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-rw-r--r--ChangeLog4
-rw-r--r--config/openaxiom-c-macros.h.in4
-rwxr-xr-xconfigure288
-rw-r--r--configure.ac3
-rw-r--r--configure.ac.pamphlet3
-rw-r--r--src/ChangeLog6
-rw-r--r--src/algebra/Makefile.in4
-rw-r--r--src/algebra/Makefile.pamphlet4
-rw-r--r--src/algebra/data.spad.pamphlet25
-rw-r--r--src/algebra/system.spad.pamphlet27
-rw-r--r--src/include/cfuns.h3
-rw-r--r--src/include/open-axiom.h5
-rw-r--r--src/interp/Makefile.in2
-rw-r--r--src/interp/nrunfast.boot25
-rw-r--r--src/interp/sys-os.boot9
-rw-r--r--src/interp/sys-utility.boot11
-rw-r--r--src/lib/cfuns-c.c15
-rw-r--r--src/share/algebra/browse.daase3552
-rw-r--r--src/share/algebra/category.daase6227
-rw-r--r--src/share/algebra/compress.daase1346
-rw-r--r--src/share/algebra/interp.daase10520
-rw-r--r--src/share/algebra/operation.daase34060
22 files changed, 28264 insertions, 27879 deletions
diff --git a/ChangeLog b/ChangeLog
index 8cf634e5..f54a7e0d 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,7 @@
+2009-02-07 Gabriel Dos Reis <gdr@cs.tamu.edu>
+
+ * configure.ac.pamphlet: Check endianness.
+
2009-01-29 Gabriel Dos Reis <gdr@cs.tamu.edu>
* OpenAxiom 1.2.1 Released.
diff --git a/config/openaxiom-c-macros.h.in b/config/openaxiom-c-macros.h.in
index d98239d6..22ac4c54 100644
--- a/config/openaxiom-c-macros.h.in
+++ b/config/openaxiom-c-macros.h.in
@@ -135,6 +135,10 @@
/* SunOS flavour */
#undef SUNplatform
+/* Define to 1 if your processor stores words with the most significant byte
+ first (like Motorola and SPARC, unlike Intel and VAX). */
+#undef WORDS_BIGENDIAN
+
/* Define to 1 if the X Window System is missing or not being used. */
#undef X_DISPLAY_MISSING
diff --git a/configure b/configure
index 6762468a..208946ae 100755
--- a/configure
+++ b/configure
@@ -20293,6 +20293,294 @@ cat >>confdefs.h <<_ACEOF
_ACEOF
+## Byte order of the host.
+{ echo "$as_me:$LINENO: checking whether byte ordering is bigendian" >&5
+echo $ECHO_N "checking whether byte ordering is bigendian... $ECHO_C" >&6; }
+if test "${ac_cv_c_bigendian+set}" = set; then
+ echo $ECHO_N "(cached) $ECHO_C" >&6
+else
+ # See if sys/param.h defines the BYTE_ORDER macro.
+cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h. */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h. */
+#include <sys/types.h>
+#include <sys/param.h>
+
+int
+main ()
+{
+#if !BYTE_ORDER || !BIG_ENDIAN || !LITTLE_ENDIAN
+ bogus endian macros
+#endif
+
+ ;
+ return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_compile") 2>conftest.er1
+ ac_status=$?
+ grep -v '^ *+' conftest.er1 >conftest.err
+ rm -f conftest.er1
+ cat conftest.err >&5
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); } &&
+ { ac_try='test -z "$ac_c_werror_flag" || test ! -s conftest.err'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; } &&
+ { ac_try='test -s conftest.$ac_objext'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; }; then
+ # It does; now see whether it defined to BIG_ENDIAN or not.
+cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h. */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h. */
+#include <sys/types.h>
+#include <sys/param.h>
+
+int
+main ()
+{
+#if BYTE_ORDER != BIG_ENDIAN
+ not big endian
+#endif
+
+ ;
+ return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_compile") 2>conftest.er1
+ ac_status=$?
+ grep -v '^ *+' conftest.er1 >conftest.err
+ rm -f conftest.er1
+ cat conftest.err >&5
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); } &&
+ { ac_try='test -z "$ac_c_werror_flag" || test ! -s conftest.err'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; } &&
+ { ac_try='test -s conftest.$ac_objext'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; }; then
+ ac_cv_c_bigendian=yes
+else
+ echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+ ac_cv_c_bigendian=no
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+else
+ echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+ # It does not; compile a test program.
+if test "$cross_compiling" = yes; then
+ # try to guess the endianness by grepping values into an object file
+ ac_cv_c_bigendian=unknown
+ cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h. */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h. */
+short int ascii_mm[] = { 0x4249, 0x4765, 0x6E44, 0x6961, 0x6E53, 0x7953, 0 };
+short int ascii_ii[] = { 0x694C, 0x5454, 0x656C, 0x6E45, 0x6944, 0x6E61, 0 };
+void _ascii () { char *s = (char *) ascii_mm; s = (char *) ascii_ii; }
+short int ebcdic_ii[] = { 0x89D3, 0xE3E3, 0x8593, 0x95C5, 0x89C4, 0x9581, 0 };
+short int ebcdic_mm[] = { 0xC2C9, 0xC785, 0x95C4, 0x8981, 0x95E2, 0xA8E2, 0 };
+void _ebcdic () { char *s = (char *) ebcdic_mm; s = (char *) ebcdic_ii; }
+int
+main ()
+{
+ _ascii (); _ebcdic ();
+ ;
+ return 0;
+}
+_ACEOF
+rm -f conftest.$ac_objext
+if { (ac_try="$ac_compile"
+case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_compile") 2>conftest.er1
+ ac_status=$?
+ grep -v '^ *+' conftest.er1 >conftest.err
+ rm -f conftest.er1
+ cat conftest.err >&5
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); } &&
+ { ac_try='test -z "$ac_c_werror_flag" || test ! -s conftest.err'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; } &&
+ { ac_try='test -s conftest.$ac_objext'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; }; then
+ if grep BIGenDianSyS conftest.$ac_objext >/dev/null ; then
+ ac_cv_c_bigendian=yes
+fi
+if grep LiTTleEnDian conftest.$ac_objext >/dev/null ; then
+ if test "$ac_cv_c_bigendian" = unknown; then
+ ac_cv_c_bigendian=no
+ else
+ # finding both strings is unlikely to happen, but who knows?
+ ac_cv_c_bigendian=unknown
+ fi
+fi
+else
+ echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+else
+ cat >conftest.$ac_ext <<_ACEOF
+/* confdefs.h. */
+_ACEOF
+cat confdefs.h >>conftest.$ac_ext
+cat >>conftest.$ac_ext <<_ACEOF
+/* end confdefs.h. */
+$ac_includes_default
+int
+main ()
+{
+
+ /* Are we little or big endian? From Harbison&Steele. */
+ union
+ {
+ long int l;
+ char c[sizeof (long int)];
+ } u;
+ u.l = 1;
+ return u.c[sizeof (long int) - 1] == 1;
+
+ ;
+ return 0;
+}
+_ACEOF
+rm -f conftest$ac_exeext
+if { (ac_try="$ac_link"
+case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_link") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); } && { ac_try='./conftest$ac_exeext'
+ { (case "(($ac_try" in
+ *\"* | *\`* | *\\*) ac_try_echo=\$ac_try;;
+ *) ac_try_echo=$ac_try;;
+esac
+eval "echo \"\$as_me:$LINENO: $ac_try_echo\"") >&5
+ (eval "$ac_try") 2>&5
+ ac_status=$?
+ echo "$as_me:$LINENO: \$? = $ac_status" >&5
+ (exit $ac_status); }; }; then
+ ac_cv_c_bigendian=no
+else
+ echo "$as_me: program exited with status $ac_status" >&5
+echo "$as_me: failed program was:" >&5
+sed 's/^/| /' conftest.$ac_ext >&5
+
+( exit $ac_status )
+ac_cv_c_bigendian=yes
+fi
+rm -f core *.core core.conftest.* gmon.out bb.out conftest$ac_exeext conftest.$ac_objext conftest.$ac_ext
+fi
+
+
+fi
+
+rm -f core conftest.err conftest.$ac_objext conftest.$ac_ext
+fi
+{ echo "$as_me:$LINENO: result: $ac_cv_c_bigendian" >&5
+echo "${ECHO_T}$ac_cv_c_bigendian" >&6; }
+case $ac_cv_c_bigendian in
+ yes)
+
+cat >>confdefs.h <<\_ACEOF
+#define WORDS_BIGENDIAN 1
+_ACEOF
+ ;;
+ no)
+ ;;
+ *)
+ { { echo "$as_me:$LINENO: error: unknown endianness
+presetting ac_cv_c_bigendian=no (or yes) will help" >&5
+echo "$as_me: error: unknown endianness
+presetting ac_cv_c_bigendian=no (or yes) will help" >&2;}
+ { (exit 1); exit 1; }; } ;;
+esac
+
+
# Find a good install program. We prefer a C program (faster),
# so one script is as good as another. But avoid the broken or
diff --git a/configure.ac b/configure.ac
index 5a268588..5b2aa386 100644
--- a/configure.ac
+++ b/configure.ac
@@ -105,6 +105,9 @@ AC_OBJEXT
AC_DEFINE_UNQUOTED([OPENAXIOM_EXEEXT], ["$ac_cv_exeext"],
[Extension of executable file.])
+## Byte order of the host.
+AC_C_BIGENDIAN
+
AC_PROG_INSTALL
# AC_PROG_LN_S
diff --git a/configure.ac.pamphlet b/configure.ac.pamphlet
index 7df5ea7e..40176e35 100644
--- a/configure.ac.pamphlet
+++ b/configure.ac.pamphlet
@@ -682,6 +682,9 @@ AC_OBJEXT
AC_DEFINE_UNQUOTED([OPENAXIOM_EXEEXT], ["$ac_cv_exeext"],
[Extension of executable file.])
+## Byte order of the host.
+AC_C_BIGENDIAN
+
@
\paragraph{File utils}
diff --git a/src/ChangeLog b/src/ChangeLog
index 92ea5f8d..9cd320fe 100644
--- a/src/ChangeLog
+++ b/src/ChangeLog
@@ -1,3 +1,9 @@
+2009-02-07 Gabriel Dos Reis <gdr@cs.tamu.edu>
+
+ * algebra/system.spad.pamphlet (hostByteOrder$System): New.
+ * algebra/data.spad.pamphlet (ByteOrder): New.
+ * algebra/Makefile.pamphlet (axiom_algebra_layer_1): Include BYTEORD.
+
2009-02-06 Alfredo Portes <doyenatccny@gmail.com>
* hyper/presea.in: Fix thinko.
diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in
index b9543285..b42c5f9f 100644
--- a/src/algebra/Makefile.in
+++ b/src/algebra/Makefile.in
@@ -287,12 +287,14 @@ $(OUT)/PROPLOG.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
$(OUT)/RETRACT.$(FASLEXT) $(OUT)/RETRACT-.$(FASLEXT): $(OUT)/KRCFROM.$(FASLEXT)
$(OUT)/MAYBE.$(FASLEXT): $(OUT)/KOERCE.$(FASLEXT) $(OUT)/RETRACT.$(FASLEXT)
+$(OUT)/BYTEORD.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+
axiom_algebra_layer_1 = \
AGG AGG- IEVALAB IEVALAB- FORTCAT ITUPLE \
PATAB PPCURVE PSCURVE REAL RESLATC RETRACT \
RETRACT- SEGCAT BINDING BMODULE LOGIC \
LOGIC- EVALAB EVALAB- FEVALAB FEVALAB- \
- OSGROUP MAYBE DATAARY PROPLOG HOMOTOP
+ OSGROUP MAYBE DATAARY PROPLOG HOMOTOP BYTEORD
axiom_algebra_layer_1_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_1))
diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet
index 94c3641c..85249ac1 100644
--- a/src/algebra/Makefile.pamphlet
+++ b/src/algebra/Makefile.pamphlet
@@ -259,12 +259,14 @@ $(OUT)/PROPLOG.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
$(OUT)/RETRACT.$(FASLEXT) $(OUT)/RETRACT-.$(FASLEXT): $(OUT)/KRCFROM.$(FASLEXT)
$(OUT)/MAYBE.$(FASLEXT): $(OUT)/KOERCE.$(FASLEXT) $(OUT)/RETRACT.$(FASLEXT)
+$(OUT)/BYTEORD.$(FASLEXT): $(OUT)/SETCAT.$(FASLEXT)
+
axiom_algebra_layer_1 = \
AGG AGG- IEVALAB IEVALAB- FORTCAT ITUPLE \
PATAB PPCURVE PSCURVE REAL RESLATC RETRACT \
RETRACT- SEGCAT BINDING BMODULE LOGIC \
LOGIC- EVALAB EVALAB- FEVALAB FEVALAB- \
- OSGROUP MAYBE DATAARY PROPLOG HOMOTOP
+ OSGROUP MAYBE DATAARY PROPLOG HOMOTOP BYTEORD
axiom_algebra_layer_1_nrlibs = \
$(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_1))
diff --git a/src/algebra/data.spad.pamphlet b/src/algebra/data.spad.pamphlet
index d52ee479..f40d8b1a 100644
--- a/src/algebra/data.spad.pamphlet
+++ b/src/algebra/data.spad.pamphlet
@@ -49,6 +49,31 @@ Byte(): Public == Private where
@
+<<domain BYTEORD ByteOrder>>=
+)abbrev domain BYTEORD ByteOrder
+++ Author: Gabriel Dos Reis
+++ Date Created: February 06, 2009
+++ Date Last Modified:
+++ Description:
+++ This datatype describes byte order of machine values stored memory.
+ByteOrder(): Public == Private where
+ Public == SetCategory with
+ littleEndian: % ++ \spad{littleEndian} describes little endian host
+ bigEndian: % ++ \spad{bigEndian} describes big endian host
+ unknownEndian: % ++ \spad{unknownEndian} for none of the above.
+ Private == add
+ unknownEndian == %unknownEndian$Lisp
+ littleEndian == %littleEndian$Lisp
+ bigEndian == %bigEndian$Lisp
+ x = y == EQ(x,y)$Lisp
+ coerce(x: %): OutputForm ==
+ outputForm
+ x = littleEndian => 'litteEndian
+ x = bigEndian => 'bigEndian
+ 'unknownEndian
+
+@
+
\section{Sized System Integer datatypes}
diff --git a/src/algebra/system.spad.pamphlet b/src/algebra/system.spad.pamphlet
index 57eb4eaa..70b31162 100644
--- a/src/algebra/system.spad.pamphlet
+++ b/src/algebra/system.spad.pamphlet
@@ -17,34 +17,39 @@
)abbrev package SYSTEM System
++ Author: Gabriel Dos Reis
++ Date Created: April 2, 2008.
+++ Date Last Modified: February 6, 2009.
++ Related Constructors:
++ Description:
++ The package \spadtype{System} provides information about
++ the runtime system and its characteristics.
System(): Public == Private where
- Public ==> with
+ Public == Type with
rootDirectory: () -> String
++ rootDirectory() returns the pathname of the root directory
++ for the running OpenAxiom system.
- hostPlatform: () -> String
- ++ hostPlatform() returns a string `triplet' description
+ hostPlatform: String
+ ++ \spad{hostPlatform} is a string `triplet' description
++ of the platform hosting the running OpenAxiom system.
- nativeModuleExtension: () -> String
- ++ nativeModuleExtension() returns a string representation
+ hostByteOrder: ByteOrder
+ ++ \sapd{hostByteOrder}
+ nativeModuleExtension: String
+ ++ \spad{nativeModuleExtension} is a string representation
++ of a filename extension for native modules.
loadNativeModule: String -> Void
++ loadNativeModule(path) loads the native modile designated
++ by \spadvar{path}.
- Private ==> add
+ Private == add
rootDirectory() ==
- systemRootDirectory()$Lisp : String
+ systemRootDirectory()$Lisp
- hostPlatform() ==
- _$hostPlatform$Lisp : String
+ hostPlatform ==
+ _$hostPlatform$Lisp
- nativeModuleExtension() ==
- _$NativeModuleExt$Lisp : String
+ hostByteOrder == %hostByteOrder$Lisp
+
+ nativeModuleExtension ==
+ _$NativeModuleExt$Lisp
loadNativeModule(path) ==
loadNativeModule(path)$Lisp
diff --git a/src/include/cfuns.h b/src/include/cfuns.h
index 99929a69..4d0a8f05 100644
--- a/src/include/cfuns.h
+++ b/src/include/cfuns.h
@@ -4,7 +4,7 @@
/*
Copyright (C) 1991-2002, The Numerical ALgorithms Group Ltd.
All rights reserved.
- Copyright (C) 2007-2008, Gabriel Dos Reis.
+ Copyright (C) 2007-2009, Gabriel Dos Reis.
All rights resrved.
Redistribution and use in source and binary forms, with or without
@@ -65,6 +65,7 @@ OPENAXIOM_EXPORT int oa_copy_file(const char*, const char*);
OPENAXIOM_EXPORT double plus_infinity(void);
OPENAXIOM_EXPORT double minus_infinity(void);
OPENAXIOM_EXPORT double NANQ(void);
+OPENAXIOM_EXPORT openaxiom_byteorder oa_get_host_byteorder(void);
#ifdef __cplusplus
diff --git a/src/include/open-axiom.h b/src/include/open-axiom.h
index d4790120..b27c9ea3 100644
--- a/src/include/open-axiom.h
+++ b/src/include/open-axiom.h
@@ -79,6 +79,11 @@ extern "C" {
# define OPENAXIOM_HAVE_GRAPHICS 1
#endif
+/* Byte order enumeration. */
+typedef enum openaxiom_byteorder {
+ oa_unknown_endian, oa_little_endian, oa_big_endian
+} openaxiom_byteorder;
+
/* Return the address of the data buffer `BUF'. */
diff --git a/src/interp/Makefile.in b/src/interp/Makefile.in
index 55cea06a..5ac93c59 100644
--- a/src/interp/Makefile.in
+++ b/src/interp/Makefile.in
@@ -135,7 +135,7 @@ YEARWEEK=(progn (defconstant timestamp "${TIMESTAMP}") \
.PRECIOUS: ${AXIOMSYS}
UNUSED= ${DOC}/construc.lisp.dvi \
- ${DOC}/domain.lisp.dvi ${DOC}/guess.boot.dvi \
+ ${DOC}/guess.boot.dvi \
${DOC}/interp-fix.boot.dvi \
${DOC}/nhyper.boot.dvi ${DOC}/pf2atree.boot.dvi \
${DOC}/redefs.boot.dvi ${DOC}/word.boot.dvi
diff --git a/src/interp/nrunfast.boot b/src/interp/nrunfast.boot
index 5ac53649..e7dc7a19 100644
--- a/src/interp/nrunfast.boot
+++ b/src/interp/nrunfast.boot
@@ -1,6 +1,6 @@
-- Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd.
-- All rights reserved.
--- Copyright (C) 2007-2008, Gabriel Dos Reis.
+-- Copyright (C) 2007-2009, Gabriel Dos Reis.
-- All rights reserved.
--
-- Redistribution and use in source and binary forms, with or without
@@ -57,9 +57,11 @@ initNewWorld() ==
$updateCatTableIfTrue := false
$doNotCompressHashTableIfTrue := true
-isNewWorldDomain domain == INTEGERP domain.3 --see HasCategory/Attribute
+isNewWorldDomain domain ==
+ INTEGERP domain.3 --see HasCategory/Attribute
-getDomainByteVector dom == CDDR dom.4
+getDomainByteVector dom ==
+ CDDR dom.4
getOpCode(op,vec,max) ==
--search Op vector for "op" returning code if found, nil otherwise
@@ -106,7 +108,6 @@ newGoGet(:l) ==
slot := replaceGoGetSlot env
APPLY(first slot,[:arglist,rest slot]) --SPADCALL it!
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
replaceGoGetSlot env ==
[thisDomain,index,:op] := env
thisDomainForm := devaluate thisDomain
@@ -142,15 +143,12 @@ replaceGoGetSlot env ==
--=======================================================
-- Lookup Function in Slot 1 (via SPADCALL)
--=======================================================
-lookupFF(op,sig,dollar,env) == newLookupInTable(op,sig,dollar,env,nil)
-
-lookupUF(op,sig,dollar,env) == newLookupInTable(op,sig,dollar,env,true)
-
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
-lookupComplete(op,sig,dollar,env) == newLookupInTable(op,sig,dollar,env,nil)
+
+lookupComplete(op,sig,dollar,env) ==
+ newLookupInTable(op,sig,dollar,env,nil)
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
-lookupIncomplete(op,sig,dollar,env) == newLookupInTable(op,sig,dollar,env,true)
+lookupIncomplete(op,sig,dollar,env) ==
+ newLookupInTable(op,sig,dollar,env,true)
newLookupInTable(op,sig,dollar,[domain,opvec],flag) ==
dollar = nil => systemError()
@@ -420,7 +418,6 @@ newCompareSig(sig, numvec, index, dollar, domain) ==
--=======================================================
lazyMatchArg(s,a,dollar,domain) == lazyMatchArg2(s,a,dollar,domain,true)
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
lazyMatchArg2(s,a,dollar,domain,typeFlag) ==
if s = '$ then
-- a = 0 => return true --needed only if extra call in newGoGet to basicLookup
@@ -525,7 +522,6 @@ newExpandTypeSlot(slot, dollar, domain) ==
newExpandLocalType(sigDomainVal(dollar, domain, slot), dollar,domain)
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
newExpandLocalType(lazyt,dollar,domain) ==
VECP lazyt => lazyt.0
ATOM lazyt => lazyt
@@ -577,7 +573,6 @@ sigDomainVal(dollar,domain,index) ==
-- Convert Lazy Domain to Domain Form
--=======================================================
---------------------> NEW DEFINITION (see interop.boot.pamphlet)
lazyDomainSet(lazyForm,thisDomain,slot) ==
form :=
lazyForm is [vec,.,:u] and VECP vec => u --old style
diff --git a/src/interp/sys-os.boot b/src/interp/sys-os.boot
index 2e9bf84b..f844fba7 100644
--- a/src/interp/sys-os.boot
+++ b/src/interp/sys-os.boot
@@ -234,4 +234,11 @@ minusInfinity() ==
++ otherwise 0.
import std__stream__is__terminal: int -> int for stdStreamIsTerminal
---%
+--% Data layout
+
+++ getHostByteOrder:
+++ returns the byte order of the host machine.
+++ 0: unknown
+++ 1: little endian
+++ 2: big endian
+import oa__get__host__byteorder: () -> int for getHostByteOrder
diff --git a/src/interp/sys-utility.boot b/src/interp/sys-utility.boot
index 2d334946..31781fae 100644
--- a/src/interp/sys-utility.boot
+++ b/src/interp/sys-utility.boot
@@ -47,6 +47,17 @@ $COMBLOCKLIST := nil
%nothing == KEYWORD::%OpenAxiomNoValue
+++ Constants describing byte order
+%littleEndian == KEYWORD::%littleEndian
+%bigEndian == KEYWORD::%bigEndian
+%unknownEndian == KEYWORD::%unknownEndian
+
+++ The byte order of the host machine running OpenAxiom.
+%hostByteOrder ==
+ getHostByteOrder() = 1 => %littleEndian
+ getHostByteOrder() = 2 => %bigEndian
+ %unknownEndian
+
--%
++ getVMType returns an approximation of the underlying object type
diff --git a/src/lib/cfuns-c.c b/src/lib/cfuns-c.c
index fb043c9f..4a443b82 100644
--- a/src/lib/cfuns-c.c
+++ b/src/lib/cfuns-c.c
@@ -2,7 +2,7 @@
Copyright (C) 1991-2002, The Numerical Algorithms Group Ltd.
All rights reserved.
- Copyright (C) 2007-2008, Gabriel Dos Reis.
+ Copyright (C) 2007-2009, Gabriel Dos Reis.
All rights reserved.
Redistribution and use in source and binary forms, with or without
@@ -672,6 +672,17 @@ NANQ(void)
#ifdef NAN
return NAN;
#else
- return sqrt(-1.0); /* Juts pick one. */
+ return sqrt(-1.0); /* Just pick one. */
#endif
}
+
+
+OPENAXIOM_EXPORT openaxiom_byteorder
+oa_get_host_byteorder(void)
+{
+#ifdef WORDS_BIGENDIAN
+ return oa_big_endian;
+#else
+ return oa_little_endian;
+#endif
+}
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase
index 958715a9..ca8b2a89 100644
--- a/src/share/algebra/browse.daase
+++ b/src/share/algebra/browse.daase
@@ -1,12 +1,12 @@
-(2282336 . 3442698064)
+(2282814 . 3443021571)
(-18 A S)
((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result.")))
NIL
NIL
(-19 S)
((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
(-20 S)
((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}.")))
@@ -38,7 +38,7 @@ NIL
NIL
(-27)
((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
(-28 S R)
((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
@@ -46,7 +46,7 @@ NIL
NIL
(-29 R)
((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}.")))
-((-4400 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4396 . T) (-4401 . T) (-4395 . T))
+((-4404 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T))
NIL
(-30)
((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted.")))
@@ -56,14 +56,14 @@ NIL
((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression.")))
NIL
NIL
-(-32 R -3196)
+(-32 R -3191)
((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))))
+((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))
(-33 S)
((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4403)))
+((|HasAttribute| |#1| (QUOTE -4407)))
(-34)
((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects.")))
NIL
@@ -74,7 +74,7 @@ NIL
NIL
(-36 |Key| |Entry|)
((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}.")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
(-37 S R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
@@ -82,20 +82,20 @@ NIL
NIL
(-38 R)
((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
(-39 UP)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an.")))
NIL
NIL
-(-40 -3196 UP UPUP -2685)
+(-40 -3191 UP UPUP -2995)
((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}")))
-((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
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-(-41 R -3196)
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+(-41 R -3191)
((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|)))))
+((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))))
(-42 OV E P)
((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}.")))
NIL
@@ -103,34 +103,34 @@ NIL
(-43 R A)
((|constructor| (NIL "AlgebraPackage assembles a variety of useful functions for general algebras.")) (|basis| (((|Vector| |#2|) (|Vector| |#2|)) "\\spad{basis(va)} selects a basis from the elements of \\spad{va}.")) (|radicalOfLeftTraceForm| (((|List| |#2|)) "\\spad{radicalOfLeftTraceForm()} returns basis for null space of \\spad{leftTraceMatrix()},{} if the algebra is associative,{} alternative or a Jordan algebra,{} then this space equals the radical (maximal nil ideal) of the algebra.")) (|basisOfCentroid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfCentroid()} returns a basis of the centroid,{} \\spadignore{i.e.} the endomorphism ring of \\spad{A} considered as \\spad{(A,{}A)}-bimodule.")) (|basisOfRightNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfRightNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as left module. Note: right nucloid coincides with right nucleus if \\spad{A} has a unit.")) (|basisOfLeftNucloid| (((|List| (|Matrix| |#1|))) "\\spad{basisOfLeftNucloid()} returns a basis of the space of endomorphisms of \\spad{A} as right module. Note: left nucloid coincides with left nucleus if \\spad{A} has a unit.")) (|basisOfCenter| (((|List| |#2|)) "\\spad{basisOfCenter()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{commutator(x,{}a) = 0} and \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfNucleus| (((|List| |#2|)) "\\spad{basisOfNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{associator(x,{}a,{}b) = associator(a,{}x,{}b) = associator(a,{}b,{}x) = 0} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfMiddleNucleus| (((|List| |#2|)) "\\spad{basisOfMiddleNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}x,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightNucleus| (((|List| |#2|)) "\\spad{basisOfRightNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(a,{}b,{}x)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfLeftNucleus| (((|List| |#2|)) "\\spad{basisOfLeftNucleus()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = associator(x,{}a,{}b)} for all \\spad{a},{}\\spad{b} in \\spad{A}.")) (|basisOfRightAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfRightAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = a*x}.")) (|basisOfLeftAnnihilator| (((|List| |#2|) |#2|) "\\spad{basisOfLeftAnnihilator(a)} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = x*a}.")) (|basisOfCommutingElements| (((|List| |#2|)) "\\spad{basisOfCommutingElements()} returns a basis of the space of all \\spad{x} of \\spad{A} satisfying \\spad{0 = commutator(x,{}a)} for all \\spad{a} in \\spad{A}.")) (|biRank| (((|NonNegativeInteger|) |#2|) "\\spad{biRank(x)} determines the number of linearly independent elements in \\spad{x},{} \\spad{x*bi},{} \\spad{bi*x},{} \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis. Note: if \\spad{A} has a unit,{} then \\spadfunFrom{doubleRank}{AlgebraPackage},{} \\spadfunFrom{weakBiRank}{AlgebraPackage} and \\spadfunFrom{biRank}{AlgebraPackage} coincide.")) (|weakBiRank| (((|NonNegativeInteger|) |#2|) "\\spad{weakBiRank(x)} determines the number of linearly independent elements in the \\spad{bi*x*bj},{} \\spad{i,{}j=1,{}...,{}n},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|doubleRank| (((|NonNegativeInteger|) |#2|) "\\spad{doubleRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|rightRank| (((|NonNegativeInteger|) |#2|) "\\spad{rightRank(x)} determines the number of linearly independent elements in \\spad{b1*x},{}...,{}\\spad{bn*x},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")) (|leftRank| (((|NonNegativeInteger|) |#2|) "\\spad{leftRank(x)} determines the number of linearly independent elements in \\spad{x*b1},{}...,{}\\spad{x*bn},{} where \\spad{b=[b1,{}...,{}bn]} is a basis.")))
NIL
-((|HasCategory| |#1| (QUOTE (-306))))
+((|HasCategory| |#1| (QUOTE (-307))))
(-44 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra.")))
-((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554))))
+((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555))))
(-45 |Key| |Entry|)
((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data.")))
-((-4403 . T) (-4404 . T))
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+((-4407 . T) (-4408 . T))
+((-4032 (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|))))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))))
(-46 S R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
NIL
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+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))))
(-47 R E)
((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
(-48)
((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562)))))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563)))))
(-49)
((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}.")))
NIL
NIL
(-50 R |lVar|)
((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}.")))
-((-4400 . T))
+((-4404 . T))
NIL
(-51 S)
((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}.")))
@@ -144,7 +144,7 @@ NIL
((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}.")))
NIL
NIL
-(-54 |Base| R -3196)
+(-54 |Base| R -3191)
((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression.")))
NIL
NIL
@@ -158,7 +158,7 @@ NIL
NIL
(-57 R |Row| |Col|)
((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
(-58 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")))
@@ -166,65 +166,65 @@ NIL
NIL
(-59 S)
((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
(-60 R)
((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-61 -3253)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-61 -3348)
((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-62 -3253)
+(-62 -3348)
((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}.")))
NIL
NIL
-(-63 -3253)
+(-63 -3348)
((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-64 -3253)
+(-64 -3348)
((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP.")))
NIL
NIL
-(-65 -3253)
+(-65 -3348)
((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")))
NIL
NIL
-(-66 -3253)
+(-66 -3348)
((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP.")))
NIL
NIL
-(-67 -3253)
+(-67 -3348)
((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}")))
NIL
NIL
-(-68 -3253)
+(-68 -3348)
((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}")))
NIL
NIL
-(-69 -3253)
+(-69 -3348)
((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}.")))
NIL
NIL
-(-70 -3253)
+(-70 -3348)
((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}")))
NIL
NIL
-(-71 -3253)
+(-71 -3348)
((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-72 -3253)
+(-72 -3348)
((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}.")))
NIL
NIL
-(-73 -3253)
+(-73 -3348)
((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}")))
NIL
NIL
-(-74 -3253)
+(-74 -3348)
((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
@@ -236,66 +236,66 @@ NIL
((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-77 -3253)
+(-77 -3348)
((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP.")))
NIL
NIL
-(-78 -3253)
+(-78 -3348)
((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP.")))
NIL
NIL
-(-79 -3253)
+(-79 -3348)
((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-80 -3253)
+(-80 -3348)
((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-81 -3253)
+(-81 -3348)
((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")))
NIL
NIL
-(-82 -3253)
+(-82 -3348)
((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-83 -3253)
+(-83 -3348)
((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-84 -3253)
+(-84 -3348)
((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-85 -3253)
+(-85 -3348)
((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-86 -3253)
+(-86 -3348)
((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-87 -3253)
+(-87 -3348)
((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP.")))
NIL
NIL
-(-88 -3253)
+(-88 -3348)
((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}")))
NIL
NIL
-(-89 -3253)
+(-89 -3348)
((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP.")))
NIL
NIL
(-90 R L)
((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op,{} m)} returns \\spad{[w,{} eq,{} lw,{} lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,{}...,{}A_n]} such that if \\spad{y = [y_1,{}...,{}y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',{}y_j'',{}...,{}y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}\\spad{'s}.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op,{} m)} returns \\spad{[M,{}w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))))
+((|HasCategory| |#1| (QUOTE (-363))))
(-91 S)
((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
(-92 S)
((|constructor| (NIL "This is the category of Spad abstract syntax trees.")))
NIL
@@ -318,15 +318,15 @@ NIL
NIL
(-97)
((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")))
-((-4403 . T))
+((-4407 . T))
NIL
(-98)
((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements.")))
-((-4403 . T) ((-4405 "*") . T) (-4404 . T) (-4400 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4401 . T) (-4395 . T) (-4394 . T) (-4393 . T) (-4392 . T) (-4391 . T) (-4399 . T) (-4402 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4390 . T))
+((-4407 . T) ((-4409 "*") . T) (-4408 . T) (-4404 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4398 . T) (-4397 . T) (-4396 . T) (-4395 . T) (-4403 . T) (-4406 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4394 . T))
NIL
(-99 R)
((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}.")))
-((-4400 . T))
+((-4404 . T))
NIL
(-100 R UP)
((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}.")))
@@ -342,15 +342,15 @@ NIL
NIL
(-103 S)
((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
(-104 R UP M |Row| |Col|)
((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}.")))
NIL
-((|HasAttribute| |#1| (QUOTE (-4405 "*"))))
+((|HasAttribute| |#1| (QUOTE (-4409 "*"))))
(-105)
((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table")))
-((-4403 . T))
+((-4407 . T))
NIL
(-106 A S)
((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed.")))
@@ -358,23 +358,23 @@ NIL
NIL
(-107 S)
((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed.")))
-((-4404 . T))
+((-4408 . T))
NIL
(-108)
((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144)))))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145)))))
(-109)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}")))
NIL
NIL
(-110)
((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-858)))))
(-111 R S)
((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
(-112)
((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant.")))
@@ -383,27 +383,27 @@ NIL
(-113 A)
((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise.")))
NIL
-((|HasCategory| |#1| (QUOTE (-845))))
+((|HasCategory| |#1| (QUOTE (-846))))
(-114)
((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}.")))
NIL
NIL
-(-115 -3196 UP)
+(-115 -3191 UP)
((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots.")))
NIL
NIL
(-116 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
(-117 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-116 |#1|) (QUOTE (-904))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-116 |#1|) (QUOTE (-1017))) (|HasCategory| (-116 |#1|) (QUOTE (-815))) (-4037 (|HasCategory| (-116 |#1|) (QUOTE (-815))) (|HasCategory| (-116 |#1|) (QUOTE (-845)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (QUOTE (-1143))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -513) (QUOTE (-1168)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-544))) (|HasCategory| (-116 |#1|) (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-904)))) (|HasCategory| (-116 |#1|) (QUOTE (-144)))))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-4032 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-1144))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145)))))
(-118 A S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)))
+((|HasAttribute| |#1| (QUOTE -4408)))
(-119 S)
((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child.")))
NIL
@@ -414,15 +414,15 @@ NIL
NIL
(-121 S)
((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
(-122 S)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
NIL
NIL
(-123)
((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
(-124 A S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
@@ -430,4643 +430,4647 @@ NIL
NIL
(-125 S)
((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
(-126 S)
((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
(-127 S)
((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
(-128)
((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-4037 (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-129) (QUOTE (-1092)))) (|HasCategory| (-129) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-129) (QUOTE (-1092))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))))
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4032 (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1093))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))))
(-129)
((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256.")))
NIL
NIL
(-130)
-((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")))
+((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host")))
NIL
NIL
(-131)
-((|constructor| (NIL "A cachable set is a set whose elements keep an integer as part of their structure.")) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) "\\spad{setPosition(x,{} n)} associates the integer \\spad{n} to \\spad{x}.")) (|position| (((|NonNegativeInteger|) $) "\\spad{position(x)} returns the integer \\spad{n} associated to \\spad{x}.")))
+((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")))
NIL
NIL
(-132)
-((|constructor| (NIL "This domain represents the capsule of a domain definition.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of top level expressions appearing in \\spad{`c'}.")))
+((|constructor| (NIL "A cachable set is a set whose elements keep an integer as part of their structure.")) (|setPosition| (((|Void|) $ (|NonNegativeInteger|)) "\\spad{setPosition(x,{} n)} associates the integer \\spad{n} to \\spad{x}.")) (|position| (((|NonNegativeInteger|) $) "\\spad{position(x)} returns the integer \\spad{n} associated to \\spad{x}.")))
NIL
NIL
(-133)
+((|constructor| (NIL "This domain represents the capsule of a domain definition.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of top level expressions appearing in \\spad{`c'}.")))
+NIL
+NIL
+(-134)
((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")))
-(((-4405 "*") . T))
+(((-4409 "*") . T))
NIL
-(-134 |minix| -2240 S T$)
+(-135 |minix| -3304 S T$)
((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}.")))
NIL
NIL
-(-135 |minix| -2240 R)
+(-136 |minix| -3304 R)
((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor.")))
NIL
NIL
-(-136)
+(-137)
((|constructor| (NIL "This domain represents a `case' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the case expression `e'.")))
NIL
NIL
-(-137)
+(-138)
((|constructor| (NIL "This domain represents the unnamed category defined \\indented{2}{by a list of exported signatures}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(c)} returns the list of exports in category syntax \\spad{`c'}.")) (|kind| (((|Symbol|) $) "\\spad{kind(c)} returns the kind of unnamed category,{} either 'domain' or 'package'.")))
NIL
NIL
-(-138)
+(-139)
((|constructor| (NIL "This domain provides representations for category constructors.")))
NIL
NIL
-(-139)
+(-140)
((|parents| (((|List| (|ConstructorCall|)) $) "\\spad{parents(c)} returns the list of all category forms directly extended by the category \\spad{`c'}.")) (|principalAncestors| (((|List| (|ConstructorCall|)) $) "\\spad{principalAncestors(c)} returns the list of all category forms that are principal ancestors of the the category \\spad{`c'}.")) (|exportedOperators| (((|List| (|OperatorSignature|)) $) "\\spad{exportedOperators(c)} returns the list of all operator signatures exported by the category \\spad{`c'},{} along with their predicates.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: December 20,{} 2008. Date Last Updated: February 16,{} 2008. Basic Operations: coerce Related Constructors: Also See: Type") (((|CategoryConstructor|) $) "\\spad{constructor(c)} returns the category constructor used to instantiate the category object \\spad{`c'}.")))
NIL
NIL
-(-140)
+(-141)
((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}.")))
-((-4403 . T) (-4393 . T) (-4404 . T))
-((-4037 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))))
-(-141 R Q A)
+((-4407 . T) (-4397 . T) (-4408 . T))
+((-4032 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))))
+(-142 R Q A)
((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}.")))
NIL
NIL
-(-142)
+(-143)
((|constructor| (NIL "Category for the usual combinatorial functions.")) (|permutation| (($ $ $) "\\spad{permutation(n,{} m)} returns the number of permutations of \\spad{n} objects taken \\spad{m} at a time. Note: \\spad{permutation(n,{}m) = n!/(n-m)!}.")) (|factorial| (($ $) "\\spad{factorial(n)} computes the factorial of \\spad{n} (denoted in the literature by \\spad{n!}) Note: \\spad{n! = n (n-1)! when n > 0}; also,{} \\spad{0! = 1}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}r)} returns the \\spad{(n,{}r)} binomial coefficient (often denoted in the literature by \\spad{C(n,{}r)}). Note: \\spad{C(n,{}r) = n!/(r!(n-r)!)} where \\spad{n >= r >= 0}.")))
NIL
NIL
-(-143)
+(-144)
((|constructor| (NIL "This domain provides the basic character data type.")) (|alphanumeric?| (((|Boolean|) $) "\\spad{alphanumeric?(c)} tests if \\spad{c} is either a letter or number,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{z} or A..\\spad{Z}.")) (|lowerCase?| (((|Boolean|) $) "\\spad{lowerCase?(c)} tests if \\spad{c} is an lower case letter,{} \\spadignore{i.e.} one of a..\\spad{z}.")) (|upperCase?| (((|Boolean|) $) "\\spad{upperCase?(c)} tests if \\spad{c} is an upper case letter,{} \\spadignore{i.e.} one of A..\\spad{Z}.")) (|alphabetic?| (((|Boolean|) $) "\\spad{alphabetic?(c)} tests if \\spad{c} is a letter,{} \\spadignore{i.e.} one of a..\\spad{z} or A..\\spad{Z}.")) (|hexDigit?| (((|Boolean|) $) "\\spad{hexDigit?(c)} tests if \\spad{c} is a hexadecimal numeral,{} \\spadignore{i.e.} one of 0..9,{} a..\\spad{f} or A..\\spad{F}.")) (|digit?| (((|Boolean|) $) "\\spad{digit?(c)} tests if \\spad{c} is a digit character,{} \\spadignore{i.e.} one of 0..9.")) (|lowerCase| (($ $) "\\spad{lowerCase(c)} converts an upper case letter to the corresponding lower case letter. If \\spad{c} is not an upper case letter,{} then it is returned unchanged.")) (|upperCase| (($ $) "\\spad{upperCase(c)} converts a lower case letter to the corresponding upper case letter. If \\spad{c} is not a lower case letter,{} then it is returned unchanged.")) (|escape| (($) "\\spad{escape()} provides the escape character,{} \\spad{_},{} which is used to allow quotes and other characters {\\em within} strings.")) (|quote| (($) "\\spad{quote()} provides the string quote character,{} \\spad{\"}.")) (|space| (($) "\\spad{space()} provides the blank character.")) (|char| (($ (|String|)) "\\spad{char(s)} provides a character from a string \\spad{s} of length one.") (($ (|NonNegativeInteger|)) "\\spad{char(i)} provides a character corresponding to the integer code \\spad{i}. It is always \\spad{true} that \\spad{ord char i = i}.")) (|ord| (((|NonNegativeInteger|) $) "\\spad{ord(c)} provides an integral code corresponding to the character \\spad{c}. It is always \\spad{true} that \\spad{char ord c = c}.")))
NIL
NIL
-(-144)
+(-145)
((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-145 R)
+(-146 R)
((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}.")))
NIL
NIL
-(-146)
+(-147)
((|constructor| (NIL "Rings of Characteristic Zero.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-147 -3196 UP UPUP)
+(-148 -3191 UP UPUP)
((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}.")))
NIL
NIL
-(-148 R CR)
+(-149 R CR)
((|constructor| (NIL "This package provides the generalized euclidean algorithm which is needed as the basic step for factoring polynomials.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} where (\\spad{fi} relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g} = sum \\spad{ai} prod \\spad{fj} (\\spad{j} \\spad{\\=} \\spad{i}) or equivalently g/prod \\spad{fj} = sum (ai/fi) or returns \"failed\" if no such list exists")))
NIL
NIL
-(-149 A S)
+(-150 A S)
((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasAttribute| |#1| (QUOTE -4403)))
-(-150 S)
+((|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasAttribute| |#1| (QUOTE -4407)))
+(-151 S)
((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List.")))
NIL
NIL
-(-151 |n| K Q)
+(-152 |n| K Q)
((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element.")))
-((-4398 . T) (-4397 . T) (-4400 . T))
+((-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-152)
+(-153)
((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,{}xMin,{}xMax,{}yMin,{}yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function.")))
NIL
NIL
-(-153)
+(-154)
((|constructor| (NIL "This domain represents list comprehension syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the expression being collected by the list comprehension `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of the iterators of the list comprehension `e'.")))
NIL
NIL
-(-154 UP |Par|)
+(-155 UP |Par|)
((|complexZeros| (((|List| (|Complex| |#2|)) |#1| |#2|) "\\spad{complexZeros(poly,{} eps)} finds the complex zeros of the univariate polynomial \\spad{poly} to precision eps with solutions returned as complex floats or rationals depending on the type of eps.")))
NIL
NIL
-(-155)
+(-156)
((|constructor| (NIL "This domain represents type specification \\indented{2}{for an identifier or expression.}")) (|rhs| (((|TypeAst|) $) "\\spad{rhs(e)} returns the right hand side of the colon expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the colon expression `e'.")))
NIL
NIL
-(-156)
+(-157)
((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.")))
NIL
NIL
-(-157 R -3196)
+(-158 R -3191)
((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator.")))
NIL
NIL
-(-158 I)
+(-159 I)
((|stirling2| ((|#1| |#1| |#1|) "\\spad{stirling2(n,{}m)} returns the Stirling number of the second kind denoted \\spad{SS[n,{}m]}.")) (|stirling1| ((|#1| |#1| |#1|) "\\spad{stirling1(n,{}m)} returns the Stirling number of the first kind denoted \\spad{S[n,{}m]}.")) (|permutation| ((|#1| |#1| |#1|) "\\spad{permutation(n)} returns \\spad{!P(n,{}r) = n!/(n-r)!}. This is the number of permutations of \\spad{n} objects taken \\spad{r} at a time.")) (|partition| ((|#1| |#1|) "\\spad{partition(n)} returns the number of partitions of the integer \\spad{n}. This is the number of distinct ways that \\spad{n} can be written as a sum of positive integers.")) (|multinomial| ((|#1| |#1| (|List| |#1|)) "\\spad{multinomial(n,{}[m1,{}m2,{}...,{}mk])} returns the multinomial coefficient \\spad{n!/(m1! m2! ... mk!)}.")) (|factorial| ((|#1| |#1|) "\\spad{factorial(n)} returns \\spad{n!}. this is the product of all integers between 1 and \\spad{n} (inclusive). Note: \\spad{0!} is defined to be 1.")) (|binomial| ((|#1| |#1| |#1|) "\\spad{binomial(n,{}r)} returns the binomial coefficient \\spad{C(n,{}r) = n!/(r! (n-r)!)},{} where \\spad{n >= r >= 0}. This is the number of combinations of \\spad{n} objects taken \\spad{r} at a time.")))
NIL
NIL
-(-159)
+(-160)
((|constructor| (NIL "CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.")) (|product| (($ $ (|SegmentBinding| $)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") (($ $ (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| (($ $ (|SegmentBinding| $)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") (($ $ (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| (($ $ (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") (($ $) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")))
NIL
NIL
-(-160)
+(-161)
((|constructor| (NIL "This domain represents the syntax of a comma-separated \\indented{2}{list of expressions.}")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions making up `e'.")))
NIL
NIL
-(-161)
+(-162)
((|constructor| (NIL "A type for basic commutators")) (|mkcomm| (($ $ $) "\\spad{mkcomm(i,{}j)} \\undocumented{}") (($ (|Integer|)) "\\spad{mkcomm(i)} \\undocumented{}")))
NIL
NIL
-(-162)
+(-163)
((|constructor| (NIL "This package exports the elementary operators,{} with some semantics already attached to them. The semantics that is attached here is not dependent on the set in which the operators will be applied.")) (|operator| (((|BasicOperator|) (|Symbol|)) "\\spad{operator(s)} returns an operator with name \\spad{s},{} with the appropriate semantics if \\spad{s} is known. If \\spad{s} is not known,{} the result has no semantics.")))
NIL
NIL
-(-163 R UP UPUP)
+(-164 R UP UPUP)
((|constructor| (NIL "A package for swapping the order of two variables in a tower of two UnivariatePolynomialCategory extensions.")) (|swap| ((|#3| |#3|) "\\spad{swap(p(x,{}y))} returns \\spad{p}(\\spad{y},{}\\spad{x}).")))
NIL
NIL
-(-164 S R)
-((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")))
+(-165 S R)
+((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})")))
NIL
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-(-165 R)
-((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")))
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+(-166 R)
+((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})")))
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NIL
-(-166 RR PR)
+(-167 RR PR)
((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients.")))
NIL
NIL
-(-167 R S)
+(-168 R S)
((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,{}u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}.")))
NIL
NIL
-(-168 R)
+(-169 R)
((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}.")))
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(QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| |#1| (QUOTE (-1053))) (-12 (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-1192)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-362)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasAttribute| |#1| (QUOTE -4399)) (|HasAttribute| |#1| (QUOTE -4402)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-348)))))
-(-169 R S CS)
+((-4400 -4032 (|has| |#1| (-555)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4403 |has| |#1| (-6 -4403)) (-4406 |has| |#1| (-6 -4406)) (-1413 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
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(QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-368)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-824)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-846)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1018)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-1193)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -611) 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(QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1193)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasAttribute| |#1| (QUOTE -4406)) (-12 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+(-170 R S CS)
((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern")))
NIL
NIL
-(-170)
+(-171)
((|constructor| (NIL "This domain implements some global properties of subspaces.")) (|copy| (($ $) "\\spad{copy(x)} \\undocumented")) (|solid| (((|Boolean|) $ (|Boolean|)) "\\spad{solid(x,{}b)} \\undocumented")) (|close| (((|Boolean|) $ (|Boolean|)) "\\spad{close(x,{}b)} \\undocumented")) (|solid?| (((|Boolean|) $) "\\spad{solid?(x)} \\undocumented")) (|closed?| (((|Boolean|) $) "\\spad{closed?(x)} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")))
NIL
NIL
-(-171)
+(-172)
((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative.")))
-(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-172)
+(-173)
((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations.")))
NIL
NIL
-(-173 R)
+(-174 R)
((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}.")))
-(((-4405 "*") . T) (-4396 . T) (-4401 . T) (-4395 . T) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") . T) (-4400 . T) (-4405 . T) (-4399 . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-174)
+(-175)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}.")))
NIL
NIL
-(-175 R)
+(-176 R)
((|constructor| (NIL "CoordinateSystems provides coordinate transformation functions for plotting. Functions in this package return conversion functions which take points expressed in other coordinate systems and return points with the corresponding Cartesian coordinates.")) (|conical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1| |#1|) "\\spad{conical(a,{}b)} transforms from conical coordinates to Cartesian coordinates: \\spad{conical(a,{}b)} is a function which will map the point \\spad{(lambda,{}mu,{}nu)} to \\spad{x = lambda*mu*nu/(a*b)},{} \\spad{y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))},{} \\spad{z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))}.")) (|toroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{toroidal(a)} transforms from toroidal coordinates to Cartesian coordinates: \\spad{toroidal(a)} is a function which will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = a*sinh(v)*cos(phi)/(cosh(v)-cos(u))},{} \\spad{y = a*sinh(v)*sin(phi)/(cosh(v)-cos(u))},{} \\spad{z = a*sin(u)/(cosh(v)-cos(u))}.")) (|bipolarCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolarCylindrical(a)} transforms from bipolar cylindrical coordinates to Cartesian coordinates: \\spad{bipolarCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))},{} \\spad{z}.")) (|bipolar| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{bipolar(a)} transforms from bipolar coordinates to Cartesian coordinates: \\spad{bipolar(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*sinh(v)/(cosh(v)-cos(u))},{} \\spad{y = a*sin(u)/(cosh(v)-cos(u))}.")) (|oblateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{oblateSpheroidal(a)} transforms from oblate spheroidal coordinates to Cartesian coordinates: \\spad{oblateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|prolateSpheroidal| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{prolateSpheroidal(a)} transforms from prolate spheroidal coordinates to Cartesian coordinates: \\spad{prolateSpheroidal(a)} is a function which will map the point \\spad{(\\spad{xi},{}eta,{}phi)} to \\spad{x = a*sinh(\\spad{xi})*sin(eta)*cos(phi)},{} \\spad{y = a*sinh(\\spad{xi})*sin(eta)*sin(phi)},{} \\spad{z = a*cosh(\\spad{xi})*cos(eta)}.")) (|ellipticCylindrical| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{ellipticCylindrical(a)} transforms from elliptic cylindrical coordinates to Cartesian coordinates: \\spad{ellipticCylindrical(a)} is a function which will map the point \\spad{(u,{}v,{}z)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)},{} \\spad{z}.")) (|elliptic| (((|Mapping| (|Point| |#1|) (|Point| |#1|)) |#1|) "\\spad{elliptic(a)} transforms from elliptic coordinates to Cartesian coordinates: \\spad{elliptic(a)} is a function which will map the point \\spad{(u,{}v)} to \\spad{x = a*cosh(u)*cos(v)},{} \\spad{y = a*sinh(u)*sin(v)}.")) (|paraboloidal| (((|Point| |#1|) (|Point| |#1|)) "\\spad{paraboloidal(pt)} transforms \\spad{pt} from paraboloidal coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}phi)} to \\spad{x = u*v*cos(phi)},{} \\spad{y = u*v*sin(phi)},{} \\spad{z = 1/2 * (u**2 - v**2)}.")) (|parabolicCylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolicCylindrical(pt)} transforms \\spad{pt} from parabolic cylindrical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v,{}z)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v},{} \\spad{z}.")) (|parabolic| (((|Point| |#1|) (|Point| |#1|)) "\\spad{parabolic(pt)} transforms \\spad{pt} from parabolic coordinates to Cartesian coordinates: the function produced will map the point \\spad{(u,{}v)} to \\spad{x = 1/2*(u**2 - v**2)},{} \\spad{y = u*v}.")) (|spherical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{spherical(pt)} transforms \\spad{pt} from spherical coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}phi)} to \\spad{x = r*sin(phi)*cos(theta)},{} \\spad{y = r*sin(phi)*sin(theta)},{} \\spad{z = r*cos(phi)}.")) (|cylindrical| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cylindrical(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta,{}z)} to \\spad{x = r * cos(theta)},{} \\spad{y = r * sin(theta)},{} \\spad{z}.")) (|polar| (((|Point| |#1|) (|Point| |#1|)) "\\spad{polar(pt)} transforms \\spad{pt} from polar coordinates to Cartesian coordinates: the function produced will map the point \\spad{(r,{}theta)} to \\spad{x = r * cos(theta)} ,{} \\spad{y = r * sin(theta)}.")) (|cartesian| (((|Point| |#1|) (|Point| |#1|)) "\\spad{cartesian(pt)} returns the Cartesian coordinates of point \\spad{pt}.")))
NIL
NIL
-(-176 R |PolR| E)
+(-177 R |PolR| E)
((|constructor| (NIL "This package implements characteristicPolynomials for monogenic algebras using resultants")) (|characteristicPolynomial| ((|#2| |#3|) "\\spad{characteristicPolynomial(e)} returns the characteristic polynomial of \\spad{e} using resultants")))
NIL
NIL
-(-177 R S CS)
+(-178 R S CS)
((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
-((|HasCategory| (-947 |#2|) (LIST (QUOTE -881) (|devaluate| |#1|))))
-(-178 R)
+((|HasCategory| (-948 |#2|) (LIST (QUOTE -882) (|devaluate| |#1|))))
+(-179 R)
((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}")))
NIL
NIL
-(-179)
+(-180)
((|constructor| (NIL "This domain represents `coerce' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-180 R UP)
+(-181 R UP)
((|constructor| (NIL "\\spadtype{ComplexRootFindingPackage} provides functions to find all roots of a polynomial \\spad{p} over the complex number by using Plesken\\spad{'s} idea to calculate in the polynomial ring modulo \\spad{f} and employing the Chinese Remainder Theorem. In this first version,{} the precision (see \\spadfunFrom{digits}{Float}) is not increased when this is necessary to avoid rounding errors. Hence it is the user\\spad{'s} responsibility to increase the precision if necessary. Note also,{} if this package is called with \\spadignore{e.g.} \\spadtype{Fraction Integer},{} the precise calculations could require a lot of time. Also note that evaluating the zeros is not necessarily a good check whether the result is correct: already evaluation can cause rounding errors.")) (|startPolynomial| (((|Record| (|:| |start| |#2|) (|:| |factors| (|Factored| |#2|))) |#2|) "\\spad{startPolynomial(p)} uses the ideas of Schoenhage\\spad{'s} variant of Graeffe\\spad{'s} method to construct circles which separate roots to get a good start polynomial,{} \\spadignore{i.e.} one whose image under the Chinese Remainder Isomorphism has both entries of norm smaller and greater or equal to 1. In case the roots are found during internal calculations. The corresponding factors are in {\\em factors} which are otherwise 1.")) (|setErrorBound| ((|#1| |#1|) "\\spad{setErrorBound(eps)} changes the internal error bound,{} by default being {\\em 10 ** (-3)} to \\spad{eps},{} if \\spad{R} is a member in the category \\spadtype{QuotientFieldCategory Integer}. The internal {\\em globalDigits} is set to {\\em ceiling(1/r)**2*10} being {\\em 10**7} by default.")) (|schwerpunkt| (((|Complex| |#1|) |#2|) "\\spad{schwerpunkt(p)} determines the 'Schwerpunkt' of the roots of the polynomial \\spad{p} of degree \\spad{n},{} \\spadignore{i.e.} the center of gravity,{} which is {\\em coeffient of \\spad{x**(n-1)}} divided by {\\em n times coefficient of \\spad{x**n}}.")) (|rootRadius| ((|#1| |#2|) "\\spad{rootRadius(p)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em 1+globalEps},{} where {\\em globalEps} is the internal error bound,{} which can be set by {\\em setErrorBound}.") ((|#1| |#2| |#1|) "\\spad{rootRadius(p,{}errQuot)} calculates the root radius of \\spad{p} with a maximal error quotient of {\\em errQuot}.")) (|reciprocalPolynomial| ((|#2| |#2|) "\\spad{reciprocalPolynomial(p)} calulates a polynomial which has exactly the inverses of the non-zero roots of \\spad{p} as roots,{} and the same number of 0-roots.")) (|pleskenSplit| (((|Factored| |#2|) |#2| |#1|) "\\spad{pleskenSplit(poly,{} eps)} determines a start polynomial {\\em start}\\\\ by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{pleskenSplit(poly,{}eps,{}info)} determines a start polynomial {\\em start} by using \"startPolynomial then it increases the exponent \\spad{n} of {\\em start ** n mod poly} to get an approximate factor of {\\em poly},{} in general of degree \"degree \\spad{poly} \\spad{-1\"}. Then a divisor cascade is calculated and the best splitting is chosen,{} as soon as the error is small enough. If {\\em info} is {\\em true},{} then information messages are issued.")) (|norm| ((|#1| |#2|) "\\spad{norm(p)} determines sum of absolute values of coefficients Note: this function depends on \\spadfunFrom{abs}{Complex}.")) (|graeffe| ((|#2| |#2|) "\\spad{graeffe p} determines \\spad{q} such that \\spad{q(-z**2) = p(z)*p(-z)}. Note that the roots of \\spad{q} are the squares of the roots of \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} tries to factor \\spad{p} into linear factors with error atmost {\\em globalEps},{} the internal error bound,{} which can be set by {\\em setErrorBound}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1|) "\\spad{factor(p,{} eps)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization.") (((|Factored| |#2|) |#2| |#1| (|Boolean|)) "\\spad{factor(p,{} eps,{} info)} tries to factor \\spad{p} into linear factors with error atmost {\\em eps}. An overall error bound {\\em eps0} is determined and iterated tree-like calls to {\\em pleskenSplit} are used to get the factorization. If {\\em info} is {\\em true},{} then information messages are given.")) (|divisorCascade| (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2|) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions is calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial.") (((|List| (|Record| (|:| |factors| (|List| |#2|)) (|:| |error| |#1|))) |#2| |#2| (|Boolean|)) "\\spad{divisorCascade(p,{}tp)} assumes that degree of polynomial {\\em tp} is smaller than degree of polynomial \\spad{p},{} both monic. A sequence of divisions are calculated using the remainder,{} made monic,{} as divisor for the the next division. The result contains also the error of the factorizations,{} \\spadignore{i.e.} the norm of the remainder polynomial. If {\\em info} is {\\em true},{} then information messages are issued.")) (|complexZeros| (((|List| (|Complex| |#1|)) |#2| |#1|) "\\spad{complexZeros(p,{} eps)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by {\\em eps}.") (((|List| (|Complex| |#1|)) |#2|) "\\spad{complexZeros(p)} tries to determine all complex zeros of the polynomial \\spad{p} with accuracy given by the package constant {\\em globalEps} which you may change by {\\em setErrorBound}.")))
NIL
NIL
-(-181 S ST)
+(-182 S ST)
((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic")))
NIL
NIL
-(-182)
+(-183)
((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") (((|Constructor|) $) "\\spad{constructor(t)} returns the name of the constructor used to make the call.")))
NIL
NIL
-(-183 S)
+(-184 S)
((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")))
NIL
NIL
-(-184)
+(-185)
((|constructor| (NIL "This category declares basic operations on all constructors.")) (|operations| (((|List| (|OverloadSet|)) $) "\\spad{operations(c)} returns the list of all operator exported by instantiations of constructor \\spad{c}. The operators are partitioned into overload sets.")) (|dualSignature| (((|List| (|Boolean|)) $) "\\spad{dualSignature(c)} returns a list \\spad{l} of Boolean values with the following meaning: \\indented{2}{\\spad{l}.(i+1) holds when the constructor takes a domain object} \\indented{10}{as the `i'th argument.\\space{2}Otherwise the argument} \\indented{10}{must be a non-domain object.}")) (|kind| (((|ConstructorKind|) $) "\\spad{kind(ctor)} returns the kind of the constructor `ctor'.")))
NIL
NIL
-(-185)
+(-186)
((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors")))
NIL
NIL
-(-186)
+(-187)
((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-187 R -3196)
+(-188 R -3191)
((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels.")))
NIL
NIL
-(-188 R)
+(-189 R)
((|constructor| (NIL "CoerceVectorMatrixPackage: an unexposed,{} technical package for data conversions")) (|coerce| (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Vector| (|Matrix| |#1|))) "\\spad{coerce(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Fraction Polynomial R}")) (|coerceP| (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|Vector| (|Matrix| |#1|))) "\\spad{coerceP(v)} coerces a vector \\spad{v} with entries in \\spadtype{Matrix R} as vector over \\spadtype{Matrix Polynomial R}")))
NIL
NIL
-(-189)
+(-190)
((|constructor| (NIL "Enumeration by cycle indices.")) (|skewSFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{skewSFunction(li1,{}li2)} is the \\spad{S}-function \\indented{1}{of the partition difference \\spad{li1 - li2}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|SFunction| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|List| (|Integer|))) "\\spad{SFunction(\\spad{li})} is the \\spad{S}-function of the partition \\spad{\\spad{li}} \\indented{1}{expressed in terms of power sum symmetric functions.}")) (|wreath| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{wreath(s1,{}s2)} is the cycle index of the wreath product \\indented{1}{of the two groups whose cycle indices are \\spad{s1} and} \\indented{1}{\\spad{s2}.}")) (|eval| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval s} is the sum of the coefficients of a cycle index.")) (|cup| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cup(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices,{} in which the} \\indented{1}{power sums are retained to produce a cycle index.}")) (|cap| (((|Fraction| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|))) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{cap(s1,{}s2)},{} introduced by Redfield,{} \\indented{1}{is the scalar product of two cycle indices.}")) (|graphs| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{graphs n} is the cycle index of the group induced on \\indented{1}{the edges of a graph by applying the symmetric function to the} \\indented{1}{\\spad{n} nodes.}")) (|dihedral| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{dihedral n} is the cycle index of the \\indented{1}{dihedral group of degree \\spad{n}.}")) (|cyclic| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{cyclic n} is the cycle index of the \\indented{1}{cyclic group of degree \\spad{n}.}")) (|alternating| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{alternating n} is the cycle index of the \\indented{1}{alternating group of degree \\spad{n}.}")) (|elementary| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{elementary n} is the \\spad{n} th elementary symmetric \\indented{1}{function expressed in terms of power sums.}")) (|powerSum| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{powerSum n} is the \\spad{n} th power sum symmetric \\indented{1}{function.}")) (|complete| (((|SymmetricPolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{complete n} is the \\spad{n} th complete homogeneous \\indented{1}{symmetric function expressed in terms of power sums.} \\indented{1}{Alternatively it is the cycle index of the symmetric} \\indented{1}{group of degree \\spad{n}.}")))
NIL
NIL
-(-190)
+(-191)
((|constructor| (NIL "This package \\undocumented{}")) (|cyclotomicFactorization| (((|Factored| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicFactorization(n)} \\undocumented{}")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} \\undocumented{}")) (|cyclotomicDecomposition| (((|List| (|SparseUnivariatePolynomial| (|Integer|))) (|Integer|)) "\\spad{cyclotomicDecomposition(n)} \\undocumented{}")))
NIL
NIL
-(-191)
+(-192)
((|constructor| (NIL "\\axiomType{d01AgentsPackage} is a package of numerical agents to be used to investigate attributes of an input function so as to decide the \\axiomFun{measure} of an appropriate numerical integration routine. It contains functions \\axiomFun{rangeIsFinite} to test the input range and \\axiomFun{functionIsContinuousAtEndPoints} to check for continuity at the end points of the range.")) (|changeName| (((|Result|) (|Symbol|) (|Symbol|) (|Result|)) "\\spad{changeName(s,{}t,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to \\axiom{\\spad{t}}.")) (|commaSeparate| (((|String|) (|List| (|String|))) "\\spad{commaSeparate(l)} produces a comma separated string from a list of strings.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{singularitiesOf(args)} returns a list of potential singularities of the function within the given range")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function if it can be retracted to \\axiomType{Polynomial DoubleFloat}.")) (|functionIsOscillatory| (((|Float|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsOscillatory(a)} tests whether the function \\spad{a.fn} has many zeros of its derivative.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(x)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{x}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(x)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{x}}")) (|functionIsContinuousAtEndPoints| (((|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsContinuousAtEndPoints(args)} uses power series limits to check for problems at the end points of the range of \\spad{args}.")) (|rangeIsFinite| (((|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{rangeIsFinite(args)} tests the endpoints of \\spad{args.range} for infinite end points.")))
NIL
NIL
-(-192)
+(-193)
((|constructor| (NIL "\\axiomType{d01ajfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AJF,{} a general numerical integration routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AJF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-193)
+(-194)
((|constructor| (NIL "\\axiomType{d01akfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AKF,{} a numerical integration routine which is is suitable for oscillating,{} non-singular functions. The function \\axiomFun{measure} measures the usefulness of the routine D01AKF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-194)
+(-195)
((|constructor| (NIL "\\axiomType{d01alfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ALF,{} a general numerical integration routine which can handle a list of singularities. The function \\axiomFun{measure} measures the usefulness of the routine D01ALF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-195)
+(-196)
((|constructor| (NIL "\\axiomType{d01amfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AMF,{} a general numerical integration routine which can handle infinite or semi-infinite range of the input function. The function \\axiomFun{measure} measures the usefulness of the routine D01AMF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-196)
+(-197)
((|constructor| (NIL "\\axiomType{d01anfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ANF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}). The function \\axiomFun{measure} measures the usefulness of the routine D01ANF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-197)
+(-198)
((|constructor| (NIL "\\axiomType{d01apfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01APF,{} a general numerical integration routine which can handle end point singularities of the algebraico-logarithmic form \\spad{w}(\\spad{x}) = (\\spad{x}-a)\\spad{^c} * (\\spad{b}-\\spad{x})\\spad{^d}. The function \\axiomFun{measure} measures the usefulness of the routine D01APF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-198)
+(-199)
((|constructor| (NIL "\\axiomType{d01aqfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01AQF,{} a general numerical integration routine which can solve an integral of the form \\newline \\centerline{\\inputbitmap{/home/bjd/Axiom/anna/hypertex/bitmaps/d01aqf.\\spad{xbm}}} The function \\axiomFun{measure} measures the usefulness of the routine D01AQF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-199)
+(-200)
((|constructor| (NIL "\\axiomType{d01asfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01ASF,{} a numerical integration routine which can handle weight functions of the form cos(\\omega \\spad{x}) or sin(\\omega \\spad{x}) on an semi-infinite range. The function \\axiomFun{measure} measures the usefulness of the routine D01ASF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-200)
+(-201)
((|constructor| (NIL "\\axiomType{d01fcfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01FCF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-201)
+(-202)
((|constructor| (NIL "\\axiomType{d01gbfAnnaType} is a domain of \\axiomType{NumericalIntegrationCategory} for the NAG routine D01GBF,{} a numerical integration routine which can handle multi-dimensional quadrature over a finite region. The function \\axiomFun{measure} measures the usefulness of the routine D01GBF for the given problem. The function \\axiomFun{numericalIntegration} performs the integration by using \\axiomType{NagIntegrationPackage}.")))
NIL
NIL
-(-202)
+(-203)
NIL
NIL
NIL
-(-203)
+(-204)
((|constructor| (NIL "\\axiom{d01WeightsPackage} is a package for functions used to investigate whether a function can be divided into a simpler function and a weight function. The types of weights investigated are those giving rise to end-point singularities of the algebraico-logarithmic type,{} and trigonometric weights.")) (|exprHasLogarithmicWeights| (((|Integer|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasLogarithmicWeights} looks for logarithmic weights giving rise to singularities of the function at the end-points.")) (|exprHasAlgebraicWeight| (((|Union| (|List| (|DoubleFloat|)) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasAlgebraicWeight} looks for algebraic weights giving rise to singularities of the function at the end-points.")) (|exprHasWeightCosWXorSinWX| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |w| (|DoubleFloat|))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\axiom{exprHasWeightCosWXorSinWX} looks for trigonometric weights in an expression of the form \\axiom{cos \\omega \\spad{x}} or \\axiom{sin \\omega \\spad{x}},{} returning the value of \\omega (\\notequal 1) and the operator.")))
NIL
NIL
-(-204)
+(-205)
((|constructor| (NIL "\\axiom{d02AgentsPackage} contains a set of computational agents for use with Ordinary Differential Equation solvers.")) (|intermediateResultsIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{intermediateResultsIF(o)} returns a value corresponding to the required number of intermediate results required and,{} therefore,{} an indication of how much this would affect the step-length of the calculation. It returns a value in the range [0,{}1].")) (|accuracyIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{accuracyIF(o)} returns the intensity value of the accuracy requirements of the input ODE. A request of accuracy of 10^-6 corresponds to the neutral intensity. It returns a value in the range [0,{}1].")) (|expenseOfEvaluationIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{expenseOfEvaluationIF(o)} returns the intensity value of the cost of evaluating the input ODE. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].\\newline\\indent{20} 400 ``operation units\\spad{''} \\spad{->} 0.75 \\newline 200 ``operation units\\spad{''} \\spad{->} 0.5 \\newline 83 ``operation units\\spad{''} \\spad{->} 0.25 \\newline\\indent{15} exponentiation = 4 units ,{} function calls = 10 units.")) (|systemSizeIF| (((|Float|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{systemSizeIF(ode)} returns the intensity value of the size of the system of ODEs. 20 equations corresponds to the neutral value. It returns a value in the range [0,{}1].")) (|stiffnessAndStabilityOfODEIF| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityOfODEIF(ode)} calculates the intensity values of stiffness of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian). \\blankline It returns two values in the range [0,{}1].")) (|stiffnessAndStabilityFactor| (((|Record| (|:| |stiffnessFactor| (|Float|)) (|:| |stabilityFactor| (|Float|))) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{stiffnessAndStabilityFactor(me)} calculates the stability and stiffness factor of a system of first-order differential equations (by evaluating the maximum difference in the real parts of the negative eigenvalues of the jacobian of the system for which \\spad{O}(10) equates to mildly stiff wheras stiffness ratios of \\spad{O}(10^6) are not uncommon) and whether the system is likely to show any oscillations (identified by the closeness to the imaginary axis of the complex eigenvalues of the jacobian).")) (|eval| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Matrix| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{eval(mat,{}symbols,{}values)} evaluates a multivariable matrix at given \\spad{values} for each of a list of variables")) (|jacobian| (((|Matrix| (|Expression| (|DoubleFloat|))) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|))) "\\spad{jacobian(v,{}w)} is a local function to make a jacobian matrix")) (|sparsityIF| (((|Float|) (|Matrix| (|Expression| (|DoubleFloat|)))) "\\spad{sparsityIF(m)} calculates the sparsity of a jacobian matrix")) (|combineFeatureCompatibility| (((|Float|) (|Float|) (|List| (|Float|))) "\\spad{combineFeatureCompatibility(C1,{}L)} is for interacting attributes") (((|Float|) (|Float|) (|Float|)) "\\spad{combineFeatureCompatibility(C1,{}C2)} is for interacting attributes")))
NIL
NIL
-(-205)
+(-206)
((|constructor| (NIL "\\axiomType{d02bbfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BBF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BBF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-206)
+(-207)
((|constructor| (NIL "\\axiomType{d02bhfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02BHF,{} a ODE routine which uses an Runge-Kutta method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02BHF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-207)
+(-208)
((|constructor| (NIL "\\axiomType{d02cjfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02CJF,{} a ODE routine which uses an Adams-Moulton-Bashworth method to solve a system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02CJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-208)
+(-209)
((|constructor| (NIL "\\axiomType{d02ejfAnnaType} is a domain of \\axiomType{OrdinaryDifferentialEquationsInitialValueProblemSolverCategory} for the NAG routine D02EJF,{} a ODE routine which uses a backward differentiation formulae method to handle a stiff system of differential equations. The function \\axiomFun{measure} measures the usefulness of the routine D02EJF for the given problem. The function \\axiomFun{ODESolve} performs the integration by using \\axiomType{NagOrdinaryDifferentialEquationsPackage}.")))
NIL
NIL
-(-209)
+(-210)
((|elliptic?| (((|Boolean|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{elliptic?(r)} \\undocumented{}")) (|central?| (((|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{central?(f,{}g,{}l)} \\undocumented{}")) (|subscriptedVariables| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{subscriptedVariables(e)} \\undocumented{}")) (|varList| (((|List| (|Symbol|)) (|Symbol|) (|NonNegativeInteger|)) "\\spad{varList(s,{}n)} \\undocumented{}")))
NIL
NIL
-(-210)
+(-211)
((|constructor| (NIL "\\axiomType{d03eefAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routines D03EEF/D03EDF.")))
NIL
NIL
-(-211)
+(-212)
((|constructor| (NIL "\\axiomType{d03fafAnnaType} is a domain of \\axiomType{PartialDifferentialEquationsSolverCategory} for the NAG routine D03FAF.")))
NIL
NIL
-(-212 N T$)
+(-213 N T$)
((|constructor| (NIL "This domain provides for a fixed-sized homogeneous data buffer.")) (|qsetelt| ((|#2| $ (|NonNegativeInteger|) |#2|) "setelt(\\spad{b},{}\\spad{i},{}\\spad{x}) sets the \\spad{i}th entry of data buffer \\spad{`b'} to \\spad{`x'}. Indexing is 0-based.")) (|qelt| ((|#2| $ (|NonNegativeInteger|)) "elt(\\spad{b},{}\\spad{i}) returns the \\spad{i}th element in buffer \\spad{`b'}. Indexing is 0-based.")) (|new| (($) "\\spad{new()} returns a fresly allocated data buffer or length \\spad{N}.")))
NIL
NIL
-(-213 S)
+(-214 S)
((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}")))
NIL
NIL
-(-214 -3196 UP UPUP R)
+(-215 -3191 UP UPUP R)
((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use.")))
NIL
NIL
-(-215 -3196 FP)
+(-216 -3191 FP)
((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}.")))
NIL
NIL
-(-216)
-((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144)))))
(-217)
+((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145)))))
+(-218)
((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-218 R -3196)
+(-219 R -3191)
((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
-(-219 R)
+(-220 R)
((|constructor| (NIL "\\spadtype{RationalFunctionDefiniteIntegration} provides functions to compute definite integrals of rational functions.")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|))) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| (|Expression| |#1|))) (|:| |f2| (|List| (|OrderedCompletion| (|Expression| |#1|)))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|OrderedCompletion| (|Expression| |#1|)))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}.")))
NIL
NIL
-(-220 R1 R2)
+(-221 R1 R2)
((|constructor| (NIL "This package \\undocumented{}")) (|expand| (((|List| (|Expression| |#2|)) (|Expression| |#2|) (|PositiveInteger|)) "\\spad{expand(f,{}n)} \\undocumented{}")) (|reduce| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#1|)) (|:| |deg| (|PositiveInteger|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reduce(p)} \\undocumented{}")))
NIL
NIL
-(-221 S)
+(-222 S)
((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-222 |CoefRing| |listIndVar|)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-223 |CoefRing| |listIndVar|)
((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-223 R -3196)
+(-224 R -3191)
((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval.")))
NIL
NIL
-(-224)
+(-225)
((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}.")))
-((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-225)
+(-226)
((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}")))
NIL
NIL
-(-226 R)
+(-227 R)
((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-227 A S)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-228 A S)
((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones.")))
NIL
NIL
-(-228 S)
+(-229 S)
((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones.")))
-((-4404 . T))
+((-4408 . T))
NIL
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((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))))
-(-230 R)
+((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))))
+(-231 R)
((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-231 S)
+(-232 S)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
NIL
NIL
-(-232)
+(-233)
((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-233 A S)
+(-234 A S)
((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4403)))
-(-234 S)
+((|HasAttribute| |#1| (QUOTE -4407)))
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((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}.")))
-((-4404 . T))
+((-4408 . T))
NIL
-(-235)
+(-236)
((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation")))
NIL
NIL
-(-236 S -2240 R)
+(-237 S -3304 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
NIL
-((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-788))) (|HasCategory| |#3| (QUOTE (-843))) (|HasAttribute| |#3| (QUOTE -4400)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-721))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1044))) (|HasCategory| |#3| (QUOTE (-1092))))
-(-237 -2240 R)
+((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1093))))
+(-238 -3304 R)
((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size")))
-((-4397 |has| |#2| (-1044)) (-4398 |has| |#2| (-1044)) (-4400 |has| |#2| (-6 -4400)) ((-4405 "*") |has| |#2| (-171)) (-4403 . T))
+((-4401 |has| |#2| (-1045)) (-4402 |has| |#2| (-1045)) (-4404 |has| |#2| (-6 -4404)) ((-4409 "*") |has| |#2| (-172)) (-4407 . T))
NIL
-(-238 -2240 A B)
+(-239 -3304 A B)
((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
NIL
NIL
-(-239 -2240 R)
+(-240 -3304 R)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation.")))
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+(-241)
((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type.")))
NIL
NIL
-(-241 S)
+(-242 S)
((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")))
NIL
NIL
-(-242)
+(-243)
((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")))
-((-4396 . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-243 S)
+(-244 S)
((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")))
NIL
NIL
-(-244 S)
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((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")))
-((-4404 . T) (-4403 . T))
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-(-245 M)
+((-4408 . T) (-4407 . T))
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+(-246 M)
((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}")))
NIL
NIL
-(-246 |vl| R)
+(-247 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial")))
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((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}.")))
NIL
NIL
-(-248)
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((|constructor| (NIL "This domain provides representations for domains constructors.")))
NIL
NIL
-(-249 |n| R M S)
+(-250 |n| R M S)
((|constructor| (NIL "This constructor provides a direct product type with a left matrix-module view.")))
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((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.")))
NIL
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((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-253 S)
+(-254 S)
((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}.")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
-(-254)
+(-255)
((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
NIL
NIL
-(-255 R |Ex|)
+(-256 R |Ex|)
((|constructor| (NIL "TopLevelDrawFunctionsForAlgebraicCurves provides top level functions for drawing non-singular algebraic curves.")) (|draw| (((|TwoDimensionalViewport|) (|Equation| |#2|) (|Symbol|) (|Symbol|) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y) = g(x,{}y),{}x,{}y,{}l)} draws the graph of a polynomial equation. The list \\spad{l} of draw options must specify a region in the plane in which the curve is to sketched.")))
NIL
NIL
-(-256)
+(-257)
((|setClipValue| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{setClipValue(x)} sets to \\spad{x} the maximum value to plot when drawing complex functions. Returns \\spad{x}.")) (|setImagSteps| (((|Integer|) (|Integer|)) "\\spad{setImagSteps(i)} sets to \\spad{i} the number of steps to use in the imaginary direction when drawing complex functions. Returns \\spad{i}.")) (|setRealSteps| (((|Integer|) (|Integer|)) "\\spad{setRealSteps(i)} sets to \\spad{i} the number of steps to use in the real direction when drawing complex functions. Returns \\spad{i}.")) (|drawComplexVectorField| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{drawComplexVectorField(f,{}rRange,{}iRange)} draws a complex vector field using arrows on the \\spad{x--y} plane. These vector fields should be viewed from the top by pressing the \"XY\" translate button on the 3-\\spad{d} viewport control panel.\\newline Sample call: \\indented{3}{\\spad{f z == sin z}} \\indented{3}{\\spad{drawComplexVectorField(f,{} -2..2,{} -2..2)}} Parameter descriptions: \\indented{2}{\\spad{f} : the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of the imaginary values} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")) (|drawComplex| (((|ThreeDimensionalViewport|) (|Mapping| (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Boolean|)) "\\spad{drawComplex(f,{}rRange,{}iRange,{}arrows?)} draws a complex function as a height field. It uses the complex norm as the height and the complex argument as the color. It will optionally draw arrows on the surface indicating the direction of the complex value.\\newline Sample call: \\indented{2}{\\spad{f z == exp(1/z)}} \\indented{2}{\\spad{drawComplex(f,{} 0.3..3,{} 0..2*\\%\\spad{pi},{} false)}} Parameter descriptions: \\indented{2}{\\spad{f:}\\space{2}the function to draw} \\indented{2}{\\spad{rRange} : the range of the real values} \\indented{2}{\\spad{iRange} : the range of imaginary values} \\indented{2}{\\spad{arrows?} : a flag indicating whether to draw the phase arrows for \\spad{f}} Call the functions \\axiomFunFrom{setRealSteps}{DrawComplex} and \\axiomFunFrom{setImagSteps}{DrawComplex} to change the number of steps used in each direction.")))
NIL
NIL
-(-257 R)
+(-258 R)
((|constructor| (NIL "Hack for the draw interface. DrawNumericHack provides a \"coercion\" from something of the form \\spad{x = a..b} where \\spad{a} and \\spad{b} are formal expressions to a binding of the form \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}. This \"coercion\" fails if \\spad{a} and \\spad{b} contains symbolic variables,{} but is meant for expressions involving \\%\\spad{pi}.")) (|coerce| (((|SegmentBinding| (|Float|)) (|SegmentBinding| (|Expression| |#1|))) "\\spad{coerce(x = a..b)} returns \\spad{x = c..d} where \\spad{c} and \\spad{d} are the numerical values of \\spad{a} and \\spad{b}.")))
NIL
NIL
-(-258 |Ex|)
+(-259 |Ex|)
((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,{}v),{}g(u,{}v),{}h(u,{}v)),{}u = a..b,{}v = c..d,{}l)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,{}y),{}x = a..b,{}y = c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; \\spad{f(x,{}y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t),{}h(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),{}g(t)),{}t = a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{(f(t),{}g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),{}x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),{}x = a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")))
NIL
NIL
-(-259)
+(-260)
((|constructor| (NIL "TopLevelDrawFunctionsForPoints provides top level functions for drawing curves and surfaces described by sets of points.")) (|draw| (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}lz,{}l)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly,{}lz)} draws the surface constructed by projecting the values in the \\axiom{\\spad{lz}} list onto the rectangular grid formed by the \\axiom{\\spad{lx} \\spad{X} \\spad{ly}}.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|))) (|List| (|DrawOption|))) "\\spad{draw(lp,{}l)} plots the curve constructed from the list of points \\spad{lp}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|Point| (|DoubleFloat|)))) "\\spad{draw(lp)} plots the curve constructed from the list of points \\spad{lp}.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{draw(lx,{}ly,{}l)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|List| (|DoubleFloat|)) (|List| (|DoubleFloat|))) "\\spad{draw(lx,{}ly)} plots the curve constructed of points (\\spad{x},{}\\spad{y}) for \\spad{x} in \\spad{lx} for \\spad{y} in \\spad{ly}.")))
NIL
NIL
-(-260)
+(-261)
((|constructor| (NIL "This package \\undocumented{}")) (|units| (((|List| (|Float|)) (|List| (|DrawOption|)) (|List| (|Float|))) "\\spad{units(l,{}u)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{unit}. If the option does not exist the value,{} \\spad{u} is returned.")) (|coord| (((|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{coord}. If the option does not exist the value,{} \\spad{p} is returned.")) (|tubeRadius| (((|Float|) (|List| (|DrawOption|)) (|Float|)) "\\spad{tubeRadius(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubeRadius}. If the option does not exist the value,{} \\spad{n} is returned.")) (|tubePoints| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{tubePoints(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{tubePoints}. If the option does not exist the value,{} \\spad{n} is returned.")) (|space| (((|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{space(l)} takes a list of draw options,{} \\spad{l},{} and checks to see if it contains the option \\spad{space}. If the the option doesn\\spad{'t} exist,{} then an empty space is returned.")) (|var2Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var2Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var2Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|var1Steps| (((|PositiveInteger|) (|List| (|DrawOption|)) (|PositiveInteger|)) "\\spad{var1Steps(l,{}n)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{var1Steps}. If the option does not exist the value,{} \\spad{n} is returned.")) (|ranges| (((|List| (|Segment| (|Float|))) (|List| (|DrawOption|)) (|List| (|Segment| (|Float|)))) "\\spad{ranges(l,{}r)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{ranges}. If the option does not exist the value,{} \\spad{r} is returned.")) (|curveColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{curveColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{curveColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|pointColorPalette| (((|Palette|) (|List| (|DrawOption|)) (|Palette|)) "\\spad{pointColorPalette(l,{}p)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{pointColorPalette}. If the option does not exist the value,{} \\spad{p} is returned.")) (|toScale| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{toScale(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{toScale}. If the option does not exist the value,{} \\spad{b} is returned.")) (|style| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{style(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{style}. If the option does not exist the value,{} \\spad{s} is returned.")) (|title| (((|String|) (|List| (|DrawOption|)) (|String|)) "\\spad{title(l,{}s)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{title}. If the option does not exist the value,{} \\spad{s} is returned.")) (|viewpoint| (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) (|List| (|DrawOption|)) (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(l,{}ls)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{viewpoint}. IF the option does not exist,{} the value \\spad{ls} is returned.")) (|clipBoolean| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{clipBoolean(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{clipBoolean}. If the option does not exist the value,{} \\spad{b} is returned.")) (|adaptive| (((|Boolean|) (|List| (|DrawOption|)) (|Boolean|)) "\\spad{adaptive(l,{}b)} takes the list of draw options,{} \\spad{l},{} and checks the list to see if it contains the option \\spad{adaptive}. If the option does not exist the value,{} \\spad{b} is returned.")))
NIL
NIL
-(-261 S)
+(-262 S)
((|constructor| (NIL "This package \\undocumented{}")) (|option| (((|Union| |#1| "failed") (|List| (|DrawOption|)) (|Symbol|)) "\\spad{option(l,{}s)} determines whether the indicated drawing option,{} \\spad{s},{} is contained in the list of drawing options,{} \\spad{l},{} which is defined by the draw command.")))
NIL
NIL
-(-262)
+(-263)
((|constructor| (NIL "DrawOption allows the user to specify defaults for the creation and rendering of plots.")) (|option?| (((|Boolean|) (|List| $) (|Symbol|)) "\\spad{option?()} is not to be used at the top level; option? internally returns \\spad{true} for drawing options which are indicated in a draw command,{} or \\spad{false} for those which are not.")) (|option| (((|Union| (|Any|) "failed") (|List| $) (|Symbol|)) "\\spad{option()} is not to be used at the top level; option determines internally which drawing options are indicated in a draw command.")) (|unit| (($ (|List| (|Float|))) "\\spad{unit(lf)} will mark off the units according to the indicated list \\spad{lf}. This option is expressed in the form \\spad{unit == [f1,{}f2]}.")) (|coord| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coord(p)} specifies a change of coordinates of point \\spad{p}. This option is expressed in the form \\spad{coord == p}.")) (|tubePoints| (($ (|PositiveInteger|)) "\\spad{tubePoints(n)} specifies the number of points,{} \\spad{n},{} defining the circle which creates the tube around a 3D curve,{} the default is 6. This option is expressed in the form \\spad{tubePoints == n}.")) (|var2Steps| (($ (|PositiveInteger|)) "\\spad{var2Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the second range variable. This option is expressed in the form \\spad{var2Steps == n}.")) (|var1Steps| (($ (|PositiveInteger|)) "\\spad{var1Steps(n)} indicates the number of subdivisions,{} \\spad{n},{} of the first range variable. This option is expressed in the form \\spad{var1Steps == n}.")) (|space| (($ (|ThreeSpace| (|DoubleFloat|))) "\\spad{space specifies} the space into which we will draw. If none is given then a new space is created.")) (|ranges| (($ (|List| (|Segment| (|Float|)))) "\\spad{ranges(l)} provides a list of user-specified ranges \\spad{l}. This option is expressed in the form \\spad{ranges == l}.")) (|range| (($ (|List| (|Segment| (|Fraction| (|Integer|))))) "\\spad{range([i])} provides a user-specified range \\spad{i}. This option is expressed in the form \\spad{range == [i]}.") (($ (|List| (|Segment| (|Float|)))) "\\spad{range([l])} provides a user-specified range \\spad{l}. This option is expressed in the form \\spad{range == [l]}.")) (|tubeRadius| (($ (|Float|)) "\\spad{tubeRadius(r)} specifies a radius,{} \\spad{r},{} for a tube plot around a 3D curve; is expressed in the form \\spad{tubeRadius == 4}.")) (|colorFunction| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(x,{}y,{}z))} specifies the color for three dimensional plots as a function of \\spad{x},{} \\spad{y},{} and \\spad{z} coordinates. This option is expressed in the form \\spad{colorFunction == f(x,{}y,{}z)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(u,{}v))} specifies the color for three dimensional plots as a function based upon the two parametric variables. This option is expressed in the form \\spad{colorFunction == f(u,{}v)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{colorFunction(f(z))} specifies the color based upon the \\spad{z}-component of three dimensional plots. This option is expressed in the form \\spad{colorFunction == f(z)}.")) (|curveColor| (($ (|Palette|)) "\\spad{curveColor(p)} specifies a color index for 2D graph curves from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{curveColor ==p}.") (($ (|Float|)) "\\spad{curveColor(v)} specifies a color,{} \\spad{v},{} for 2D graph curves. This option is expressed in the form \\spad{curveColor == v}.")) (|pointColor| (($ (|Palette|)) "\\spad{pointColor(p)} specifies a color index for 2D graph points from the spadcolors palette \\spad{p}. This option is expressed in the form \\spad{pointColor == p}.") (($ (|Float|)) "\\spad{pointColor(v)} specifies a color,{} \\spad{v},{} for 2D graph points. This option is expressed in the form \\spad{pointColor == v}.")) (|coordinates| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)))) "\\spad{coordinates(p)} specifies a change of coordinate systems of point \\spad{p}. This option is expressed in the form \\spad{coordinates == p}.")) (|toScale| (($ (|Boolean|)) "\\spad{toScale(b)} specifies whether or not a plot is to be drawn to scale; if \\spad{b} is \\spad{true} it is drawn to scale,{} if \\spad{b} is \\spad{false} it is not. This option is expressed in the form \\spad{toScale == b}.")) (|style| (($ (|String|)) "\\spad{style(s)} specifies the drawing style in which the graph will be plotted by the indicated string \\spad{s}. This option is expressed in the form \\spad{style == s}.")) (|title| (($ (|String|)) "\\spad{title(s)} specifies a title for a plot by the indicated string \\spad{s}. This option is expressed in the form \\spad{title == s}.")) (|viewpoint| (($ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(vp)} creates a viewpoint data structure corresponding to the list of values. The values are interpreted as [theta,{} phi,{} scale,{} scaleX,{} scaleY,{} scaleZ,{} deltaX,{} deltaY]. This option is expressed in the form \\spad{viewpoint == ls}.")) (|clip| (($ (|List| (|Segment| (|Float|)))) "\\spad{clip([l])} provides ranges for user-defined clipping as specified in the list \\spad{l}. This option is expressed in the form \\spad{clip == [l]}.") (($ (|Boolean|)) "\\spad{clip(b)} turns 2D clipping on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{clip == b}.")) (|adaptive| (($ (|Boolean|)) "\\spad{adaptive(b)} turns adaptive 2D plotting on if \\spad{b} is \\spad{true},{} or off if \\spad{b} is \\spad{false}. This option is expressed in the form \\spad{adaptive == b}.")))
NIL
NIL
-(-263 R S V)
+(-264 R S V)
((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
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((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate.")))
NIL
NIL
-(-265 S)
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((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#1| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#1| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate.")))
NIL
NIL
-(-266)
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((|optAttributes| (((|List| (|String|)) (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{optAttributes(o)} is a function for supplying a list of attributes of an optimization problem.")) (|expenseOfEvaluation| (((|Float|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{expenseOfEvaluation(o)} returns the intensity value of the cost of evaluating the input set of functions. This is in terms of the number of ``operational units\\spad{''}. It returns a value in the range [0,{}1].")) (|changeNameToObjf| (((|Result|) (|Symbol|) (|Result|)) "\\spad{changeNameToObjf(s,{}r)} changes the name of item \\axiom{\\spad{s}} in \\axiom{\\spad{r}} to objf.")) (|varList| (((|List| (|Symbol|)) (|Expression| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{varList(e,{}n)} returns a list of \\axiom{\\spad{n}} indexed variables with name as in \\axiom{\\spad{e}}.")) (|variables| (((|List| (|Symbol|)) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{variables(args)} returns the list of variables in \\axiom{\\spad{args}.\\spad{lfn}}")) (|quadratic?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{quadratic?(e)} tests if \\axiom{\\spad{e}} is a quadratic function.")) (|nonLinearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{nonLinearPart(l)} returns the list of non-linear functions of \\axiom{\\spad{l}}.")) (|linearPart| (((|List| (|Expression| (|DoubleFloat|))) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linearPart(l)} returns the list of linear functions of \\axiom{\\spad{l}}.")) (|linearMatrix| (((|Matrix| (|DoubleFloat|)) (|List| (|Expression| (|DoubleFloat|))) (|NonNegativeInteger|)) "\\spad{linearMatrix(l,{}n)} returns a matrix of coefficients of the linear functions in \\axiom{\\spad{l}}. If \\spad{l} is empty,{} the matrix has at least one row.")) (|linear?| (((|Boolean|) (|Expression| (|DoubleFloat|))) "\\spad{linear?(e)} tests if \\axiom{\\spad{e}} is a linear function.") (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{linear?(l)} returns \\spad{true} if all the bounds \\spad{l} are either linear or simple.")) (|simpleBounds?| (((|Boolean|) (|List| (|Expression| (|DoubleFloat|)))) "\\spad{simpleBounds?(l)} returns \\spad{true} if the list of expressions \\spad{l} are simple.")) (|splitLinear| (((|Expression| (|DoubleFloat|)) (|Expression| (|DoubleFloat|))) "\\spad{splitLinear(f)} splits the linear part from an expression which it returns.")) (|sumOfSquares| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{sumOfSquares(f)} returns either an expression for which the square is the original function of \"failed\".")) (|sortConstraints| (((|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|))))) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{sortConstraints(args)} uses a simple bubblesort on the list of constraints using the degree of the expression on which to sort. Of course,{} it must match the bounds to the constraints.")) (|finiteBound| (((|List| (|DoubleFloat|)) (|List| (|OrderedCompletion| (|DoubleFloat|))) (|DoubleFloat|)) "\\spad{finiteBound(l,{}b)} repaces all instances of an infinite entry in \\axiom{\\spad{l}} by a finite entry \\axiom{\\spad{b}} or \\axiom{\\spad{-b}}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04dgfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04DGF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04DGF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04fdfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04FDF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04FDF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04gcfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04GCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04GCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04jafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04JAF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04JAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04mbfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04MBF,{} an optimization routine for Linear functions. The function \\axiomFun{measure} measures the usefulness of the routine E04MBF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04nafAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04NAF,{} an optimization routine for Quadratic functions. The function \\axiomFun{measure} measures the usefulness of the routine E04NAF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "\\axiomType{e04ucfAnnaType} is a domain of \\axiomType{NumericalOptimization} for the NAG routine E04UCF,{} a general optimization routine which can handle some singularities in the input function. The function \\axiomFun{measure} measures the usefulness of the routine E04UCF for the given problem. The function \\axiomFun{numericalOptimization} performs the optimization by using \\axiomType{NagOptimisationPackage}.")))
NIL
NIL
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((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1.")))
NIL
NIL
-(-275 R -3196)
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((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}")))
NIL
NIL
-(-276 R -3196)
+(-277 R -3191)
((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels.")))
NIL
NIL
-(-277 |Coef| UTS ULS)
+(-278 |Coef| UTS ULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of Laurent series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of Laurent series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of Laurent series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of Laurent series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of Laurent series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of Laurent series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of Laurent series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of Laurent series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of Laurent series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of Laurent series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of Laurent series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of Laurent series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of Laurent series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of Laurent series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of Laurent series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of Laurent series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of Laurent series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of Laurent series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of Laurent series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of Laurent series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of Laurent series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of Laurent series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of Laurent series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of Laurent series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of Laurent series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of Laurent series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{s ** r} raises a Laurent series \\spad{s} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))))
-(-278 |Coef| ULS UPXS EFULS)
+((|HasCategory| |#1| (QUOTE (-363))))
+(-279 |Coef| ULS UPXS EFULS)
((|constructor| (NIL "\\indented{1}{This package provides elementary functions on any Laurent series} domain over a field which was constructed from a Taylor series domain. These functions are implemented by calling the corresponding functions on the Taylor series domain. We also provide 'partial functions' which compute transcendental functions of Laurent series when possible and return \"failed\" when this is not possible.")) (|acsch| ((|#3| |#3|) "\\spad{acsch(z)} returns the inverse hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|asech| ((|#3| |#3|) "\\spad{asech(z)} returns the inverse hyperbolic secant of a Puiseux series \\spad{z}.")) (|acoth| ((|#3| |#3|) "\\spad{acoth(z)} returns the inverse hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|atanh| ((|#3| |#3|) "\\spad{atanh(z)} returns the inverse hyperbolic tangent of a Puiseux series \\spad{z}.")) (|acosh| ((|#3| |#3|) "\\spad{acosh(z)} returns the inverse hyperbolic cosine of a Puiseux series \\spad{z}.")) (|asinh| ((|#3| |#3|) "\\spad{asinh(z)} returns the inverse hyperbolic sine of a Puiseux series \\spad{z}.")) (|csch| ((|#3| |#3|) "\\spad{csch(z)} returns the hyperbolic cosecant of a Puiseux series \\spad{z}.")) (|sech| ((|#3| |#3|) "\\spad{sech(z)} returns the hyperbolic secant of a Puiseux series \\spad{z}.")) (|coth| ((|#3| |#3|) "\\spad{coth(z)} returns the hyperbolic cotangent of a Puiseux series \\spad{z}.")) (|tanh| ((|#3| |#3|) "\\spad{tanh(z)} returns the hyperbolic tangent of a Puiseux series \\spad{z}.")) (|cosh| ((|#3| |#3|) "\\spad{cosh(z)} returns the hyperbolic cosine of a Puiseux series \\spad{z}.")) (|sinh| ((|#3| |#3|) "\\spad{sinh(z)} returns the hyperbolic sine of a Puiseux series \\spad{z}.")) (|acsc| ((|#3| |#3|) "\\spad{acsc(z)} returns the arc-cosecant of a Puiseux series \\spad{z}.")) (|asec| ((|#3| |#3|) "\\spad{asec(z)} returns the arc-secant of a Puiseux series \\spad{z}.")) (|acot| ((|#3| |#3|) "\\spad{acot(z)} returns the arc-cotangent of a Puiseux series \\spad{z}.")) (|atan| ((|#3| |#3|) "\\spad{atan(z)} returns the arc-tangent of a Puiseux series \\spad{z}.")) (|acos| ((|#3| |#3|) "\\spad{acos(z)} returns the arc-cosine of a Puiseux series \\spad{z}.")) (|asin| ((|#3| |#3|) "\\spad{asin(z)} returns the arc-sine of a Puiseux series \\spad{z}.")) (|csc| ((|#3| |#3|) "\\spad{csc(z)} returns the cosecant of a Puiseux series \\spad{z}.")) (|sec| ((|#3| |#3|) "\\spad{sec(z)} returns the secant of a Puiseux series \\spad{z}.")) (|cot| ((|#3| |#3|) "\\spad{cot(z)} returns the cotangent of a Puiseux series \\spad{z}.")) (|tan| ((|#3| |#3|) "\\spad{tan(z)} returns the tangent of a Puiseux series \\spad{z}.")) (|cos| ((|#3| |#3|) "\\spad{cos(z)} returns the cosine of a Puiseux series \\spad{z}.")) (|sin| ((|#3| |#3|) "\\spad{sin(z)} returns the sine of a Puiseux series \\spad{z}.")) (|log| ((|#3| |#3|) "\\spad{log(z)} returns the logarithm of a Puiseux series \\spad{z}.")) (|exp| ((|#3| |#3|) "\\spad{exp(z)} returns the exponential of a Puiseux series \\spad{z}.")) (** ((|#3| |#3| (|Fraction| (|Integer|))) "\\spad{z ** r} raises a Puiseaux series \\spad{z} to a rational power \\spad{r}")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))))
-(-279)
+((|HasCategory| |#1| (QUOTE (-363))))
+(-280)
((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Symbol|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Symbol|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|ConstructorCall|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter.")))
NIL
NIL
-(-280 A S)
+(-281 A S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))))
-(-281 S)
+((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))))
+(-282 S)
((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}.")))
-((-4404 . T))
+((-4408 . T))
NIL
-(-282 S)
+(-283 S)
((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}.")))
NIL
NIL
-(-283)
+(-284)
((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}.")))
NIL
NIL
-(-284 |Coef| UTS)
+(-285 |Coef| UTS)
((|constructor| (NIL "The elliptic functions \\spad{sn},{} \\spad{sc} and \\spad{dn} are expanded as Taylor series.")) (|sncndn| (((|List| (|Stream| |#1|)) (|Stream| |#1|) |#1|) "\\spad{sncndn(s,{}c)} is used internally.")) (|dn| ((|#2| |#2| |#1|) "\\spad{dn(x,{}k)} expands the elliptic function \\spad{dn} as a Taylor \\indented{1}{series.}")) (|cn| ((|#2| |#2| |#1|) "\\spad{cn(x,{}k)} expands the elliptic function \\spad{cn} as a Taylor \\indented{1}{series.}")) (|sn| ((|#2| |#2| |#1|) "\\spad{sn(x,{}k)} expands the elliptic function \\spad{sn} as a Taylor \\indented{1}{series.}")))
NIL
NIL
-(-285 S |Index|)
+(-286 S |Index|)
((|constructor| (NIL "An eltable over domains \\spad{D} and \\spad{I} is a structure which can be viewed as a function from \\spad{D} to \\spad{I}. Examples of eltable structures range from data structures,{} \\spadignore{e.g.} those of type \\spadtype{List},{} to algebraic structures,{} \\spadignore{e.g.} \\spadtype{Polynomial}.")) (|elt| ((|#2| $ |#1|) "\\spad{elt(u,{}i)} (also written: \\spad{u} . \\spad{i}) returns the element of \\spad{u} indexed by \\spad{i}. Error: if \\spad{i} is not an index of \\spad{u}.")))
NIL
NIL
-(-286 S |Dom| |Im|)
+(-287 S |Dom| |Im|)
((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)))
-(-287 |Dom| |Im|)
+((|HasAttribute| |#1| (QUOTE -4408)))
+(-288 |Dom| |Im|)
((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range.")))
NIL
NIL
-(-288 S R |Mod| -3834 -4103 |exactQuo|)
+(-289 S R |Mod| -2472 -3164 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-289)
+(-290)
((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero.")))
-((-4396 . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-290)
+(-291)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment")))
NIL
NIL
-(-291 R)
+(-292 R)
((|constructor| (NIL "This is a package for the exact computation of eigenvalues and eigenvectors. This package can be made to work for matrices with coefficients which are rational functions over a ring where we can factor polynomials. Rational eigenvalues are always explicitly computed while the non-rational ones are expressed in terms of their minimal polynomial.")) (|eigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvectors(m)} returns the eigenvalues and eigenvectors for the matrix \\spad{m}. The rational eigenvalues and the correspondent eigenvectors are explicitely computed,{} while the non rational ones are given via their minimal polynomial and the corresponding eigenvectors are expressed in terms of a \"generic\" root of such a polynomial.")) (|generalizedEigenvectors| (((|List| (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |geneigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|))))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvectors(m)} returns the generalized eigenvectors of the matrix \\spad{m}.")) (|generalizedEigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Record| (|:| |eigval| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|:| |eigmult| (|NonNegativeInteger|)) (|:| |eigvec| (|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{generalizedEigenvector(eigen,{}m)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{eigen},{} as returned by the function eigenvectors.") (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generalizedEigenvector(alpha,{}m,{}k,{}g)} returns the generalized eigenvectors of the matrix relative to the eigenvalue \\spad{alpha}. The integers \\spad{k} and \\spad{g} are respectively the algebraic and the geometric multiplicity of tye eigenvalue \\spad{alpha}. \\spad{alpha} can be either rational or not. In the seconda case apha is the minimal polynomial of the eigenvalue.")) (|eigenvector| (((|List| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvector(eigval,{}m)} returns the eigenvectors belonging to the eigenvalue \\spad{eigval} for the matrix \\spad{m}.")) (|eigenvalues| (((|List| (|Union| (|Fraction| (|Polynomial| |#1|)) (|SuchThat| (|Symbol|) (|Polynomial| |#1|)))) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eigenvalues(m)} returns the eigenvalues of the matrix \\spad{m} which are expressible as rational functions over the rational numbers.")) (|characteristicPolynomial| (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{characteristicPolynomial(m)} returns the characteristicPolynomial of the matrix \\spad{m} using a new generated symbol symbol as the main variable.") (((|Polynomial| |#1|) (|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}var)} returns the characteristicPolynomial of the matrix \\spad{m} using the symbol \\spad{var} as the main variable.")))
NIL
NIL
-(-292 S R)
+(-293 S R)
((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,{}eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}")))
NIL
NIL
-(-293 S)
+(-294 S)
((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation.")))
-((-4400 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4397 |has| |#1| (-1044)) (-4398 |has| |#1| (-1044)))
-((|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1044)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721)))) (|HasCategory| |#1| (QUOTE (-472))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-1092)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1104)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-301))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-472)))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721)))) (-4037 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-171))))
-(-294 |Key| |Entry|)
+((-4404 -4032 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-1045)) (-4402 |has| |#1| (-1045)))
+((|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1045)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722)))) (|HasCategory| |#1| (QUOTE (-473))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-302))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-473)))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722)))) (-4032 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-172))))
+(-295 |Key| |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-295)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-296)
((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates.")))
NIL
NIL
-(-296 -3196 S)
+(-297 -3191 S)
((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}.")))
NIL
NIL
-(-297 E -3196)
+(-298 E -3191)
((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}.")))
NIL
NIL
-(-298 A B)
+(-299 A B)
((|constructor| (NIL "ExpertSystemContinuityPackage1 exports a function to check range inclusion")) (|in?| (((|Boolean|) (|DoubleFloat|)) "\\spad{in?(p)} tests whether point \\spad{p} is internal to the range [\\spad{A..B}]")))
NIL
NIL
-(-299)
+(-300)
((|constructor| (NIL "ExpertSystemContinuityPackage is a package of functions for the use of domains belonging to the category \\axiomType{NumericalIntegration}.")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a Stream of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a List of \\axiomType{DoubleFloat} to \\axiomType{List}(\\axiomType{String})")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|polynomialZeros| (((|List| (|DoubleFloat|)) (|Polynomial| (|Fraction| (|Integer|))) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{polynomialZeros(fn,{}var,{}range)} calculates the real zeros of the polynomial which are contained in the given interval. It returns a list of points (\\axiomType{Doublefloat}) for which the univariate polynomial \\spad{fn} is zero.")) (|singularitiesOf| (((|Stream| (|DoubleFloat|)) (|Vector| (|Expression| (|DoubleFloat|))) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(v,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{v} will most likely produce an error. This includes those points which evaluate to 0/0.") (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{singularitiesOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error. This includes those points which evaluate to 0/0.")) (|zerosOf| (((|Stream| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|List| (|Symbol|)) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{zerosOf(e,{}vars,{}range)} returns a list of points (\\axiomType{Doublefloat}) at which a NAG fortran version of \\spad{e} will most likely produce an error.")) (|problemPoints| (((|List| (|DoubleFloat|)) (|Expression| (|DoubleFloat|)) (|Symbol|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{problemPoints(f,{}var,{}range)} returns a list of possible problem points by looking at the zeros of the denominator of the function \\spad{f} if it can be retracted to \\axiomType{Polynomial(DoubleFloat)}.")) (|functionIsFracPolynomial?| (((|Boolean|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{functionIsFracPolynomial?(args)} tests whether the function can be retracted to \\axiomType{Fraction(Polynomial(DoubleFloat))}")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\axiom{\\spad{u}}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\axiom{\\spad{u}}")))
NIL
NIL
-(-300 S)
+(-301 S)
((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-1044))))
-(-301)
+((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-1045))))
+(-302)
((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} f)} replaces every \\spad{s(a1,{}..,{}am)} in \\spad{x} by \\spad{f(a1,{}..,{}am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x,{} s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x,{} y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f,{} k)} returns \\spad{op(f(x1),{}...,{}f(xn))} where \\spad{k = op(x1,{}...,{}xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op,{} [f1,{}...,{}fn])} constructs \\spad{op(f1,{}...,{}fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op,{} x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x,{} s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x,{} op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}\\spad{fn},{} \\spad{op(f1,{}...,{}fn)} has height equal to \\spad{1 + max(height(f1),{}...,{}height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f,{} g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x,{} 2])} returns the formal kernel \\spad{atan((x,{} 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,{}...,{}fn])} returns \\spad{(f1,{}...,{}fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x,{} 2])} returns the formal kernel \\spad{atan(x,{} 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f,{} [k1...,{}kn],{} [g1,{}...,{}gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f,{} [k1 = g1,{}...,{}kn = gn])} replaces the kernels \\spad{k1},{}...,{}\\spad{kn} by \\spad{g1},{}...,{}\\spad{gn} formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f,{} k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{}[x1,{}...,{}xn])} or \\spad{op}([\\spad{x1},{}...,{}\\spad{xn}]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}\\spad{xn}.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,{}x,{}y,{}z,{}t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,{}x,{}y,{}z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,{}x,{}y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,{}x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}.")))
NIL
NIL
-(-302 R1)
+(-303 R1)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage1} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|neglist| (((|List| |#1|) (|List| |#1|)) "\\spad{neglist(l)} returns only the negative elements of the list \\spad{l}")))
NIL
NIL
-(-303 R1 R2)
+(-304 R1 R2)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage2} contains some useful functions for use by the computational agents of Ordinary Differential Equation solvers.")) (|map| (((|Matrix| |#2|) (|Mapping| |#2| |#1|) (|Matrix| |#1|)) "\\spad{map(f,{}m)} applies a mapping f:R1 \\spad{->} \\spad{R2} onto a matrix \\spad{m} in \\spad{R1} returning a matrix in \\spad{R2}")))
NIL
NIL
-(-304)
+(-305)
((|constructor| (NIL "\\axiom{ExpertSystemToolsPackage} contains some useful functions for use by the computational agents of numerical solvers.")) (|mat| (((|Matrix| (|DoubleFloat|)) (|List| (|DoubleFloat|)) (|NonNegativeInteger|)) "\\spad{mat(a,{}n)} constructs a one-dimensional matrix of a.")) (|fi2df| (((|DoubleFloat|) (|Fraction| (|Integer|))) "\\spad{fi2df(f)} coerces a \\axiomType{Fraction Integer} to \\axiomType{DoubleFloat}")) (|df2ef| (((|Expression| (|Float|)) (|DoubleFloat|)) "\\spad{df2ef(a)} coerces a \\axiomType{DoubleFloat} to \\axiomType{Expression Float}")) (|pdf2df| (((|DoubleFloat|) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2df(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{DoubleFloat}. It is an error if \\axiom{\\spad{p}} is not retractable to DoubleFloat.")) (|pdf2ef| (((|Expression| (|Float|)) (|Polynomial| (|DoubleFloat|))) "\\spad{pdf2ef(p)} coerces a \\axiomType{Polynomial DoubleFloat} to \\axiomType{Expression Float}")) (|iflist2Result| (((|Result|) (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))) "\\spad{iflist2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|att2Result| (((|Result|) (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) "\\spad{att2Result(m)} converts a attributes record into a \\axiomType{Result}")) (|measure2Result| (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|)))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}") (((|Result|) (|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))))) "\\spad{measure2Result(m)} converts a measure record into a \\axiomType{Result}")) (|outputMeasure| (((|String|) (|Float|)) "\\spad{outputMeasure(n)} rounds \\spad{n} to 3 decimal places and outputs it as a string")) (|concat| (((|Result|) (|List| (|Result|))) "\\spad{concat(l)} concatenates a list of aggregates of type \\axiomType{Result}") (((|Result|) (|Result|) (|Result|)) "\\spad{concat(a,{}b)} adds two aggregates of type \\axiomType{Result}.")) (|gethi| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{gethi(u)} gets the \\axiomType{DoubleFloat} equivalent of the second endpoint of the range \\spad{u}")) (|getlo| (((|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{getlo(u)} gets the \\axiomType{DoubleFloat} equivalent of the first endpoint of the range \\spad{u}")) (|sdf2lst| (((|List| (|String|)) (|Stream| (|DoubleFloat|))) "\\spad{sdf2lst(ln)} coerces a \\axiomType{Stream DoubleFloat} to \\axiomType{String}")) (|ldf2lst| (((|List| (|String|)) (|List| (|DoubleFloat|))) "\\spad{ldf2lst(ln)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List String}")) (|f2st| (((|String|) (|Float|)) "\\spad{f2st(n)} coerces a \\axiomType{Float} to \\axiomType{String}")) (|df2st| (((|String|) (|DoubleFloat|)) "\\spad{df2st(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{String}")) (|in?| (((|Boolean|) (|DoubleFloat|) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{in?(p,{}range)} tests whether point \\spad{p} is internal to the \\spad{range} \\spad{range}")) (|vedf2vef| (((|Vector| (|Expression| (|Float|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{vedf2vef(v)} maps \\axiomType{Vector Expression DoubleFloat} to \\axiomType{Vector Expression Float}")) (|edf2ef| (((|Expression| (|Float|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2ef(e)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Expression Float}")) (|ldf2vmf| (((|Vector| (|MachineFloat|)) (|List| (|DoubleFloat|))) "\\spad{ldf2vmf(l)} coerces a \\axiomType{List DoubleFloat} to \\axiomType{List MachineFloat}")) (|df2mf| (((|MachineFloat|) (|DoubleFloat|)) "\\spad{df2mf(n)} coerces a \\axiomType{DoubleFloat} to \\axiomType{MachineFloat}")) (|dflist| (((|List| (|DoubleFloat|)) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{dflist(l)} returns a list of \\axiomType{DoubleFloat} equivalents of list \\spad{l}")) (|dfRange| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) "\\spad{dfRange(r)} converts a range including \\inputbitmap{\\htbmdir{}/plusminus.bitmap} \\infty to \\axiomType{DoubleFloat} equavalents.")) (|edf2efi| (((|Expression| (|Fraction| (|Integer|))) (|Expression| (|DoubleFloat|))) "\\spad{edf2efi(e)} coerces \\axiomType{Expression DoubleFloat} into \\axiomType{Expression Fraction Integer}")) (|numberOfOperations| (((|Record| (|:| |additions| (|Integer|)) (|:| |multiplications| (|Integer|)) (|:| |exponentiations| (|Integer|)) (|:| |functionCalls| (|Integer|))) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{numberOfOperations(ode)} counts additions,{} multiplications,{} exponentiations and function calls in the input set of expressions.")) (|expenseOfEvaluation| (((|Float|) (|Vector| (|Expression| (|DoubleFloat|)))) "\\spad{expenseOfEvaluation(o)} gives an approximation of the cost of evaluating a list of expressions in terms of the number of basic operations. < 0.3 inexpensive ; 0.5 neutral ; > 0.7 very expensive 400 `operation units' \\spad{->} 0.75 200 `operation units' \\spad{->} 0.5 83 `operation units' \\spad{->} 0.25 \\spad{**} = 4 units ,{} function calls = 10 units.")) (|isQuotient| (((|Union| (|Expression| (|DoubleFloat|)) "failed") (|Expression| (|DoubleFloat|))) "\\spad{isQuotient(expr)} returns the quotient part of the input expression or \\spad{\"failed\"} if the expression is not of that form.")) (|edf2df| (((|DoubleFloat|) (|Expression| (|DoubleFloat|))) "\\spad{edf2df(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{DoubleFloat} It is an error if \\spad{n} is not coercible to DoubleFloat")) (|edf2fi| (((|Fraction| (|Integer|)) (|Expression| (|DoubleFloat|))) "\\spad{edf2fi(n)} maps \\axiomType{Expression DoubleFloat} to \\axiomType{Fraction Integer} It is an error if \\spad{n} is not coercible to Fraction Integer")) (|df2fi| (((|Fraction| (|Integer|)) (|DoubleFloat|)) "\\spad{df2fi(n)} is a function to convert a \\axiomType{DoubleFloat} to a \\axiomType{Fraction Integer}")) (|convert| (((|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{convert(l)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|socf2socdf| (((|Segment| (|OrderedCompletion| (|DoubleFloat|))) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{socf2socdf(a)} is a function to convert a \\axiomType{Segment OrderedCompletion Float} to a \\axiomType{Segment OrderedCompletion DoubleFloat}")) (|ocf2ocdf| (((|OrderedCompletion| (|DoubleFloat|)) (|OrderedCompletion| (|Float|))) "\\spad{ocf2ocdf(a)} is a function to convert an \\axiomType{OrderedCompletion Float} to an \\axiomType{OrderedCompletion DoubleFloat}")) (|ef2edf| (((|Expression| (|DoubleFloat|)) (|Expression| (|Float|))) "\\spad{ef2edf(f)} is a function to convert an \\axiomType{Expression Float} to an \\axiomType{Expression DoubleFloat}")) (|f2df| (((|DoubleFloat|) (|Float|)) "\\spad{f2df(f)} is a function to convert a \\axiomType{Float} to a \\axiomType{DoubleFloat}")))
NIL
NIL
-(-305 S)
+(-306 S)
((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
NIL
NIL
-(-306)
+(-307)
((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-307 S R)
+(-308 S R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-308 R)
+(-309 R)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-309 -3196)
+(-310 -3191)
((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}")))
NIL
NIL
-(-310)
+(-311)
((|constructor| (NIL "This domain represents exit expressions.")) (|level| (((|Integer|) $) "\\spad{level(e)} returns the nesting exit level of `e'")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the exit expression of `e'.")))
NIL
NIL
-(-311)
+(-312)
((|constructor| (NIL "A function which does not return directly to its caller should have Exit as its return type. \\blankline Note: It is convenient to have a formal \\spad{coerce} into each type from type Exit. This allows,{} for example,{} errors to be raised in one half of a type-balanced \\spad{if}.")))
NIL
NIL
-(-312 R FE |var| |cen|)
+(-313 R FE |var| |cen|)
((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
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((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}.")))
NIL
NIL
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((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,{}x = a,{}n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,{}x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,{}n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}x = a,{}n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,{}x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,{}n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,{}x = a,{}n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,{}x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,{}n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,{}x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,{}n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series.")))
NIL
NIL
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((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations.")))
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((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}.")))
NIL
NIL
-(-317)
+(-318)
((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tubePlot| (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|) (|String|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n,{}s)} puts a tube of radius \\spad{r(t)} with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. If \\spad{s} = \"closed\",{} the tube is considered to be closed; if \\spad{s} = \"open\",{} the tube is considered to be open.") (((|TubePlot| (|Plot3D|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Integer|)) "\\spad{tubePlot(f,{}g,{}h,{}colorFcn,{}a..b,{}r,{}n)} puts a tube of radius \\spad{r}(\\spad{t}) with \\spad{n} points on each circle about the curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} for \\spad{t} in \\spad{[a,{}b]}. The tube is considered to be open.")) (|constantToUnaryFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|DoubleFloat|)) "\\spad{constantToUnaryFunction(s)} is a local function which takes the value of \\spad{s},{} which may be a function of a constant,{} and returns a function which always returns the value \\spadtype{DoubleFloat} \\spad{s}.")))
NIL
NIL
-(-318 FE |var| |cen|)
+(-319 FE |var| |cen|)
((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms.")))
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-(-319 M)
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+(-320 M)
((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}.")))
NIL
NIL
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((|constructor| (NIL "This package provides utilities used by the factorizers which operate on polynomials represented as univariate polynomials with multivariate coefficients.")) (|ran| ((|#3| (|Integer|)) "\\spad{ran(k)} computes a random integer between \\spad{-k} and \\spad{k} as a member of \\spad{R}.")) (|normalDeriv| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|Integer|)) "\\spad{normalDeriv(poly,{}i)} computes the \\spad{i}th derivative of \\spad{poly} divided by i!.")) (|raisePolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|)) "\\spad{raisePolynomial(rpoly)} converts \\spad{rpoly} from a univariate polynomial over \\spad{r} to be a univariate polynomial with polynomial coefficients.")) (|lowerPolynomial| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{lowerPolynomial(upoly)} converts \\spad{upoly} to be a univariate polynomial over \\spad{R}. An error if the coefficients contain variables.")) (|variables| (((|List| |#2|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{variables(upoly)} returns the list of variables for the coefficients of \\spad{upoly}.")) (|degree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|)) "\\spad{degree(upoly,{} lvar)} returns a list containing the maximum degree for each variable in lvar.")) (|completeEval| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|)) "\\spad{completeEval(upoly,{} lvar,{} lval)} evaluates the polynomial \\spad{upoly} with each variable in \\spad{lvar} replaced by the corresponding value in lval. Substitutions are done for all variables in \\spad{upoly} producing a univariate polynomial over \\spad{R}.")))
NIL
NIL
-(-321 S)
+(-322 S)
((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative.")))
-((-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-787))))
-(-322 S E)
+((-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-788))))
+(-323 S E)
((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}.")))
NIL
NIL
-(-323 S)
+(-324 S)
((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative.")))
NIL
-((|HasCategory| (-766) (QUOTE (-787))))
-(-324 S R E)
+((|HasCategory| (-767) (QUOTE (-788))))
+(-325 S R E)
((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring.")))
NIL
-((|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))))
-(-325 R E)
+((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))))
+(-326 R E)
((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-326 S)
+(-327 S)
((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-327 S -3196)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-328 S -3191)
((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace.")))
NIL
-((|HasCategory| |#2| (QUOTE (-367))))
-(-328 -3196)
+((|HasCategory| |#2| (QUOTE (-368))))
+(-329 -3191)
((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-329)
+(-330)
((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")))
NIL
NIL
-(-330 E)
+(-331 E)
((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series")))
NIL
NIL
-(-331)
+(-332)
((|constructor| (NIL "\\spadtype{FortranCodePackage1} provides some utilities for producing useful objects in FortranCode domain. The Package may be used with the FortranCode domain and its \\spad{printCode} or possibly via an outputAsFortran. (The package provides items of use in connection with ASPs in the AXIOM-NAG link and,{} where appropriate,{} naming accords with that in IRENA.) The easy-to-use functions use Fortran loop variables I1,{} I2,{} and it is users' responsibility to check that this is sensible. The advanced functions use SegmentBinding to allow users control over Fortran loop variable names.")) (|identitySquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{identitySquareMatrix(s,{}p)} \\undocumented{}")) (|zeroSquareMatrix| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroSquareMatrix(s,{}p)} \\undocumented{}")) (|zeroMatrix| (((|FortranCode|) (|Symbol|) (|SegmentBinding| (|Polynomial| (|Integer|))) (|SegmentBinding| (|Polynomial| (|Integer|)))) "\\spad{zeroMatrix(s,{}b,{}d)} in this version gives the user control over names of Fortran variables used in loops.") (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|)) (|Polynomial| (|Integer|))) "\\spad{zeroMatrix(s,{}p,{}q)} uses loop variables in the Fortran,{} I1 and I2")) (|zeroVector| (((|FortranCode|) (|Symbol|) (|Polynomial| (|Integer|))) "\\spad{zeroVector(s,{}p)} \\undocumented{}")))
NIL
NIL
-(-332 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
+(-333 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}")))
NIL
NIL
-(-333 S -3196 UP UPUP R)
+(-334 S -3191 UP UPUP R)
((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}.")))
NIL
NIL
-(-334 -3196 UP UPUP R)
+(-335 -3191 UP UPUP R)
((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}.")))
NIL
NIL
-(-335 -3196 UP UPUP R)
+(-336 -3191 UP UPUP R)
((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}.")))
NIL
NIL
-(-336 S R)
+(-337 S R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))))
-(-337 R)
+((|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))))
+(-338 R)
((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex.")))
NIL
NIL
-(-338 |basicSymbols| |subscriptedSymbols| R)
+(-339 |basicSymbols| |subscriptedSymbols| R)
((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#3| (LIST (QUOTE -1033) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-339 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-340 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2)
((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}.")))
NIL
NIL
-(-340 S -3196 UP UPUP)
+(-341 S -3191 UP UPUP)
((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components.")))
NIL
-((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-362))))
-(-341 -3196 UP UPUP)
+((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-363))))
+(-342 -3191 UP UPUP)
((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components.")))
-((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-342 |p| |extdeg|)
+(-343 |p| |extdeg|)
((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144))))
-(-343 GF |defpol|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145))))
+(-344 GF |defpol|)
((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-344 GF |extdeg|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-345 GF |extdeg|)
((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-345 GF)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-346 GF)
((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}.")))
NIL
NIL
-(-346 F1 GF F2)
+(-347 F1 GF F2)
((|constructor| (NIL "FiniteFieldHomomorphisms(\\spad{F1},{}\\spad{GF},{}\\spad{F2}) exports coercion functions of elements between the fields {\\em F1} and {\\em F2},{} which both must be finite simple algebraic extensions of the finite ground field {\\em GF}.")) (|coerce| ((|#1| |#3|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F2} in {\\em F1},{} where {\\em coerce} is a field homomorphism between the fields extensions {\\em F2} and {\\em F1} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F2} doesn\\spad{'t} divide the extension degree of {\\em F1}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.") ((|#3| |#1|) "\\spad{coerce(x)} is the homomorphic image of \\spad{x} from {\\em F1} in {\\em F2}. Thus {\\em coerce} is a field homomorphism between the fields extensions {\\em F1} and {\\em F2} both over ground field {\\em GF} (the second argument to the package). Error: if the extension degree of {\\em F1} doesn\\spad{'t} divide the extension degree of {\\em F2}. Note that the other coercion function in the \\spadtype{FiniteFieldHomomorphisms} is a left inverse.")))
NIL
NIL
-(-347 S)
+(-348 S)
((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields.")))
NIL
NIL
-(-348)
+(-349)
((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-349 R UP -3196)
+(-350 R UP -3191)
((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
-(-350 |p| |extdeg|)
+(-351 |p| |extdeg|)
((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144))))
-(-351 GF |uni|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145))))
+(-352 GF |uni|)
((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-352 GF |extdeg|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-353 GF |extdeg|)
((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-353 |p| |n|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-354 |p| |n|)
((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| (-905 |#1|) (QUOTE (-144))) (|HasCategory| (-905 |#1|) (QUOTE (-367)))) (|HasCategory| (-905 |#1|) (QUOTE (-146))) (|HasCategory| (-905 |#1|) (QUOTE (-367))) (|HasCategory| (-905 |#1|) (QUOTE (-144))))
-(-354 GF |defpol|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145))))
+(-355 GF |defpol|)
((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-355 -3196 GF)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-356 -3191 GF)
((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-356 GF)
+(-357 GF)
((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive.")))
NIL
NIL
-(-357 -3196 FP FPP)
+(-358 -3191 FP FPP)
((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
-(-358 GF |n|)
+(-359 GF |n|)
((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144))))
-(-359 R |ls|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145))))
+(-360 R |ls|)
((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}.")))
NIL
NIL
-(-360 S)
+(-361 S)
((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-361 S)
+(-362 S)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
NIL
NIL
-(-362)
+(-363)
((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-363 |Name| S)
+(-364 |Name| S)
((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input.")))
NIL
NIL
-(-364 S)
+(-365 S)
((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result.")))
NIL
NIL
-(-365 S R)
+(-366 S R)
((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
NIL
-((|HasCategory| |#2| (QUOTE (-554))))
-(-366 R)
+((|HasCategory| |#2| (QUOTE (-555))))
+(-367 R)
((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis.")))
-((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T))
+((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T))
NIL
-(-367)
+(-368)
((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set.")))
NIL
NIL
-(-368 S R UP)
+(-369 S R UP)
((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#3| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#3| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#2| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#2| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#2| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
NIL
-((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-362))))
-(-369 R UP)
+((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-363))))
+(-370 R UP)
((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-370 S A R B)
+(-371 S A R B)
((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain.")))
NIL
NIL
-(-371 A S)
+(-372 A S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))))
-(-372 S)
+((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))))
+(-373 S)
((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}.")))
-((-4403 . T))
+((-4407 . T))
NIL
-(-373 |VarSet| R)
+(-374 |VarSet| R)
((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T))
NIL
-(-374 S V)
+(-375 S V)
((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm.")))
NIL
NIL
-(-375 S R)
+(-376 S R)
((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))))
-(-376 R)
+((|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))))
+(-377 R)
((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-377 |Par|)
+(-378 |Par|)
((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}.")))
NIL
NIL
-(-378)
+(-379)
((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}.")))
-((-4386 . T) (-4394 . T) (-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4390 . T) (-4398 . T) (-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-379 |Par|)
+(-380 |Par|)
((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.")))
NIL
NIL
-(-380 R S)
+(-381 R S)
((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}")))
-((-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-171))))
-(-381 R |Basis|)
+((-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-172))))
+(-382 R |Basis|)
((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}.")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-382)
+(-383)
((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}.")))
NIL
NIL
-(-383)
+(-384)
((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
NIL
NIL
-(-384 R S)
+(-385 R S)
((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored.")))
-((-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-171))))
-(-385 S)
+((-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-172))))
+(-386 S)
((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
NIL
-((|HasCategory| |#1| (QUOTE (-845))))
-(-386)
+((|HasCategory| |#1| (QUOTE (-846))))
+(-387)
((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-387)
+(-388)
((|constructor| (NIL "This domain provides an interface to names in the file system.")))
NIL
NIL
-(-388)
+(-389)
((|constructor| (NIL "This category provides an interface to names in the file system.")) (|new| (($ (|String|) (|String|) (|String|)) "\\spad{new(d,{}pref,{}e)} constructs the name of a new writable file with \\spad{d} as its directory,{} \\spad{pref} as a prefix of its name and \\spad{e} as its extension. When \\spad{d} or \\spad{t} is the empty string,{} a default is used. An error occurs if a new file cannot be written in the given directory.")) (|writable?| (((|Boolean|) $) "\\spad{writable?(f)} tests if the named file be opened for writing. The named file need not already exist.")) (|readable?| (((|Boolean|) $) "\\spad{readable?(f)} tests if the named file exist and can it be opened for reading.")) (|exists?| (((|Boolean|) $) "\\spad{exists?(f)} tests if the file exists in the file system.")) (|extension| (((|String|) $) "\\spad{extension(f)} returns the type part of the file name.")) (|name| (((|String|) $) "\\spad{name(f)} returns the name part of the file name.")) (|directory| (((|String|) $) "\\spad{directory(f)} returns the directory part of the file name.")) (|filename| (($ (|String|) (|String|) (|String|)) "\\spad{filename(d,{}n,{}e)} creates a file name with \\spad{d} as its directory,{} \\spad{n} as its name and \\spad{e} as its extension. This is a portable way to create file names. When \\spad{d} or \\spad{t} is the empty string,{} a default is used.")))
NIL
NIL
-(-389 |n| |class| R)
+(-390 |n| |class| R)
((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-390)
+(-391)
((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack")))
NIL
NIL
-(-391 -3196 UP UPUP R)
+(-392 -3191 UP UPUP R)
((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented")))
NIL
NIL
-(-392 S)
+(-393 S)
((|constructor| (NIL "\\spadtype{ScriptFormulaFormat1} provides a utility coercion for changing to SCRIPT formula format anything that has a coercion to the standard output format.")) (|coerce| (((|ScriptFormulaFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from an expression \\spad{s} of domain \\spad{S} to SCRIPT formula format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to SCRIPT formula format.")))
NIL
NIL
-(-393)
+(-394)
((|constructor| (NIL "\\spadtype{ScriptFormulaFormat} provides a coercion from \\spadtype{OutputForm} to IBM SCRIPT/VS Mathematical Formula Format. The basic SCRIPT formula format object consists of three parts: a prologue,{} a formula part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{formula} and \\spadfun{epilogue} extract these parts,{} respectively. The central parts of the expression go into the formula part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \":df.\" and \":edf.\" so that the formula section will be printed in display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a formatted object \\spad{t} to \\spad{strings}.")) (|setFormula!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setFormula!(t,{}strings)} sets the formula section of a formatted object \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a formatted object \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a formatted object \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setFormula!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|formula| (((|List| (|String|)) $) "\\spad{formula(t)} extracts the formula section of a formatted object \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a formatted object \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to SCRIPT formula format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")))
NIL
NIL
-(-394)
+(-395)
((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram.")))
NIL
NIL
-(-395)
+(-396)
((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
NIL
NIL
-(-396)
+(-397)
((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}")))
NIL
NIL
-(-397 -3253 |returnType| -3433 |symbols|)
+(-398 -3348 |returnType| -4093 |symbols|)
((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}")))
NIL
NIL
-(-398 -3196 UP)
+(-399 -3191 UP)
((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}")))
NIL
NIL
-(-399 R)
+(-400 R)
((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers).")))
NIL
NIL
-(-400 S)
+(-401 S)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
NIL
NIL
-(-401)
+(-402)
((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-402 S)
+(-403 S)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\".")))
NIL
-((|HasAttribute| |#1| (QUOTE -4386)) (|HasAttribute| |#1| (QUOTE -4394)))
-(-403)
+((|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#1| (QUOTE -4398)))
+(-404)
((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\".")))
-((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-404 R S)
+(-405 R S)
((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type.")))
NIL
NIL
-(-405 A B)
+(-406 A B)
((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}.")))
NIL
NIL
-(-406 S)
+(-407 S)
((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical.")))
-((-4390 -12 (|has| |#1| (-6 -4401)) (|has| |#1| (-451)) (|has| |#1| (-6 -4390))) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
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-(-407 S R UP)
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+(-408 S R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
NIL
-(-408 R UP)
+(-409 R UP)
((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-409 A S)
+(-410 A S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-410 S)
+((|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-411 S)
((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991")))
NIL
NIL
-(-411 R1 F1 U1 A1 R2 F2 U2 A2)
+(-412 R1 F1 U1 A1 R2 F2 U2 A2)
((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}")))
NIL
NIL
-(-412 R -3196 UP A)
+(-413 R -3191 UP A)
((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-413 R -3196 UP A |ibasis|)
+(-414 R -3191 UP A |ibasis|)
((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")))
NIL
-((|HasCategory| |#4| (LIST (QUOTE -1033) (|devaluate| |#2|))))
-(-414 AR R AS S)
+((|HasCategory| |#4| (LIST (QUOTE -1034) (|devaluate| |#2|))))
+(-415 AR R AS S)
((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}.")))
NIL
NIL
-(-415 S R)
+(-416 S R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#2|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#2|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#2|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#2|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#2|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#2|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#2| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))))
-(-416 R)
+((|HasCategory| |#2| (QUOTE (-363))))
+(-417 R)
((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis.")))
-((-4400 |has| |#1| (-554)) (-4398 . T) (-4397 . T))
+((-4404 |has| |#1| (-555)) (-4402 . T) (-4401 . T))
NIL
-(-417 R)
-((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1211))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-1211)))) (|HasCategory| |#1| (QUOTE (-1017))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-451))))
(-418 R)
+((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically.")))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1212))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1212)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452))))
+(-419 R)
((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}.")))
NIL
NIL
-(-419 R FE |x| |cen|)
+(-420 R FE |x| |cen|)
((|constructor| (NIL "This package converts expressions in some function space to exponential expansions.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToXXP| (((|Union| (|:| |%expansion| (|ExponentialExpansion| |#1| |#2| |#3| |#4|)) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|)) "\\spad{exprToXXP(fcn,{}posCheck?)} converts the expression \\spad{fcn} to an exponential expansion. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed.")))
NIL
NIL
-(-420 R A S B)
+(-421 R A S B)
((|constructor| (NIL "This package allows a mapping \\spad{R} \\spad{->} \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}.")))
NIL
NIL
-(-421 R FE |Expon| UPS TRAN |x|)
+(-422 R FE |Expon| UPS TRAN |x|)
((|constructor| (NIL "This package converts expressions in some function space to power series in a variable \\spad{x} with coefficients in that function space. The function \\spadfun{exprToUPS} converts expressions to power series whose coefficients do not contain the variable \\spad{x}. The function \\spadfun{exprToGenUPS} converts functional expressions to power series whose coefficients may involve functions of \\spad{log(x)}.")) (|localAbs| ((|#2| |#2|) "\\spad{localAbs(fcn)} = \\spad{abs(fcn)} or \\spad{sqrt(fcn**2)} depending on whether or not FE has a function \\spad{abs}. This should be a local function,{} but the compiler won\\spad{'t} allow it.")) (|exprToGenUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToGenUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a generalized power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} we return a record containing the name of the function that caused the problem and a brief description of the problem. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|exprToUPS| (((|Union| (|:| |%series| |#4|) (|:| |%problem| (|Record| (|:| |func| (|String|)) (|:| |prob| (|String|))))) |#2| (|Boolean|) (|String|)) "\\spad{exprToUPS(fcn,{}posCheck?,{}atanFlag)} converts the expression \\spad{fcn} to a power series. If \\spad{posCheck?} is \\spad{true},{} log\\spad{'s} of negative numbers are not allowed nor are \\spad{n}th roots of negative numbers with \\spad{n} even. If \\spad{posCheck?} is \\spad{false},{} these are allowed. \\spad{atanFlag} determines how the case \\spad{atan(f(x))},{} where \\spad{f(x)} has a pole,{} will be treated. The possible values of \\spad{atanFlag} are \\spad{\"complex\"},{} \\spad{\"real: two sides\"},{} \\spad{\"real: left side\"},{} \\spad{\"real: right side\"},{} and \\spad{\"just do it\"}. If \\spad{atanFlag} is \\spad{\"complex\"},{} then no series expansion will be computed because,{} viewed as a function of a complex variable,{} \\spad{atan(f(x))} has an essential singularity. Otherwise,{} the sign of the leading coefficient of the series expansion of \\spad{f(x)} determines the constant coefficient in the series expansion of \\spad{atan(f(x))}. If this sign cannot be determined,{} a series expansion is computed only when \\spad{atanFlag} is \\spad{\"just do it\"}. When the leading term in the series expansion of \\spad{f(x)} is of odd degree (or is a rational degree with odd numerator),{} then the constant coefficient in the series expansion of \\spad{atan(f(x))} for values to the left differs from that for values to the right. If \\spad{atanFlag} is \\spad{\"real: two sides\"},{} no series expansion will be computed. If \\spad{atanFlag} is \\spad{\"real: left side\"} the constant coefficient for values to the left will be used and if \\spad{atanFlag} \\spad{\"real: right side\"} the constant coefficient for values to the right will be used. If there is a problem in converting the function to a power series,{} a record containing the name of the function that caused the problem and a brief description of the problem is returned. When expanding the expression into a series it is assumed that the series is centered at 0. For a series centered at a,{} the user should perform the substitution \\spad{x -> x + a} before calling this function.")) (|integrate| (($ $) "\\spad{integrate(x)} returns the integral of \\spad{x} since we need to be able to integrate a power series")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x} since we need to be able to differentiate a power series")))
NIL
NIL
-(-422 S A R B)
+(-423 S A R B)
((|constructor| (NIL "FiniteSetAggregateFunctions2 provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad {[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain.")))
NIL
NIL
-(-423 A S)
+(-424 A S)
((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-367))))
-(-424 S)
+((|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-368))))
+(-425 S)
((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}.")))
-((-4403 . T) (-4393 . T) (-4404 . T))
+((-4407 . T) (-4397 . T) (-4408 . T))
NIL
-(-425 R -3196)
+(-426 R -3191)
((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")))
NIL
NIL
-(-426 R E)
+(-427 R E)
((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series")))
-((-4390 -12 (|has| |#1| (-6 -4390)) (|has| |#2| (-6 -4390))) (-4397 . T) (-4398 . T) (-4400 . T))
-((-12 (|HasAttribute| |#1| (QUOTE -4390)) (|HasAttribute| |#2| (QUOTE -4390))))
-(-427 R -3196)
+((-4394 -12 (|has| |#1| (-6 -4394)) (|has| |#2| (-6 -4394))) (-4401 . T) (-4402 . T) (-4404 . T))
+((-12 (|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#2| (QUOTE -4394))))
+(-428 R -3191)
((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable.")))
NIL
NIL
-(-428 S R)
+(-429 S R)
((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-1104))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))))
-(-429 R)
+((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))))
+(-430 R)
((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}.")))
-((-4400 -4037 (|has| |#1| (-1044)) (|has| |#1| (-472))) (-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) ((-4405 "*") |has| |#1| (-554)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-554)) (-4395 |has| |#1| (-554)))
+((-4404 -4032 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) ((-4409 "*") |has| |#1| (-555)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-555)) (-4399 |has| |#1| (-555)))
NIL
-(-430 R -3196)
+(-431 R -3191)
((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator.")))
NIL
NIL
-(-431 R -3196)
+(-432 R -3191)
((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.")))
NIL
((|HasCategory| |#2| (QUOTE (-27))))
-(-432 R -3196)
+(-433 R -3191)
((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,{}k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented")))
NIL
NIL
-(-433)
+(-434)
((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\"")))
NIL
NIL
-(-434 R -3196 UP)
+(-435 R -3191 UP)
((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-48)))))
-(-435)
+((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-48)))))
+(-436)
((|constructor| (NIL "Code to manipulate Fortran templates")) (|fortranCarriageReturn| (((|Void|)) "\\spad{fortranCarriageReturn()} produces a carriage return on the current Fortran output stream")) (|fortranLiteral| (((|Void|) (|String|)) "\\spad{fortranLiteral(s)} writes \\spad{s} to the current Fortran output stream")) (|fortranLiteralLine| (((|Void|) (|String|)) "\\spad{fortranLiteralLine(s)} writes \\spad{s} to the current Fortran output stream,{} followed by a carriage return")) (|processTemplate| (((|FileName|) (|FileName|)) "\\spad{processTemplate(tp)} processes the template \\spad{tp},{} writing the result to the current FORTRAN output stream.") (((|FileName|) (|FileName|) (|FileName|)) "\\spad{processTemplate(tp,{}fn)} processes the template \\spad{tp},{} writing the result out to \\spad{fn}.")))
NIL
NIL
-(-436)
+(-437)
((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,{}dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type")))
NIL
NIL
-(-437 |f|)
+(-438 |f|)
((|constructor| (NIL "This domain implements named functions")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-438)
+(-439)
((|constructor| (NIL "This is the datatype for exported function descriptor. A function descriptor consists of: (1) a signature; (2) a predicate; and (3) a slot into the scope object.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of function described by \\spad{x}.")))
NIL
NIL
-(-439)
+(-440)
((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}.")))
NIL
NIL
-(-440)
+(-441)
((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}")))
NIL
NIL
-(-441 UP)
+(-442 UP)
((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object.")))
NIL
NIL
-(-442 R UP -3196)
+(-443 R UP -3191)
((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}.")))
NIL
NIL
-(-443 R UP)
+(-444 R UP)
((|constructor| (NIL "\\spadtype{GaloisGroupPolynomialUtilities} provides useful functions for univariate polynomials which should be added to \\spadtype{UnivariatePolynomialCategory} or to \\spadtype{Factored} (July 1994).")) (|factorsOfDegree| (((|List| |#2|) (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorsOfDegree(d,{}f)} returns the factors of degree \\spad{d} of the factored polynomial \\spad{f}.")) (|factorOfDegree| ((|#2| (|PositiveInteger|) (|Factored| |#2|)) "\\spad{factorOfDegree(d,{}f)} returns a factor of degree \\spad{d} of the factored polynomial \\spad{f}. Such a factor shall exist.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|Factored| |#2|)) "\\spad{degreePartition(f)} returns the degree partition (\\spadignore{i.e.} the multiset of the degrees of the irreducible factors) of the polynomial \\spad{f}.")) (|shiftRoots| ((|#2| |#2| |#1|) "\\spad{shiftRoots(p,{}c)} returns the polynomial which has for roots \\spad{c} added to the roots of \\spad{p}.")) (|scaleRoots| ((|#2| |#2| |#1|) "\\spad{scaleRoots(p,{}c)} returns the polynomial which has \\spad{c} times the roots of \\spad{p}.")) (|reverse| ((|#2| |#2|) "\\spad{reverse(p)} returns the reverse polynomial of \\spad{p}.")) (|unvectorise| ((|#2| (|Vector| |#1|)) "\\spad{unvectorise(v)} returns the polynomial which has for coefficients the entries of \\spad{v} in the increasing order.")) (|monic?| (((|Boolean|) |#2|) "\\spad{monic?(p)} tests if \\spad{p} is monic (\\spadignore{i.e.} leading coefficient equal to 1).")))
NIL
NIL
-(-444 R)
+(-445 R)
((|constructor| (NIL "\\spadtype{GaloisGroupUtilities} provides several useful functions.")) (|safetyMargin| (((|NonNegativeInteger|)) "\\spad{safetyMargin()} returns the number of low weight digits we do not trust in the floating point representation (used by \\spadfun{safeCeiling}).") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{safetyMargin(n)} sets to \\spad{n} the number of low weight digits we do not trust in the floating point representation and returns the previous value (for use by \\spadfun{safeCeiling}).")) (|safeFloor| (((|Integer|) |#1|) "\\spad{safeFloor(x)} returns the integer which is lower or equal to the largest integer which has the same floating point number representation.")) (|safeCeiling| (((|Integer|) |#1|) "\\spad{safeCeiling(x)} returns the integer which is greater than any integer with the same floating point number representation.")) (|fillPascalTriangle| (((|Void|)) "\\spad{fillPascalTriangle()} fills the stored table.")) (|sizePascalTriangle| (((|NonNegativeInteger|)) "\\spad{sizePascalTriangle()} returns the number of entries currently stored in the table.")) (|rangePascalTriangle| (((|NonNegativeInteger|)) "\\spad{rangePascalTriangle()} returns the maximal number of lines stored.") (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rangePascalTriangle(n)} sets the maximal number of lines which are stored and returns the previous value.")) (|pascalTriangle| ((|#1| (|NonNegativeInteger|) (|Integer|)) "\\spad{pascalTriangle(n,{}r)} returns the binomial coefficient \\spad{C(n,{}r)=n!/(r! (n-r)!)} and stores it in a table to prevent recomputation.")))
NIL
-((|HasCategory| |#1| (QUOTE (-403))))
-(-445)
+((|HasCategory| |#1| (QUOTE (-404))))
+(-446)
((|constructor| (NIL "Package for the factorization of complex or gaussian integers.")) (|prime?| (((|Boolean|) (|Complex| (|Integer|))) "\\spad{prime?(\\spad{zi})} tests if the complex integer \\spad{zi} is prime.")) (|sumSquares| (((|List| (|Integer|)) (|Integer|)) "\\spad{sumSquares(p)} construct \\spad{a} and \\spad{b} such that \\spad{a**2+b**2} is equal to the integer prime \\spad{p},{} and otherwise returns an error. It will succeed if the prime number \\spad{p} is 2 or congruent to 1 mod 4.")) (|factor| (((|Factored| (|Complex| (|Integer|))) (|Complex| (|Integer|))) "\\spad{factor(\\spad{zi})} produces the complete factorization of the complex integer \\spad{zi}.")))
NIL
NIL
-(-446 |Dom| |Expon| |VarSet| |Dpol|)
+(-447 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{EuclideanGroebnerBasisPackage} computes groebner bases for polynomial ideals over euclidean domains. The basic computation provides a distinguished set of generators for these ideals. This basis allows an easy test for membership: the operation \\spadfun{euclideanNormalForm} returns zero on ideal members. The string \"info\" and \"redcrit\" can be given as additional args to provide incremental information during the computation. If \"info\" is given,{} \\indented{1}{a computational summary is given for each \\spad{s}-polynomial. If \"redcrit\"} is given,{} the reduced critical pairs are printed. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|euclideanGroebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{euclideanGroebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. If the second argument is \\spad{\"info\"},{} a summary is given of the critical pairs. If the third argument is \"redcrit\",{} critical pairs are printed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{euclideanGroebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}. During computation,{} additional information is printed out if infoflag is given as either \"info\" (for summary information) or \"redcrit\" (for reduced critical pairs)") (((|List| |#4|) (|List| |#4|)) "\\spad{euclideanGroebner(lp)} computes a groebner basis for a polynomial ideal over a euclidean domain generated by the list of polynomials \\spad{lp}.")) (|euclideanNormalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{euclideanNormalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")))
NIL
NIL
-(-447 |Dom| |Expon| |VarSet| |Dpol|)
+(-448 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerFactorizationPackage} provides the function groebnerFactor\" which uses the factorization routines of \\Language{} to factor each polynomial under consideration while doing the groebner basis algorithm. Then it writes the ideal as an intersection of ideals determined by the irreducible factors. Note that the whole ring may occur as well as other redundancies. We also use the fact,{} that from the second factor on we can assume that the preceding factors are not equal to 0 and we divide all polynomials under considerations by the elements of this list of \"nonZeroRestrictions\". The result is a list of groebner bases,{} whose union of solutions of the corresponding systems of equations is the solution of the system of equation corresponding to the input list. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|groebnerFactorize| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} info)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys)} returns a list of groebner bases. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys}. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions,{} info)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|) (|List| |#4|)) "\\spad{groebnerFactorize(listOfPolys,{} nonZeroRestrictions)} returns a list of groebner basis. The union of their solutions is the solution of the system of equations given by {\\em listOfPolys} under the restriction that the polynomials of {\\em nonZeroRestrictions} don\\spad{'t} vanish. At each stage the polynomial \\spad{p} under consideration (either from the given basis or obtained from a reduction of the next \\spad{S}-polynomial) is factorized. For each irreducible factors of \\spad{p},{} a new {\\em createGroebnerBasis} is started doing the usual updates with the factor in place of \\spad{p}.")) (|factorGroebnerBasis| (((|List| (|List| |#4|)) (|List| |#4|) (|Boolean|)) "\\spad{factorGroebnerBasis(basis,{}info)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}. If argument {\\em info} is \\spad{true},{} information is printed about partial results.") (((|List| (|List| |#4|)) (|List| |#4|)) "\\spad{factorGroebnerBasis(basis)} checks whether the \\spad{basis} contains reducible polynomials and uses these to split the \\spad{basis}.")))
NIL
NIL
-(-448 |Dom| |Expon| |VarSet| |Dpol|)
+(-449 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Keywords: Description This package provides low level tools for Groebner basis computations")) (|virtualDegree| (((|NonNegativeInteger|) |#4|) "\\spad{virtualDegree }\\undocumented")) (|makeCrit| (((|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)) |#4| (|NonNegativeInteger|)) "\\spad{makeCrit }\\undocumented")) (|critpOrder| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critpOrder }\\undocumented")) (|prinb| (((|Void|) (|Integer|)) "\\spad{prinb }\\undocumented")) (|prinpolINFO| (((|Void|) (|List| |#4|)) "\\spad{prinpolINFO }\\undocumented")) (|fprindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{fprindINFO }\\undocumented")) (|prindINFO| (((|Integer|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)) |#4| |#4| (|Integer|) (|Integer|) (|Integer|)) "\\spad{prindINFO }\\undocumented")) (|prinshINFO| (((|Void|) |#4|) "\\spad{prinshINFO }\\undocumented")) (|lepol| (((|Integer|) |#4|) "\\spad{lepol }\\undocumented")) (|minGbasis| (((|List| |#4|) (|List| |#4|)) "\\spad{minGbasis }\\undocumented")) (|updatD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{updatD }\\undocumented")) (|sPol| ((|#4| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{sPol }\\undocumented")) (|updatF| (((|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|))) |#4| (|NonNegativeInteger|) (|List| (|Record| (|:| |totdeg| (|NonNegativeInteger|)) (|:| |pol| |#4|)))) "\\spad{updatF }\\undocumented")) (|hMonic| ((|#4| |#4|) "\\spad{hMonic }\\undocumented")) (|redPo| (((|Record| (|:| |poly| |#4|) (|:| |mult| |#1|)) |#4| (|List| |#4|)) "\\spad{redPo }\\undocumented")) (|critMonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#2| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMonD1 }\\undocumented")) (|critMTonD1| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critMTonD1 }\\undocumented")) (|critBonD| (((|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) |#4| (|List| (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|)))) "\\spad{critBonD }\\undocumented")) (|critB| (((|Boolean|) |#2| |#2| |#2| |#2|) "\\spad{critB }\\undocumented")) (|critM| (((|Boolean|) |#2| |#2|) "\\spad{critM }\\undocumented")) (|critT| (((|Boolean|) (|Record| (|:| |lcmfij| |#2|) (|:| |totdeg| (|NonNegativeInteger|)) (|:| |poli| |#4|) (|:| |polj| |#4|))) "\\spad{critT }\\undocumented")) (|gbasis| (((|List| |#4|) (|List| |#4|) (|Integer|) (|Integer|)) "\\spad{gbasis }\\undocumented")) (|redPol| ((|#4| |#4| (|List| |#4|)) "\\spad{redPol }\\undocumented")) (|credPol| ((|#4| |#4| (|List| |#4|)) "\\spad{credPol }\\undocumented")))
NIL
NIL
-(-449 |Dom| |Expon| |VarSet| |Dpol|)
+(-450 |Dom| |Expon| |VarSet| |Dpol|)
((|constructor| (NIL "\\spadtype{GroebnerPackage} computes groebner bases for polynomial ideals. The basic computation provides a distinguished set of generators for polynomial ideals over fields. This basis allows an easy test for membership: the operation \\spadfun{normalForm} returns zero on ideal members. When the provided coefficient domain,{} Dom,{} is not a field,{} the result is equivalent to considering the extended ideal with \\spadtype{Fraction(Dom)} as coefficients,{} but considerably more efficient since all calculations are performed in Dom. Additional argument \"info\" and \"redcrit\" can be given to provide incremental information during computation. Argument \"info\" produces a computational summary for each \\spad{s}-polynomial. Argument \"redcrit\" prints out the reduced critical pairs. The term ordering is determined by the polynomial type used. Suggested types include \\spadtype{DistributedMultivariatePolynomial},{} \\spadtype{HomogeneousDistributedMultivariatePolynomial},{} \\spadtype{GeneralDistributedMultivariatePolynomial}.")) (|normalForm| ((|#4| |#4| (|List| |#4|)) "\\spad{normalForm(poly,{}gb)} reduces the polynomial \\spad{poly} modulo the precomputed groebner basis \\spad{gb} giving a canonical representative of the residue class.")) (|groebner| (((|List| |#4|) (|List| |#4|) (|String|) (|String|)) "\\spad{groebner(lp,{} \"info\",{} \"redcrit\")} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp},{} displaying both a summary of the critical pairs considered (\\spad{\"info\"}) and the result of reducing each critical pair (\"redcrit\"). If the second or third arguments have any other string value,{} the indicated information is suppressed.") (((|List| |#4|) (|List| |#4|) (|String|)) "\\spad{groebner(lp,{} infoflag)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}. Argument infoflag is used to get information on the computation. If infoflag is \"info\",{} then summary information is displayed for each \\spad{s}-polynomial generated. If infoflag is \"redcrit\",{} the reduced critical pairs are displayed. If infoflag is any other string,{} no information is printed during computation.") (((|List| |#4|) (|List| |#4|)) "\\spad{groebner(lp)} computes a groebner basis for a polynomial ideal generated by the list of polynomials \\spad{lp}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))))
-(-450 S)
+((|HasCategory| |#1| (QUOTE (-363))))
+(-451 S)
((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-451)
+(-452)
((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-452 R |n| |ls| |gamma|)
+(-453 R |n| |ls| |gamma|)
((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed")))
-((-4400 |has| (-406 (-947 |#1|)) (-554)) (-4398 . T) (-4397 . T))
-((|HasCategory| (-406 (-947 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| (-406 (-947 |#1|)) (QUOTE (-554))))
-(-453 |vl| R E)
+((-4404 |has| (-407 (-948 |#1|)) (-555)) (-4402 . T) (-4401 . T))
+((|HasCategory| (-407 (-948 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-407 (-948 |#1|)) (QUOTE (-555))))
+(-454 |vl| R E)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial")))
-(((-4405 "*") |has| |#2| (-171)) (-4396 |has| |#2| (-554)) (-4401 |has| |#2| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
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-(-454 R BP)
+(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
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+(-455 R BP)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional.")))
NIL
NIL
-(-455 OV E S R P)
+(-456 OV E S R P)
((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| |#5|) |#5|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-456 E OV R P)
+(-457 E OV R P)
((|constructor| (NIL "This package provides operations for \\spad{GCD} computations on polynomials")) (|randomR| ((|#3|) "\\spad{randomR()} should be local but conditional")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{GCD} of \\spad{p} and \\spad{q}")))
NIL
NIL
-(-457 R)
+(-458 R)
((|constructor| (NIL "\\indented{1}{Description} This package provides operations for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" the finite \"berlekamp's\" factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{factor(p)} returns the factorisation of \\spad{p}")))
NIL
NIL
-(-458 R FE)
+(-459 R FE)
((|constructor| (NIL "\\spadtype{GenerateUnivariatePowerSeries} provides functions that create power series from explicit formulas for their \\spad{n}th coefficient.")) (|series| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{series(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{series(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{series(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{series(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.")) (|puiseux| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(a(n),{}n,{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(a(n),{}n,{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Fraction| (|Integer|))) (|Equation| |#2|) (|UniversalSegment| (|Fraction| (|Integer|))) (|Fraction| (|Integer|))) "\\spad{puiseux(n +-> a(n),{}x = a,{}r0..,{}r)} returns \\spad{sum(n = r0,{}r0 + r,{}r0 + 2*r...,{} a(n) * (x - a)**n)}; \\spad{puiseux(n +-> a(n),{}x = a,{}r0..r1,{}r)} returns \\spad{sum(n = r0 + k*r while n <= r1,{} a(n) * (x - a)**n)}.")) (|laurent| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(a(n),{}n,{}x=a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(a(n),{}n,{}x=a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|Integer|))) "\\spad{laurent(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n) * (x - a)**n)}; \\spad{laurent(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..n1,{}a(n) * (x - a)**n)}.")) (|taylor| (((|Any|) |#2| (|Symbol|) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(a(n),{}n,{}x = a,{}n0..)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(a(n),{}n,{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|) (|UniversalSegment| (|NonNegativeInteger|))) "\\spad{taylor(n +-> a(n),{}x = a,{}n0..)} returns \\spad{sum(n=n0..,{}a(n)*(x-a)**n)}; \\spad{taylor(n +-> a(n),{}x = a,{}n0..n1)} returns \\spad{sum(n = n0..,{}a(n)*(x-a)**n)}.") (((|Any|) |#2| (|Symbol|) (|Equation| |#2|)) "\\spad{taylor(a(n),{}n,{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.") (((|Any|) (|Mapping| |#2| (|Integer|)) (|Equation| |#2|)) "\\spad{taylor(n +-> a(n),{}x = a)} returns \\spad{sum(n = 0..,{}a(n)*(x-a)**n)}.")))
NIL
NIL
-(-459 RP TP)
+(-460 RP TP)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni} General Hensel Lifting Used for Factorization of bivariate polynomials over a finite field.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(u,{}pol)} computes the symmetric reduction of \\spad{u} mod \\spad{pol}")) (|completeHensel| (((|List| |#2|) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{completeHensel(pol,{}lfact,{}prime,{}bound)} lifts \\spad{lfact},{} the factorization mod \\spad{prime} of \\spad{pol},{} to the factorization mod prime**k>bound. Factors are recombined on the way.")) (|HenselLift| (((|Record| (|:| |plist| (|List| |#2|)) (|:| |modulo| |#1|)) |#2| (|List| |#2|) |#1| (|PositiveInteger|)) "\\spad{HenselLift(pol,{}lfacts,{}prime,{}bound)} lifts \\spad{lfacts},{} that are the factors of \\spad{pol} mod \\spad{prime},{} to factors of \\spad{pol} mod prime**k > \\spad{bound}. No recombining is done .")))
NIL
NIL
-(-460 |vl| R IS E |ff| P)
+(-461 |vl| R IS E |ff| P)
((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-461 E V R P Q)
+(-462 E V R P Q)
((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}.")))
NIL
NIL
-(-462 R E |VarSet| P)
+(-463 R E |VarSet| P)
((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-463 S R E)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-464 S R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}.")))
NIL
NIL
-(-464 R E)
+(-465 R E)
((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}.")))
NIL
NIL
-(-465)
+(-466)
((|constructor| (NIL "GrayCode provides a function for efficiently running through all subsets of a finite set,{} only changing one element by another one.")) (|firstSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{firstSubsetGray(n)} creates the first vector {\\em ww} to start a loop using {\\em nextSubsetGray(ww,{}n)}")) (|nextSubsetGray| (((|Vector| (|Vector| (|Integer|))) (|Vector| (|Vector| (|Integer|))) (|PositiveInteger|)) "\\spad{nextSubsetGray(ww,{}n)} returns a vector {\\em vv} whose components have the following meanings:\\begin{items} \\item {\\em vv.1}: a vector of length \\spad{n} whose entries are 0 or 1. This \\indented{3}{can be interpreted as a code for a subset of the set 1,{}...,{}\\spad{n};} \\indented{3}{{\\em vv.1} differs from {\\em ww.1} by exactly one entry;} \\item {\\em vv.2.1} is the number of the entry of {\\em vv.1} which \\indented{3}{will be changed next time;} \\item {\\em vv.2.1 = n+1} means that {\\em vv.1} is the last subset; \\indented{3}{trying to compute nextSubsetGray(\\spad{vv}) if {\\em vv.2.1 = n+1}} \\indented{3}{will produce an error!} \\end{items} The other components of {\\em vv.2} are needed to compute nextSubsetGray efficiently. Note: this is an implementation of [Williamson,{} Topic II,{} 3.54,{} \\spad{p}. 112] for the special case {\\em r1 = r2 = ... = rn = 2}; Note: nextSubsetGray produces a side-effect,{} \\spadignore{i.e.} {\\em nextSubsetGray(vv)} and {\\em vv := nextSubsetGray(vv)} will have the same effect.")))
NIL
NIL
-(-466)
+(-467)
((|constructor| (NIL "TwoDimensionalPlotSettings sets global flags and constants for 2-dimensional plotting.")) (|screenResolution| (((|Integer|) (|Integer|)) "\\spad{screenResolution(n)} sets the screen resolution to \\spad{n}.") (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution \\spad{n}.")) (|minPoints| (((|Integer|) (|Integer|)) "\\spad{minPoints()} sets the minimum number of points in a plot.") (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot.")) (|maxPoints| (((|Integer|) (|Integer|)) "\\spad{maxPoints()} sets the maximum number of points in a plot.") (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot.")) (|adaptive| (((|Boolean|) (|Boolean|)) "\\spad{adaptive(true)} turns adaptive plotting on; \\spad{adaptive(false)} turns adaptive plotting off.") (((|Boolean|)) "\\spad{adaptive()} determines whether plotting will be done adaptively.")) (|drawToScale| (((|Boolean|) (|Boolean|)) "\\spad{drawToScale(true)} causes plots to be drawn to scale. \\spad{drawToScale(false)} causes plots to be drawn so that they fill up the viewport window. The default setting is \\spad{false}.") (((|Boolean|)) "\\spad{drawToScale()} determines whether or not plots are to be drawn to scale.")) (|clipPointsDefault| (((|Boolean|) (|Boolean|)) "\\spad{clipPointsDefault(true)} turns on automatic clipping; \\spad{clipPointsDefault(false)} turns off automatic clipping. The default setting is \\spad{true}.") (((|Boolean|)) "\\spad{clipPointsDefault()} determines whether or not automatic clipping is to be done.")))
NIL
NIL
-(-467)
+(-468)
((|constructor| (NIL "TwoDimensionalGraph creates virtual two dimensional graphs (to be displayed on TwoDimensionalViewports).")) (|putColorInfo| (((|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|))) "\\spad{putColorInfo(llp,{}lpal)} takes a list of list of points,{} \\spad{llp},{} and returns the points with their hue and shade components set according to the list of palette colors,{} \\spad{lpal}.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(\\spad{gi})} returns the indicated graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage} as output of the domain \\spadtype{OutputForm}.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{coerce(llp)} component(\\spad{gi},{}\\spad{pt}) creates and returns a graph of the domain \\spadtype{GraphImage} which is composed of the list of list of points given by \\spad{llp},{} and whose point colors,{} line colors and point sizes are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.")) (|point| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|)) "\\spad{point(\\spad{gi},{}pt,{}pal)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to be the palette color \\spad{pal},{} and whose line color and point size are determined by the default functions \\spadfun{lineColorDefault} and \\spadfun{pointSizeDefault}.")) (|appendPoint| (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{appendPoint(\\spad{gi},{}pt)} appends the point \\spad{pt} to the end of the list of points component for the graph,{} \\spad{\\spad{gi}},{} which is of the domain \\spadtype{GraphImage}.")) (|component| (((|Void|) $ (|Point| (|DoubleFloat|)) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}pt,{}pal1,{}pal2,{}ps)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color is set to the palette color \\spad{pal1},{} line color is set to the palette color \\spad{pal2},{} and point size is set to the positive integer \\spad{ps}.") (((|Void|) $ (|Point| (|DoubleFloat|))) "\\spad{component(\\spad{gi},{}pt)} modifies the graph \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage} to contain one point component,{} \\spad{pt} whose point color,{} line color and point size are determined by the default functions \\spadfun{pointColorDefault},{} \\spadfun{lineColorDefault},{} and \\spadfun{pointSizeDefault}.") (((|Void|) $ (|List| (|Point| (|DoubleFloat|))) (|Palette|) (|Palette|) (|PositiveInteger|)) "\\spad{component(\\spad{gi},{}lp,{}pal1,{}pal2,{}p)} sets the components of the graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to the values given. The point list for \\spad{\\spad{gi}} is set to the list \\spad{lp},{} the color of the points in \\spad{lp} is set to the palette color \\spad{pal1},{} the color of the lines which connect the points \\spad{lp} is set to the palette color \\spad{pal2},{} and the size of the points in \\spad{lp} is given by the integer \\spad{p}.")) (|units| (((|List| (|Float|)) $ (|List| (|Float|))) "\\spad{units(\\spad{gi},{}lu)} modifies the list of unit increments for the \\spad{x} and \\spad{y} axes of the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of unit increments,{} \\spad{lu},{} and returns the new list of units for \\spad{\\spad{gi}}.") (((|List| (|Float|)) $) "\\spad{units(\\spad{gi})} returns the list of unit increments for the \\spad{x} and \\spad{y} axes of the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|ranges| (((|List| (|Segment| (|Float|))) $ (|List| (|Segment| (|Float|)))) "\\spad{ranges(\\spad{gi},{}lr)} modifies the list of ranges for the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} to be that of the list of range segments,{} \\spad{lr},{} and returns the new range list for \\spad{\\spad{gi}}.") (((|List| (|Segment| (|Float|))) $) "\\spad{ranges(\\spad{gi})} returns the list of ranges of the point components from the indicated graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|key| (((|Integer|) $) "\\spad{key(\\spad{gi})} returns the process ID of the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|pointLists| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{pointLists(\\spad{gi})} returns the list of lists of points which compose the given graph,{} \\spad{\\spad{gi}},{} of the domain \\spadtype{GraphImage}.")) (|makeGraphImage| (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|)) (|List| (|DrawOption|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp,{}lopt)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points,{} and \\spad{lopt} is the list of draw command options. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|Palette|)) (|List| (|Palette|)) (|List| (|PositiveInteger|))) "\\spad{makeGraphImage(llp,{}lpal1,{}lpal2,{}lp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} whose point colors are indicated by the list of palette colors,{} \\spad{lpal1},{} and whose lines are colored according to the list of palette colors,{} \\spad{lpal2}. The paramater \\spad{lp} is a list of integers which denote the size of the data points. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{makeGraphImage(llp)} returns a graph of the domain \\spadtype{GraphImage} which is composed of the points and lines from the list of lists of points,{} \\spad{llp},{} with default point size and default point and line colours. The graph data is then sent to the viewport manager where it waits to be included in a two-dimensional viewport window.") (($ $) "\\spad{makeGraphImage(\\spad{gi})} takes the given graph,{} \\spad{\\spad{gi}} of the domain \\spadtype{GraphImage},{} and sends it\\spad{'s} data to the viewport manager where it waits to be included in a two-dimensional viewport window. \\spad{\\spad{gi}} cannot be an empty graph,{} and it\\spad{'s} elements must have been created using the \\spadfun{point} or \\spadfun{component} functions,{} not by a previous \\spadfun{makeGraphImage}.")) (|graphImage| (($) "\\spad{graphImage()} returns an empty graph with 0 point lists of the domain \\spadtype{GraphImage}. A graph image contains the graph data component of a two dimensional viewport.")))
NIL
NIL
-(-468 S R E)
+(-469 S R E)
((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#2|) "\\spad{g*r} is right module multiplication.") (($ |#2| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#3| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-469 R E)
+(-470 R E)
((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module.")))
NIL
NIL
-(-470 |lv| -3196 R)
+(-471 |lv| -3191 R)
((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}.")))
NIL
NIL
-(-471 S)
+(-472 S)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
NIL
NIL
-(-472)
+(-473)
((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-473 |Coef| |var| |cen|)
+(-474 |Coef| |var| |cen|)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-562)) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|)))))))
-(-474 |Key| |Entry| |Tbl| |dent|)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-563)) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1193))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -3698) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1169))))) (|HasSignature| |#1| (LIST (QUOTE -2606) (LIST (LIST (QUOTE -640) (QUOTE (-1169))) (|devaluate| |#1|)))))))
+(-475 |Key| |Entry| |Tbl| |dent|)
((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key.")))
-((-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))))
-(-475 R E V P)
+((-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))))
+(-476 R E V P)
((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-476)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-477)
((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-477)
+(-478)
((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'.")))
NIL
NIL
-(-478 |Key| |Entry| |hashfn|)
+(-479 |Key| |Entry| |hashfn|)
((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-479)
+((-4407 . T) (-4408 . T))
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((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2")))
NIL
NIL
-(-480 |vl| R)
+(-481 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial")))
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((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered first by the sum of their components,{} and then refined using a reverse lexicographic ordering. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
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+(-483)
((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header.")))
NIL
NIL
-(-483 S)
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((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}.")))
-((-4403 . T) (-4404 . T))
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-(-484 -3196 UP UPUP R)
+((-4407 . T) (-4408 . T))
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+(-485 -3191 UP UPUP R)
((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree.")))
NIL
NIL
-(-485 BP)
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((|constructor| (NIL "This package provides the functions for the heuristic integer \\spad{gcd}. Geddes\\spad{'s} algorithm,{}for univariate polynomials with integer coefficients")) (|lintgcd| (((|Integer|) (|List| (|Integer|))) "\\spad{lintgcd([a1,{}..,{}ak])} = \\spad{gcd} of a list of integers")) (|content| (((|List| (|Integer|)) (|List| |#1|)) "\\spad{content([f1,{}..,{}fk])} = content of a list of univariate polynonials")) (|gcdcofactprim| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofactprim([f1,{}..fk])} = \\spad{gcd} and cofactors of \\spad{k} primitive polynomials.")) (|gcdcofact| (((|List| |#1|) (|List| |#1|)) "\\spad{gcdcofact([f1,{}..fk])} = \\spad{gcd} and cofactors of \\spad{k} univariate polynomials.")) (|gcdprim| ((|#1| (|List| |#1|)) "\\spad{gcdprim([f1,{}..,{}fk])} = \\spad{gcd} of \\spad{k} PRIMITIVE univariate polynomials")) (|gcd| ((|#1| (|List| |#1|)) "\\spad{gcd([f1,{}..,{}fk])} = \\spad{gcd} of the polynomials \\spad{fi}.")))
NIL
NIL
-(-486)
+(-487)
((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
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-(-487 A S)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
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+(-488 A S)
((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
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-(-488 S)
+((|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-489 S)
((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}.")))
NIL
NIL
-(-489 S)
+(-490 S)
((|constructor| (NIL "A is homotopic to \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain \\spad{B},{} and nay element of domain \\spad{B} can be automatically converted into an A.")))
NIL
NIL
-(-490)
+(-491)
((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}.")))
NIL
NIL
-(-491 S)
+(-492 S)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-492)
+(-493)
((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}.")))
NIL
NIL
-(-493 -3196 UP |AlExt| |AlPol|)
+(-494 -3191 UP |AlExt| |AlPol|)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP.")))
NIL
NIL
-(-494)
+(-495)
((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| $ (QUOTE (-1044))) (|HasCategory| $ (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-495 S |mn|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-496 S |mn|)
((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-496 R |mnRow| |mnCol|)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-497 R |mnRow| |mnCol|)
((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-497 K R UP)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-498 K R UP)
((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented")))
NIL
NIL
-(-498 R UP -3196)
+(-499 R UP -3191)
((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}")))
NIL
NIL
-(-499 |mn|)
+(-500 |mn|)
((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-112) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-112) (QUOTE (-1092))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-500 K R UP L)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-112) (QUOTE (-1093))) (|HasCategory| (-112) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-501 K R UP L)
((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.")))
NIL
NIL
-(-501)
+(-502)
((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|coerce| (($ (|String|)) "\\spad{coerce(s)} converts \\axiom{\\spad{s}} into an \\axiom{IndexCard}. Warning: if \\axiom{\\spad{s}} is not of the right format then an error will occur when using it.")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,{}s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}.")))
NIL
NIL
-(-502 R Q A B)
+(-503 R Q A B)
((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}.")))
NIL
NIL
-(-503 -3196 |Expon| |VarSet| |DPoly|)
+(-504 -3191 |Expon| |VarSet| |DPoly|)
((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}.")))
NIL
-((|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-1168)))))
-(-504 |vl| |nv|)
+((|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-1169)))))
+(-505 |vl| |nv|)
((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime.")))
NIL
NIL
-(-505)
+(-506)
((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")))
NIL
NIL
-(-506 A S)
+(-507 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-507 A S)
+(-508 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored.")))
NIL
NIL
-(-508 A S)
+(-509 A S)
((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,{}s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}.")))
NIL
NIL
-(-509 A S)
+(-510 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-510 A S)
+(-511 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored.")))
NIL
NIL
-(-511 A S)
+(-512 A S)
((|constructor| (NIL "\\indented{1}{Indexed direct products of objects over a set \\spad{A}} of generators indexed by an ordered set \\spad{S}. All items have finite support.")))
NIL
NIL
-(-512 S A B)
+(-513 S A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-513 A B)
+(-514 A B)
((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f,{} [x1,{}...,{}xn],{} [v1,{}...,{}vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f,{} x,{} v)} replaces \\spad{x} by \\spad{v} in \\spad{f}.")))
NIL
NIL
-(-514 S E |un|)
+(-515 S E |un|)
((|constructor| (NIL "Internal implementation of a free abelian monoid.")))
NIL
-((|HasCategory| |#2| (QUOTE (-787))))
-(-515 S |mn|)
+((|HasCategory| |#2| (QUOTE (-788))))
+(-516 S |mn|)
((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-516)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-517)
((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'.")))
NIL
NIL
-(-517 |p| |n|)
+(-518 |p| |n|)
((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| (-579 |#1|) (QUOTE (-144))) (|HasCategory| (-579 |#1|) (QUOTE (-367)))) (|HasCategory| (-579 |#1|) (QUOTE (-146))) (|HasCategory| (-579 |#1|) (QUOTE (-367))) (|HasCategory| (-579 |#1|) (QUOTE (-144))))
-(-518 R |mnRow| |mnCol| |Row| |Col|)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((-4032 (|HasCategory| (-580 |#1|) (QUOTE (-145))) (|HasCategory| (-580 |#1|) (QUOTE (-368)))) (|HasCategory| (-580 |#1|) (QUOTE (-147))) (|HasCategory| (-580 |#1|) (QUOTE (-368))) (|HasCategory| (-580 |#1|) (QUOTE (-145))))
+(-519 R |mnRow| |mnCol| |Row| |Col|)
((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-519 S |mn|)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-520 S |mn|)
((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-520 R |Row| |Col| M)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-521 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")))
NIL
-((|HasAttribute| |#3| (QUOTE -4404)))
-(-521 R |Row| |Col| M QF |Row2| |Col2| M2)
+((|HasAttribute| |#3| (QUOTE -4408)))
+(-522 R |Row| |Col| M QF |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field.")))
NIL
-((|HasAttribute| |#7| (QUOTE -4404)))
-(-522 R |mnRow| |mnCol|)
+((|HasAttribute| |#7| (QUOTE -4408)))
+(-523 R |mnRow| |mnCol|)
((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-523)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-524)
((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'.")))
NIL
NIL
-(-524)
+(-525)
((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Symbol|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'")))
NIL
NIL
-(-525 S)
+(-526 S)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}.")))
NIL
NIL
-(-526)
+(-527)
((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}.")))
NIL
NIL
-(-527 GF)
+(-528 GF)
((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}.")))
NIL
NIL
-(-528)
+(-529)
((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file \\spad{`f'}.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
NIL
NIL
-(-529 R)
+(-530 R)
((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} \\spad{:=} increment()} then \\spad{f x} is \\spad{x+1}.")))
NIL
NIL
-(-530 |Varset|)
+(-531 |Varset|)
((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables")))
NIL
NIL
-(-531 K -3196 |Par|)
+(-532 K -3191 |Par|)
((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}")))
NIL
NIL
-(-532)
+(-533)
NIL
NIL
NIL
-(-533)
+(-534)
((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity.")))
NIL
NIL
-(-534 R)
+(-535 R)
((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}.")))
NIL
NIL
-(-535)
+(-536)
((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f,{} [t1,{}...,{}tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,{}...,{}tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}\\spad{'s} are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) ((|One|) (($) "\\spad{1} returns the input form corresponding to 1.")) ((|Zero|) (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code,{} [x1,{}...,{}xn])} returns the input form corresponding to \\spad{(x1,{}...,{}xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code,{} [x1,{}...,{}xn],{} f)} returns the input form corresponding to \\spad{f(x1,{}...,{}xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op,{} [a1,{}...,{}an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter.")))
NIL
NIL
-(-536 |Coef| UTS)
+(-537 |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-537 K -3196 |Par|)
+(-538 K -3191 |Par|)
((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}.")))
NIL
NIL
-(-538 R BP |pMod| |nextMod|)
+(-539 R BP |pMod| |nextMod|)
((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,{}p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the \\spad{gcd} of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,{}f2)} computes the \\spad{gcd} of the two polynomials \\spad{f1} and \\spad{f2} by modular methods.")))
NIL
NIL
-(-539 OV E R P)
+(-540 OV E R P)
((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,{}ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}.")))
NIL
NIL
-(-540 K UP |Coef| UTS)
+(-541 K UP |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-541 |Coef| UTS)
+(-542 |Coef| UTS)
((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-542 R UP)
+(-543 R UP)
((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) "failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}r,{}i,{}f)} \\undocumented") (((|Union| (|Integer|) "failed") |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) "failed") |#1|)) "\\spad{signAround(u,{}i,{}f)} \\undocumented")))
NIL
NIL
-(-543 S)
+(-544 S)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
NIL
NIL
-(-544)
+(-545)
((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd.")))
-((-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-545)
+(-546)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits.")))
NIL
NIL
-(-546)
+(-547)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits.")))
NIL
NIL
-(-547)
+(-548)
((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits.")))
NIL
NIL
-(-548 |Key| |Entry| |addDom|)
+(-549 |Key| |Entry| |addDom|)
((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-549 R -3196)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-550 R -3191)
((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f,{} x,{} y,{} d)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}.")))
NIL
NIL
-(-550 R0 -3196 UP UPUP R)
+(-551 R0 -3191 UP UPUP R)
((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f,{} d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f,{} d)} integrates \\spad{f} with respect to the derivation \\spad{d}.")))
NIL
NIL
-(-551)
+(-552)
((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,{}m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,{}m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})")))
NIL
NIL
-(-552 R)
+(-553 R)
((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise.")))
-((-1406 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-1403 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-553 S)
+(-554 S)
((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found.")))
NIL
NIL
-(-554)
+(-555)
((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-555 R -3196)
+(-556 R -3191)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise.")))
NIL
NIL
-(-556 I)
+(-557 I)
((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra\\spad{'s} eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}")))
NIL
NIL
-(-557)
+(-558)
((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions.")))
NIL
NIL
-(-558 R -3196 L)
+(-559 R -3191 L)
((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}.")))
NIL
-((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|))))
-(-559)
+((|HasCategory| |#3| (LIST (QUOTE -651) (|devaluate| |#2|))))
+(-560)
((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial.")))
NIL
NIL
-(-560 -3196 UP UPUP R)
+(-561 -3191 UP UPUP R)
((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} ')} returns \\spad{[g,{}h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles.")))
NIL
NIL
-(-561 -3196 UP)
+(-562 -3191 UP)
((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f,{} D)} returns \\spad{[g,{} h,{} s,{} p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}.")))
NIL
NIL
-(-562)
+(-563)
((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")))
-((-4385 . T) (-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4389 . T) (-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-563)
+(-564)
((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.")))
NIL
NIL
-(-564 R -3196 L)
+(-565 R -3191 L)
((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}.")))
NIL
-((|HasCategory| |#3| (LIST (QUOTE -650) (|devaluate| |#2|))))
-(-565 R -3196)
+((|HasCategory| |#3| (LIST (QUOTE -651) (|devaluate| |#2|))))
+(-566 R -3191)
((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}.")))
NIL
-((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1131)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-625)))))
-(-566 -3196 UP)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-626)))))
+(-567 -3191 UP)
((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}.")))
NIL
NIL
-(-567 S)
+(-568 S)
((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer.")))
NIL
NIL
-(-568 -3196)
+(-569 -3191)
((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}.")))
NIL
NIL
-(-569 R)
+(-570 R)
((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals.")))
-((-1406 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-1403 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-570)
+(-571)
((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")))
NIL
NIL
-(-571 R -3196)
+(-572 R -3191)
((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}.")))
NIL
-((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-625))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-554))))
-(-572 -3196 UP)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-626))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-555))))
+(-573 -3191 UP)
((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}.")))
NIL
NIL
-(-573 R -3196)
+(-574 R -3191)
((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f,{} s,{} t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form.")))
NIL
NIL
-(-574)
+(-575)
((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations.")))
NIL
NIL
-(-575)
+(-576)
((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if \\spad{`f'} is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by \\spad{`f'} as a binary file.")))
NIL
NIL
-(-576)
+(-577)
((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|bothWays| (($) "`bothWays' indicates that an IO conduit is for both input and output.")) (|output| (($) "`output' indicates that an IO conduit is for output")) (|input| (($) "`input' indicates that an IO conduit is for input.")))
NIL
NIL
-(-577)
+(-578)
((|constructor| (NIL "This domain provides representation for ARPA Internet IP4 addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the IP4 address of host \\spad{`h'}.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address \\spad{`x'}.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'.")))
NIL
NIL
-(-578 |p| |unBalanced?|)
+(-579 |p| |unBalanced?|)
((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-579 |p|)
+(-580 |p|)
((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367))))
-(-580)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368))))
+(-581)
((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor.")))
NIL
NIL
-(-581 R -3196)
+(-582 R -3191)
((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}.")))
NIL
NIL
-(-582 E -3196)
+(-583 E -3191)
((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,{}ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,{}ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,{}ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,{}ire)} \\undocumented")))
NIL
NIL
-(-583 -3196)
+(-584 -3191)
((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}.")))
-((-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-1168)))))
-(-584 I)
+((-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1169)))))
+(-585 I)
((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise")))
NIL
NIL
-(-585 GF)
+(-586 GF)
((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field.")))
NIL
NIL
-(-586 R)
+(-587 R)
((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-146))))
-(-587)
+((|HasCategory| |#1| (QUOTE (-147))))
+(-588)
((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,{}2,{}...,{}n}} in Young\\spad{'s} natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,{}3,{}3,{}1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,{}listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young\\spad{'s} natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young\\spad{'s} natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,{}\\spad{pi})} is the irreducible representation corresponding to partition {\\em lambda} in Young\\spad{'s} natural form of the permutation {\\em \\spad{pi}} in the symmetric group,{} whose elements permute {\\em {1,{}2,{}...,{}n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|Integer|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented.")))
NIL
NIL
-(-588 R E V P TS)
+(-589 R E V P TS)
((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,{}lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,{}univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial.")))
NIL
NIL
-(-589)
+(-590)
((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'.")))
NIL
NIL
-(-590 |mn|)
+(-591 |mn|)
((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-4037 (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092)))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))))
-(-591 E V R P)
+((-4408 . T) (-4407 . T))
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+(-592 E V R P)
((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}.")))
NIL
NIL
-(-592 |Coef|)
-((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-562)) (|devaluate| |#1|)))) (|HasCategory| (-562) (QUOTE (-1104))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-562))))))
(-593 |Coef|)
+((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}.")))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-563)) (|devaluate| |#1|)))) (|HasCategory| (-563) (QUOTE (-1105))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563))))) (|HasSignature| |#1| (LIST (QUOTE -1693) (LIST (|devaluate| |#1|) (QUOTE (-1169)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-563))))))
+(-594 |Coef|)
((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}")))
-((-4398 |has| |#1| (-554)) (-4397 |has| |#1| (-554)) ((-4405 "*") |has| |#1| (-554)) (-4396 |has| |#1| (-554)) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-554))))
-(-594 A B)
+((-4402 |has| |#1| (-555)) (-4401 |has| |#1| (-555)) ((-4409 "*") |has| |#1| (-555)) (-4400 |has| |#1| (-555)) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-555))))
+(-595 A B)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}.")))
NIL
NIL
-(-595 A B C)
+(-596 A B C)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented")))
NIL
NIL
-(-596 R -3196 FG)
+(-597 R -3191 FG)
((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain.")))
NIL
NIL
-(-597 S)
+(-598 S)
((|constructor| (NIL "\\indented{1}{This package implements 'infinite tuples' for the interpreter.} The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}s)} returns \\spad{[s,{}f(s),{}f(f(s)),{}...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}.")))
NIL
NIL
-(-598 R |mn|)
+(-599 R |mn|)
((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-599 S |Index| |Entry|)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-600 S |Index| |Entry|)
((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-845))) (|HasAttribute| |#1| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-1092))))
-(-600 |Index| |Entry|)
+((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-846))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasCategory| |#3| (QUOTE (-1093))))
+(-601 |Index| |Entry|)
((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order.")))
NIL
NIL
-(-601)
+(-602)
((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")))
NIL
NIL
-(-602)
+(-603)
((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join \\spad{`x'}.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'.")))
NIL
NIL
-(-603 R A)
+(-604 R A)
((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A).")))
-((-4400 -4037 (-2245 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4398 . T) (-4397 . T))
-((-4037 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))))
-(-604 |Entry|)
+((-4404 -4032 (-2190 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4402 . T) (-4401 . T))
+((-4032 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))))
+(-605 |Entry|)
((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| (-1150) (QUOTE (-845))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-605 S |Key| |Entry|)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-606 S |Key| |Entry|)
((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}.")))
NIL
NIL
-(-606 |Key| |Entry|)
+(-607 |Key| |Entry|)
((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}.")))
-((-4404 . T))
+((-4408 . T))
NIL
-(-607 R S)
+(-608 R S)
((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented")))
NIL
NIL
-(-608 S)
+(-609 S)
((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))))
-(-609 S)
+((|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))))
+(-610 S)
((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-610 S)
+(-611 S)
((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}.")))
NIL
NIL
-(-611 -3196 UP)
+(-612 -3191 UP)
((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions.")))
NIL
NIL
-(-612 S)
+(-613 S)
((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms \\spad{`s'} into an element of `\\%'.")))
NIL
NIL
-(-613)
+(-614)
((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value")))
NIL
NIL
-(-614 S)
+(-615 S)
((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'.")))
NIL
NIL
-(-615 S R)
+(-616 S R)
((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra.")))
NIL
NIL
-(-616 R)
+(-617 R)
((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-617 A R S)
+(-618 A R S)
((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-843))))
-(-618 R -3196)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-844))))
+(-619 R -3191)
((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f,{} t,{} s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t),{} t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f,{} t,{} s)} if it cannot compute the transform.")))
NIL
NIL
-(-619 R UP)
+(-620 R UP)
((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented")))
-((-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4396 . T) (-4400 . T))
-((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-620 R E V P TS ST)
+((-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4400 . T) (-4404 . T))
+((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-621 R E V P TS ST)
((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional.")))
NIL
NIL
-(-621 OV E Z P)
+(-622 OV E Z P)
((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \\spad{\"F\"}.")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,{}unilist,{}plead,{}vl,{}lvar,{}lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod,{} numFacts,{} evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation.")))
NIL
NIL
-(-622)
+(-623)
((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'.")))
NIL
NIL
-(-623 |VarSet| R |Order|)
+(-624 |VarSet| R |Order|)
((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-624 R |ls|)
+(-625 R |ls|)
((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}.")))
NIL
NIL
-(-625)
+(-626)
((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}.")))
NIL
NIL
-(-626 R -3196)
+(-627 R -3191)
((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian")))
NIL
NIL
-(-627 |lv| -3196)
+(-628 |lv| -3191)
((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented")))
NIL
NIL
-(-628)
+(-629)
((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file.")))
-((-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1150) (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 (-52))) (QUOTE (-1092))))
-(-629 S R)
+((-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1151) (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 (-52))) (QUOTE (-1093))))
+(-630 S R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))))
-(-630 R)
+((|HasCategory| |#2| (QUOTE (-363))))
+(-631 R)
((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T))
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T))
NIL
-(-631 R A)
+(-632 R A)
((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A).")))
-((-4400 -4037 (-2245 (|has| |#2| (-366 |#1|)) (|has| |#1| (-554))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-554)))) (-4398 . T) (-4397 . T))
-((-4037 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))))
-(-632 R FE)
+((-4404 -4032 (-2190 (|has| |#2| (-367 |#1|)) (|has| |#1| (-555))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-555)))) (-4402 . T) (-4401 . T))
+((-4032 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))))
+(-633 R FE)
((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}.")))
NIL
NIL
-(-633 R)
+(-634 R)
((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),{}x,{}a,{}\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) "failed"))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),{}x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")))
NIL
NIL
-(-634 S R)
+(-635 S R)
((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise.")))
NIL
-((-2234 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362))))
-(-635 R)
+((-2176 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363))))
+(-636 R)
((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-636 A B)
+(-637 A B)
((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}.")))
NIL
NIL
-(-637 A B)
+(-638 A B)
((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,{}u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,{}[1,{}2,{}3]) = [1,{}4,{}9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,{}[1,{}2,{}3],{}0) = fn(3,{}fn(2,{}fn(1,{}0)))} and \\spad{reduce(*,{}[2,{}3],{}1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,{}u,{}ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,{}[1,{}2],{}0) = [fn(2,{}fn(1,{}0)),{}fn(1,{}0)]} and \\spad{scan(*,{}[2,{}3],{}1) = [2 * 1,{} 3 * (2 * 1)]}.")))
NIL
NIL
-(-638 A B C)
+(-639 A B C)
((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,{}list1,{} u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,{}[1,{}2,{}3],{}[4,{}5,{}6]) = [1/4,{}2/4,{}1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}.")))
NIL
NIL
-(-639 S)
+(-640 S)
((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list.")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-823))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-640 T$)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-641 T$)
((|constructor| (NIL "This domain represents AST for Spad literals.")))
NIL
NIL
-(-641 S)
+(-642 S)
((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-642 R)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-643 R)
((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}.")))
NIL
NIL
-(-643 S E |un|)
+(-644 S E |un|)
((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,{}y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x,{} y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s,{} e,{} x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s,{} a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a,{} s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l,{} n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l,{} n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s,{} e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l,{} fop,{} fexp,{} unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a,{} b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a,{} n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n}).")))
NIL
NIL
-(-644 A S)
+(-645 A S)
((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)))
-(-645 S)
+((|HasAttribute| |#1| (QUOTE -4408)))
+(-646 S)
((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}.")))
NIL
NIL
-(-646 R -3196 L)
+(-647 R -3191 L)
((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable.")))
NIL
NIL
-(-647 A)
+(-648 A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362))))
-(-648 A M)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363))))
+(-649 A M)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362))))
-(-649 S A)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363))))
+(-650 S A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))))
-(-650 A)
+((|HasCategory| |#2| (QUOTE (-363))))
+(-651 A)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-651 -3196 UP)
+(-652 -3191 UP)
((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a,{} zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}.")))
NIL
((|HasCategory| |#1| (QUOTE (-27))))
-(-652 A -3679)
+(-653 A -3397)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362))))
-(-653 A L)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363))))
+(-654 A L)
((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")))
NIL
NIL
-(-654 S)
+(-655 S)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-655)
+(-656)
((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}.")))
NIL
NIL
-(-656 M R S)
+(-657 M R S)
((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}.")))
-((-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-786))))
-(-657 R)
+((-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-787))))
+(-658 R)
((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists.")))
NIL
NIL
-(-658 |VarSet| R)
+(-659 |VarSet| R)
((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned.")))
-((|JacobiIdentity| . T) (|NullSquare| . T) (-4398 . T) (-4397 . T))
-((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-171))))
-(-659 A S)
+((|JacobiIdentity| . T) (|NullSquare| . T) (-4402 . T) (-4401 . T))
+((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-172))))
+(-660 A S)
((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}.")))
NIL
NIL
-(-660 S)
+(-661 S)
((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-661 -3196)
+(-662 -3191)
((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.")))
NIL
NIL
-(-662 -3196 |Row| |Col| M)
+(-663 -3191 |Row| |Col| M)
((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.")))
NIL
NIL
-(-663 R E OV P)
+(-664 R E OV P)
((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,{}lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}.")))
NIL
NIL
-(-664 |n| R)
+(-665 |n| R)
((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication.")))
-((-4400 . T) (-4403 . T) (-4397 . T) (-4398 . T))
-((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554))) (-4037 (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171))))
-(-665)
+((-4404 . T) (-4407 . T) (-4401 . T) (-4402 . T))
+((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555))) (-4032 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172))))
+(-666)
((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'.")))
NIL
NIL
-(-666 |VarSet|)
+(-667 |VarSet|)
((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")))
NIL
NIL
-(-667 A S)
+(-668 A S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.")))
NIL
NIL
-(-668 S)
+(-669 S)
((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}.")))
NIL
NIL
-(-669 R)
+(-670 R)
((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms")))
NIL
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-670)
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-671)
((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any.")))
NIL
NIL
-(-671 |VarSet|)
+(-672 |VarSet|)
((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}.")))
NIL
NIL
-(-672 A)
+(-673 A)
((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,{}g,{}x)} is \\spad{g(n,{}g(n-1,{}..g(1,{}x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,{}n,{}x)} applies \\spad{f n} times to \\spad{x}.")))
NIL
NIL
-(-673 A C)
+(-674 A C)
((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,{}c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,{}c)} selects its first argument.")))
NIL
NIL
-(-674 A B C)
+(-675 A B C)
((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,{}g,{}x)} is \\spad{f(g x)}.")))
NIL
NIL
-(-675)
+(-676)
((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for \\spad{`s'}.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of \\spad{`s'}.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,{}t)} builds the mapping AST \\spad{s} \\spad{->} \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'.")))
NIL
NIL
-(-676 A)
+(-677 A)
((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,{}x)= g(n,{}g(n-1,{}..g(1,{}x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,{}n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}")))
NIL
NIL
-(-677 A C)
+(-678 A C)
((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,{}a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}")))
NIL
NIL
-(-678 A B C)
+(-679 A B C)
((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f(b,{}a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,{}b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,{}a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,{}b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,{}b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,{}b)}.}")))
NIL
NIL
-(-679 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+(-680 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.")))
NIL
NIL
-(-680 S R |Row| |Col|)
+(-681 S R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
NIL
-((|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-554))))
-(-681 R |Row| |Col|)
+((|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-555))))
+(-682 R |Row| |Col|)
((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
-(-682 R |Row| |Col| M)
+(-683 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))))
-(-683 R)
-((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal.")))
-((-4403 . T) (-4404 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-554))) (|HasAttribute| |#1| (QUOTE (-4405 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
+((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))))
(-684 R)
+((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal.")))
+((-4407 . T) (-4408 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-555))) (|HasAttribute| |#1| (QUOTE (-4409 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-685 R)
((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")))
NIL
NIL
-(-685 T$)
+(-686 T$)
((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%.")))
NIL
NIL
-(-686 S -3196 FLAF FLAS)
+(-687 S -3191 FLAF FLAS)
((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")))
NIL
NIL
-(-687 R Q)
+(-688 R Q)
((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}.")))
NIL
NIL
-(-688)
+(-689)
((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex")))
-((-4396 . T) (-4401 |has| (-693) (-362)) (-4395 |has| (-693) (-362)) (-4402 |has| (-693) (-6 -4402)) (-4399 |has| (-693) (-6 -4399)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
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-(-689 S)
+((-4400 . T) (-4405 |has| (-694) (-363)) (-4399 |has| (-694) (-363)) (-1413 . T) (-4406 |has| (-694) (-6 -4406)) (-4403 |has| (-694) (-6 -4403)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
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+(-690 S)
((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}.")))
-((-4404 . T))
+((-4408 . T))
NIL
-(-690 U)
+(-691 U)
((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}.")))
NIL
NIL
-(-691)
+(-692)
((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented")))
NIL
NIL
-(-692 OV E -3196 PG)
+(-693 OV E -3191 PG)
((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field.")))
NIL
NIL
-(-693)
+(-694)
((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}")))
-((-1406 . T) (-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-1403 . T) (-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-694 R)
+(-695 R)
((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus.")))
NIL
NIL
-(-695)
+(-696)
((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}")))
-((-4402 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4406 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-696 S D1 D2 I)
+(-697 S D1 D2 I)
((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function")))
NIL
NIL
-(-697 S)
+(-698 S)
((|constructor| (NIL "MakeCachableSet(\\spad{S}) returns a cachable set which is equal to \\spad{S} as a set.")))
NIL
NIL
-(-698 S)
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((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x,{} y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat},{} \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr,{} x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}.")))
NIL
NIL
-(-699 S)
+(-700 S)
((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e,{} foo,{} [x1,{}...,{}xn])} creates a function \\spad{foo(x1,{}...,{}xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x,{} y)} creates a function \\spad{foo(x,{} y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e,{} foo,{} x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e,{} foo)} creates a function \\spad{foo() == e}.")))
NIL
NIL
-(-700 S T$)
+(-701 S T$)
((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}.")))
NIL
NIL
-(-701 S -3113 I)
+(-702 S -3209 I)
((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function")))
NIL
NIL
-(-702 E OV R P)
+(-703 E OV R P)
((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,{}lv,{}lu,{}lr,{}lp,{}lt,{}ln,{}t,{}r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,{}lv,{}lu,{}lr,{}lp,{}ln,{}r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,{}lv,{}lr,{}ln,{}lu,{}t,{}r)} \\undocumented")))
NIL
NIL
-(-703 R)
+(-704 R)
((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-704 R1 UP1 UPUP1 R2 UP2 UPUP2)
+(-705 R1 UP1 UPUP1 R2 UP2 UPUP2)
((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}.")))
NIL
NIL
-(-705)
+(-706)
((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format.")))
NIL
NIL
-(-706 R |Mod| -3834 -4103 |exactQuo|)
+(-707 R |Mod| -2472 -3164 |exactQuo|)
((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-707 R |Rep|)
+(-708 R |Rep|)
((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented")))
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-(-708 IS E |ff|)
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+(-709 IS E |ff|)
((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented")))
NIL
NIL
-(-709 R M)
+(-710 R M)
((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}.")))
-((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))))
-(-710 R |Mod| -3834 -4103 |exactQuo|)
+((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))))
+(-711 R |Mod| -2472 -3164 |exactQuo|)
((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-711 S R)
+(-712 S R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
NIL
NIL
-(-712 R)
+(-713 R)
((|constructor| (NIL "The category of modules over a commutative ring. \\blankline")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-713 -3196)
+(-714 -3191)
((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-714 S)
+(-715 S)
((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation.")))
NIL
NIL
-(-715)
+(-716)
((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation.")))
NIL
NIL
-(-716 S)
+(-717 S)
((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1.")))
NIL
NIL
-(-717)
+(-718)
((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)\\spad{->}\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn\\spad{'t} a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) ((|One|) (($) "1 returns the unit element,{} denoted by 1.")))
NIL
NIL
-(-718 S R UP)
+(-719 S R UP)
((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain.")))
NIL
-((|HasCategory| |#2| (QUOTE (-348))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-367))))
-(-719 R UP)
+((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368))))
+(-720 R UP)
((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain.")))
-((-4396 |has| |#1| (-362)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-720 S)
+(-721 S)
((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity.")))
NIL
NIL
-(-721)
+(-722)
((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity.")))
NIL
NIL
-(-722 -3196 UP)
+(-723 -3191 UP)
((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use.")))
NIL
NIL
-(-723 |VarSet| E1 E2 R S PR PS)
+(-724 |VarSet| E1 E2 R S PR PS)
((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (\\spad{PG})")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,{}p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,{}p)} \\undocumented")))
NIL
NIL
-(-724 |Vars1| |Vars2| E1 E2 R PR1 PR2)
+(-725 |Vars1| |Vars2| E1 E2 R PR1 PR2)
((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-725 E OV R PPR)
+(-726 E OV R PPR)
((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-726 |vl| R)
+(-727 |vl| R)
((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")))
-(((-4405 "*") |has| |#2| (-171)) (-4396 |has| |#2| (-554)) (-4401 |has| |#2| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-904))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (-4037 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-554)))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-859 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144)))))
-(-727 E OV R PRF)
+(((-4409 "*") |has| |#2| (-172)) (-4400 |has| |#2| (-555)) (-4405 |has| |#2| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-905))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (-4032 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-555)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145)))))
+(-728 E OV R PRF)
((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-728 E OV R P)
+(-729 E OV R P)
((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}.")))
NIL
NIL
-(-729 R S M)
+(-730 R S M)
((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,{}u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}.")))
NIL
NIL
-(-730 R M)
+(-731 R M)
((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}.")))
-((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-845))))
-(-731 S)
+((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-846))))
+(-732 S)
((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements.")))
-((-4393 . T) (-4404 . T))
+((-4397 . T) (-4408 . T))
NIL
-(-732 S)
+(-733 S)
((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}.")))
-((-4403 . T) (-4393 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-733)
+((-4407 . T) (-4397 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-734)
((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned.")))
NIL
NIL
-(-734 S)
+(-735 S)
((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,{}l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}.")))
NIL
NIL
-(-735 |Coef| |Var|)
+(-736 |Coef| |Var|)
((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-736 OV E R P)
+(-737 OV E R P)
((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain")))
NIL
NIL
-(-737 E OV R P)
+(-738 E OV R P)
((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}.")))
NIL
NIL
-(-738 S R)
+(-739 S R)
((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}.")))
NIL
NIL
-(-739 R)
+(-740 R)
((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}.")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-740)
+(-741)
((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}.")))
NIL
NIL
-(-741)
+(-742)
((|constructor| (NIL "This package uses the NAG Library to calculate real zeros of continuous real functions of one or more variables. (Complex equations must be expressed in terms of the equivalent larger system of real equations.) See \\downlink{Manual Page}{manpageXXc05}.")) (|c05pbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp35| FCN)))) "\\spad{c05pbf(n,{}ldfjac,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. The user must provide the Jacobian. See \\downlink{Manual Page}{manpageXXc05pbf}.")) (|c05nbf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp6| FCN)))) "\\spad{c05nbf(n,{}lwa,{}x,{}xtol,{}ifail,{}fcn)} is an easy-to-use routine to find a solution of a system of nonlinear equations by a modification of the Powell hybrid method. See \\downlink{Manual Page}{manpageXXc05nbf}.")) (|c05adf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{c05adf(a,{}b,{}eps,{}eta,{}ifail,{}f)} locates a zero of a continuous function in a given interval by a combination of the methods of linear interpolation,{} extrapolation and bisection. See \\downlink{Manual Page}{manpageXXc05adf}.")))
NIL
NIL
-(-742)
+(-743)
((|constructor| (NIL "This package uses the NAG Library to calculate the discrete Fourier transform of a sequence of real or complex data values,{} and applies it to calculate convolutions and correlations. See \\downlink{Manual Page}{manpageXXc06}.")) (|c06gsf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gsf(m,{}n,{}x,{}ifail)} takes \\spad{m} Hermitian sequences,{} each containing \\spad{n} data values,{} and forms the real and imaginary parts of the \\spad{m} corresponding complex sequences. See \\downlink{Manual Page}{manpageXXc06gsf}.")) (|c06gqf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gqf(m,{}n,{}x,{}ifail)} forms the complex conjugates,{} each containing \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gqf}.")) (|c06gcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gcf(n,{}y,{}ifail)} forms the complex conjugate of a sequence of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gcf}.")) (|c06gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06gbf(n,{}x,{}ifail)} forms the complex conjugate of \\spad{n} data values. See \\downlink{Manual Page}{manpageXXc06gbf}.")) (|c06fuf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fuf(m,{}n,{}init,{}x,{}y,{}trigm,{}trign,{}ifail)} computes the two-dimensional discrete Fourier transform of a bivariate sequence of complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fuf}.")) (|c06frf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06frf(m,{}n,{}init,{}x,{}y,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06frf}.")) (|c06fqf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fqf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} Hermitian sequences,{} each containing \\spad{n} complex data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fqf}.")) (|c06fpf| (((|Result|) (|Integer|) (|Integer|) (|String|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06fpf(m,{}n,{}init,{}x,{}trig,{}ifail)} computes the discrete Fourier transforms of \\spad{m} sequences,{} each containing \\spad{n} real data values. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXc06fpf}.")) (|c06ekf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ekf(job,{}n,{}x,{}y,{}ifail)} calculates the circular convolution of two real vectors of period \\spad{n}. No extra workspace is required. See \\downlink{Manual Page}{manpageXXc06ekf}.")) (|c06ecf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ecf(n,{}x,{}y,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ecf}.")) (|c06ebf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06ebf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a Hermitian sequence of \\spad{n} complex data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06ebf}.")) (|c06eaf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{c06eaf(n,{}x,{}ifail)} calculates the discrete Fourier transform of a sequence of \\spad{n} real data values. (No extra workspace required.) See \\downlink{Manual Page}{manpageXXc06eaf}.")))
NIL
NIL
-(-743)
+(-744)
((|constructor| (NIL "This package uses the NAG Library to calculate the numerical value of definite integrals in one or more dimensions and to evaluate weights and abscissae of integration rules. See \\downlink{Manual Page}{manpageXXd01}.")) (|d01gbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01gbf(ndim,{}a,{}b,{}maxcls,{}eps,{}lenwrk,{}mincls,{}wrkstr,{}ifail,{}functn)} returns an approximation to the integral of a function over a hyper-rectangular region,{} using a Monte Carlo method. An approximate relative error estimate is also returned. This routine is suitable for low accuracy work. See \\downlink{Manual Page}{manpageXXd01gbf}.")) (|d01gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|)) "\\spad{d01gaf(x,{}y,{}n,{}ifail)} integrates a function which is specified numerically at four or more points,{} over the whole of its specified range,{} using third-order finite-difference formulae with error estimates,{} according to a method due to Gill and Miller. See \\downlink{Manual Page}{manpageXXd01gaf}.")) (|d01fcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp4| FUNCTN)))) "\\spad{d01fcf(ndim,{}a,{}b,{}maxpts,{}eps,{}lenwrk,{}minpts,{}ifail,{}functn)} attempts to evaluate a multi-dimensional integral (up to 15 dimensions),{} with constant and finite limits,{} to a specified relative accuracy,{} using an adaptive subdivision strategy. See \\downlink{Manual Page}{manpageXXd01fcf}.")) (|d01bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{d01bbf(a,{}b,{}itype,{}n,{}gtype,{}ifail)} returns the weight appropriate to a Gaussian quadrature. The formulae provided are Gauss-Legendre,{} Gauss-Rational,{} Gauss- Laguerre and Gauss-Hermite. See \\downlink{Manual Page}{manpageXXd01bbf}.")) (|d01asf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01asf(a,{}omega,{}key,{}epsabs,{}limlst,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}infty): See \\downlink{Manual Page}{manpageXXd01asf}.")) (|d01aqf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01aqf(a,{}b,{}c,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the Hilbert transform of a function \\spad{g}(\\spad{x}) over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01aqf}.")) (|d01apf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01apf(a,{}b,{}alfa,{}beta,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} is an adaptive integrator which calculates an approximation to the integral of a function \\spad{g}(\\spad{x})\\spad{w}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01apf}.")) (|d01anf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| G)))) "\\spad{d01anf(a,{}b,{}omega,{}key,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}g)} calculates an approximation to the sine or the cosine transform of a function \\spad{g} over [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01anf}.")) (|d01amf| (((|Result|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01amf(bound,{}inf,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over an infinite or semi-infinite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01amf}.")) (|d01alf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01alf(a,{}b,{}npts,{}points,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01alf}.")) (|d01akf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01akf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is an adaptive integrator,{} especially suited to oscillating,{} non-singular integrands,{} which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01akf}.")) (|d01ajf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp1| F)))) "\\spad{d01ajf(a,{}b,{}epsabs,{}epsrel,{}lw,{}liw,{}ifail,{}f)} is a general-purpose integrator which calculates an approximation to the integral of a function \\spad{f}(\\spad{x}) over a finite interval [a,{}\\spad{b}]: See \\downlink{Manual Page}{manpageXXd01ajf}.")))
NIL
NIL
-(-744)
+(-745)
((|constructor| (NIL "This package uses the NAG Library to calculate the numerical solution of ordinary differential equations. There are two main types of problem,{} those in which all boundary conditions are specified at one point (initial-value problems),{} and those in which the boundary conditions are distributed between two or more points (boundary- value problems and eigenvalue problems). Routines are available for initial-value problems,{} two-point boundary-value problems and Sturm-Liouville eigenvalue problems. See \\downlink{Manual Page}{manpageXXd02}.")) (|d02raf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp41| FCN JACOBF JACEPS))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp42| G JACOBG JACGEP)))) "\\spad{d02raf(n,{}mnp,{}numbeg,{}nummix,{}tol,{}init,{}iy,{}ijac,{}lwork,{}liwork,{}np,{}x,{}y,{}deleps,{}ifail,{}fcn,{}g)} solves the two-point boundary-value problem with general boundary conditions for a system of ordinary differential equations,{} using a deferred correction technique and Newton iteration. See \\downlink{Manual Page}{manpageXXd02raf}.")) (|d02kef| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL))) (|FileName|) (|FileName|)) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval,{}monit,{}report)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. Files \\spad{monit} and \\spad{report} will be used to define the subroutines for the MONIT and REPORT arguments. See \\downlink{Manual Page}{manpageXXd02gbf}.") (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp10| COEFFN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp80| BDYVAL)))) "\\spad{d02kef(xpoint,{}m,{}k,{}tol,{}maxfun,{}match,{}elam,{}delam,{}hmax,{}maxit,{}ifail,{}coeffn,{}bdyval)} finds a specified eigenvalue of a regular singular second- order Sturm-Liouville system on a finite or infinite range,{} using a Pruefer transformation and a shooting method. It also reports values of the eigenfunction and its derivatives. Provision is made for discontinuities in the coefficient functions or their derivatives. See \\downlink{Manual Page}{manpageXXd02kef}. ASP domains Asp12 and Asp33 are used to supply default subroutines for the MONIT and REPORT arguments via their \\axiomOp{outputAsFortran} operation.")) (|d02gbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp77| FCNF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp78| FCNG)))) "\\spad{d02gbf(a,{}b,{}n,{}tol,{}mnp,{}lw,{}liw,{}c,{}d,{}gam,{}x,{}np,{}ifail,{}fcnf,{}fcng)} solves a general linear two-point boundary value problem for a system of ordinary differential equations using a deferred correction technique. See \\downlink{Manual Page}{manpageXXd02gbf}.")) (|d02gaf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02gaf(u,{}v,{}n,{}a,{}b,{}tol,{}mnp,{}lw,{}liw,{}x,{}np,{}ifail,{}fcn)} solves the two-point boundary-value problem with assigned boundary values for a system of ordinary differential equations,{} using a deferred correction technique and a Newton iteration. See \\downlink{Manual Page}{manpageXXd02gaf}.")) (|d02ejf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp31| PEDERV))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02ejf(xend,{}m,{}n,{}relabs,{}iw,{}x,{}y,{}tol,{}ifail,{}g,{}fcn,{}pederv,{}output)} integrates a stiff system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a variable-order,{} variable-step method implementing the Backward Differentiation Formulae (\\spad{BDF}),{} until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02ejf}.")) (|d02cjf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|String|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02cjf(xend,{}m,{}n,{}tol,{}relabs,{}x,{}y,{}ifail,{}g,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over a range with suitable initial conditions,{} using a variable-order,{} variable-step Adams method until a user-specified function,{} if supplied,{} of the solution is zero,{} and returns the solution at points specified by the user,{} if desired. See \\downlink{Manual Page}{manpageXXd02cjf}.")) (|d02bhf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp9| G))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN)))) "\\spad{d02bhf(xend,{}n,{}irelab,{}hmax,{}x,{}y,{}tol,{}ifail,{}g,{}fcn)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} until a user-specified function of the solution is zero. See \\downlink{Manual Page}{manpageXXd02bhf}.")) (|d02bbf| (((|Result|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp7| FCN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp8| OUTPUT)))) "\\spad{d02bbf(xend,{}m,{}n,{}irelab,{}x,{}y,{}tol,{}ifail,{}fcn,{}output)} integrates a system of first-order ordinary differential equations over an interval with suitable initial conditions,{} using a Runge-Kutta-Merson method,{} and returns the solution at points specified by the user. See \\downlink{Manual Page}{manpageXXd02bbf}.")))
NIL
NIL
-(-745)
+(-746)
((|constructor| (NIL "This package uses the NAG Library to solve partial differential equations. See \\downlink{Manual Page}{manpageXXd03}.")) (|d03faf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|ThreeDimensionalMatrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03faf(xs,{}xf,{}l,{}lbdcnd,{}bdxs,{}bdxf,{}ys,{}yf,{}m,{}mbdcnd,{}bdys,{}bdyf,{}zs,{}zf,{}n,{}nbdcnd,{}bdzs,{}bdzf,{}lambda,{}ldimf,{}mdimf,{}lwrk,{}f,{}ifail)} solves the Helmholtz equation in Cartesian co-ordinates in three dimensions using the standard seven-point finite difference approximation. This routine is designed to be particularly efficient on vector processors. See \\downlink{Manual Page}{manpageXXd03faf}.")) (|d03eef| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|String|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp73| PDEF))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp74| BNDY)))) "\\spad{d03eef(xmin,{}xmax,{}ymin,{}ymax,{}ngx,{}ngy,{}lda,{}scheme,{}ifail,{}pdef,{}bndy)} discretizes a second order elliptic partial differential equation (PDE) on a rectangular region. See \\downlink{Manual Page}{manpageXXd03eef}.")) (|d03edf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{d03edf(ngx,{}ngy,{}lda,{}maxit,{}acc,{}iout,{}a,{}rhs,{}ub,{}ifail)} solves seven-diagonal systems of linear equations which arise from the discretization of an elliptic partial differential equation on a rectangular region. This routine uses a multigrid technique. See \\downlink{Manual Page}{manpageXXd03edf}.")))
NIL
NIL
-(-746)
+(-747)
((|constructor| (NIL "This package uses the NAG Library to calculate the interpolation of a function of one or two variables. When provided with the value of the function (and possibly one or more of its lowest-order derivatives) at each of a number of values of the variable(\\spad{s}),{} the routines provide either an interpolating function or an interpolated value. For some of the interpolating functions,{} there are supporting routines to evaluate,{} differentiate or integrate them. See \\downlink{Manual Page}{manpageXXe01}.")) (|e01sff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sff(m,{}x,{}y,{}f,{}rnw,{}fnodes,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolating function computed by E01SEF. See \\downlink{Manual Page}{manpageXXe01sff}.")) (|e01sef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sef(m,{}x,{}y,{}f,{}nw,{}nq,{}rnw,{}rnq,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using a modified Shepard method. See \\downlink{Manual Page}{manpageXXe01sef}.")) (|e01sbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01sbf(m,{}x,{}y,{}f,{}triang,{}grads,{}px,{}py,{}ifail)} evaluates at a given point the two-dimensional interpolant function computed by E01SAF. See \\downlink{Manual Page}{manpageXXe01sbf}.")) (|e01saf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01saf(m,{}x,{}y,{}f,{}ifail)} generates a two-dimensional surface interpolating a set of scattered data points,{} using the method of Renka and Cline. See \\downlink{Manual Page}{manpageXXe01saf}.")) (|e01daf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01daf(mx,{}my,{}x,{}y,{}f,{}ifail)} computes a bicubic spline interpolating surface through a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. See \\downlink{Manual Page}{manpageXXe01daf}.")) (|e01bhf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{e01bhf(n,{}x,{}f,{}d,{}a,{}b,{}ifail)} evaluates the definite integral of a piecewise cubic Hermite interpolant over the interval [a,{}\\spad{b}]. See \\downlink{Manual Page}{manpageXXe01bhf}.")) (|e01bgf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bgf(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant and its first derivative at a set of points. See \\downlink{Manual Page}{manpageXXe01bgf}.")) (|e01bff| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bff(n,{}x,{}f,{}d,{}m,{}px,{}ifail)} evaluates a piecewise cubic Hermite interpolant at a set of points. See \\downlink{Manual Page}{manpageXXe01bff}.")) (|e01bef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e01bef(n,{}x,{}f,{}ifail)} computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points. See \\downlink{Manual Page}{manpageXXe01bef}.")) (|e01baf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e01baf(m,{}x,{}y,{}lck,{}lwrk,{}ifail)} determines a cubic spline to a given set of data. See \\downlink{Manual Page}{manpageXXe01baf}.")))
NIL
NIL
-(-747)
+(-748)
((|constructor| (NIL "This package uses the NAG Library to find a function which approximates a set of data points. Typically the data contain random errors,{} as of experimental measurement,{} which need to be smoothed out. To seek an approximation to the data,{} it is first necessary to specify for the approximating function a mathematical form (a polynomial,{} for example) which contains a number of unspecified coefficients: the appropriate fitting routine then derives for the coefficients the values which provide the best fit of that particular form. The package deals mainly with curve and surface fitting (\\spadignore{i.e.} fitting with functions of one and of two variables) when a polynomial or a cubic spline is used as the fitting function,{} since these cover the most common needs. However,{} fitting with other functions and/or more variables can be undertaken by means of general linear or nonlinear routines (some of which are contained in other packages) depending on whether the coefficients in the function occur linearly or nonlinearly. Cases where a graph rather than a set of data points is given can be treated simply by first reading a suitable set of points from the graph. The package also contains routines for evaluating,{} differentiating and integrating polynomial and spline curves and surfaces,{} once the numerical values of their coefficients have been determined. See \\downlink{Manual Page}{manpageXXe02}.")) (|e02zaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02zaf(px,{}py,{}lamda,{}mu,{}m,{}x,{}y,{}npoint,{}nadres,{}ifail)} sorts two-dimensional data into rectangular panels. See \\downlink{Manual Page}{manpageXXe02zaf}.")) (|e02gaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02gaf(m,{}la,{}nplus2,{}toler,{}a,{}b,{}ifail)} calculates an \\spad{l} solution to an over-determined system of \\indented{22}{1} linear equations. See \\downlink{Manual Page}{manpageXXe02gaf}.")) (|e02dff| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02dff(mx,{}my,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}lwrk,{}liwrk,{}ifail)} calculates values of a bicubic spline representation. The spline is evaluated at all points on a rectangular grid. See \\downlink{Manual Page}{manpageXXe02dff}.")) (|e02def| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02def(m,{}px,{}py,{}x,{}y,{}lamda,{}mu,{}c,{}ifail)} calculates values of a bicubic spline representation. See \\downlink{Manual Page}{manpageXXe02def}.")) (|e02ddf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02ddf(start,{}m,{}x,{}y,{}f,{}w,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}ifail)} computes a bicubic spline approximation to a set of scattered data are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02ddf}.")) (|e02dcf| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{e02dcf(start,{}mx,{}x,{}my,{}y,{}f,{}s,{}nxest,{}nyest,{}lwrk,{}liwrk,{}nx,{}lamda,{}ny,{}mu,{}wrk,{}iwrk,{}ifail)} computes a bicubic spline approximation to a set of data values,{} given on a rectangular grid in the \\spad{x}-\\spad{y} plane. The knots of the spline are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02dcf}.")) (|e02daf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02daf(m,{}px,{}py,{}x,{}y,{}f,{}w,{}mu,{}point,{}npoint,{}nc,{}nws,{}eps,{}lamda,{}ifail)} forms a minimal,{} weighted least-squares bicubic spline surface fit with prescribed knots to a given set of data points. See \\downlink{Manual Page}{manpageXXe02daf}.")) (|e02bef| (((|Result|) (|String|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|))) "\\spad{e02bef(start,{}m,{}x,{}y,{}w,{}s,{}nest,{}lwrk,{}n,{}lamda,{}ifail,{}wrk,{}iwrk)} computes a cubic spline approximation to an arbitrary set of data points. The knot are located automatically,{} but a single parameter must be specified to control the trade-off between closeness of fit and smoothness of fit. See \\downlink{Manual Page}{manpageXXe02bef}.")) (|e02bdf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02bdf(ncap7,{}lamda,{}c,{}ifail)} computes the definite integral from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bdf}.")) (|e02bcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|) (|Integer|)) "\\spad{e02bcf(ncap7,{}lamda,{}c,{}x,{}left,{}ifail)} evaluates a cubic spline and its first three derivatives from its \\spad{B}-spline representation. See \\downlink{Manual Page}{manpageXXe02bcf}.")) (|e02bbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02bbf(ncap7,{}lamda,{}c,{}x,{}ifail)} evaluates a cubic spline representation. See \\downlink{Manual Page}{manpageXXe02bbf}.")) (|e02baf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02baf(m,{}ncap7,{}x,{}y,{}w,{}lamda,{}ifail)} computes a weighted least-squares approximation to an arbitrary set of data points by a cubic splines prescribed by the user. Cubic spline can also be carried out. See \\downlink{Manual Page}{manpageXXe02baf}.")) (|e02akf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|)) "\\spad{e02akf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}x,{}ifail)} evaluates a polynomial from its Chebyshev-series representation,{} allowing an arbitrary index increment for accessing the array of coefficients. See \\downlink{Manual Page}{manpageXXe02akf}.")) (|e02ajf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ajf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}qatm1,{}iaint1,{}laint,{}ifail)} determines the coefficients in the Chebyshev-series representation of the indefinite integral of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ajf}.")) (|e02ahf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02ahf(np1,{}xmin,{}xmax,{}a,{}ia1,{}la,{}iadif1,{}ladif,{}ifail)} determines the coefficients in the Chebyshev-series representation of the derivative of a polynomial given in Chebyshev-series form. See \\downlink{Manual Page}{manpageXXe02ahf}.")) (|e02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{e02agf(m,{}kplus1,{}nrows,{}xmin,{}xmax,{}x,{}y,{}w,{}mf,{}xf,{}yf,{}lyf,{}ip,{}lwrk,{}liwrk,{}ifail)} computes constrained weighted least-squares polynomial approximations in Chebyshev-series form to an arbitrary set of data points. The values of the approximations and any number of their derivatives can be specified at selected points. See \\downlink{Manual Page}{manpageXXe02agf}.")) (|e02aef| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|DoubleFloat|) (|Integer|)) "\\spad{e02aef(nplus1,{}a,{}xcap,{}ifail)} evaluates a polynomial from its Chebyshev-series representation. See \\downlink{Manual Page}{manpageXXe02aef}.")) (|e02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e02adf(m,{}kplus1,{}nrows,{}x,{}y,{}w,{}ifail)} computes weighted least-squares polynomial approximations to an arbitrary set of data points. See \\downlink{Manual Page}{manpageXXe02adf}.")))
NIL
NIL
-(-748)
+(-749)
((|constructor| (NIL "This package uses the NAG Library to perform optimization. An optimization problem involves minimizing a function (called the objective function) of several variables,{} possibly subject to restrictions on the values of the variables defined by a set of constraint functions. The routines in the NAG Foundation Library are concerned with function minimization only,{} since the problem of maximizing a given function can be transformed into a minimization problem simply by multiplying the function by \\spad{-1}. See \\downlink{Manual Page}{manpageXXe04}.")) (|e04ycf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04ycf(job,{}m,{}n,{}fsumsq,{}s,{}lv,{}v,{}ifail)} returns estimates of elements of the variance matrix of the estimated regression coefficients for a nonlinear least squares problem. The estimates are derived from the Jacobian of the function \\spad{f}(\\spad{x}) at the solution. See \\downlink{Manual Page}{manpageXXe04ycf}.")) (|e04ucf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Boolean|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp55| CONFUN))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04ucf(n,{}nclin,{}ncnln,{}nrowa,{}nrowj,{}nrowr,{}a,{}bl,{}bu,{}liwork,{}lwork,{}sta,{}cra,{}der,{}fea,{}fun,{}hes,{}infb,{}infs,{}linf,{}lint,{}list,{}maji,{}majp,{}mini,{}minp,{}mon,{}nonf,{}opt,{}ste,{}stao,{}stac,{}stoo,{}stoc,{}ve,{}istate,{}cjac,{}clamda,{}r,{}x,{}ifail,{}confun,{}objfun)} is designed to minimize an arbitrary smooth function subject to constraints on the variables,{} linear constraints. (E04UCF may be used for unconstrained,{} bound-constrained and linearly constrained optimization.) The user must provide subroutines that define the objective and constraint functions and as many of their first partial derivatives as possible. Unspecified derivatives are approximated by finite differences. All matrices are treated as dense,{} and hence E04UCF is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04ucf}.")) (|e04naf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Boolean|) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp20| QPHESS)))) "\\spad{e04naf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}nrowh,{}ncolh,{}bigbnd,{}a,{}bl,{}bu,{}cvec,{}featol,{}hess,{}cold,{}lpp,{}orthog,{}liwork,{}lwork,{}x,{}istate,{}ifail,{}qphess)} is a comprehensive programming (\\spad{QP}) or linear programming (\\spad{LP}) problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04naf}.")) (|e04mbf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{e04mbf(itmax,{}msglvl,{}n,{}nclin,{}nctotl,{}nrowa,{}a,{}bl,{}bu,{}cvec,{}linobj,{}liwork,{}lwork,{}x,{}ifail)} is an easy-to-use routine for solving linear programming problems,{} or for finding a feasible point for such problems. It is not intended for large sparse problems. See \\downlink{Manual Page}{manpageXXe04mbf}.")) (|e04jaf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp24| FUNCT1)))) "\\spad{e04jaf(n,{}ibound,{}liw,{}lw,{}bl,{}bu,{}x,{}ifail,{}funct1)} is an easy-to-use quasi-Newton algorithm for finding a minimum of a function \\spad{F}(\\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ),{} subject to fixed upper and \\indented{25}{1\\space{2}2\\space{6}\\spad{n}} lower bounds of the independent variables \\spad{x} ,{}\\spad{x} ,{}...,{}\\spad{x} ,{} using \\indented{43}{1\\space{2}2\\space{6}\\spad{n}} function values only. See \\downlink{Manual Page}{manpageXXe04jaf}.")) (|e04gcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp19| LSFUN2)))) "\\spad{e04gcf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun2)} is an easy-to-use quasi-Newton algorithm for finding an unconstrained minimum of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). First derivatives are required. See \\downlink{Manual Page}{manpageXXe04gcf}.")) (|e04fdf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp50| LSFUN1)))) "\\spad{e04fdf(m,{}n,{}liw,{}lw,{}x,{}ifail,{}lsfun1)} is an easy-to-use algorithm for finding an unconstrained minimum of a sum of squares of \\spad{m} nonlinear functions in \\spad{n} variables (m>=n). No derivatives are required. See \\downlink{Manual Page}{manpageXXe04fdf}.")) (|e04dgf| (((|Result|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp49| OBJFUN)))) "\\spad{e04dgf(n,{}es,{}fu,{}it,{}lin,{}list,{}ma,{}op,{}pr,{}sta,{}sto,{}ve,{}x,{}ifail,{}objfun)} minimizes an unconstrained nonlinear function of several variables using a pre-conditioned,{} limited memory quasi-Newton conjugate gradient method. First derivatives are required. The routine is intended for use on large scale problems. See \\downlink{Manual Page}{manpageXXe04dgf}.")))
NIL
NIL
-(-749)
+(-750)
((|constructor| (NIL "This package uses the NAG Library to provide facilities for matrix factorizations and associated transformations. See \\downlink{Manual Page}{manpageXXf01}.")) (|f01ref| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01ref(wheret,{}m,{}n,{}ncolq,{}lda,{}theta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the complex \\spad{m} by \\spad{m} unitary matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01ref}.")) (|f01rdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}theta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01rdf}.")) (|f01rcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f01rcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the complex \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01rcf}.")) (|f01qef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qef(wheret,{}m,{}n,{}ncolq,{}lda,{}zeta,{}a,{}ifail)} returns the first \\spad{ncolq} columns of the real \\spad{m} by \\spad{m} orthogonal matrix \\spad{Q},{} where \\spad{Q} is given as the product of Householder transformation matrices. See \\downlink{Manual Page}{manpageXXf01qef}.")) (|f01qdf| (((|Result|) (|String|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qdf(trans,{}wheret,{}m,{}n,{}a,{}lda,{}zeta,{}ncolb,{}ldb,{}b,{}ifail)} performs one of the transformations See \\downlink{Manual Page}{manpageXXf01qdf}.")) (|f01qcf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01qcf(m,{}n,{}lda,{}a,{}ifail)} finds the \\spad{QR} factorization of the real \\spad{m} by \\spad{n} matrix A,{} where m>=n. See \\downlink{Manual Page}{manpageXXf01qcf}.")) (|f01mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01mcf(n,{}avals,{}lal,{}nrow,{}ifail)} computes the Cholesky factorization of a real symmetric positive-definite variable-bandwidth matrix. See \\downlink{Manual Page}{manpageXXf01mcf}.")) (|f01maf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{f01maf(n,{}nz,{}licn,{}lirn,{}abort,{}avals,{}irn,{}icn,{}droptl,{}densw,{}ifail)} computes an incomplete Cholesky factorization of a real sparse symmetric positive-definite matrix A. See \\downlink{Manual Page}{manpageXXf01maf}.")) (|f01bsf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Boolean|) (|DoubleFloat|) (|Boolean|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f01bsf(n,{}nz,{}licn,{}ivect,{}jvect,{}icn,{}ikeep,{}grow,{}eta,{}abort,{}idisp,{}avals,{}ifail)} factorizes a real sparse matrix using the pivotal sequence previously obtained by F01BRF when a matrix of the same sparsity pattern was factorized. See \\downlink{Manual Page}{manpageXXf01bsf}.")) (|f01brf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Boolean|) (|List| (|Boolean|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f01brf(n,{}nz,{}licn,{}lirn,{}pivot,{}lblock,{}grow,{}abort,{}a,{}irn,{}icn,{}ifail)} factorizes a real sparse matrix. The routine either forms the LU factorization of a permutation of the entire matrix,{} or,{} optionally,{} first permutes the matrix to block lower triangular form and then only factorizes the diagonal blocks. See \\downlink{Manual Page}{manpageXXf01brf}.")))
NIL
NIL
-(-750)
+(-751)
((|constructor| (NIL "This package uses the NAG Library to compute \\begin{items} \\item eigenvalues and eigenvectors of a matrix \\item eigenvalues and eigenvectors of generalized matrix eigenvalue problems \\item singular values and singular vectors of a matrix. \\end{items} See \\downlink{Manual Page}{manpageXXf02}.")) (|f02xef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f02xef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldph,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general complex matrix. See \\downlink{Manual Page}{manpageXXf02xef}.")) (|f02wef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Boolean|) (|Integer|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02wef(m,{}n,{}lda,{}ncolb,{}ldb,{}wantq,{}ldq,{}wantp,{}ldpt,{}a,{}b,{}ifail)} returns all,{} or part,{} of the singular value decomposition of a general real matrix. See \\downlink{Manual Page}{manpageXXf02wef}.")) (|f02fjf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE))) (|FileName|)) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image,{}monit)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.") (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp27| DOT))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| IMAGE)))) "\\spad{f02fjf(n,{}k,{}tol,{}novecs,{}nrx,{}lwork,{}lrwork,{}liwork,{}m,{}noits,{}x,{}ifail,{}dot,{}image)} finds eigenvalues of a real sparse symmetric or generalized symmetric eigenvalue problem. See \\downlink{Manual Page}{manpageXXf02fjf}.")) (|f02bjf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Boolean|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bjf(n,{}ia,{}ib,{}eps1,{}matv,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues and,{} if required,{} all the eigenvectors of the generalized eigenproblem Ax=(lambda)\\spad{Bx} where A and \\spad{B} are real,{} square matrices,{} using the \\spad{QZ} algorithm. See \\downlink{Manual Page}{manpageXXf02bjf}.")) (|f02bbf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02bbf(ia,{}n,{}alb,{}ub,{}m,{}iv,{}a,{}ifail)} calculates selected eigenvalues of a real symmetric matrix by reduction to tridiagonal form,{} bisection and inverse iteration,{} where the selected eigenvalues lie within a given interval. See \\downlink{Manual Page}{manpageXXf02bbf}.")) (|f02axf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02axf(ar,{}iar,{}\\spad{ai},{}iai,{}n,{}ivr,{}ivi,{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02axf}.")) (|f02awf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02awf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex Hermitian matrix. See \\downlink{Manual Page}{manpageXXf02awf}.")) (|f02akf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02akf(iar,{}iai,{}n,{}ivr,{}ivi,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalues of a complex matrix. See \\downlink{Manual Page}{manpageXXf02akf}.")) (|f02ajf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02ajf(iar,{}iai,{}n,{}ar,{}\\spad{ai},{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02ajf}.")) (|f02agf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02agf(ia,{}n,{}ivr,{}ivi,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02agf}.")) (|f02aff| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aff(ia,{}n,{}a,{}ifail)} calculates all the eigenvalues of a real unsymmetric matrix. See \\downlink{Manual Page}{manpageXXf02aff}.")) (|f02aef| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aef(ia,{}ib,{}n,{}iv,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf02aef}.")) (|f02adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02adf(ia,{}ib,{}n,{}a,{}b,{}ifail)} calculates all the eigenvalues of Ax=(lambda)\\spad{Bx},{} where A is a real symmetric matrix and \\spad{B} is a real symmetric positive- definite matrix. See \\downlink{Manual Page}{manpageXXf02adf}.")) (|f02abf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f02abf(a,{}ia,{}n,{}iv,{}ifail)} calculates all the eigenvalues of a real symmetric matrix. See \\downlink{Manual Page}{manpageXXf02abf}.")) (|f02aaf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f02aaf(ia,{}n,{}a,{}ifail)} calculates all the eigenvalue. See \\downlink{Manual Page}{manpageXXf02aaf}.")))
NIL
NIL
-(-751)
+(-752)
((|constructor| (NIL "This package uses the NAG Library to solve the matrix equation \\axiom{AX=B},{} where \\axiom{\\spad{B}} may be a single vector or a matrix of multiple right-hand sides. The matrix \\axiom{A} may be real,{} complex,{} symmetric,{} Hermitian positive- definite,{} or sparse. It may also be rectangular,{} in which case a least-squares solution is obtained. See \\downlink{Manual Page}{manpageXXf04}.")) (|f04qaf| (((|Result|) (|Integer|) (|Integer|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp30| APROD)))) "\\spad{f04qaf(m,{}n,{}damp,{}atol,{}btol,{}conlim,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}b,{}ifail,{}aprod)} solves sparse unsymmetric equations,{} sparse linear least- squares problems and sparse damped linear least-squares problems,{} using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04qaf}.")) (|f04mcf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04mcf(n,{}al,{}lal,{}d,{}nrow,{}ir,{}b,{}nrb,{}iselct,{}nrx,{}ifail)} computes the approximate solution of a system of real linear equations with multiple right-hand sides,{} AX=B,{} where A is a symmetric positive-definite variable-bandwidth matrix,{} which has previously been factorized by F01MCF. Related systems may also be solved. See \\downlink{Manual Page}{manpageXXf04mcf}.")) (|f04mbf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Boolean|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp28| APROD))) (|Union| (|:| |fn| (|FileName|)) (|:| |fp| (|Asp34| MSOLVE)))) "\\spad{f04mbf(n,{}b,{}precon,{}shift,{}itnlim,{}msglvl,{}lrwork,{}liwork,{}rtol,{}ifail,{}aprod,{}msolve)} solves a system of real sparse symmetric linear equations using a Lanczos algorithm. See \\downlink{Manual Page}{manpageXXf04mbf}.")) (|f04maf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|Integer|)) (|Integer|)) "\\spad{f04maf(n,{}nz,{}avals,{}licn,{}irn,{}lirn,{}icn,{}wkeep,{}ikeep,{}inform,{}b,{}acc,{}noits,{}ifail)} \\spad{e} a sparse symmetric positive-definite system of linear equations,{} Ax=b,{} using a pre-conditioned conjugate gradient method,{} where A has been factorized by F01MAF. See \\downlink{Manual Page}{manpageXXf04maf}.")) (|f04jgf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|DoubleFloat|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04jgf(m,{}n,{}nra,{}tol,{}lwork,{}a,{}b,{}ifail)} finds the solution of a linear least-squares problem,{} Ax=b ,{} where A is a real \\spad{m} by \\spad{n} (m>=n) matrix and \\spad{b} is an \\spad{m} element vector. If the matrix of observations is not of full rank,{} then the minimal least-squares solution is returned. See \\downlink{Manual Page}{manpageXXf04jgf}.")) (|f04faf| (((|Result|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04faf(job,{}n,{}d,{}e,{}b,{}ifail)} calculates the approximate solution of a set of real symmetric positive-definite tridiagonal linear equations. See \\downlink{Manual Page}{manpageXXf04faf}.")) (|f04axf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|Integer|)) (|Matrix| (|DoubleFloat|))) "\\spad{f04axf(n,{}a,{}licn,{}icn,{}ikeep,{}mtype,{}idisp,{}rhs)} calculates the approximate solution of a set of real sparse linear equations with a single right-hand side,{} Ax=b or \\indented{1}{\\spad{T}} A \\spad{x=b},{} where A has been factorized by F01BRF or F01BSF. See \\downlink{Manual Page}{manpageXXf04axf}.")) (|f04atf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{f04atf(a,{}ia,{}b,{}n,{}iaa,{}ifail)} calculates the accurate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting,{} and iterative refinement. See \\downlink{Manual Page}{manpageXXf04atf}.")) (|f04asf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04asf(ia,{}b,{}n,{}a,{}ifail)} calculates the accurate solution of a set of real symmetric positive-definite linear equations with a single right- hand side,{} Ax=b,{} using a Cholesky factorization and iterative refinement. See \\downlink{Manual Page}{manpageXXf04asf}.")) (|f04arf| (((|Result|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|)) "\\spad{f04arf(ia,{}b,{}n,{}a,{}ifail)} calculates the approximate solution of a set of real linear equations with a single right-hand side,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04arf}.")) (|f04adf| (((|Result|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|Complex| (|DoubleFloat|))) (|Integer|)) "\\spad{f04adf(ia,{}b,{}ib,{}n,{}m,{}ic,{}a,{}ifail)} calculates the approximate solution of a set of complex linear equations with multiple right-hand sides,{} using an LU factorization with partial pivoting. See \\downlink{Manual Page}{manpageXXf04adf}.")))
NIL
NIL
-(-752)
+(-753)
((|constructor| (NIL "This package uses the NAG Library to compute matrix factorizations,{} and to solve systems of linear equations following the matrix factorizations. See \\downlink{Manual Page}{manpageXXf07}.")) (|f07fef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fef(uplo,{}n,{}nrhs,{}a,{}lda,{}ldb,{}b)} (DPOTRS) solves a real symmetric positive-definite system of linear equations with multiple right-hand sides,{} AX=B,{} where A has been factorized by F07FDF (DPOTRF). See \\downlink{Manual Page}{manpageXXf07fef}.")) (|f07fdf| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07fdf(uplo,{}n,{}lda,{}a)} (DPOTRF) computes the Cholesky factorization of a real symmetric positive-definite matrix. See \\downlink{Manual Page}{manpageXXf07fdf}.")) (|f07aef| (((|Result|) (|String|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Matrix| (|Integer|)) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07aef(trans,{}n,{}nrhs,{}a,{}lda,{}ipiv,{}ldb,{}b)} (DGETRS) solves a real system of linear equations with \\indented{36}{\\spad{T}} multiple right-hand sides,{} AX=B or A \\spad{X=B},{} where A has been factorized by F07ADF (DGETRF). See \\downlink{Manual Page}{manpageXXf07aef}.")) (|f07adf| (((|Result|) (|Integer|) (|Integer|) (|Integer|) (|Matrix| (|DoubleFloat|))) "\\spad{f07adf(m,{}n,{}lda,{}a)} (DGETRF) computes the LU factorization of a real \\spad{m} by \\spad{n} matrix. See \\downlink{Manual Page}{manpageXXf07adf}.")))
NIL
NIL
-(-753)
+(-754)
((|constructor| (NIL "This package uses the NAG Library to compute some commonly occurring physical and mathematical functions. See \\downlink{Manual Page}{manpageXXs}.")) (|s21bdf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bdf(x,{}y,{}z,{}r,{}ifail)} returns a value of the symmetrised elliptic integral of the third kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bdf}.")) (|s21bcf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bcf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the second kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bcf}.")) (|s21bbf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21bbf(x,{}y,{}z,{}ifail)} returns a value of the symmetrised elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21bbf}.")) (|s21baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s21baf(x,{}y,{}ifail)} returns a value of an elementary integral,{} which occurs as a degenerate case of an elliptic integral of the first kind,{} via the routine name. See \\downlink{Manual Page}{manpageXXs21baf}.")) (|s20adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20adf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{C}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20adf}.")) (|s20acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s20acf(x,{}ifail)} returns a value for the Fresnel Integral \\spad{S}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs20acf}.")) (|s19adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19adf(x,{}ifail)} returns a value for the Kelvin function kei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19adf}.")) (|s19acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19acf(x,{}ifail)} returns a value for the Kelvin function ker(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs19acf}.")) (|s19abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19abf(x,{}ifail)} returns a value for the Kelvin function bei(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19abf}.")) (|s19aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s19aaf(x,{}ifail)} returns a value for the Kelvin function ber(\\spad{x}) via the routine name. See \\downlink{Manual Page}{manpageXXs19aaf}.")) (|s18def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{I}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18def}.")) (|s18dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s18dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the modified Bessel functions \\indented{1}{\\spad{K}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs18dcf}.")) (|s18aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aff(x,{}ifail)} returns a value for the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18aff}.")) (|s18aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18aef(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{I} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18aef}.")) (|s18adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18adf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs18adf}.")) (|s18acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s18acf(x,{}ifail)} returns the value of the modified Bessel Function \\indented{1}{\\spad{K} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs18acf}.")) (|s17dlf| (((|Result|) (|Integer|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dlf(m,{}fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Hankel functions \\indented{2}{(1)\\space{11}(2)} \\indented{1}{\\spad{H}\\space{6}(\\spad{z}) or \\spad{H}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and} \\indented{2}{(nu)\\spad{+n}\\space{8}(nu)\\spad{+n}} \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dlf}.")) (|s17dhf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dhf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Bi}(\\spad{z}) or its derivative Bi'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dhf}.")) (|s17dgf| (((|Result|) (|String|) (|Complex| (|DoubleFloat|)) (|String|) (|Integer|)) "\\spad{s17dgf(deriv,{}z,{}scale,{}ifail)} returns the value of the Airy function \\spad{Ai}(\\spad{z}) or its derivative Ai'(\\spad{z}) for complex \\spad{z},{} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dgf}.")) (|s17def| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17def(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{J}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17def}.")) (|s17dcf| (((|Result|) (|DoubleFloat|) (|Complex| (|DoubleFloat|)) (|Integer|) (|String|) (|Integer|)) "\\spad{s17dcf(fnu,{}z,{}n,{}scale,{}ifail)} returns a sequence of values for the Bessel functions \\indented{1}{\\spad{Y}\\space{6}(\\spad{z}) for complex \\spad{z},{} non-negative (nu) and \\spad{n=0},{}1,{}...,{}\\spad{N}-1,{}} \\indented{2}{(nu)\\spad{+n}} with an option for exponential scaling. See \\downlink{Manual Page}{manpageXXs17dcf}.")) (|s17akf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17akf(x,{}ifail)} returns a value for the derivative of the Airy function \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17akf}.")) (|s17ajf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ajf(x,{}ifail)} returns a value of the derivative of the Airy function \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ajf}.")) (|s17ahf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17ahf(x,{}ifail)} returns a value of the Airy function,{} \\spad{Bi}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17ahf}.")) (|s17agf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17agf(x,{}ifail)} returns a value for the Airy function,{} \\spad{Ai}(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs17agf}.")) (|s17aff| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aff(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17aff}.")) (|s17aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17aef(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{J} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17aef}.")) (|s17adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17adf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs17adf}.")) (|s17acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s17acf(x,{}ifail)} returns the value of the Bessel Function \\indented{1}{\\spad{Y} (\\spad{x}),{} via the routine name.} \\indented{2}{0} See \\downlink{Manual Page}{manpageXXs17acf}.")) (|s15aef| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15aef(x,{}ifail)} returns the value of the error function erf(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15aef}.")) (|s15adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s15adf(x,{}ifail)} returns the value of the complementary error function,{} erfc(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs15adf}.")) (|s14baf| (((|Result|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|)) "\\spad{s14baf(a,{}x,{}tol,{}ifail)} computes values for the incomplete gamma functions \\spad{P}(a,{}\\spad{x}) and \\spad{Q}(a,{}\\spad{x}). See \\downlink{Manual Page}{manpageXXs14baf}.")) (|s14abf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14abf(x,{}ifail)} returns a value for the log,{} \\spad{ln}(Gamma(\\spad{x})),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14abf}.")) (|s14aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s14aaf(x,{}ifail)} returns the value of the Gamma function (Gamma)(\\spad{x}),{} via the routine name. See \\downlink{Manual Page}{manpageXXs14aaf}.")) (|s13adf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13adf(x,{}ifail)} returns the value of the sine integral See \\downlink{Manual Page}{manpageXXs13adf}.")) (|s13acf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13acf(x,{}ifail)} returns the value of the cosine integral See \\downlink{Manual Page}{manpageXXs13acf}.")) (|s13aaf| (((|Result|) (|DoubleFloat|) (|Integer|)) "\\spad{s13aaf(x,{}ifail)} returns the value of the exponential integral \\indented{1}{\\spad{E} (\\spad{x}),{} via the routine name.} \\indented{2}{1} See \\downlink{Manual Page}{manpageXXs13aaf}.")) (|s01eaf| (((|Result|) (|Complex| (|DoubleFloat|)) (|Integer|)) "\\spad{s01eaf(z,{}ifail)} S01EAF evaluates the exponential function exp(\\spad{z}) ,{} for complex \\spad{z}. See \\downlink{Manual Page}{manpageXXs01eaf}.")))
NIL
NIL
-(-754)
+(-755)
((|constructor| (NIL "Support functions for the NAG Library Link functions")) (|restorePrecision| (((|Void|)) "\\spad{restorePrecision()} \\undocumented{}")) (|checkPrecision| (((|Boolean|)) "\\spad{checkPrecision()} \\undocumented{}")) (|dimensionsOf| (((|SExpression|) (|Symbol|) (|Matrix| (|Integer|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|Matrix| (|DoubleFloat|))) "\\spad{dimensionsOf(s,{}m)} \\undocumented{}")) (|aspFilename| (((|String|) (|String|)) "\\spad{aspFilename(\"f\")} returns a String consisting of \\spad{\"f\"} suffixed with \\indented{1}{an extension identifying the current AXIOM session.}")) (|fortranLinkerArgs| (((|String|)) "\\spad{fortranLinkerArgs()} returns the current linker arguments")) (|fortranCompilerName| (((|String|)) "\\spad{fortranCompilerName()} returns the name of the currently selected \\indented{1}{Fortran compiler}")))
NIL
NIL
-(-755 S)
+(-756 S)
((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-756)
+(-757)
((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,{}b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,{}b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,{}b,{}c)} returns \\spad{(a*b)*c-a*(b*c)}.")))
NIL
NIL
-(-757 S)
+(-758 S)
((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring.")))
NIL
NIL
-(-758)
+(-759)
((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring.")))
NIL
NIL
-(-759 |Par|)
+(-760 |Par|)
((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable.")))
NIL
NIL
-(-760 -3196)
+(-761 -3191)
((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction.")))
NIL
NIL
-(-761 P -3196)
+(-762 P -3191)
((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")))
NIL
NIL
-(-762 T$)
+(-763 T$)
NIL
NIL
NIL
-(-763 UP -3196)
+(-764 UP -3191)
((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}.")))
NIL
NIL
-(-764)
+(-765)
((|retract| (((|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |nia| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |mdnia| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-765 R)
+(-766 R)
((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")))
NIL
NIL
-(-766)
+(-767)
((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder.")))
-(((-4405 "*") . T))
+(((-4409 "*") . T))
NIL
-(-767 R -3196)
+(-768 R -3191)
((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found.")))
NIL
NIL
-(-768 S)
+(-769 S)
((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}.")))
NIL
NIL
-(-769)
+(-770)
((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code).")))
NIL
NIL
-(-770 R |PolR| E |PolE|)
+(-771 R |PolR| E |PolE|)
((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}.")))
NIL
NIL
-(-771 R E V P TS)
+(-772 R E V P TS)
((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")))
NIL
NIL
-(-772 -3196 |ExtF| |SUEx| |ExtP| |n|)
+(-773 -3191 |ExtF| |SUEx| |ExtP| |n|)
((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented")))
NIL
NIL
-(-773 BP E OV R P)
+(-774 BP E OV R P)
((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented")))
NIL
NIL
-(-774 |Par|)
+(-775 |Par|)
((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,{}eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with variable \\spad{x}. Fraction \\spad{P} \\spad{RN}.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over \\spad{RN} with a new symbol as variable.")))
NIL
NIL
-(-775 R |VarSet|)
+(-776 R |VarSet|)
((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))) (-2234 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))) (-2234 (|HasCategory| |#1| (QUOTE (-544)))) (-2234 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))) (-2234 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-562))))) (-2234 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-1168)))) (-2234 (|HasCategory| |#1| (LIST (QUOTE -987) (QUOTE (-562))))))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))))
-(-776 R S)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
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+(-777 R S)
((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
-(-777 R)
-((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4399 |has| |#1| (-362)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
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(-778 R)
+((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}")))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
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+(-779 R)
((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))
-(-779 R E V P)
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))
+(-780 R E V P)
((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-780 S)
+(-781 S)
((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-1044))) (|HasCategory| |#1| (QUOTE (-171))))
-(-781)
+((-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (QUOTE (-172))))
+(-782)
((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}.")))
NIL
NIL
-(-782)
+(-783)
((|numericalIntegration| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) (|Result|)) "\\spad{numericalIntegration(args,{}hints)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|List| (|Segment| (|OrderedCompletion| (|DoubleFloat|))))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|)) (|:| |extra| (|Result|))) (|RoutinesTable|) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.")))
NIL
NIL
-(-783)
+(-784)
((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,{}y,{}x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})\\spad{**}(-1/5)}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try ,{} did ,{} next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is the same as \\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation\\spad{'s} right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,{}n,{}x1,{}x2,{}ns,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs,{}t1,{}t2,{}t3,{}t4,{}t5,{}t6,{}t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |try| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,{}n,{}x1,{}step,{}eps,{}yscal,{}derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,{}n,{}x1,{}x2,{}eps,{}h,{}ns,{}derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs,{}t1,{}t2,{}t3,{}t4)} is the same as \\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,{}n,{}x1,{}h,{}derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,{}x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}.")))
NIL
NIL
-(-784)
+(-785)
((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,{}a,{}b,{}epsrel,{}epsabs,{}nmin,{}nmax,{}nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")))
NIL
NIL
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((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,{}r,{}n)} creates a tube of radius \\spad{r} around the curve \\spad{c}.")))
NIL
NIL
-(-786)
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((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")))
NIL
NIL
-(-787)
+(-788)
((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")))
NIL
NIL
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((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,{}y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted.")))
NIL
NIL
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((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}")))
NIL
NIL
-(-790)
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((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering.")))
NIL
NIL
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((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-367))))
-(-792 R)
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+(-793 R)
((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-793 -4037 R OS S)
+(-794 -4032 R OS S)
((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}.")))
NIL
NIL
-(-794 R)
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((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-4037 (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (-4037 (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-994 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-795)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4032 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (-4032 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-796)
((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.")))
NIL
NIL
-(-796 R -3196 L)
+(-797 R -3191 L)
((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}.")))
NIL
NIL
-(-797 R -3196)
+(-798 R -3191)
((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.")))
NIL
NIL
-(-798)
+(-799)
((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions.")))
NIL
NIL
-(-799 R -3196)
+(-800 R -3191)
((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}.")))
NIL
NIL
-(-800)
+(-801)
((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.")))
NIL
NIL
-(-801 -3196 UP UPUP R)
+(-802 -3191 UP UPUP R)
((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation.")))
NIL
NIL
-(-802 -3196 UP L LQ)
+(-803 -3191 UP L LQ)
((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution.")))
NIL
NIL
-(-803)
+(-804)
((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-804 -3196 UP L LQ)
+(-805 -3191 UP L LQ)
((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}.")))
NIL
NIL
-(-805 -3196 UP)
+(-806 -3191 UP)
((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.")))
NIL
NIL
-(-806 -3196 L UP A LO)
+(-807 -3191 L UP A LO)
((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}.")))
NIL
NIL
-(-807 -3196 UP)
+(-808 -3191 UP)
((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")))
NIL
((|HasCategory| |#1| (QUOTE (-27))))
-(-808 -3196 LO)
+(-809 -3191 LO)
((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}.")))
NIL
NIL
-(-809 -3196 LODO)
+(-810 -3191 LODO)
((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.")))
NIL
NIL
-(-810 -2240 S |f|)
+(-811 -3304 S |f|)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
-((-4397 |has| |#2| (-1044)) (-4398 |has| |#2| (-1044)) (-4400 |has| |#2| (-6 -4400)) ((-4405 "*") |has| |#2| (-171)) (-4403 . T))
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(|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169))))) (-4032 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-1093)))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))))
+(-812 R)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-813 (-1168)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))))
-(-812 |Kernels| R |var|)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-814 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))))
+(-813 |Kernels| R |var|)
((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")))
-(((-4405 "*") |has| |#2| (-362)) (-4396 |has| |#2| (-362)) (-4401 |has| |#2| (-362)) (-4395 |has| |#2| (-362)) (-4400 . T) (-4398 . T) (-4397 . T))
-((|HasCategory| |#2| (QUOTE (-362))))
-(-813 S)
+(((-4409 "*") |has| |#2| (-363)) (-4400 |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 . T) (-4402 . T) (-4401 . T))
+((|HasCategory| |#2| (QUOTE (-363))))
+(-814 S)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u})).")))
NIL
NIL
-(-814 S)
+(-815 S)
((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l,{} r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,{}y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left.")))
NIL
NIL
-(-815)
+(-816)
((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-816)
+(-817)
((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}")))
NIL
NIL
-(-817)
+(-818)
((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}.")))
NIL
NIL
-(-818)
+(-819)
((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device.")))
NIL
NIL
-(-819)
+(-820)
((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error.")))
NIL
NIL
-(-820)
+(-821)
((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents.")))
NIL
NIL
-(-821 R)
+(-822 R)
((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath.")))
NIL
NIL
-(-822 P R)
+(-823 P R)
((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-232))))
-(-823)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233))))
+(-824)
((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object.")))
NIL
NIL
-(-824)
+(-825)
((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM.")))
NIL
NIL
-(-825 S)
+(-826 S)
((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}.")))
-((-4403 . T) (-4393 . T) (-4404 . T))
+((-4407 . T) (-4397 . T) (-4408 . T))
NIL
-(-826)
+(-827)
((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object.")))
NIL
NIL
-(-827 R S)
+(-828 R S)
((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity.")))
NIL
NIL
-(-828 R)
+(-829 R)
((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity.")))
-((-4400 |has| |#1| (-843)))
-((|HasCategory| |#1| (QUOTE (-843))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-21))))
-(-829 A S)
+((-4404 |has| |#1| (-844)))
+((|HasCategory| |#1| (QUOTE (-844))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21))))
+(-830 A S)
((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'.")))
NIL
NIL
-(-830 S)
+(-831 S)
((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of `op'.")))
NIL
NIL
-(-831 R)
+(-832 R)
((|constructor| (NIL "Algebra of ADDITIVE operators over a ring.")))
-((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))))
-(-832)
+((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))))
+(-833)
((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages).")))
NIL
NIL
-(-833)
+(-834)
((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,{}sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of \\spad{`x'}.")))
NIL
NIL
-(-834)
+(-835)
((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.")))
NIL
NIL
-(-835)
+(-836)
((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")))
NIL
NIL
-(-836)
+(-837)
((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-837 R S)
+(-838 R S)
((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity.")))
NIL
NIL
-(-838 R)
+(-839 R)
((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity.")))
-((-4400 |has| |#1| (-843)))
-((|HasCategory| |#1| (QUOTE (-843))) (-4037 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (-4037 (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-544))) (|HasCategory| |#1| (QUOTE (-21))))
-(-839)
+((-4404 |has| |#1| (-844)))
+((|HasCategory| |#1| (QUOTE (-844))) (-4032 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (-4032 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21))))
+(-840)
((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%.")))
NIL
NIL
-(-840 -2240 S)
+(-841 -3304 S)
((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering.")))
NIL
NIL
-(-841)
+(-842)
((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline")))
NIL
NIL
-(-842 S)
+(-843 S)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
NIL
NIL
-(-843)
+(-844)
((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-844 S)
+(-845 S)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set.")))
NIL
NIL
-(-845)
+(-846)
((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set.")))
NIL
NIL
-(-846 S R)
+(-847 S R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))))
-(-847 R)
+((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))))
+(-848 R)
((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-848 R C)
+(-849 R C)
((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use.")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-554))))
-(-849 R |sigma| -3756)
+((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-555))))
+(-850 R |sigma| -1648)
((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-362))))
-(-850 |x| R |sigma| -3756)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363))))
+(-851 |x| R |sigma| -1648)
((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")))
-((-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-362))))
-(-851 R)
+((-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363))))
+(-852 R)
((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")))
NIL
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))
-(-852)
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))
+(-853)
((|constructor| (NIL "Semigroups with compatible ordering.")))
NIL
NIL
-(-853)
+(-854)
((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}")))
NIL
NIL
-(-854 S)
+(-855 S)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-855)
+(-856)
((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}.")))
NIL
NIL
-(-856)
+(-857)
((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by \\spad{`f'} as a binary file.")))
NIL
NIL
-(-857)
+(-858)
((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}.")))
NIL
NIL
-(-858)
+(-859)
((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.")))
NIL
NIL
-(-859 |VariableList|)
+(-860 |VariableList|)
((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed")))
NIL
NIL
-(-860)
+(-861)
((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}.")))
NIL
NIL
-(-861 R |vl| |wl| |wtlevel|)
+(-862 R |vl| |wl| |wtlevel|)
((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")))
-((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))))
-(-862 R PS UP)
+((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))))
+(-863 R PS UP)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")))
NIL
NIL
-(-863 R |x| |pt|)
+(-864 R |x| |pt|)
((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")))
NIL
NIL
-(-864 |p|)
+(-865 |p|)
((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-865 |p|)
+(-866 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1).")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-866 |p|)
+(-867 |p|)
((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1).")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-865 |#1|) (QUOTE (-904))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-865 |#1|) (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-146))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-865 |#1|) (QUOTE (-1017))) (|HasCategory| (-865 |#1|) (QUOTE (-815))) (-4037 (|HasCategory| (-865 |#1|) (QUOTE (-815))) (|HasCategory| (-865 |#1|) (QUOTE (-845)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (QUOTE (-1143))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| (-865 |#1|) (QUOTE (-232))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -513) (QUOTE (-1168)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -865) (|devaluate| |#1|)) (LIST (QUOTE -865) (|devaluate| |#1|)))) (|HasCategory| (-865 |#1|) (QUOTE (-306))) (|HasCategory| (-865 |#1|) (QUOTE (-544))) (|HasCategory| (-865 |#1|) (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-865 |#1|) (QUOTE (-904)))) (|HasCategory| (-865 |#1|) (QUOTE (-144)))))
-(-867 |p| PADIC)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-4032 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-1144))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1169)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145)))))
+(-868 |p| PADIC)
((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-815))) (-4037 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-845)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-845))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-904)))) (|HasCategory| |#2| (QUOTE (-144)))))
-(-868 S T$)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-4032 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145)))))
+(-869 S T$)
((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))))
-(-869)
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))))
+(-870)
((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value.")))
NIL
NIL
-(-870)
+(-871)
((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.")))
NIL
NIL
-(-871 CF1 CF2)
+(-872 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-872 |ComponentFunction|)
+(-873 |ComponentFunction|)
((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}.")))
NIL
NIL
-(-873 CF1 CF2)
+(-874 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-874 |ComponentFunction|)
+(-875 |ComponentFunction|)
((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}.")))
NIL
NIL
-(-875)
+(-876)
((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result.")))
NIL
NIL
-(-876 CF1 CF2)
+(-877 CF1 CF2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented")))
NIL
NIL
-(-877 |ComponentFunction|)
+(-878 |ComponentFunction|)
((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}.")))
NIL
NIL
-(-878)
+(-879)
((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}")))
NIL
NIL
-(-879 R)
+(-880 R)
((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself.")))
NIL
NIL
-(-880 R S L)
+(-881 R S L)
((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match.")))
NIL
NIL
-(-881 S)
+(-882 S)
((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches.")))
NIL
NIL
-(-882 |Base| |Subject| |Pat|)
+(-883 |Base| |Subject| |Pat|)
((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat.")))
NIL
-((-12 (-2234 (|HasCategory| |#2| (QUOTE (-1044)))) (-2234 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (-12 (|HasCategory| |#2| (QUOTE (-1044))) (-2234 (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))))
-(-883 R A B)
+((-12 (-2176 (|HasCategory| |#2| (QUOTE (-1045)))) (-2176 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2176 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))))
+(-884 R A B)
((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))].")))
NIL
NIL
-(-884 R S)
+(-885 R S)
((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match.")))
NIL
NIL
-(-885 R -3113)
+(-886 R -3209)
((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned.")))
NIL
NIL
-(-886 R S)
+(-887 R S)
((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}.")))
NIL
NIL
-(-887 R)
+(-888 R)
((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0")))
NIL
NIL
-(-888 |VarSet|)
+(-889 |VarSet|)
((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list.")))
NIL
NIL
-(-889 UP R)
+(-890 UP R)
((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented")))
NIL
NIL
-(-890)
+(-891)
((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far.")))
NIL
NIL
-(-891 UP -3196)
+(-892 UP -3191)
((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented")))
NIL
NIL
-(-892)
+(-893)
((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}")))
NIL
NIL
-(-893)
+(-894)
((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}")))
NIL
NIL
-(-894 A S)
+(-895 A S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
NIL
NIL
-(-895 S)
+(-896 S)
((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-896 S)
+(-897 S)
((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-897 |n| R)
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-898 |n| R)
((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}")))
NIL
NIL
-(-898 S)
+(-899 S)
((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-899 S)
+(-900 S)
((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}.")))
NIL
NIL
-(-900 S)
+(-901 S)
((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation.")))
-((-4400 . T))
-((-4037 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-845))))
-(-901 R E |VarSet| S)
+((-4404 . T))
+((-4032 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846))))
+(-902 R E |VarSet| S)
((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned.")))
NIL
NIL
-(-902 R S)
+(-903 R S)
((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned.")))
NIL
NIL
-(-903 S)
+(-904 S)
((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-144))))
-(-904)
+((|HasCategory| |#1| (QUOTE (-145))))
+(-905)
((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-905 |p|)
+(-906 |p|)
((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367))))
-(-906 R0 -3196 UP UPUP R)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368))))
+(-907 R0 -3191 UP UPUP R)
((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented")))
NIL
NIL
-(-907 UP UPUP R)
+(-908 UP UPUP R)
((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented")))
NIL
NIL
-(-908 UP UPUP)
+(-909 UP UPUP)
((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}")))
NIL
NIL
-(-909 R)
+(-910 R)
((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-910 R)
+(-911 R)
((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var.")))
NIL
NIL
-(-911 E OV R P)
+(-912 E OV R P)
((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-912)
+(-913)
((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}.")))
NIL
NIL
-(-913 -3196)
+(-914 -3191)
((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}.")))
NIL
NIL
-(-914 R)
+(-915 R)
((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R}).")))
NIL
NIL
-(-915)
+(-916)
((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-916)
+(-917)
((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}.")))
-(((-4405 "*") . T))
+(((-4409 "*") . T))
NIL
-(-917 -3196 P)
+(-918 -3191 P)
((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented")))
NIL
NIL
-(-918 |xx| -3196)
+(-919 |xx| -3191)
((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented")))
NIL
NIL
-(-919 R |Var| |Expon| GR)
+(-920 R |Var| |Expon| GR)
((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}")))
NIL
NIL
-(-920 S)
+(-921 S)
((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval")))
NIL
NIL
-(-921)
+(-922)
((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")))
NIL
NIL
-(-922)
+(-923)
((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}.")))
NIL
NIL
-(-923)
+(-924)
((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented")))
NIL
NIL
-(-924 R -3196)
+(-925 R -3191)
((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol.")))
NIL
NIL
-(-925)
+(-926)
((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}.")))
NIL
NIL
-(-926 S A B)
+(-927 S A B)
((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B).")))
NIL
NIL
-(-927 S R -3196)
+(-928 S R -3191)
((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-928 I)
+(-929 I)
((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-929 S E)
+(-930 S E)
((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-930 S R L)
+(-931 S R L)
((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-931 S E V R P)
+(-932 S E V R P)
((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables.")))
NIL
-((|HasCategory| |#3| (LIST (QUOTE -881) (|devaluate| |#1|))))
-(-932 R -3196 -3113)
+((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|))))
+(-933 R -3191 -3209)
((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol.")))
NIL
NIL
-(-933 -3113)
+(-934 -3209)
((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}.")))
NIL
NIL
-(-934 S R Q)
+(-935 S R Q)
((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches.")))
NIL
NIL
-(-935 S)
+(-936 S)
((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion).")))
NIL
NIL
-(-936 S R P)
+(-937 S R P)
((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}.")))
NIL
NIL
-(-937)
+(-938)
((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}.")))
NIL
NIL
-(-938 R)
+(-939 R)
((|constructor| (NIL "This domain implements points in coordinate space")))
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092)))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#1| (QUOTE (-1044))) (-12 (|HasCategory| |#1| (QUOTE (-997))) (|HasCategory| |#1| (QUOTE (-1044)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-939 |lv| R)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-940 |lv| R)
((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}.")))
NIL
NIL
-(-940 |TheField| |ThePols|)
+(-941 |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term")))
NIL
-((|HasCategory| |#1| (QUOTE (-843))))
-(-941 R S)
+((|HasCategory| |#1| (QUOTE (-844))))
+(-942 R S)
((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}.")))
NIL
NIL
-(-942 |x| R)
+(-943 |x| R)
((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}.")))
NIL
NIL
-(-943 S R E |VarSet|)
+(-944 S R E |VarSet|)
((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-904))) (|HasAttribute| |#2| (QUOTE -4401)) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-845))))
-(-944 R E |VarSet|)
+((|HasCategory| |#2| (QUOTE (-905))) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-846))))
+(-945 R E |VarSet|)
((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-945 E V R P -3196)
+(-946 E V R P -3191)
((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}.")))
NIL
NIL
-(-946 E |Vars| R P S)
+(-947 E |Vars| R P S)
((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}")))
NIL
NIL
-(-947 R)
+(-948 R)
((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| (-1168) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))))
-(-948 E V R P -3196)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
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+(-949 E V R P -3191)
((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented")))
NIL
-((|HasCategory| |#3| (QUOTE (-451))))
-(-949)
+((|HasCategory| |#3| (QUOTE (-452))))
+(-950)
((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}.")))
NIL
NIL
-(-950)
+(-951)
((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
NIL
NIL
-(-951 R L)
+(-952 R L)
((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}.")))
NIL
NIL
-(-952 A B)
+(-953 A B)
((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")))
NIL
NIL
-(-953 S)
+(-954 S)
((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed")))
-((-4404 . T) (-4403 . T))
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-(-954)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-955)
((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}.")))
NIL
NIL
-(-955 -3196)
+(-956 -3191)
((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}.")))
NIL
NIL
-(-956 I)
+(-957 I)
((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime")))
NIL
NIL
-(-957)
+(-958)
((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter.")))
NIL
NIL
-(-958 R E)
+(-959 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4397 . T) (-4398 . T) (-4400 . T))
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-(-959 A B)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4405)))
+(-960 A B)
((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented")))
-((-4400 -12 (|has| |#2| (-472)) (|has| |#1| (-472))))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-845))))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-472))) (|HasCategory| |#2| (QUOTE (-472)))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-788))) (|HasCategory| |#2| (QUOTE (-788))))) (-12 (|HasCategory| |#1| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-721)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-845)))))
-(-960)
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+(-961)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}")))
NIL
NIL
-(-961 T$)
+(-962 T$)
((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the variable name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula")))
NIL
NIL
-(-962)
+(-963)
((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")))
NIL
NIL
-(-963 S)
+(-964 S)
((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}.")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
-(-964 R |polR|)
+(-965 R |polR|)
((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")))
NIL
-((|HasCategory| |#1| (QUOTE (-451))))
-(-965)
+((|HasCategory| |#1| (QUOTE (-452))))
+(-966)
((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-966)
+(-967)
((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(\\spad{li})} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(\\spad{li})} converts a list of integers \\spad{li} to a partition")))
NIL
NIL
-(-967 S |Coef| |Expon| |Var|)
+(-968 S |Coef| |Expon| |Var|)
((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}.")))
NIL
NIL
-(-968 |Coef| |Expon| |Var|)
+(-969 |Coef| |Expon| |Var|)
((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-969)
+(-970)
((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}.")))
NIL
NIL
-(-970 S R E |VarSet| P)
+(-971 S R E |VarSet| P)
((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
NIL
-((|HasCategory| |#2| (QUOTE (-554))))
-(-971 R E |VarSet| P)
+((|HasCategory| |#2| (QUOTE (-555))))
+(-972 R E |VarSet| P)
((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned.")))
-((-4403 . T))
+((-4407 . T))
NIL
-(-972 R E V P)
+(-973 R E V P)
((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-306)))) (|HasCategory| |#1| (QUOTE (-451))))
-(-973 K)
+((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307)))) (|HasCategory| |#1| (QUOTE (-452))))
+(-974 K)
((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m,{} v)} returns \\spad{[[C_1,{} g_1],{}...,{}[C_k,{} g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,{}...,{}C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M,{} A,{} sig,{} der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M,{} sig,{} der)} returns \\spad{[R,{} A,{} A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation.")))
NIL
NIL
-(-974 |VarSet| E RC P)
+(-975 |VarSet| E RC P)
((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary \\spad{gcd} domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")))
NIL
NIL
-(-975 R)
+(-976 R)
((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-976 R1 R2)
+(-977 R1 R2)
((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented")))
NIL
NIL
-(-977 R)
+(-978 R)
((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")))
NIL
NIL
-(-978 K)
+(-979 K)
((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns \\spad{csc}(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,{}n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise.")))
NIL
NIL
-(-979 R E OV PPR)
+(-980 R E OV PPR)
((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol")))
NIL
NIL
-(-980 K R UP -3196)
+(-981 K R UP -3191)
((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")))
NIL
NIL
-(-981 |vl| |nv|)
+(-982 |vl| |nv|)
((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals")))
NIL
NIL
-(-982 R |Var| |Expon| |Dpoly|)
+(-983 R |Var| |Expon| |Dpoly|)
((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-306)))))
-(-983 R E V P TS)
+((-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-307)))))
+(-984 R E V P TS)
((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
NIL
NIL
-(-984)
+(-985)
((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,{}\"a\")} creates a new equation.")))
NIL
NIL
-(-985 A B R S)
+(-986 A B R S)
((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,{}frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}.")))
NIL
NIL
-(-986 A S)
+(-987 A S)
((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-904))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-1017))) (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-1143))))
-(-987 S)
+((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-1144))))
+(-988 S)
((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-988 |n| K)
+(-989 |n| K)
((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}.")))
NIL
NIL
-(-989)
+(-990)
((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted.")))
NIL
NIL
-(-990 S)
+(-991 S)
((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end.")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
-(-991 S R)
+(-992 S R)
((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (QUOTE (-1053))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-289))))
-(-992 R)
+((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-290))))
+(-993 R)
((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}.")))
-((-4396 |has| |#1| (-289)) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-993 QR R QS S)
+(-994 QR R QS S)
((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}.")))
NIL
NIL
-(-994 R)
+(-995 R)
((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}")))
-((-4396 |has| |#1| (-289)) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-1053))) (|HasCategory| |#1| (QUOTE (-544))))
-(-995 S)
-((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}.")))
-((-4403 . T) (-4404 . T))
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+((-4400 |has| |#1| (-290)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4032 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1169)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))))
(-996 S)
+((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}.")))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-997 S)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-997)
+(-998)
((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}.")))
NIL
NIL
-(-998 -3196 UP UPUP |radicnd| |n|)
+(-999 -3191 UP UPUP |radicnd| |n|)
((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x}).")))
-((-4396 |has| (-406 |#2|) (-362)) (-4401 |has| (-406 |#2|) (-362)) (-4395 |has| (-406 |#2|) (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4037 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4037 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4037 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))))
-(-999 |bb|)
+((-4400 |has| (-407 |#2|) (-363)) (-4405 |has| (-407 |#2|) (-363)) (-4399 |has| (-407 |#2|) (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4032 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4032 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4032 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))))
+(-1000 |bb|)
((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| (-562) (QUOTE (-904))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-1168)))) (|HasCategory| (-562) (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-146))) (|HasCategory| (-562) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-1017))) (|HasCategory| (-562) (QUOTE (-815))) (-4037 (|HasCategory| (-562) (QUOTE (-815))) (|HasCategory| (-562) (QUOTE (-845)))) (|HasCategory| (-562) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-1143))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| (-562) (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| (-562) (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| (-562) (QUOTE (-232))) (|HasCategory| (-562) (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| (-562) (LIST (QUOTE -513) (QUOTE (-1168)) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -308) (QUOTE (-562)))) (|HasCategory| (-562) (LIST (QUOTE -285) (QUOTE (-562)) (QUOTE (-562)))) (|HasCategory| (-562) (QUOTE (-306))) (|HasCategory| (-562) (QUOTE (-544))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-562) (LIST (QUOTE -635) (QUOTE (-562)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-562) (QUOTE (-904)))) (|HasCategory| (-562) (QUOTE (-144)))))
-(-1000)
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-563) (QUOTE (-905))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-1169)))) (|HasCategory| (-563) (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-147))) (|HasCategory| (-563) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-1018))) (|HasCategory| (-563) (QUOTE (-816))) (-4032 (|HasCategory| (-563) (QUOTE (-816))) (|HasCategory| (-563) (QUOTE (-846)))) (|HasCategory| (-563) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-1144))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-563) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-563) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| (-563) (QUOTE (-233))) (|HasCategory| (-563) (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| (-563) (LIST (QUOTE -514) (QUOTE (-1169)) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -309) (QUOTE (-563)))) (|HasCategory| (-563) (LIST (QUOTE -286) (QUOTE (-563)) (QUOTE (-563)))) (|HasCategory| (-563) (QUOTE (-307))) (|HasCategory| (-563) (QUOTE (-545))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-563) (LIST (QUOTE -636) (QUOTE (-563)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-563) (QUOTE (-905)))) (|HasCategory| (-563) (QUOTE (-145)))))
+(-1001)
((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}.")))
NIL
NIL
-(-1001)
+(-1002)
((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size().")))
NIL
NIL
-(-1002 RP)
+(-1003 RP)
((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers.")))
NIL
NIL
-(-1003 S)
+(-1004 S)
((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number.")))
NIL
NIL
-(-1004 A S)
+(-1005 A S)
((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-1092))))
-(-1005 S)
+((|HasAttribute| |#1| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-1093))))
+(-1006 S)
((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}.")))
NIL
NIL
-(-1006 S)
+(-1007 S)
((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}")))
NIL
NIL
-(-1007)
+(-1008)
((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}")))
-((-4396 . T) (-4401 . T) (-4395 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4400 . T))
+((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T))
NIL
-(-1008 R -3196)
+(-1009 R -3191)
((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function.")))
NIL
NIL
-(-1009 R -3196)
+(-1010 R -3191)
((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function.")))
NIL
NIL
-(-1010 -3196 UP)
+(-1011 -3191 UP)
((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use.")))
NIL
NIL
-(-1011 -3196 UP)
+(-1012 -3191 UP)
((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use.")))
NIL
NIL
-(-1012 S)
+(-1013 S)
((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,{}u,{}n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented")))
NIL
NIL
-(-1013 F1 UP UPUP R F2)
+(-1014 F1 UP UPUP R F2)
((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,{}u,{}g)} \\undocumented")))
NIL
NIL
-(-1014)
+(-1015)
((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied.")))
NIL
NIL
-(-1015 |Pol|)
+(-1016 |Pol|)
((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}.")))
NIL
NIL
-(-1016 |Pol|)
+(-1017 |Pol|)
((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol,{} int,{} range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol,{} int,{} eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} int,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol,{} eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol,{} range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}.")))
NIL
NIL
-(-1017)
+(-1018)
((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats.")))
NIL
NIL
-(-1018)
+(-1019)
((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,{}lv,{}eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,{}eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}.")))
NIL
NIL
-(-1019 |TheField|)
+(-1020 |TheField|)
((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number")))
-((-4396 . T) (-4401 . T) (-4395 . T) (-4398 . T) (-4397 . T) ((-4405 "*") . T) (-4400 . T))
-((-4037 (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| (-406 (-562)) (LIST (QUOTE -1033) (QUOTE (-562)))))
-(-1020 -3196 L)
+((-4400 . T) (-4405 . T) (-4399 . T) (-4402 . T) (-4401 . T) ((-4409 "*") . T) (-4404 . T))
+((-4032 (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-407 (-563)) (LIST (QUOTE -1034) (QUOTE (-563)))))
+(-1021 -3191 L)
((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}.")))
NIL
NIL
-(-1021 S)
+(-1022 S)
((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(n,{}m)} same as \\spad{setelt(n,{}m)}.")) (|deref| ((|#1| $) "\\spad{deref(n)} is equivalent to \\spad{elt(n)}.")) (|setelt| ((|#1| $ |#1|) "\\spad{setelt(n,{}m)} changes the value of the object \\spad{n} to \\spad{m}.")) (|elt| ((|#1| $) "\\spad{elt(n)} returns the object \\spad{n}.")) (|ref| (($ |#1|) "\\spad{ref(n)} creates a pointer (reference) to the object \\spad{n}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-1092))))
-(-1022 R E V P)
+((|HasCategory| |#1| (QUOTE (-1093))))
+(-1023 R E V P)
((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1023 R)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1024 R)
((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.")))
NIL
-((|HasAttribute| |#1| (QUOTE (-4405 "*"))))
-(-1024 R)
+((|HasAttribute| |#1| (QUOTE (-4409 "*"))))
+(-1025 R)
((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis.")))
NIL
-((-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))))
-(-1025 S)
+((-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))))
+(-1026 S)
((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i,{} r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1026)
+(-1027)
((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,{}m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals.")))
NIL
NIL
-(-1027 S)
+(-1028 S)
((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r,{} i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}")))
NIL
NIL
-(-1028 S)
+(-1029 S)
((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used.")))
NIL
NIL
-(-1029 -3196 |Expon| |VarSet| |FPol| |LFPol|)
+(-1030 -3191 |Expon| |VarSet| |FPol| |LFPol|)
((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring")))
-(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1030)
-((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))))
(-1031)
+((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}")))
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1032)
((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'.")))
NIL
NIL
-(-1032 A S)
+(-1033 A S)
((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")))
NIL
NIL
-(-1033 S)
+(-1034 S)
((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")))
NIL
NIL
-(-1034 Q R)
+(-1035 Q R)
((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible.")))
NIL
NIL
-(-1035)
+(-1036)
((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,{}m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,{}m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,{}g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,{}g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented")))
NIL
NIL
-(-1036 UP)
+(-1037 UP)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}.")))
NIL
NIL
-(-1037 R)
+(-1038 R)
((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}.")))
NIL
NIL
-(-1038 R)
+(-1039 R)
((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f,{} [v1 = g1,{}...,{}vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f,{} [v1,{}...,{}vn],{} [g1,{}...,{}gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}\\spad{'s} appearing inside the \\spad{gi}\\spad{'s} are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f,{} v,{} g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}.")))
NIL
NIL
-(-1039 T$)
+(-1040 T$)
((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of \\spad{`c'}.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of \\spad{`c'}.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}.")))
NIL
NIL
-(-1040 T$)
+(-1041 T$)
((|constructor| (NIL "This category defines the common interface for \\spad{RGB} color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space.")))
NIL
NIL
-(-1041 R |ls|)
+(-1042 R |ls|)
((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| (-775 |#1| (-859 |#2|)) (QUOTE (-1092))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -775) (|devaluate| |#1|) (LIST (QUOTE -859) (|devaluate| |#2|)))))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-775 |#1| (-859 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| (-859 |#2|) (QUOTE (-367))) (|HasCategory| (-775 |#1| (-859 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1042)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -776) (|devaluate| |#1|) (LIST (QUOTE -860) (|devaluate| |#2|)))))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-776 |#1| (-860 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| (-860 |#2|) (QUOTE (-368))) (|HasCategory| (-776 |#1| (-860 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1043)
((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented")))
NIL
NIL
-(-1043 S)
+(-1044 S)
((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists.")))
NIL
NIL
-(-1044)
+(-1045)
((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists.")))
-((-4400 . T))
+((-4404 . T))
NIL
-(-1045 |xx| -3196)
+(-1046 |xx| -3191)
((|constructor| (NIL "This package exports rational interpolation algorithms")))
NIL
NIL
-(-1046 S |m| |n| R |Row| |Col|)
+(-1047 S |m| |n| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite")))
NIL
-((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-554))) (|HasCategory| |#4| (QUOTE (-171))))
-(-1047 |m| |n| R |Row| |Col|)
+((|HasCategory| |#4| (QUOTE (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-555))) (|HasCategory| |#4| (QUOTE (-172))))
+(-1048 |m| |n| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite")))
-((-4403 . T) (-4398 . T) (-4397 . T))
+((-4407 . T) (-4402 . T) (-4401 . T))
NIL
-(-1048 |m| |n| R)
+(-1049 |m| |n| R)
((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}.")))
-((-4403 . T) (-4398 . T) (-4397 . T))
-((-4037 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-535)))) (-4037 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1092))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1049 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
+((-4407 . T) (-4402 . T) (-4401 . T))
+((-4032 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-536)))) (-4032 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1050 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2)
((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.")))
NIL
NIL
-(-1050 R)
+(-1051 R)
((|constructor| (NIL "The category of right modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ $ |#1|) "\\spad{x*r} returns the right multiplication of the module element \\spad{x} by the ring element \\spad{r}.")))
NIL
NIL
-(-1051)
+(-1052)
((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")))
NIL
NIL
-(-1052 S)
+(-1053 S)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
NIL
NIL
-(-1053)
+(-1054)
((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1054 |TheField| |ThePolDom|)
+(-1055 |TheField| |ThePolDom|)
((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval")))
NIL
NIL
-(-1055)
+(-1056)
((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")))
-((-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1056)
+(-1057)
((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1168))) (LIST (QUOTE |:|) (QUOTE -2693) (QUOTE (-52))))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-52) (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| (-52) (QUOTE (-1092))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (QUOTE (-1092))) (|HasCategory| (-1168) (QUOTE (-845))) (|HasCategory| (-52) (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-52) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1168)) (|:| -2693 (-52))) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1057 S R E V)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1169))) (LIST (QUOTE |:|) (QUOTE -2557) (QUOTE (-52))))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-52) (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1093))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (QUOTE (-1093))) (|HasCategory| (-1169) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1169)) (|:| -2557 (-52))) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1058 S R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#2| (QUOTE (-544))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -987) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-1168)))))
-(-1058 R E V)
+((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -988) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-1169)))))
+(-1059 R E V)
((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-1059)
+(-1060)
((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'.")))
NIL
NIL
-(-1060 S |TheField| |ThePols|)
+(-1061 S |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}")))
NIL
NIL
-(-1061 |TheField| |ThePols|)
+(-1062 |TheField| |ThePols|)
((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}")))
NIL
NIL
-(-1062 R E V P TS)
+(-1063 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}\\spad{TS}). The same way it does not care about the way univariate polynomial \\spad{gcd} (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these \\spad{gcd} need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
NIL
NIL
-(-1063 S R E V P)
+(-1064 S R E V P)
((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#5| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")))
NIL
NIL
-(-1064 R E V P)
+(-1065 R E V P)
((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1065 R E V P TS)
+(-1066 R E V P TS)
((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
NIL
NIL
-(-1066)
+(-1067)
((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted.")))
NIL
NIL
-(-1067 |f|)
+(-1068 |f|)
((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol")))
NIL
NIL
-(-1068 |Base| R -3196)
+(-1069 |Base| R -3191)
((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}.")))
NIL
NIL
-(-1069 |Base| R -3196)
+(-1070 |Base| R -3191)
((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}.")))
NIL
NIL
-(-1070 R |ls|)
+(-1071 R |ls|)
((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,{}univ?,{}check?)} returns the same as \\spad{rur(lp,{}true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,{}true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,{}univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,{}univ?)} returns a list of items \\spad{[u,{}lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,{}lc]} in \\spad{rur(lp,{}univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor.")))
NIL
NIL
-(-1071 UP SAE UPA)
+(-1072 UP SAE UPA)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}.")))
NIL
NIL
-(-1072 R UP M)
+(-1073 R UP M)
((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself.")))
-((-4396 |has| |#1| (-362)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4037 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))))
-(-1073 UP SAE UPA)
+((-4400 |has| |#1| (-363)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4032 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))))
+(-1074 UP SAE UPA)
((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}.")))
NIL
NIL
-(-1074)
+(-1075)
((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable")))
NIL
NIL
-(-1075)
+(-1076)
((|constructor| (NIL "This is the category of Spad syntax objects.")))
NIL
NIL
-(-1076 S)
+(-1077 S)
((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(x,{} y)} to determine whether \\spad{x < y (f(x,{}y) < 0),{} x = y (f(x,{}y) = 0)},{} or \\spad{x > y (f(x,{}y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x,{} f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache.")))
NIL
NIL
-(-1077)
+(-1078)
((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,{}s)} pushs a new contour with sole binding \\spad{`b'}.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(n,{}s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `failed'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope.")))
NIL
NIL
-(-1078 R)
+(-1079 R)
((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,{}mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}")))
NIL
NIL
-(-1079 R)
+(-1080 R)
((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
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-(-1080 S)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| (-1081 (-1169)) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))))
+(-1081 S)
((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u})).")))
NIL
NIL
-(-1081 R S)
+(-1082 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-843))))
-(-1082)
+((|HasCategory| |#1| (QUOTE (-844))))
+(-1083)
((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list.")))
NIL
NIL
-(-1083 R S)
+(-1084 R S)
((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}.")))
NIL
NIL
-(-1084 S)
+(-1085 S)
((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions.")) (|segment| (((|Segment| |#1|) $) "\\spad{segment(segb)} returns the segment from the right hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{segment(segb)} returns \\spad{a..b}.")) (|variable| (((|Symbol|) $) "\\spad{variable(segb)} returns the variable from the left hand side of the \\spadtype{SegmentBinding}. For example,{} if \\spad{segb} is \\spad{v=a..b},{} then \\spad{variable(segb)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) (|Segment| |#1|)) "\\spad{equation(v,{}a..b)} creates a segment binding value with variable \\spad{v} and segment \\spad{a..b}. Note that the interpreter parses \\spad{v=a..b} to this form.")))
NIL
-((|HasCategory| |#1| (QUOTE (-1092))))
-(-1085 S)
+((|HasCategory| |#1| (QUOTE (-1093))))
+(-1086 S)
((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints.")))
NIL
NIL
-(-1086 S)
+(-1087 S)
((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1092))))
-(-1087 S L)
+((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1093))))
+(-1088 S L)
((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}.")))
NIL
NIL
-(-1088)
+(-1089)
((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'.")))
NIL
NIL
-(-1089 A S)
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((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
NIL
NIL
-(-1090 S)
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((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}.")))
-((-4393 . T))
+((-4397 . T))
NIL
-(-1091 S)
+(-1092 S)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1092)
+(-1093)
((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}.")))
NIL
NIL
-(-1093 |m| |n|)
+(-1094 |m| |n|)
((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,{}k,{}p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the \\spad{k^}{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p,{} s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,{}...,{}a_m])} returns the set {a_1,{}...,{}a_m}. Error if {a_1,{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ "failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,{}k,{}p)} replaces the \\spad{k^}{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ "failed") $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,{}k)} increments the \\spad{k^}{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")))
NIL
NIL
-(-1094 S)
+(-1095 S)
((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}")))
-((-4403 . T) (-4393 . T) (-4404 . T))
-((-4037 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))))
-(-1095 |Str| |Sym| |Int| |Flt| |Expr|)
+((-4407 . T) (-4397 . T) (-4408 . T))
+((-4032 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))))
+(-1096 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp.")))
NIL
NIL
-(-1096)
+(-1097)
((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values.")))
NIL
NIL
-(-1097 |Str| |Sym| |Int| |Flt| |Expr|)
+(-1098 |Str| |Sym| |Int| |Flt| |Expr|)
((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types.")))
NIL
NIL
-(-1098 R FS)
+(-1099 R FS)
((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|Symbol|) (|FortranScalarType|) |#2|) "\\spad{fortran(fname,{}ftype,{}body)} builds an object of type \\axiomType{FortranProgramCategory}. The three arguments specify the name,{} the type and the \\spad{body} of the program.")))
NIL
NIL
-(-1099 R E V P TS)
+(-1100 R E V P TS)
((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}\\spad{ts},{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(\\spad{lp},{}\\spad{lts},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(lpwt1,{}lpwt2)} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(\\spad{lts})} removes from \\axiom{\\spad{lts}} any \\spad{ts} such that \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for another \\spad{us} in \\axiom{\\spad{lts}}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(\\spad{ts},{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(\\spad{ts},{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(\\spad{ts},{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(\\spad{ts},{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{\\spad{ts}} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(\\spad{ts},{}us)} returns \\spad{false} iff \\axiom{\\spad{ts}} and \\axiom{us} are both empty,{} or \\axiom{\\spad{ts}} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(\\spad{lts})} sorts \\axiom{\\spad{lts}} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(\\spad{ts},{}us)} returns \\spad{true} iff \\axiom{\\spad{ts}} has less elements than \\axiom{us} otherwise if \\axiom{\\spad{ts}} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")))
NIL
NIL
-(-1100 R E V P TS)
+(-1101 R E V P TS)
((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
NIL
NIL
-(-1101 R E V P)
+(-1102 R E V P)
((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1102)
+(-1103)
((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber.")))
NIL
NIL
-(-1103 S)
+(-1104 S)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1104)
+(-1105)
((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}.")))
NIL
NIL
-(-1105 |dimtot| |dim1| S)
+(-1106 |dimtot| |dim1| S)
((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}.")))
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(LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (|HasCategory| (-563) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1169))))) (-4032 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563)))))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-563))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#3| (QUOTE (-1093)))) (|HasAttribute| |#3| (QUOTE -4404)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1093))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))))
+(-1107 R |x|)
((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}")))
NIL
-((|HasCategory| |#1| (QUOTE (-451))))
-(-1107)
+((|HasCategory| |#1| (QUOTE (-452))))
+(-1108)
((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}")))
NIL
NIL
-(-1108 R -3196)
+(-1109 R -3191)
((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1109 R)
+(-1110 R)
((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere.")))
NIL
NIL
-(-1110)
+(-1111)
((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of \\spad{`s'}.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature \\spad{`s'}.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,{}t)} constructs a Signature object with parameter types indicaded by \\spad{`s'},{} and return type indicated by \\spad{`t'}.")))
NIL
NIL
-(-1111)
+(-1112)
((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}")))
NIL
NIL
-(-1112)
+(-1113)
((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality.")))
-((-4391 . T) (-4395 . T) (-4390 . T) (-4401 . T) (-4402 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4395 . T) (-4399 . T) (-4394 . T) (-4405 . T) (-4406 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1113 S)
+(-1114 S)
((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}.")))
-((-4403 . T) (-4404 . T))
+((-4407 . T) (-4408 . T))
NIL
-(-1114 S |ndim| R |Row| |Col|)
+(-1115 S |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")))
NIL
-((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4405 "*"))) (|HasCategory| |#3| (QUOTE (-171))))
-(-1115 |ndim| R |Row| |Col|)
+((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4409 "*"))) (|HasCategory| |#3| (QUOTE (-172))))
+(-1116 |ndim| R |Row| |Col|)
((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")))
-((-4403 . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4407 . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1116 R |Row| |Col| M)
+(-1117 R |Row| |Col| M)
((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}.")))
NIL
NIL
-(-1117 R |VarSet|)
+(-1118 R |VarSet|)
((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-904))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (|HasCategory| |#1| (QUOTE (-451))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-171))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -881) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -881) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (-4037 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-904)))) (|HasCategory| |#1| (QUOTE (-144)))))
-(-1118 |Coef| |Var| SMP)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-905))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-172))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-563))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (QUOTE (-563)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4405)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-4032 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))))
+(-1119 |Coef| |Var| SMP)
((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362))))
-(-1119 R E V P)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363))))
+(-1120 R E V P)
((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1120 UP -3196)
+(-1121 UP -3191)
((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented")))
NIL
NIL
-(-1121 R)
+(-1122 R)
((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,{}lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,{}x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,{}lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,{}x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,{}x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function.")))
NIL
NIL
-(-1122 R)
+(-1123 R)
((|constructor| (NIL "This package finds the function func3 where func1 and func2 \\indented{1}{are given and\\space{2}func1 = func3(func2) .\\space{2}If there is no solution then} \\indented{1}{function func1 will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect,{} var,{} n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1,{} func2,{} newvar)} returns a function func3 where \\spad{func1} = func3(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned.")))
NIL
NIL
-(-1123 R)
+(-1124 R)
((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs,{} lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,{}x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,{}x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq.")))
NIL
NIL
-(-1124 S A)
+(-1125 S A)
((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented")))
NIL
-((|HasCategory| |#1| (QUOTE (-845))))
-(-1125 R)
+((|HasCategory| |#1| (QUOTE (-846))))
+(-1126 R)
((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")))
NIL
NIL
-(-1126 R)
+(-1127 R)
((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} creates a surface defined over a list of curves,{} \\spad{p0} through \\spad{pn},{} which are lists of points; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); close2 set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],{}[p1],{}...,{}[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through \\spad{pn},{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and close2 indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if close2 is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{} close1,{} close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and close2 indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument close2 equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[ [[r10]...,{}[r1m]],{} [[r20]...,{}[r2m]],{}...,{} [[rn0]...,{}[rnm]] ],{} [props],{} prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size \\spad{WxH} where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,{}[[p0],{}[p1],{}...,{}[pn]],{}[props],{}prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,{}p1,{}...,{}pn])} creates a polygon defined by a list of points,{} \\spad{p0} through \\spad{pn},{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,{}[[r0],{}[r1],{}...,{}[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,{}[p0,{}p1,{}...,{}pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,{}R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,{}[[lr0],{}[lr1],{}...,{}[lrn],{}[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,{}[p0,{}p1,{}...,{}pn,{}p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,{}p1,{}p2,{}...,{}pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,{}[[p0],{}[p1],{}...,{}[pn]])} adds a space curve which is a list of points \\spad{p0} through \\spad{pn} defined by lists of elements from the domain \\spad{PointDomain(m,{}R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,{}[p0,{}p1,{}...,{}pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,{}i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,{}[x,{}y,{}z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,{}p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,{}i,{}p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,{}[p0,{}p1,{}...,{}pn])} adds a list of points from \\spad{p0} through \\spad{pn} to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,{}s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,{}s2,{}...,{}sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination.")))
NIL
NIL
-(-1127)
+(-1128)
((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}")))
NIL
NIL
-(-1128)
+(-1129)
((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful.")))
NIL
NIL
-(-1129)
+(-1130)
((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of \\spad{`s'}. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of \\spad{`s'}. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of \\spad{`s'}. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of \\spad{`s'}. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if \\spad{`s'} represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if \\spad{`s'} represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if \\spad{`s'} represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if \\spad{`s'} represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if \\spad{`s'} represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if \\spad{`s'} represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if \\spad{`s'} represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if \\spad{`s'} represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if \\spad{`s'} represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if \\spad{`s'} represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if \\spad{`s'} represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if \\spad{`s'} represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if \\spad{`s'} represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if \\spad{`s'} represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if \\spad{`s'} represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if \\spad{`s'} represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if \\spad{`s'} represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if \\spad{`s'} represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if \\spad{`s'} represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if \\spad{`s'} represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if \\spad{`s'} represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if \\spad{`s'} represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if \\spad{`s'} represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if \\spad{`s'} represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if \\spad{`s'} represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if \\spad{`s'} represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if \\spad{`s'} represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if \\spad{`s'} represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if \\spad{`s'} represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement.")))
NIL
NIL
-(-1130)
+(-1131)
((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.")))
NIL
NIL
-(-1131)
+(-1132)
((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")))
NIL
NIL
-(-1132 V C)
+(-1133 V C)
((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}")))
NIL
NIL
-(-1133 V C)
+(-1134 V C)
((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1132) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092))) (-4037 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1132) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1132 |#1| |#2|) (QUOTE (-1092))))) (|HasCategory| (-1132 |#1| |#2|) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1134 |ndim| R)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))) (-4032 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1133) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1133 |#1| |#2|) (QUOTE (-1093))))) (|HasCategory| (-1133 |#1| |#2|) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1135 |ndim| R)
((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}.")))
-((-4400 . T) (-4392 |has| |#2| (-6 (-4405 "*"))) (-4403 . T) (-4397 . T) (-4398 . T))
-((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (LIST (QUOTE -1033) (QUOTE (-562)))) (-4037 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-362))) (-4037 (|HasAttribute| |#2| (QUOTE (-4405 "*"))) (|HasCategory| |#2| (LIST (QUOTE -635) (QUOTE (-562)))) (|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171))))
-(-1135 S)
+((-4404 . T) (-4396 |has| |#2| (-6 (-4409 "*"))) (-4407 . T) (-4401 . T) (-4402 . T))
+((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-563)))) (-4032 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-363))) (-4032 (|HasAttribute| |#2| (QUOTE (-4409 "*"))) (|HasCategory| |#2| (LIST (QUOTE -636) (QUOTE (-563)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1169)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172))))
+(-1136 S)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
NIL
NIL
-(-1136)
+(-1137)
((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1137 R E V P TS)
+(-1138 R E V P TS)
((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")))
NIL
NIL
-(-1138 R E V P)
+(-1139 R E V P)
((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1139 S)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1140 S)
((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1140 A S)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1141 A S)
((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}.")))
NIL
NIL
-(-1141 S)
+(-1142 S)
((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}.")))
NIL
NIL
-(-1142 |Key| |Ent| |dent|)
+(-1143 |Key| |Ent| |dent|)
((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key.")))
-((-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-845))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))))
-(-1143)
+((-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))))
+(-1144)
((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping.")))
NIL
NIL
-(-1144 |Coef|)
+(-1145 |Coef|)
((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")))
NIL
NIL
-(-1145 S)
+(-1146 S)
((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}.")))
NIL
NIL
-(-1146 A B)
+(-1147 A B)
((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}.")))
NIL
NIL
-(-1147 A B C)
+(-1148 A B C)
((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}.")))
NIL
NIL
-(-1148 S)
+(-1149 S)
((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries.")))
-((-4404 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1149)
+((-4408 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1150)
((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1150)
+(-1151)
NIL
-((-4404 . T) (-4403 . T))
-((-4037 (-12 (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| (-143) (QUOTE (-845))) (|HasCategory| (-562) (QUOTE (-845))) (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-857)))) (-12 (|HasCategory| (-143) (QUOTE (-1092))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))))
-(-1151 |Entry|)
+((-4408 . T) (-4407 . T))
+((-4032 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-563) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -610) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1093))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))))
+(-1152 |Entry|)
((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used.")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (QUOTE (-1150))) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#1|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (QUOTE (-1092))) (|HasCategory| (-1150) (QUOTE (-845))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 (-1150)) (|:| -2693 |#1|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1152 A)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (QUOTE (-1151))) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#1|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (QUOTE (-1093))) (|HasCategory| (-1151) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 (-1151)) (|:| -2557 |#1|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1153 A)
((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}")))
NIL
-((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))))
-(-1153 |Coef|)
+((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))))
+(-1154 |Coef|)
((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}.")))
NIL
NIL
-(-1154 |Coef|)
+(-1155 |Coef|)
((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}.")))
NIL
NIL
-(-1155 R UP)
+(-1156 R UP)
((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}.")))
NIL
-((|HasCategory| |#1| (QUOTE (-306))))
-(-1156 |n| R)
+((|HasCategory| |#1| (QUOTE (-307))))
+(-1157 |n| R)
((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,{}s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) (|deepCopy| (($ $) "\\spad{deepCopy(x)} \\undocumented")) (|shallowCopy| (($ $) "\\spad{shallowCopy(x)} \\undocumented")) (|numberOfChildren| (((|NonNegativeInteger|) $) "\\spad{numberOfChildren(x)} \\undocumented")) (|children| (((|List| $) $) "\\spad{children(x)} \\undocumented")) (|child| (($ $ (|NonNegativeInteger|)) "\\spad{child(x,{}n)} \\undocumented")) (|birth| (($ $) "\\spad{birth(x)} \\undocumented")) (|subspace| (($) "\\spad{subspace()} \\undocumented")) (|new| (($) "\\spad{new()} \\undocumented")) (|internal?| (((|Boolean|) $) "\\spad{internal?(x)} \\undocumented")) (|root?| (((|Boolean|) $) "\\spad{root?(x)} \\undocumented")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(x)} \\undocumented")))
NIL
NIL
-(-1157 S1 S2)
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((|constructor| (NIL "This domain implements \"such that\" forms")) (|rhs| ((|#2| $) "\\spad{rhs(f)} returns the right side of \\spad{f}")) (|lhs| ((|#1| $) "\\spad{lhs(f)} returns the left side of \\spad{f}")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} makes a form \\spad{s:t}")))
NIL
NIL
-(-1158)
+(-1159)
((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'.")))
NIL
NIL
-(-1159 |Coef| |var| |cen|)
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((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series.")))
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((|constructor| (NIL "computes sums of top-level expressions.")) (|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n}).")))
NIL
NIL
-(-1161 R)
+(-1162 R)
((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n),{} n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.")))
NIL
NIL
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((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
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((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}.")))
NIL
NIL
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((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{}var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable.")))
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(-1166 |Coef| |var| |cen|)
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+(-1167 |Coef| |var| |cen|)
((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}.")))
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((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}")))
NIL
NIL
-(-1168)
+(-1169)
((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s,{} [a,{}b,{}c,{}d,{}e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s,{} [a,{}b,{}c])} is equivalent to \\spad{script(s,{}[a,{}b,{}c,{}[],{}[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%.")))
NIL
NIL
-(-1169 R)
+(-1170 R)
((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r,{} n)} returns the vector of the elementary symmetric functions in \\spad{[r,{}r,{}...,{}r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,{}...,{}rn])} returns the vector of the elementary symmetric functions in the \\spad{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}.")))
NIL
NIL
-(-1170 R)
+(-1171 R)
((|constructor| (NIL "This domain implements symmetric polynomial")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-6 -4401)) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562)))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (LIST (QUOTE -1033) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-451))) (-12 (|HasCategory| (-966) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasAttribute| |#1| (QUOTE -4401)))
-(-1171)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-6 -4405)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-555))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4032 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasAttribute| |#1| (QUOTE -4405)))
+(-1172)
((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table.")))
NIL
NIL
-(-1172)
+(-1173)
((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,{}tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,{}tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,{}t,{}tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,{}t,{}tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}")))
NIL
NIL
-(-1173)
+(-1174)
((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{symbols,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: Integer,{} DoubleFloat,{} Symbol,{} String,{} SExpression. See Also: SExpression. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax.")))
NIL
NIL
-(-1174 N)
+(-1175 N)
((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")))
NIL
NIL
-(-1175 N)
+(-1176 N)
((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")))
NIL
NIL
-(-1176 R)
+(-1177 R)
((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,{}lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,{}v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,{}v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,{}lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")))
NIL
NIL
-(-1177)
+(-1178)
((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system.")))
NIL
NIL
-(-1178 S)
+(-1179 S)
((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record")))
NIL
NIL
-(-1179 S)
+(-1180 S)
((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau.")))
NIL
NIL
-(-1180 |Key| |Entry|)
+(-1181 |Key| |Entry|)
((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}")))
-((-4403 . T) (-4404 . T))
-((-12 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2319) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2693) (|devaluate| |#2|)))))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#2| (QUOTE (-1092)))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -610) (QUOTE (-535)))) (-12 (|HasCategory| |#2| (QUOTE (-1092))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#2| (QUOTE (-1092))) (-4037 (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-857)))) (|HasCategory| (-2 (|:| -2319 |#1|) (|:| -2693 |#2|)) (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1181 R)
+((-4407 . T) (-4408 . T))
+((-12 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2387) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2557) (|devaluate| |#2|)))))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#2| (QUOTE (-1093)))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -611) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1093))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1093))) (-4032 (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -2387 |#1|) (|:| -2557 |#2|)) (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1182 R)
((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}.")))
NIL
NIL
-(-1182 S |Key| |Entry|)
+(-1183 S |Key| |Entry|)
((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}.")))
NIL
NIL
-(-1183 |Key| |Entry|)
+(-1184 |Key| |Entry|)
((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}.")))
-((-4404 . T))
+((-4408 . T))
NIL
-(-1184 |Key| |Entry|)
+(-1185 |Key| |Entry|)
((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table.")))
NIL
NIL
-(-1185)
+(-1186)
((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it.")))
NIL
NIL
-(-1186 S)
+(-1187 S)
((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format.")))
NIL
NIL
-(-1187)
+(-1188)
((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")))
NIL
NIL
-(-1188)
+(-1189)
((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned.")))
NIL
NIL
-(-1189 R)
+(-1190 R)
((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented")))
NIL
NIL
-(-1190)
+(-1191)
((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination.")))
NIL
NIL
-(-1191 S)
+(-1192 S)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1192)
+(-1193)
((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}.")))
NIL
NIL
-(-1193 S)
-((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1092))) (-4037 (-12 (|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
(-1194 S)
+((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}.")))
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1093))) (-4032 (-12 (|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1195 S)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1195)
+(-1196)
((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}.")))
NIL
NIL
-(-1196 R -3196)
+(-1197 R -3191)
((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels.")))
NIL
NIL
-(-1197 R |Row| |Col| M)
+(-1198 R |Row| |Col| M)
((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")))
NIL
NIL
-(-1198 R -3196)
+(-1199 R -3191)
((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}")))
NIL
-((-12 (|HasCategory| |#1| (LIST (QUOTE -610) (LIST (QUOTE -887) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -881) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -610) (LIST (QUOTE -887) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -881) (|devaluate| |#1|)))))
-(-1199 S R E V P)
+((-12 (|HasCategory| |#1| (LIST (QUOTE -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -611) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|)))))
+(-1200 S R E V P)
((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
NIL
-((|HasCategory| |#4| (QUOTE (-367))))
-(-1200 R E V P)
+((|HasCategory| |#4| (QUOTE (-368))))
+(-1201 R E V P)
((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
-(-1201 |Coef|)
+(-1202 |Coef|)
((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#1| (QUOTE (-362))))
-(-1202 |Curve|)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4032 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-555)))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#1| (QUOTE (-363))))
+(-1203 |Curve|)
((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}.")))
NIL
NIL
-(-1203)
+(-1204)
((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point.")))
NIL
NIL
-(-1204 S)
+(-1205 S)
((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")))
NIL
-((|HasCategory| |#1| (QUOTE (-1092))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1205 -3196)
+((|HasCategory| |#1| (QUOTE (-1093))) (|HasCategory| |#1| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1206 -3191)
((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")))
NIL
NIL
-(-1206)
+(-1207)
((|constructor| (NIL "This domain represents a type AST.")))
NIL
NIL
-(-1207)
+(-1208)
((|constructor| (NIL "The fundamental Type.")))
NIL
NIL
-(-1208 S)
+(-1209 S)
((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}")))
NIL
-((|HasCategory| |#1| (QUOTE (-845))))
-(-1209)
+((|HasCategory| |#1| (QUOTE (-846))))
+(-1210)
((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}.")))
NIL
NIL
-(-1210 S)
+(-1211 S)
((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
NIL
NIL
-(-1211)
+(-1212)
((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element.")))
-((-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1212)
+(-1213)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits.")))
NIL
NIL
-(-1213)
+(-1214)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits.")))
NIL
NIL
-(-1214)
+(-1215)
((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits.")))
NIL
NIL
-(-1215 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
+(-1216 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}.")))
NIL
NIL
-(-1216 |Coef|)
+(-1217 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1217 S |Coef| UTS)
+(-1218 S |Coef| UTS)
((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-362))))
-(-1218 |Coef| UTS)
+((|HasCategory| |#2| (QUOTE (-363))))
+(-1219 |Coef| UTS)
((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4405 |has| |#1| (-363)) (-4399 |has| |#1| (-363)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1219 |Coef| UTS)
+(-1220 |Coef| UTS)
((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T))
-((-4037 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -513) (QUOTE (-1168)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-845)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-904)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1017)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1143)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -610) (QUOTE (-535))))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1033) 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((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}")))
NIL
NIL
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((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}.")))
NIL
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((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound.")))
NIL
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((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly.")))
NIL
NIL
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((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}.")))
NIL
NIL
-(-1226 R UP)
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((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")))
NIL
NIL
-(-1227 R UP)
+(-1228 R UP)
((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded.")))
NIL
NIL
-(-1228 R U)
+(-1229 R U)
((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all.")))
NIL
NIL
-(-1229 |x| R)
+(-1230 |x| R)
((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")))
-(((-4405 "*") |has| |#2| (-171)) (-4396 |has| |#2| (-554)) (-4399 |has| |#2| (-362)) (-4401 |has| |#2| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
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-(-1230 R PR S PS)
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+(-1231 R PR S PS)
((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero.")))
NIL
NIL
-(-1231 S R)
+(-1232 S R)
((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-451))) (|HasCategory| |#2| (QUOTE (-554))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1143))))
-(-1232 R)
+((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-555))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1144))))
+(-1233 R)
((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4399 |has| |#1| (-362)) (-4401 |has| |#1| (-6 -4401)) (-4398 . T) (-4397 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4403 |has| |#1| (-363)) (-4405 |has| |#1| (-6 -4405)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-1233 S |Coef| |Expon|)
+(-1234 S |Coef| |Expon|)
((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
NIL
-((|HasCategory| |#2| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1104))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4053) (LIST (|devaluate| |#2|) (QUOTE (-1168))))))
-(-1234 |Coef| |Expon|)
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+(-1235 |Coef| |Expon|)
((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1235 RC P)
+(-1236 RC P)
((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}.")))
NIL
NIL
-(-1236 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
+(-1237 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|)
((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}.")))
NIL
NIL
-(-1237 |Coef|)
+(-1238 |Coef|)
((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms.")))
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NIL
-(-1238 S |Coef| ULS)
+(-1239 S |Coef| ULS)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}.")))
NIL
NIL
-(-1239 |Coef| ULS)
+(-1240 |Coef| ULS)
((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4401 |has| |#1| (-362)) (-4395 |has| |#1| (-362)) (-4397 . T) (-4398 . T) (-4400 . T))
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NIL
-(-1240 |Coef| ULS)
+(-1241 |Coef| ULS)
((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")))
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-(-1241 |Coef| |var| |cen|)
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+(-1242 |Coef| |var| |cen|)
((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")))
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-(-1242 R FE |var| |cen|)
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+(-1243 R FE |var| |cen|)
((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}.")))
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-(-1243 A S)
+(((-4409 "*") |has| (-1242 |#2| |#3| |#4|) (-172)) (-4400 |has| (-1242 |#2| |#3| |#4|) (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
+((|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-172))) (-4032 (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563)))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasCategory| (-1242 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-563)))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1242 |#2| |#3| |#4|) (QUOTE (-555))))
+(-1244 A S)
((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
-((|HasAttribute| |#1| (QUOTE -4404)))
-(-1244 S)
+((|HasAttribute| |#1| (QUOTE -4408)))
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((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}.")))
NIL
NIL
-(-1245 |Coef1| |Coef2| UTS1 UTS2)
+(-1246 |Coef1| |Coef2| UTS1 UTS2)
((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}")))
NIL
NIL
-(-1246 S |Coef|)
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((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")))
NIL
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-(-1247 |Coef|)
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((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1248 |Coef| |var| |cen|)
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((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}.")))
-(((-4405 "*") |has| |#1| (-171)) (-4396 |has| |#1| (-554)) (-4397 . T) (-4398 . T) (-4400 . T))
-((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasCategory| |#1| (QUOTE (-554))) (-4037 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-554)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -895) (QUOTE (-1168)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-766)) (|devaluate| |#1|)))) (|HasCategory| (-766) (QUOTE (-1104))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasSignature| |#1| (LIST (QUOTE -4053) (LIST (|devaluate| |#1|) (QUOTE (-1168)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-766))))) (|HasCategory| |#1| (QUOTE (-362))) (-4037 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-562)))) (|HasCategory| |#1| (QUOTE (-954))) (|HasCategory| |#1| (QUOTE (-1192))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasSignature| |#1| (LIST (QUOTE -3081) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1168))))) (|HasSignature| |#1| (LIST (QUOTE -1401) (LIST (LIST (QUOTE -639) (QUOTE (-1168))) (|devaluate| |#1|)))))))
-(-1249 |Coef| UTS)
+(((-4409 "*") |has| |#1| (-172)) (-4400 |has| |#1| (-555)) (-4401 . T) (-4402 . T) (-4404 . T))
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((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")))
NIL
NIL
-(-1250 -3196 UP L UTS)
+(-1251 -3191 UP L UTS)
((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series.")))
NIL
-((|HasCategory| |#1| (QUOTE (-554))))
-(-1251)
+((|HasCategory| |#1| (QUOTE (-555))))
+(-1252)
((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators.")))
NIL
NIL
-(-1252 |sym|)
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((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol")))
NIL
NIL
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((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
NIL
-((|HasCategory| |#2| (QUOTE (-997))) (|HasCategory| |#2| (QUOTE (-1044))) (|HasCategory| |#2| (QUOTE (-721))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
-(-1254 R)
+((|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25))))
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((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")))
-((-4404 . T) (-4403 . T))
+((-4408 . T) (-4407 . T))
NIL
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((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}.")))
NIL
NIL
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((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector.")))
-((-4404 . T) (-4403 . T))
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((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc.")))
NIL
NIL
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((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians.")))
NIL
NIL
-(-1259)
+(-1260)
((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport.")))
NIL
NIL
-(-1260)
+(-1261)
((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}.")))
NIL
NIL
-(-1261)
+(-1262)
((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object.")))
NIL
NIL
-(-1262 A S)
+(-1263 A S)
((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}.")))
NIL
NIL
-(-1263 S)
+(-1264 S)
((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}.")))
-((-4398 . T) (-4397 . T))
+((-4402 . T) (-4401 . T))
NIL
-(-1264 R)
+(-1265 R)
((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally.")))
NIL
NIL
-(-1265 K R UP -3196)
+(-1266 K R UP -3191)
((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")))
NIL
NIL
-(-1266)
+(-1267)
((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'.")))
NIL
NIL
-(-1267)
+(-1268)
((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'.")))
NIL
NIL
-(-1268 R |VarSet| E P |vl| |wl| |wtlevel|)
+(-1269 R |VarSet| E P |vl| |wl| |wtlevel|)
((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")))
-((-4398 |has| |#1| (-171)) (-4397 |has| |#1| (-171)) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))))
-(-1269 R E V P)
+((-4402 |has| |#1| (-172)) (-4401 |has| |#1| (-172)) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))))
+(-1270 R E V P)
((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}.")))
-((-4404 . T) (-4403 . T))
-((-12 (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-535)))) (|HasCategory| |#4| (QUOTE (-1092))) (|HasCategory| |#1| (QUOTE (-554))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-857)))))
-(-1270 R)
+((-4408 . T) (-4407 . T))
+((-12 (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1093))) (|HasCategory| |#1| (QUOTE (-555))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -610) (QUOTE (-858)))))
+(-1271 R)
((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")))
-((-4397 . T) (-4398 . T) (-4400 . T))
+((-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1271 |vl| R)
+(-1272 |vl| R)
((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute.")))
-((-4400 . T) (-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T))
-((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4396)))
-(-1272 R |VarSet| XPOLY)
+((-4404 . T) (-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T))
+((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400)))
+(-1273 R |VarSet| XPOLY)
((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")))
NIL
NIL
-(-1273 |vl| R)
+(-1274 |vl| R)
((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}.")))
-((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T))
+((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-1274 S -3196)
+(-1275 S -3191)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
NIL
-((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))))
-(-1275 -3196)
+((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))))
+(-1276 -3191)
((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}.")))
-((-4395 . T) (-4401 . T) (-4396 . T) ((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+((-4399 . T) (-4405 . T) (-4400 . T) ((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
-(-1276 |VarSet| R)
+(-1277 |VarSet| R)
((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}.")))
-((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -712) (LIST (QUOTE -406) (QUOTE (-562))))) (|HasAttribute| |#2| (QUOTE -4396)))
-(-1277 |vl| R)
+((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -713) (LIST (QUOTE -407) (QUOTE (-563))))) (|HasAttribute| |#2| (QUOTE -4400)))
+(-1278 |vl| R)
((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}.")))
-((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T))
+((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T))
NIL
-(-1278 R)
+(-1279 R)
((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute.")))
-((-4396 |has| |#1| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4396)))
-(-1279 R E)
+((-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4400)))
+(-1280 R E)
((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}.")))
-((-4400 . T) (-4401 |has| |#1| (-6 -4401)) (-4396 |has| |#1| (-6 -4396)) (-4398 . T) (-4397 . T))
-((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4401)) (|HasAttribute| |#1| (QUOTE -4396)))
-(-1280 |VarSet| R)
+((-4404 . T) (-4405 |has| |#1| (-6 -4405)) (-4400 |has| |#1| (-6 -4400)) (-4402 . T) (-4401 . T))
+((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4405)) (|HasAttribute| |#1| (QUOTE -4400)))
+(-1281 |VarSet| R)
((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form.")))
-((-4396 |has| |#2| (-6 -4396)) (-4398 . T) (-4397 . T) (-4400 . T))
-((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4396)))
-(-1281 A)
+((-4400 |has| |#2| (-6 -4400)) (-4402 . T) (-4401 . T) (-4404 . T))
+((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4400)))
+(-1282 A)
((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}.")))
NIL
NIL
-(-1282 R |ls| |ls2|)
+(-1283 R |ls| |ls2|)
((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.")))
NIL
NIL
-(-1283 R)
+(-1284 R)
((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise.")))
NIL
NIL
-(-1284 |p|)
+(-1285 |p|)
((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}.")))
-(((-4405 "*") . T) (-4397 . T) (-4398 . T) (-4400 . T))
+(((-4409 "*") . T) (-4401 . T) (-4402 . T) (-4404 . T))
NIL
NIL
NIL
@@ -5084,4 +5088,4 @@ NIL
NIL
NIL
NIL
-((-3 NIL 2282316 2282321 2282326 2282331) (-2 NIL 2282296 2282301 2282306 2282311) (-1 NIL 2282276 2282281 2282286 2282291) (0 NIL 2282256 2282261 2282266 2282271) (-1284 "ZMOD.spad" 2282065 2282078 2282194 2282251) (-1283 "ZLINDEP.spad" 2281109 2281120 2282055 2282060) (-1282 "ZDSOLVE.spad" 2270958 2270980 2281099 2281104) (-1281 "YSTREAM.spad" 2270451 2270462 2270948 2270953) (-1280 "XRPOLY.spad" 2269671 2269691 2270307 2270376) (-1279 "XPR.spad" 2267462 2267475 2269389 2269488) (-1278 "XPOLY.spad" 2267017 2267028 2267318 2267387) (-1277 "XPOLYC.spad" 2266334 2266350 2266943 2267012) (-1276 "XPBWPOLY.spad" 2264771 2264791 2266114 2266183) (-1275 "XF.spad" 2263232 2263247 2264673 2264766) (-1274 "XF.spad" 2261673 2261690 2263116 2263121) (-1273 "XFALG.spad" 2258697 2258713 2261599 2261668) (-1272 "XEXPPKG.spad" 2257948 2257974 2258687 2258692) (-1271 "XDPOLY.spad" 2257562 2257578 2257804 2257873) (-1270 "XALG.spad" 2257222 2257233 2257518 2257557) (-1269 "WUTSET.spad" 2253061 2253078 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"STACK.spad" 1969319 1969330 1969575 1969602) (-1138 "SREGSET.spad" 1967023 1967040 1968965 1968992) (-1137 "SRDCMPK.spad" 1965568 1965588 1967013 1967018) (-1136 "SRAGG.spad" 1960665 1960674 1965536 1965563) (-1135 "SRAGG.spad" 1955782 1955793 1960655 1960660) (-1134 "SQMATRIX.spad" 1953398 1953416 1954314 1954401) (-1133 "SPLTREE.spad" 1947950 1947963 1952834 1952861) (-1132 "SPLNODE.spad" 1944538 1944551 1947940 1947945) (-1131 "SPFCAT.spad" 1943315 1943324 1944528 1944533) (-1130 "SPECOUT.spad" 1941865 1941874 1943305 1943310) (-1129 "SPADXPT.spad" 1934004 1934013 1941855 1941860) (-1128 "spad-parser.spad" 1933469 1933478 1933994 1933999) (-1127 "SPADAST.spad" 1933170 1933179 1933459 1933464) (-1126 "SPACEC.spad" 1917183 1917194 1933160 1933165) (-1125 "SPACE3.spad" 1916959 1916970 1917173 1917178) (-1124 "SORTPAK.spad" 1916504 1916517 1916915 1916920) (-1123 "SOLVETRA.spad" 1914261 1914272 1916494 1916499) (-1122 "SOLVESER.spad" 1912781 1912792 1914251 1914256) (-1121 "SOLVERAD.spad" 1908791 1908802 1912771 1912776) (-1120 "SOLVEFOR.spad" 1907211 1907229 1908781 1908786) (-1119 "SNTSCAT.spad" 1906811 1906828 1907179 1907206) (-1118 "SMTS.spad" 1905071 1905097 1906376 1906473) (-1117 "SMP.spad" 1902510 1902530 1902900 1903027) (-1116 "SMITH.spad" 1901353 1901378 1902500 1902505) (-1115 "SMATCAT.spad" 1899463 1899493 1901297 1901348) (-1114 "SMATCAT.spad" 1897505 1897537 1899341 1899346) (-1113 "SKAGG.spad" 1896466 1896477 1897473 1897500) (-1112 "SINT.spad" 1895292 1895301 1896332 1896461) (-1111 "SIMPAN.spad" 1895020 1895029 1895282 1895287) (-1110 "SIG.spad" 1894348 1894357 1895010 1895015) (-1109 "SIGNRF.spad" 1893456 1893467 1894338 1894343) (-1108 "SIGNEF.spad" 1892725 1892742 1893446 1893451) (-1107 "SIGAST.spad" 1892106 1892115 1892715 1892720) (-1106 "SHP.spad" 1890024 1890039 1892062 1892067) (-1105 "SHDP.spad" 1879735 1879762 1880244 1880375) (-1104 "SGROUP.spad" 1879343 1879352 1879725 1879730) (-1103 "SGROUP.spad" 1878949 1878960 1879333 1879338) (-1102 "SGCF.spad" 1871830 1871839 1878939 1878944) (-1101 "SFRTCAT.spad" 1870758 1870775 1871798 1871825) (-1100 "SFRGCD.spad" 1869821 1869841 1870748 1870753) (-1099 "SFQCMPK.spad" 1864458 1864478 1869811 1869816) (-1098 "SFORT.spad" 1863893 1863907 1864448 1864453) (-1097 "SEXOF.spad" 1863736 1863776 1863883 1863888) (-1096 "SEX.spad" 1863628 1863637 1863726 1863731) (-1095 "SEXCAT.spad" 1861179 1861219 1863618 1863623) (-1094 "SET.spad" 1859479 1859490 1860600 1860639) (-1093 "SETMN.spad" 1857913 1857930 1859469 1859474) (-1092 "SETCAT.spad" 1857398 1857407 1857903 1857908) (-1091 "SETCAT.spad" 1856881 1856892 1857388 1857393) (-1090 "SETAGG.spad" 1853402 1853413 1856861 1856876) (-1089 "SETAGG.spad" 1849931 1849944 1853392 1853397) (-1088 "SEQAST.spad" 1849634 1849643 1849921 1849926) (-1087 "SEGXCAT.spad" 1848756 1848769 1849624 1849629) (-1086 "SEG.spad" 1848569 1848580 1848675 1848680) (-1085 "SEGCAT.spad" 1847476 1847487 1848559 1848564) (-1084 "SEGBIND.spad" 1846548 1846559 1847431 1847436) (-1083 "SEGBIND2.spad" 1846244 1846257 1846538 1846543) (-1082 "SEGAST.spad" 1845958 1845967 1846234 1846239) (-1081 "SEG2.spad" 1845383 1845396 1845914 1845919) (-1080 "SDVAR.spad" 1844659 1844670 1845373 1845378) (-1079 "SDPOL.spad" 1842049 1842060 1842340 1842467) (-1078 "SCPKG.spad" 1840128 1840139 1842039 1842044) (-1077 "SCOPE.spad" 1839273 1839282 1840118 1840123) (-1076 "SCACHE.spad" 1837955 1837966 1839263 1839268) (-1075 "SASTCAT.spad" 1837864 1837873 1837945 1837950) (-1074 "SAOS.spad" 1837736 1837745 1837854 1837859) (-1073 "SAERFFC.spad" 1837449 1837469 1837726 1837731) (-1072 "SAE.spad" 1835624 1835640 1836235 1836370) (-1071 "SAEFACT.spad" 1835325 1835345 1835614 1835619) (-1070 "RURPK.spad" 1832966 1832982 1835315 1835320) (-1069 "RULESET.spad" 1832407 1832431 1832956 1832961) (-1068 "RULE.spad" 1830611 1830635 1832397 1832402) (-1067 "RULECOLD.spad" 1830463 1830476 1830601 1830606) (-1066 "RSTRCAST.spad" 1830180 1830189 1830453 1830458) (-1065 "RSETGCD.spad" 1826558 1826578 1830170 1830175) (-1064 "RSETCAT.spad" 1816342 1816359 1826526 1826553) (-1063 "RSETCAT.spad" 1806146 1806165 1816332 1816337) (-1062 "RSDCMPK.spad" 1804598 1804618 1806136 1806141) (-1061 "RRCC.spad" 1802982 1803012 1804588 1804593) (-1060 "RRCC.spad" 1801364 1801396 1802972 1802977) (-1059 "RPTAST.spad" 1801066 1801075 1801354 1801359) (-1058 "RPOLCAT.spad" 1780426 1780441 1800934 1801061) (-1057 "RPOLCAT.spad" 1759500 1759517 1780010 1780015) (-1056 "ROUTINE.spad" 1755363 1755372 1758147 1758174) (-1055 "ROMAN.spad" 1754691 1754700 1755229 1755358) (-1054 "ROIRC.spad" 1753771 1753803 1754681 1754686) (-1053 "RNS.spad" 1752674 1752683 1753673 1753766) (-1052 "RNS.spad" 1751663 1751674 1752664 1752669) (-1051 "RNG.spad" 1751398 1751407 1751653 1751658) (-1050 "RMODULE.spad" 1751036 1751047 1751388 1751393) (-1049 "RMCAT2.spad" 1750444 1750501 1751026 1751031) (-1048 "RMATRIX.spad" 1749268 1749287 1749611 1749650) (-1047 "RMATCAT.spad" 1744801 1744832 1749224 1749263) (-1046 "RMATCAT.spad" 1740224 1740257 1744649 1744654) (-1045 "RINTERP.spad" 1740112 1740132 1740214 1740219) (-1044 "RING.spad" 1739582 1739591 1740092 1740107) (-1043 "RING.spad" 1739060 1739071 1739572 1739577) (-1042 "RIDIST.spad" 1738444 1738453 1739050 1739055) (-1041 "RGCHAIN.spad" 1737023 1737039 1737929 1737956) (-1040 "RGBCSPC.spad" 1736804 1736816 1737013 1737018) (-1039 "RGBCMDL.spad" 1736334 1736346 1736794 1736799) (-1038 "RF.spad" 1733948 1733959 1736324 1736329) (-1037 "RFFACTOR.spad" 1733410 1733421 1733938 1733943) (-1036 "RFFACT.spad" 1733145 1733157 1733400 1733405) (-1035 "RFDIST.spad" 1732133 1732142 1733135 1733140) (-1034 "RETSOL.spad" 1731550 1731563 1732123 1732128) (-1033 "RETRACT.spad" 1730978 1730989 1731540 1731545) (-1032 "RETRACT.spad" 1730404 1730417 1730968 1730973) (-1031 "RETAST.spad" 1730216 1730225 1730394 1730399) (-1030 "RESULT.spad" 1728276 1728285 1728863 1728890) (-1029 "RESRING.spad" 1727623 1727670 1728214 1728271) (-1028 "RESLATC.spad" 1726947 1726958 1727613 1727618) (-1027 "REPSQ.spad" 1726676 1726687 1726937 1726942) (-1026 "REP.spad" 1724228 1724237 1726666 1726671) (-1025 "REPDB.spad" 1723933 1723944 1724218 1724223) (-1024 "REP2.spad" 1713505 1713516 1723775 1723780) (-1023 "REP1.spad" 1707495 1707506 1713455 1713460) (-1022 "REGSET.spad" 1705292 1705309 1707141 1707168) (-1021 "REF.spad" 1704621 1704632 1705247 1705252) (-1020 "REDORDER.spad" 1703797 1703814 1704611 1704616) (-1019 "RECLOS.spad" 1702580 1702600 1703284 1703377) (-1018 "REALSOLV.spad" 1701712 1701721 1702570 1702575) (-1017 "REAL.spad" 1701584 1701593 1701702 1701707) (-1016 "REAL0Q.spad" 1698866 1698881 1701574 1701579) (-1015 "REAL0.spad" 1695694 1695709 1698856 1698861) (-1014 "RDUCEAST.spad" 1695415 1695424 1695684 1695689) (-1013 "RDIV.spad" 1695066 1695091 1695405 1695410) (-1012 "RDIST.spad" 1694629 1694640 1695056 1695061) (-1011 "RDETRS.spad" 1693425 1693443 1694619 1694624) (-1010 "RDETR.spad" 1691532 1691550 1693415 1693420) (-1009 "RDEEFS.spad" 1690605 1690622 1691522 1691527) (-1008 "RDEEF.spad" 1689601 1689618 1690595 1690600) (-1007 "RCFIELD.spad" 1686787 1686796 1689503 1689596) (-1006 "RCFIELD.spad" 1684059 1684070 1686777 1686782) (-1005 "RCAGG.spad" 1681971 1681982 1684049 1684054) (-1004 "RCAGG.spad" 1679810 1679823 1681890 1681895) (-1003 "RATRET.spad" 1679170 1679181 1679800 1679805) (-1002 "RATFACT.spad" 1678862 1678874 1679160 1679165) (-1001 "RANDSRC.spad" 1678181 1678190 1678852 1678857) (-1000 "RADUTIL.spad" 1677935 1677944 1678171 1678176) (-999 "RADIX.spad" 1674837 1674850 1676402 1676495) (-998 "RADFF.spad" 1673251 1673287 1673369 1673525) (-997 "RADCAT.spad" 1672845 1672853 1673241 1673246) (-996 "RADCAT.spad" 1672437 1672447 1672835 1672840) (-995 "QUEUE.spad" 1671780 1671790 1672044 1672071) (-994 "QUAT.spad" 1670362 1670372 1670704 1670769) (-993 "QUATCT2.spad" 1669981 1669999 1670352 1670357) (-992 "QUATCAT.spad" 1668146 1668156 1669911 1669976) (-991 "QUATCAT.spad" 1666062 1666074 1667829 1667834) (-990 "QUAGG.spad" 1664888 1664898 1666030 1666057) (-989 "QQUTAST.spad" 1664657 1664665 1664878 1664883) (-988 "QFORM.spad" 1664120 1664134 1664647 1664652) (-987 "QFCAT.spad" 1662823 1662833 1664022 1664115) (-986 "QFCAT.spad" 1661117 1661129 1662318 1662323) (-985 "QFCAT2.spad" 1660808 1660824 1661107 1661112) (-984 "QEQUAT.spad" 1660365 1660373 1660798 1660803) (-983 "QCMPACK.spad" 1655112 1655131 1660355 1660360) (-982 "QALGSET.spad" 1651187 1651219 1655026 1655031) (-981 "QALGSET2.spad" 1649183 1649201 1651177 1651182) (-980 "PWFFINTB.spad" 1646493 1646514 1649173 1649178) (-979 "PUSHVAR.spad" 1645822 1645841 1646483 1646488) (-978 "PTRANFN.spad" 1641948 1641958 1645812 1645817) (-977 "PTPACK.spad" 1639036 1639046 1641938 1641943) (-976 "PTFUNC2.spad" 1638857 1638871 1639026 1639031) (-975 "PTCAT.spad" 1638106 1638116 1638825 1638852) (-974 "PSQFR.spad" 1637413 1637437 1638096 1638101) (-973 "PSEUDLIN.spad" 1636271 1636281 1637403 1637408) (-972 "PSETPK.spad" 1621704 1621720 1636149 1636154) (-971 "PSETCAT.spad" 1615624 1615647 1621684 1621699) (-970 "PSETCAT.spad" 1609518 1609543 1615580 1615585) (-969 "PSCURVE.spad" 1608501 1608509 1609508 1609513) (-968 "PSCAT.spad" 1607268 1607297 1608399 1608496) (-967 "PSCAT.spad" 1606125 1606156 1607258 1607263) (-966 "PRTITION.spad" 1605070 1605078 1606115 1606120) (-965 "PRTDAST.spad" 1604789 1604797 1605060 1605065) (-964 "PRS.spad" 1594351 1594368 1604745 1604750) (-963 "PRQAGG.spad" 1593782 1593792 1594319 1594346) (-962 "PROPLOG.spad" 1593185 1593193 1593772 1593777) (-961 "PROPFRML.spad" 1591103 1591114 1593175 1593180) (-960 "PROPERTY.spad" 1590597 1590605 1591093 1591098) (-959 "PRODUCT.spad" 1588277 1588289 1588563 1588618) (-958 "PR.spad" 1586663 1586675 1587368 1587495) (-957 "PRINT.spad" 1586415 1586423 1586653 1586658) (-956 "PRIMES.spad" 1584666 1584676 1586405 1586410) (-955 "PRIMELT.spad" 1582647 1582661 1584656 1584661) (-954 "PRIMCAT.spad" 1582270 1582278 1582637 1582642) (-953 "PRIMARR.spad" 1581275 1581285 1581453 1581480) (-952 "PRIMARR2.spad" 1579998 1580010 1581265 1581270) (-951 "PREASSOC.spad" 1579370 1579382 1579988 1579993) (-950 "PPCURVE.spad" 1578507 1578515 1579360 1579365) (-949 "PORTNUM.spad" 1578282 1578290 1578497 1578502) (-948 "POLYROOT.spad" 1577111 1577133 1578238 1578243) (-947 "POLY.spad" 1574408 1574418 1574925 1575052) (-946 "POLYLIFT.spad" 1573669 1573692 1574398 1574403) (-945 "POLYCATQ.spad" 1571771 1571793 1573659 1573664) (-944 "POLYCAT.spad" 1565177 1565198 1571639 1571766) (-943 "POLYCAT.spad" 1557885 1557908 1564349 1564354) (-942 "POLY2UP.spad" 1557333 1557347 1557875 1557880) (-941 "POLY2.spad" 1556928 1556940 1557323 1557328) (-940 "POLUTIL.spad" 1555869 1555898 1556884 1556889) (-939 "POLTOPOL.spad" 1554617 1554632 1555859 1555864) (-938 "POINT.spad" 1553456 1553466 1553543 1553570) (-937 "PNTHEORY.spad" 1550122 1550130 1553446 1553451) (-936 "PMTOOLS.spad" 1548879 1548893 1550112 1550117) (-935 "PMSYM.spad" 1548424 1548434 1548869 1548874) (-934 "PMQFCAT.spad" 1548011 1548025 1548414 1548419) (-933 "PMPRED.spad" 1547480 1547494 1548001 1548006) (-932 "PMPREDFS.spad" 1546924 1546946 1547470 1547475) (-931 "PMPLCAT.spad" 1545994 1546012 1546856 1546861) (-930 "PMLSAGG.spad" 1545575 1545589 1545984 1545989) (-929 "PMKERNEL.spad" 1545142 1545154 1545565 1545570) (-928 "PMINS.spad" 1544718 1544728 1545132 1545137) (-927 "PMFS.spad" 1544291 1544309 1544708 1544713) (-926 "PMDOWN.spad" 1543577 1543591 1544281 1544286) (-925 "PMASS.spad" 1542589 1542597 1543567 1543572) (-924 "PMASSFS.spad" 1541558 1541574 1542579 1542584) (-923 "PLOTTOOL.spad" 1541338 1541346 1541548 1541553) (-922 "PLOT.spad" 1536169 1536177 1541328 1541333) (-921 "PLOT3D.spad" 1532589 1532597 1536159 1536164) (-920 "PLOT1.spad" 1531730 1531740 1532579 1532584) (-919 "PLEQN.spad" 1518946 1518973 1531720 1531725) (-918 "PINTERP.spad" 1518562 1518581 1518936 1518941) (-917 "PINTERPA.spad" 1518344 1518360 1518552 1518557) (-916 "PI.spad" 1517951 1517959 1518318 1518339) (-915 "PID.spad" 1516907 1516915 1517877 1517946) (-914 "PICOERCE.spad" 1516564 1516574 1516897 1516902) (-913 "PGROEB.spad" 1515161 1515175 1516554 1516559) (-912 "PGE.spad" 1506414 1506422 1515151 1515156) (-911 "PGCD.spad" 1505296 1505313 1506404 1506409) (-910 "PFRPAC.spad" 1504439 1504449 1505286 1505291) (-909 "PFR.spad" 1501096 1501106 1504341 1504434) (-908 "PFOTOOLS.spad" 1500354 1500370 1501086 1501091) (-907 "PFOQ.spad" 1499724 1499742 1500344 1500349) (-906 "PFO.spad" 1499143 1499170 1499714 1499719) (-905 "PF.spad" 1498717 1498729 1498948 1499041) (-904 "PFECAT.spad" 1496383 1496391 1498643 1498712) (-903 "PFECAT.spad" 1494077 1494087 1496339 1496344) (-902 "PFBRU.spad" 1491947 1491959 1494067 1494072) (-901 "PFBR.spad" 1489485 1489508 1491937 1491942) (-900 "PERM.spad" 1485166 1485176 1489315 1489330) (-899 "PERMGRP.spad" 1479902 1479912 1485156 1485161) (-898 "PERMCAT.spad" 1478454 1478464 1479882 1479897) (-897 "PERMAN.spad" 1476986 1477000 1478444 1478449) (-896 "PENDTREE.spad" 1476325 1476335 1476615 1476620) (-895 "PDRING.spad" 1474816 1474826 1476305 1476320) (-894 "PDRING.spad" 1473315 1473327 1474806 1474811) (-893 "PDEPROB.spad" 1472330 1472338 1473305 1473310) (-892 "PDEPACK.spad" 1466332 1466340 1472320 1472325) (-891 "PDECOMP.spad" 1465794 1465811 1466322 1466327) (-890 "PDECAT.spad" 1464148 1464156 1465784 1465789) (-889 "PCOMP.spad" 1463999 1464012 1464138 1464143) (-888 "PBWLB.spad" 1462581 1462598 1463989 1463994) (-887 "PATTERN.spad" 1457012 1457022 1462571 1462576) (-886 "PATTERN2.spad" 1456748 1456760 1457002 1457007) (-885 "PATTERN1.spad" 1455050 1455066 1456738 1456743) (-884 "PATRES.spad" 1452597 1452609 1455040 1455045) (-883 "PATRES2.spad" 1452259 1452273 1452587 1452592) (-882 "PATMATCH.spad" 1450416 1450447 1451967 1451972) (-881 "PATMAB.spad" 1449841 1449851 1450406 1450411) (-880 "PATLRES.spad" 1448925 1448939 1449831 1449836) (-879 "PATAB.spad" 1448689 1448699 1448915 1448920) (-878 "PARTPERM.spad" 1446051 1446059 1448679 1448684) (-877 "PARSURF.spad" 1445479 1445507 1446041 1446046) (-876 "PARSU2.spad" 1445274 1445290 1445469 1445474) (-875 "script-parser.spad" 1444794 1444802 1445264 1445269) (-874 "PARSCURV.spad" 1444222 1444250 1444784 1444789) (-873 "PARSC2.spad" 1444011 1444027 1444212 1444217) (-872 "PARPCURV.spad" 1443469 1443497 1444001 1444006) (-871 "PARPC2.spad" 1443258 1443274 1443459 1443464) (-870 "PAN2EXPR.spad" 1442670 1442678 1443248 1443253) (-869 "PALETTE.spad" 1441640 1441648 1442660 1442665) (-868 "PAIR.spad" 1440623 1440636 1441228 1441233) (-867 "PADICRC.spad" 1437953 1437971 1439128 1439221) (-866 "PADICRAT.spad" 1435968 1435980 1436189 1436282) (-865 "PADIC.spad" 1435663 1435675 1435894 1435963) (-864 "PADICCT.spad" 1434204 1434216 1435589 1435658) (-863 "PADEPAC.spad" 1432883 1432902 1434194 1434199) (-862 "PADE.spad" 1431623 1431639 1432873 1432878) (-861 "OWP.spad" 1430863 1430893 1431481 1431548) (-860 "OVERSET.spad" 1430436 1430444 1430853 1430858) (-859 "OVAR.spad" 1430217 1430240 1430426 1430431) (-858 "OUT.spad" 1429301 1429309 1430207 1430212) (-857 "OUTFORM.spad" 1418597 1418605 1429291 1429296) (-856 "OUTBFILE.spad" 1418015 1418023 1418587 1418592) (-855 "OUTBCON.spad" 1417013 1417021 1418005 1418010) (-854 "OUTBCON.spad" 1416009 1416019 1417003 1417008) (-853 "OSI.spad" 1415484 1415492 1415999 1416004) (-852 "OSGROUP.spad" 1415402 1415410 1415474 1415479) (-851 "ORTHPOL.spad" 1413863 1413873 1415319 1415324) (-850 "OREUP.spad" 1413316 1413344 1413543 1413582) (-849 "ORESUP.spad" 1412615 1412639 1412996 1413035) (-848 "OREPCTO.spad" 1410434 1410446 1412535 1412540) (-847 "OREPCAT.spad" 1404491 1404501 1410390 1410429) (-846 "OREPCAT.spad" 1398438 1398450 1404339 1404344) (-845 "ORDSET.spad" 1397604 1397612 1398428 1398433) (-844 "ORDSET.spad" 1396768 1396778 1397594 1397599) (-843 "ORDRING.spad" 1396158 1396166 1396748 1396763) (-842 "ORDRING.spad" 1395556 1395566 1396148 1396153) (-841 "ORDMON.spad" 1395411 1395419 1395546 1395551) (-840 "ORDFUNS.spad" 1394537 1394553 1395401 1395406) (-839 "ORDFIN.spad" 1394357 1394365 1394527 1394532) (-838 "ORDCOMP.spad" 1392822 1392832 1393904 1393933) (-837 "ORDCOMP2.spad" 1392107 1392119 1392812 1392817) (-836 "OPTPROB.spad" 1390745 1390753 1392097 1392102) (-835 "OPTPACK.spad" 1383130 1383138 1390735 1390740) (-834 "OPTCAT.spad" 1380805 1380813 1383120 1383125) (-833 "OPSIG.spad" 1380457 1380465 1380795 1380800) (-832 "OPQUERY.spad" 1380006 1380014 1380447 1380452) (-831 "OP.spad" 1379748 1379758 1379828 1379895) (-830 "OPERCAT.spad" 1379336 1379346 1379738 1379743) (-829 "OPERCAT.spad" 1378922 1378934 1379326 1379331) (-828 "ONECOMP.spad" 1377667 1377677 1378469 1378498) (-827 "ONECOMP2.spad" 1377085 1377097 1377657 1377662) (-826 "OMSERVER.spad" 1376087 1376095 1377075 1377080) (-825 "OMSAGG.spad" 1375875 1375885 1376043 1376082) (-824 "OMPKG.spad" 1374487 1374495 1375865 1375870) (-823 "OM.spad" 1373452 1373460 1374477 1374482) (-822 "OMLO.spad" 1372877 1372889 1373338 1373377) (-821 "OMEXPR.spad" 1372711 1372721 1372867 1372872) (-820 "OMERR.spad" 1372254 1372262 1372701 1372706) (-819 "OMERRK.spad" 1371288 1371296 1372244 1372249) (-818 "OMENC.spad" 1370632 1370640 1371278 1371283) (-817 "OMDEV.spad" 1364921 1364929 1370622 1370627) (-816 "OMCONN.spad" 1364330 1364338 1364911 1364916) (-815 "OINTDOM.spad" 1364093 1364101 1364256 1364325) (-814 "OFMONOID.spad" 1360280 1360290 1364083 1364088) (-813 "ODVAR.spad" 1359541 1359551 1360270 1360275) (-812 "ODR.spad" 1359185 1359211 1359353 1359502) (-811 "ODPOL.spad" 1356531 1356541 1356871 1356998) (-810 "ODP.spad" 1346378 1346398 1346751 1346882) (-809 "ODETOOLS.spad" 1344961 1344980 1346368 1346373) (-808 "ODESYS.spad" 1342611 1342628 1344951 1344956) (-807 "ODERTRIC.spad" 1338552 1338569 1342568 1342573) (-806 "ODERED.spad" 1337939 1337963 1338542 1338547) (-805 "ODERAT.spad" 1335490 1335507 1337929 1337934) (-804 "ODEPRRIC.spad" 1332381 1332403 1335480 1335485) (-803 "ODEPROB.spad" 1331638 1331646 1332371 1332376) (-802 "ODEPRIM.spad" 1328912 1328934 1331628 1331633) (-801 "ODEPAL.spad" 1328288 1328312 1328902 1328907) (-800 "ODEPACK.spad" 1314890 1314898 1328278 1328283) (-799 "ODEINT.spad" 1314321 1314337 1314880 1314885) (-798 "ODEIFTBL.spad" 1311716 1311724 1314311 1314316) (-797 "ODEEF.spad" 1307083 1307099 1311706 1311711) (-796 "ODECONST.spad" 1306602 1306620 1307073 1307078) (-795 "ODECAT.spad" 1305198 1305206 1306592 1306597) (-794 "OCT.spad" 1303336 1303346 1304052 1304091) (-793 "OCTCT2.spad" 1302980 1303001 1303326 1303331) (-792 "OC.spad" 1300754 1300764 1302936 1302975) (-791 "OC.spad" 1298253 1298265 1300437 1300442) (-790 "OCAMON.spad" 1298101 1298109 1298243 1298248) (-789 "OASGP.spad" 1297916 1297924 1298091 1298096) (-788 "OAMONS.spad" 1297436 1297444 1297906 1297911) (-787 "OAMON.spad" 1297297 1297305 1297426 1297431) (-786 "OAGROUP.spad" 1297159 1297167 1297287 1297292) (-785 "NUMTUBE.spad" 1296746 1296762 1297149 1297154) (-784 "NUMQUAD.spad" 1284608 1284616 1296736 1296741) (-783 "NUMODE.spad" 1275744 1275752 1284598 1284603) (-782 "NUMINT.spad" 1273302 1273310 1275734 1275739) (-781 "NUMFMT.spad" 1272142 1272150 1273292 1273297) (-780 "NUMERIC.spad" 1264214 1264224 1271947 1271952) (-779 "NTSCAT.spad" 1262716 1262732 1264182 1264209) (-778 "NTPOLFN.spad" 1262261 1262271 1262633 1262638) (-777 "NSUP.spad" 1255271 1255281 1259811 1259964) (-776 "NSUP2.spad" 1254663 1254675 1255261 1255266) (-775 "NSMP.spad" 1250858 1250877 1251166 1251293) (-774 "NREP.spad" 1249230 1249244 1250848 1250853) (-773 "NPCOEF.spad" 1248476 1248496 1249220 1249225) (-772 "NORMRETR.spad" 1248074 1248113 1248466 1248471) (-771 "NORMPK.spad" 1245976 1245995 1248064 1248069) (-770 "NORMMA.spad" 1245664 1245690 1245966 1245971) (-769 "NONE.spad" 1245405 1245413 1245654 1245659) (-768 "NONE1.spad" 1245081 1245091 1245395 1245400) (-767 "NODE1.spad" 1244550 1244566 1245071 1245076) (-766 "NNI.spad" 1243437 1243445 1244524 1244545) (-765 "NLINSOL.spad" 1242059 1242069 1243427 1243432) (-764 "NIPROB.spad" 1240600 1240608 1242049 1242054) (-763 "NFINTBAS.spad" 1238060 1238077 1240590 1240595) (-762 "NETCLT.spad" 1238034 1238045 1238050 1238055) (-761 "NCODIV.spad" 1236232 1236248 1238024 1238029) (-760 "NCNTFRAC.spad" 1235874 1235888 1236222 1236227) (-759 "NCEP.spad" 1234034 1234048 1235864 1235869) (-758 "NASRING.spad" 1233630 1233638 1234024 1234029) (-757 "NASRING.spad" 1233224 1233234 1233620 1233625) (-756 "NARNG.spad" 1232568 1232576 1233214 1233219) (-755 "NARNG.spad" 1231910 1231920 1232558 1232563) (-754 "NAGSP.spad" 1230983 1230991 1231900 1231905) (-753 "NAGS.spad" 1220508 1220516 1230973 1230978) (-752 "NAGF07.spad" 1218901 1218909 1220498 1220503) (-751 "NAGF04.spad" 1213133 1213141 1218891 1218896) (-750 "NAGF02.spad" 1206942 1206950 1213123 1213128) (-749 "NAGF01.spad" 1202545 1202553 1206932 1206937) (-748 "NAGE04.spad" 1196005 1196013 1202535 1202540) (-747 "NAGE02.spad" 1186347 1186355 1195995 1196000) (-746 "NAGE01.spad" 1182231 1182239 1186337 1186342) (-745 "NAGD03.spad" 1180151 1180159 1182221 1182226) (-744 "NAGD02.spad" 1172682 1172690 1180141 1180146) (-743 "NAGD01.spad" 1166795 1166803 1172672 1172677) (-742 "NAGC06.spad" 1162582 1162590 1166785 1166790) (-741 "NAGC05.spad" 1161051 1161059 1162572 1162577) (-740 "NAGC02.spad" 1160306 1160314 1161041 1161046) (-739 "NAALG.spad" 1159841 1159851 1160274 1160301) (-738 "NAALG.spad" 1159396 1159408 1159831 1159836) (-737 "MULTSQFR.spad" 1156354 1156371 1159386 1159391) (-736 "MULTFACT.spad" 1155737 1155754 1156344 1156349) (-735 "MTSCAT.spad" 1153771 1153792 1155635 1155732) (-734 "MTHING.spad" 1153428 1153438 1153761 1153766) (-733 "MSYSCMD.spad" 1152862 1152870 1153418 1153423) (-732 "MSET.spad" 1150804 1150814 1152568 1152607) (-731 "MSETAGG.spad" 1150649 1150659 1150772 1150799) (-730 "MRING.spad" 1147620 1147632 1150357 1150424) (-729 "MRF2.spad" 1147188 1147202 1147610 1147615) (-728 "MRATFAC.spad" 1146734 1146751 1147178 1147183) (-727 "MPRFF.spad" 1144764 1144783 1146724 1146729) (-726 "MPOLY.spad" 1142199 1142214 1142558 1142685) (-725 "MPCPF.spad" 1141463 1141482 1142189 1142194) (-724 "MPC3.spad" 1141278 1141318 1141453 1141458) (-723 "MPC2.spad" 1140920 1140953 1141268 1141273) (-722 "MONOTOOL.spad" 1139255 1139272 1140910 1140915) (-721 "MONOID.spad" 1138574 1138582 1139245 1139250) (-720 "MONOID.spad" 1137891 1137901 1138564 1138569) (-719 "MONOGEN.spad" 1136637 1136650 1137751 1137886) (-718 "MONOGEN.spad" 1135405 1135420 1136521 1136526) (-717 "MONADWU.spad" 1133419 1133427 1135395 1135400) (-716 "MONADWU.spad" 1131431 1131441 1133409 1133414) (-715 "MONAD.spad" 1130575 1130583 1131421 1131426) (-714 "MONAD.spad" 1129717 1129727 1130565 1130570) (-713 "MOEBIUS.spad" 1128403 1128417 1129697 1129712) (-712 "MODULE.spad" 1128273 1128283 1128371 1128398) (-711 "MODULE.spad" 1128163 1128175 1128263 1128268) (-710 "MODRING.spad" 1127494 1127533 1128143 1128158) (-709 "MODOP.spad" 1126153 1126165 1127316 1127383) (-708 "MODMONOM.spad" 1125882 1125900 1126143 1126148) (-707 "MODMON.spad" 1122641 1122657 1123360 1123513) (-706 "MODFIELD.spad" 1121999 1122038 1122543 1122636) (-705 "MMLFORM.spad" 1120859 1120867 1121989 1121994) (-704 "MMAP.spad" 1120599 1120633 1120849 1120854) (-703 "MLO.spad" 1119026 1119036 1120555 1120594) (-702 "MLIFT.spad" 1117598 1117615 1119016 1119021) (-701 "MKUCFUNC.spad" 1117131 1117149 1117588 1117593) (-700 "MKRECORD.spad" 1116733 1116746 1117121 1117126) (-699 "MKFUNC.spad" 1116114 1116124 1116723 1116728) (-698 "MKFLCFN.spad" 1115070 1115080 1116104 1116109) (-697 "MKCHSET.spad" 1114935 1114945 1115060 1115065) (-696 "MKBCFUNC.spad" 1114420 1114438 1114925 1114930) (-695 "MINT.spad" 1113859 1113867 1114322 1114415) (-694 "MHROWRED.spad" 1112360 1112370 1113849 1113854) (-693 "MFLOAT.spad" 1110876 1110884 1112250 1112355) (-692 "MFINFACT.spad" 1110276 1110298 1110866 1110871) (-691 "MESH.spad" 1108008 1108016 1110266 1110271) (-690 "MDDFACT.spad" 1106201 1106211 1107998 1108003) (-689 "MDAGG.spad" 1105488 1105498 1106181 1106196) (-688 "MCMPLX.spad" 1101474 1101482 1102088 1102277) (-687 "MCDEN.spad" 1100682 1100694 1101464 1101469) (-686 "MCALCFN.spad" 1097784 1097810 1100672 1100677) (-685 "MAYBE.spad" 1097068 1097079 1097774 1097779) (-684 "MATSTOR.spad" 1094344 1094354 1097058 1097063) (-683 "MATRIX.spad" 1093048 1093058 1093532 1093559) (-682 "MATLIN.spad" 1090374 1090398 1092932 1092937) (-681 "MATCAT.spad" 1081959 1081981 1090342 1090369) (-680 "MATCAT.spad" 1073416 1073440 1081801 1081806) (-679 "MATCAT2.spad" 1072684 1072732 1073406 1073411) (-678 "MAPPKG3.spad" 1071583 1071597 1072674 1072679) (-677 "MAPPKG2.spad" 1070917 1070929 1071573 1071578) (-676 "MAPPKG1.spad" 1069735 1069745 1070907 1070912) (-675 "MAPPAST.spad" 1069048 1069056 1069725 1069730) (-674 "MAPHACK3.spad" 1068856 1068870 1069038 1069043) (-673 "MAPHACK2.spad" 1068621 1068633 1068846 1068851) (-672 "MAPHACK1.spad" 1068251 1068261 1068611 1068616) (-671 "MAGMA.spad" 1066041 1066058 1068241 1068246) (-670 "MACROAST.spad" 1065620 1065628 1066031 1066036) (-669 "M3D.spad" 1063316 1063326 1064998 1065003) (-668 "LZSTAGG.spad" 1060544 1060554 1063306 1063311) (-667 "LZSTAGG.spad" 1057770 1057782 1060534 1060539) (-666 "LWORD.spad" 1054475 1054492 1057760 1057765) (-665 "LSTAST.spad" 1054259 1054267 1054465 1054470) (-664 "LSQM.spad" 1052485 1052499 1052883 1052934) (-663 "LSPP.spad" 1052018 1052035 1052475 1052480) (-662 "LSMP.spad" 1050858 1050886 1052008 1052013) (-661 "LSMP1.spad" 1048662 1048676 1050848 1050853) (-660 "LSAGG.spad" 1048331 1048341 1048630 1048657) (-659 "LSAGG.spad" 1048020 1048032 1048321 1048326) (-658 "LPOLY.spad" 1046974 1046993 1047876 1047945) (-657 "LPEFRAC.spad" 1046231 1046241 1046964 1046969) (-656 "LO.spad" 1045632 1045646 1046165 1046192) (-655 "LOGIC.spad" 1045234 1045242 1045622 1045627) (-654 "LOGIC.spad" 1044834 1044844 1045224 1045229) (-653 "LODOOPS.spad" 1043752 1043764 1044824 1044829) (-652 "LODO.spad" 1043136 1043152 1043432 1043471) (-651 "LODOF.spad" 1042180 1042197 1043093 1043098) (-650 "LODOCAT.spad" 1040838 1040848 1042136 1042175) (-649 "LODOCAT.spad" 1039494 1039506 1040794 1040799) (-648 "LODO2.spad" 1038767 1038779 1039174 1039213) (-647 "LODO1.spad" 1038167 1038177 1038447 1038486) (-646 "LODEEF.spad" 1036939 1036957 1038157 1038162) (-645 "LNAGG.spad" 1032741 1032751 1036929 1036934) (-644 "LNAGG.spad" 1028507 1028519 1032697 1032702) (-643 "LMOPS.spad" 1025243 1025260 1028497 1028502) (-642 "LMODULE.spad" 1024885 1024895 1025233 1025238) (-641 "LMDICT.spad" 1024168 1024178 1024436 1024463) (-640 "LITERAL.spad" 1024074 1024085 1024158 1024163) (-639 "LIST.spad" 1021792 1021802 1023221 1023248) (-638 "LIST3.spad" 1021083 1021097 1021782 1021787) (-637 "LIST2.spad" 1019723 1019735 1021073 1021078) (-636 "LIST2MAP.spad" 1016600 1016612 1019713 1019718) (-635 "LINEXP.spad" 1016032 1016042 1016580 1016595) (-634 "LINDEP.spad" 1014809 1014821 1015944 1015949) (-633 "LIMITRF.spad" 1012723 1012733 1014799 1014804) (-632 "LIMITPS.spad" 1011606 1011619 1012713 1012718) (-631 "LIE.spad" 1009620 1009632 1010896 1011041) (-630 "LIECAT.spad" 1009096 1009106 1009546 1009615) (-629 "LIECAT.spad" 1008600 1008612 1009052 1009057) (-628 "LIB.spad" 1006648 1006656 1007259 1007274) (-627 "LGROBP.spad" 1004001 1004020 1006638 1006643) (-626 "LF.spad" 1002920 1002936 1003991 1003996) (-625 "LFCAT.spad" 1001939 1001947 1002910 1002915) (-624 "LEXTRIPK.spad" 997442 997457 1001929 1001934) (-623 "LEXP.spad" 995445 995472 997422 997437) (-622 "LETAST.spad" 995144 995152 995435 995440) (-621 "LEADCDET.spad" 993528 993545 995134 995139) (-620 "LAZM3PK.spad" 992232 992254 993518 993523) (-619 "LAUPOL.spad" 990921 990934 991825 991894) (-618 "LAPLACE.spad" 990494 990510 990911 990916) (-617 "LA.spad" 989934 989948 990416 990455) (-616 "LALG.spad" 989710 989720 989914 989929) (-615 "LALG.spad" 989494 989506 989700 989705) (-614 "KVTFROM.spad" 989229 989239 989484 989489) (-613 "KTVLOGIC.spad" 988652 988660 989219 989224) (-612 "KRCFROM.spad" 988390 988400 988642 988647) (-611 "KOVACIC.spad" 987103 987120 988380 988385) (-610 "KONVERT.spad" 986825 986835 987093 987098) (-609 "KOERCE.spad" 986562 986572 986815 986820) (-608 "KERNEL.spad" 985097 985107 986346 986351) (-607 "KERNEL2.spad" 984800 984812 985087 985092) (-606 "KDAGG.spad" 983903 983925 984780 984795) (-605 "KDAGG.spad" 983014 983038 983893 983898) (-604 "KAFILE.spad" 981977 981993 982212 982239) (-603 "JORDAN.spad" 979804 979816 981267 981412) (-602 "JOINAST.spad" 979498 979506 979794 979799) (-601 "JAVACODE.spad" 979364 979372 979488 979493) (-600 "IXAGG.spad" 977487 977511 979354 979359) (-599 "IXAGG.spad" 975465 975491 977334 977339) (-598 "IVECTOR.spad" 974236 974251 974391 974418) (-597 "ITUPLE.spad" 973381 973391 974226 974231) (-596 "ITRIGMNP.spad" 972192 972211 973371 973376) (-595 "ITFUN3.spad" 971686 971700 972182 972187) (-594 "ITFUN2.spad" 971416 971428 971676 971681) (-593 "ITAYLOR.spad" 969208 969223 971252 971377) (-592 "ISUPS.spad" 961619 961634 968182 968279) (-591 "ISUMP.spad" 961116 961132 961609 961614) (-590 "ISTRING.spad" 960119 960132 960285 960312) (-589 "ISAST.spad" 959838 959846 960109 960114) (-588 "IRURPK.spad" 958551 958570 959828 959833) (-587 "IRSN.spad" 956511 956519 958541 958546) (-586 "IRRF2F.spad" 954986 954996 956467 956472) (-585 "IRREDFFX.spad" 954587 954598 954976 954981) (-584 "IROOT.spad" 952918 952928 954577 954582) (-583 "IR.spad" 950707 950721 952773 952800) (-582 "IR2.spad" 949727 949743 950697 950702) (-581 "IR2F.spad" 948927 948943 949717 949722) (-580 "IPRNTPK.spad" 948687 948695 948917 948922) (-579 "IPF.spad" 948252 948264 948492 948585) (-578 "IPADIC.spad" 948013 948039 948178 948247) (-577 "IP4ADDR.spad" 947570 947578 948003 948008) (-576 "IOMODE.spad" 947191 947199 947560 947565) (-575 "IOBFILE.spad" 946552 946560 947181 947186) (-574 "IOBCON.spad" 946417 946425 946542 946547) (-573 "INVLAPLA.spad" 946062 946078 946407 946412) (-572 "INTTR.spad" 939308 939325 946052 946057) (-571 "INTTOOLS.spad" 937019 937035 938882 938887) (-570 "INTSLPE.spad" 936325 936333 937009 937014) (-569 "INTRVL.spad" 935891 935901 936239 936320) (-568 "INTRF.spad" 934255 934269 935881 935886) (-567 "INTRET.spad" 933687 933697 934245 934250) (-566 "INTRAT.spad" 932362 932379 933677 933682) (-565 "INTPM.spad" 930725 930741 932005 932010) (-564 "INTPAF.spad" 928493 928511 930657 930662) (-563 "INTPACK.spad" 918803 918811 928483 928488) (-562 "INT.spad" 918164 918172 918657 918798) (-561 "INTHERTR.spad" 917430 917447 918154 918159) (-560 "INTHERAL.spad" 917096 917120 917420 917425) (-559 "INTHEORY.spad" 913509 913517 917086 917091) (-558 "INTG0.spad" 906972 906990 913441 913446) (-557 "INTFTBL.spad" 901001 901009 906962 906967) (-556 "INTFACT.spad" 900060 900070 900991 900996) (-555 "INTEF.spad" 898375 898391 900050 900055) (-554 "INTDOM.spad" 896990 896998 898301 898370) (-553 "INTDOM.spad" 895667 895677 896980 896985) (-552 "INTCAT.spad" 893920 893930 895581 895662) (-551 "INTBIT.spad" 893423 893431 893910 893915) (-550 "INTALG.spad" 892605 892632 893413 893418) (-549 "INTAF.spad" 892097 892113 892595 892600) (-548 "INTABL.spad" 890615 890646 890778 890805) (-547 "INT8.spad" 890495 890503 890605 890610) (-546 "INT32.spad" 890374 890382 890485 890490) (-545 "INT16.spad" 890253 890261 890364 890369) (-544 "INS.spad" 887720 887728 890155 890248) (-543 "INS.spad" 885273 885283 887710 887715) (-542 "INPSIGN.spad" 884707 884720 885263 885268) (-541 "INPRODPF.spad" 883773 883792 884697 884702) (-540 "INPRODFF.spad" 882831 882855 883763 883768) (-539 "INNMFACT.spad" 881802 881819 882821 882826) (-538 "INMODGCD.spad" 881286 881316 881792 881797) (-537 "INFSP.spad" 879571 879593 881276 881281) (-536 "INFPROD0.spad" 878621 878640 879561 879566) (-535 "INFORM.spad" 875782 875790 878611 878616) (-534 "INFORM1.spad" 875407 875417 875772 875777) (-533 "INFINITY.spad" 874959 874967 875397 875402) (-532 "INETCLTS.spad" 874936 874944 874949 874954) (-531 "INEP.spad" 873468 873490 874926 874931) (-530 "INDE.spad" 873197 873214 873458 873463) (-529 "INCRMAPS.spad" 872618 872628 873187 873192) (-528 "INBFILE.spad" 871690 871698 872608 872613) (-527 "INBFF.spad" 867460 867471 871680 871685) (-526 "INBCON.spad" 865748 865756 867450 867455) (-525 "INBCON.spad" 864034 864044 865738 865743) (-524 "INAST.spad" 863699 863707 864024 864029) (-523 "IMPTAST.spad" 863407 863415 863689 863694) (-522 "IMATRIX.spad" 862352 862378 862864 862891) (-521 "IMATQF.spad" 861446 861490 862308 862313) (-520 "IMATLIN.spad" 860051 860075 861402 861407) (-519 "ILIST.spad" 858707 858722 859234 859261) (-518 "IIARRAY2.spad" 858095 858133 858314 858341) (-517 "IFF.spad" 857505 857521 857776 857869) (-516 "IFAST.spad" 857119 857127 857495 857500) (-515 "IFARRAY.spad" 854606 854621 856302 856329) (-514 "IFAMON.spad" 854468 854485 854562 854567) (-513 "IEVALAB.spad" 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"D02BHFA.spad" 241384 241392 241884 241889) (-205 "D02BBFA.spad" 240874 240882 241374 241379) (-204 "D02AGNT.spad" 235678 235686 240864 240869) (-203 "D01WGTS.spad" 233997 234005 235668 235673) (-202 "D01TRNS.spad" 233974 233982 233987 233992) (-201 "D01GBFA.spad" 233496 233504 233964 233969) (-200 "D01FCFA.spad" 233018 233026 233486 233491) (-199 "D01ASFA.spad" 232486 232494 233008 233013) (-198 "D01AQFA.spad" 231932 231940 232476 232481) (-197 "D01APFA.spad" 231356 231364 231922 231927) (-196 "D01ANFA.spad" 230850 230858 231346 231351) (-195 "D01AMFA.spad" 230360 230368 230840 230845) (-194 "D01ALFA.spad" 229900 229908 230350 230355) (-193 "D01AKFA.spad" 229426 229434 229890 229895) (-192 "D01AJFA.spad" 228949 228957 229416 229421) (-191 "D01AGNT.spad" 225008 225016 228939 228944) (-190 "CYCLOTOM.spad" 224514 224522 224998 225003) (-189 "CYCLES.spad" 221346 221354 224504 224509) (-188 "CVMP.spad" 220763 220773 221336 221341) (-187 "CTRIGMNP.spad" 219253 219269 220753 220758) (-186 "CTOR.spad" 218948 218956 219243 219248) (-185 "CTORKIND.spad" 218551 218559 218938 218943) (-184 "CTORCAT.spad" 217800 217808 218541 218546) (-183 "CTORCAT.spad" 217047 217057 217790 217795) (-182 "CTORCALL.spad" 216627 216635 217037 217042) (-181 "CSTTOOLS.spad" 215870 215883 216617 216622) (-180 "CRFP.spad" 209574 209587 215860 215865) (-179 "CRCEAST.spad" 209294 209302 209564 209569) (-178 "CRAPACK.spad" 208337 208347 209284 209289) (-177 "CPMATCH.spad" 207837 207852 208262 208267) (-176 "CPIMA.spad" 207542 207561 207827 207832) (-175 "COORDSYS.spad" 202435 202445 207532 207537) (-174 "CONTOUR.spad" 201837 201845 202425 202430) (-173 "CONTFRAC.spad" 197449 197459 201739 201832) (-172 "CONDUIT.spad" 197207 197215 197439 197444) (-171 "COMRING.spad" 196881 196889 197145 197202) (-170 "COMPPROP.spad" 196395 196403 196871 196876) (-169 "COMPLPAT.spad" 196162 196177 196385 196390) (-168 "COMPLEX.spad" 190198 190208 190442 190691) (-167 "COMPLEX2.spad" 189911 189923 190188 190193) (-166 "COMPFACT.spad" 189513 189527 189901 189906) (-165 "COMPCAT.spad" 187651 187661 189259 189508) (-164 "COMPCAT.spad" 185470 185482 187080 187085) (-163 "COMMUPC.spad" 185216 185234 185460 185465) (-162 "COMMONOP.spad" 184749 184757 185206 185211) (-161 "COMM.spad" 184558 184566 184739 184744) (-160 "COMMAAST.spad" 184321 184329 184548 184553) (-159 "COMBOPC.spad" 183226 183234 184311 184316) (-158 "COMBINAT.spad" 181971 181981 183216 183221) (-157 "COMBF.spad" 179339 179355 181961 181966) (-156 "COLOR.spad" 178176 178184 179329 179334) (-155 "COLONAST.spad" 177842 177850 178166 178171) (-154 "CMPLXRT.spad" 177551 177568 177832 177837) (-153 "CLLCTAST.spad" 177213 177221 177541 177546) (-152 "CLIP.spad" 173305 173313 177203 177208) (-151 "CLIF.spad" 171944 171960 173261 173300) (-150 "CLAGG.spad" 168429 168439 171934 171939) (-149 "CLAGG.spad" 164785 164797 168292 168297) (-148 "CINTSLPE.spad" 164110 164123 164775 164780) (-147 "CHVAR.spad" 162188 162210 164100 164105) (-146 "CHARZ.spad" 162103 162111 162168 162183) (-145 "CHARPOL.spad" 161611 161621 162093 162098) (-144 "CHARNZ.spad" 161364 161372 161591 161606) (-143 "CHAR.spad" 159232 159240 161354 161359) (-142 "CFCAT.spad" 158548 158556 159222 159227) (-141 "CDEN.spad" 157706 157720 158538 158543) (-140 "CCLASS.spad" 155855 155863 157117 157156) (-139 "CATEGORY.spad" 154945 154953 155845 155850) (-138 "CATCTOR.spad" 154836 154844 154935 154940) (-137 "CATAST.spad" 154463 154471 154826 154831) (-136 "CASEAST.spad" 154177 154185 154453 154458) (-135 "CARTEN.spad" 149280 149304 154167 154172) (-134 "CARTEN2.spad" 148666 148693 149270 149275) (-133 "CARD.spad" 145955 145963 148640 148661) (-132 "CAPSLAST.spad" 145729 145737 145945 145950) (-131 "CACHSET.spad" 145351 145359 145719 145724) (-130 "CABMON.spad" 144904 144912 145341 145346) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865)) \ No newline at end of file
+((-3 NIL 2282794 2282799 2282804 2282809) (-2 NIL 2282774 2282779 2282784 2282789) (-1 NIL 2282754 2282759 2282764 2282769) (0 NIL 2282734 2282739 2282744 2282749) (-1285 "ZMOD.spad" 2282543 2282556 2282672 2282729) (-1284 "ZLINDEP.spad" 2281587 2281598 2282533 2282538) (-1283 "ZDSOLVE.spad" 2271436 2271458 2281577 2281582) (-1282 "YSTREAM.spad" 2270929 2270940 2271426 2271431) (-1281 "XRPOLY.spad" 2270149 2270169 2270785 2270854) (-1280 "XPR.spad" 2267940 2267953 2269867 2269966) (-1279 "XPOLY.spad" 2267495 2267506 2267796 2267865) (-1278 "XPOLYC.spad" 2266812 2266828 2267421 2267490) (-1277 "XPBWPOLY.spad" 2265249 2265269 2266592 2266661) (-1276 "XF.spad" 2263710 2263725 2265151 2265244) (-1275 "XF.spad" 2262151 2262168 2263594 2263599) (-1274 "XFALG.spad" 2259175 2259191 2262077 2262146) (-1273 "XEXPPKG.spad" 2258426 2258452 2259165 2259170) (-1272 "XDPOLY.spad" 2258040 2258056 2258282 2258351) (-1271 "XALG.spad" 2257700 2257711 2257996 2258035) (-1270 "WUTSET.spad" 2253539 2253556 2257346 2257373) (-1269 "WP.spad" 2252738 2252782 2253397 2253464) (-1268 "WHILEAST.spad" 2252536 2252545 2252728 2252733) (-1267 "WHEREAST.spad" 2252207 2252216 2252526 2252531) (-1266 "WFFINTBS.spad" 2249770 2249792 2252197 2252202) (-1265 "WEIER.spad" 2247984 2247995 2249760 2249765) (-1264 "VSPACE.spad" 2247657 2247668 2247952 2247979) (-1263 "VSPACE.spad" 2247350 2247363 2247647 2247652) (-1262 "VOID.spad" 2247027 2247036 2247340 2247345) (-1261 "VIEW.spad" 2244649 2244658 2247017 2247022) (-1260 "VIEWDEF.spad" 2239846 2239855 2244639 2244644) (-1259 "VIEW3D.spad" 2223681 2223690 2239836 2239841) (-1258 "VIEW2D.spad" 2211418 2211427 2223671 2223676) (-1257 "VECTOR.spad" 2210093 2210104 2210344 2210371) (-1256 "VECTOR2.spad" 2208720 2208733 2210083 2210088) (-1255 "VECTCAT.spad" 2206620 2206631 2208688 2208715) (-1254 "VECTCAT.spad" 2204328 2204341 2206398 2206403) (-1253 "VARIABLE.spad" 2204108 2204123 2204318 2204323) (-1252 "UTYPE.spad" 2203752 2203761 2204098 2204103) (-1251 "UTSODETL.spad" 2203045 2203069 2203708 2203713) (-1250 "UTSODE.spad" 2201233 2201253 2203035 2203040) (-1249 "UTS.spad" 2196022 2196050 2199700 2199797) (-1248 "UTSCAT.spad" 2193473 2193489 2195920 2196017) (-1247 "UTSCAT.spad" 2190568 2190586 2193017 2193022) (-1246 "UTS2.spad" 2190161 2190196 2190558 2190563) (-1245 "URAGG.spad" 2184793 2184804 2190151 2190156) (-1244 "URAGG.spad" 2179389 2179402 2184749 2184754) (-1243 "UPXSSING.spad" 2177032 2177058 2178470 2178603) (-1242 "UPXS.spad" 2174180 2174208 2175164 2175313) (-1241 "UPXSCONS.spad" 2171937 2171957 2172312 2172461) (-1240 "UPXSCCA.spad" 2170502 2170522 2171783 2171932) (-1239 "UPXSCCA.spad" 2169209 2169231 2170492 2170497) (-1238 "UPXSCAT.spad" 2167790 2167806 2169055 2169204) (-1237 "UPXS2.spad" 2167331 2167384 2167780 2167785) (-1236 "UPSQFREE.spad" 2165743 2165757 2167321 2167326) (-1235 "UPSCAT.spad" 2163336 2163360 2165641 2165738) (-1234 "UPSCAT.spad" 2160635 2160661 2162942 2162947) (-1233 "UPOLYC.spad" 2155613 2155624 2160477 2160630) (-1232 "UPOLYC.spad" 2150483 2150496 2155349 2155354) (-1231 "UPOLYC2.spad" 2149952 2149971 2150473 2150478) (-1230 "UP.spad" 2147109 2147124 2147502 2147655) (-1229 "UPMP.spad" 2145999 2146012 2147099 2147104) (-1228 "UPDIVP.spad" 2145562 2145576 2145989 2145994) (-1227 "UPDECOMP.spad" 2143799 2143813 2145552 2145557) (-1226 "UPCDEN.spad" 2143006 2143022 2143789 2143794) (-1225 "UP2.spad" 2142368 2142389 2142996 2143001) (-1224 "UNISEG.spad" 2141721 2141732 2142287 2142292) (-1223 "UNISEG2.spad" 2141214 2141227 2141677 2141682) (-1222 "UNIFACT.spad" 2140315 2140327 2141204 2141209) (-1221 "ULS.spad" 2130867 2130895 2131960 2132389) (-1220 "ULSCONS.spad" 2123261 2123281 2123633 2123782) (-1219 "ULSCCAT.spad" 2120990 2121010 2123107 2123256) (-1218 "ULSCCAT.spad" 2118827 2118849 2120946 2120951) (-1217 "ULSCAT.spad" 2117043 2117059 2118673 2118822) (-1216 "ULS2.spad" 2116555 2116608 2117033 2117038) (-1215 "UINT8.spad" 2116432 2116441 2116545 2116550) (-1214 "UINT32.spad" 2116308 2116317 2116422 2116427) (-1213 "UINT16.spad" 2116184 2116193 2116298 2116303) (-1212 "UFD.spad" 2115249 2115258 2116110 2116179) (-1211 "UFD.spad" 2114376 2114387 2115239 2115244) (-1210 "UDVO.spad" 2113223 2113232 2114366 2114371) (-1209 "UDPO.spad" 2110650 2110661 2113179 2113184) (-1208 "TYPE.spad" 2110582 2110591 2110640 2110645) (-1207 "TYPEAST.spad" 2110501 2110510 2110572 2110577) (-1206 "TWOFACT.spad" 2109151 2109166 2110491 2110496) (-1205 "TUPLE.spad" 2108635 2108646 2109050 2109055) (-1204 "TUBETOOL.spad" 2105472 2105481 2108625 2108630) (-1203 "TUBE.spad" 2104113 2104130 2105462 2105467) (-1202 "TS.spad" 2102702 2102718 2103678 2103775) (-1201 "TSETCAT.spad" 2089829 2089846 2102670 2102697) (-1200 "TSETCAT.spad" 2076942 2076961 2089785 2089790) (-1199 "TRMANIP.spad" 2071308 2071325 2076648 2076653) (-1198 "TRIMAT.spad" 2070267 2070292 2071298 2071303) (-1197 "TRIGMNIP.spad" 2068784 2068801 2070257 2070262) (-1196 "TRIGCAT.spad" 2068296 2068305 2068774 2068779) (-1195 "TRIGCAT.spad" 2067806 2067817 2068286 2068291) (-1194 "TREE.spad" 2066377 2066388 2067413 2067440) (-1193 "TRANFUN.spad" 2066208 2066217 2066367 2066372) (-1192 "TRANFUN.spad" 2066037 2066048 2066198 2066203) (-1191 "TOPSP.spad" 2065711 2065720 2066027 2066032) (-1190 "TOOLSIGN.spad" 2065374 2065385 2065701 2065706) (-1189 "TEXTFILE.spad" 2063931 2063940 2065364 2065369) (-1188 "TEX.spad" 2061063 2061072 2063921 2063926) (-1187 "TEX1.spad" 2060619 2060630 2061053 2061058) (-1186 "TEMUTL.spad" 2060174 2060183 2060609 2060614) (-1185 "TBCMPPK.spad" 2058267 2058290 2060164 2060169) (-1184 "TBAGG.spad" 2057303 2057326 2058247 2058262) (-1183 "TBAGG.spad" 2056347 2056372 2057293 2057298) (-1182 "TANEXP.spad" 2055723 2055734 2056337 2056342) (-1181 "TABLE.spad" 2054134 2054157 2054404 2054431) (-1180 "TABLEAU.spad" 2053615 2053626 2054124 2054129) (-1179 "TABLBUMP.spad" 2050398 2050409 2053605 2053610) (-1178 "SYSTEM.spad" 2049672 2049681 2050388 2050393) (-1177 "SYSSOLP.spad" 2047145 2047156 2049662 2049667) (-1176 "SYSNNI.spad" 2046321 2046332 2047135 2047140) (-1175 "SYSINT.spad" 2045794 2045805 2046311 2046316) (-1174 "SYNTAX.spad" 2042064 2042073 2045784 2045789) (-1173 "SYMTAB.spad" 2040120 2040129 2042054 2042059) (-1172 "SYMS.spad" 2036105 2036114 2040110 2040115) (-1171 "SYMPOLY.spad" 2035112 2035123 2035194 2035321) (-1170 "SYMFUNC.spad" 2034587 2034598 2035102 2035107) (-1169 "SYMBOL.spad" 2032014 2032023 2034577 2034582) (-1168 "SWITCH.spad" 2028771 2028780 2032004 2032009) (-1167 "SUTS.spad" 2025670 2025698 2027238 2027335) (-1166 "SUPXS.spad" 2022805 2022833 2023802 2023951) (-1165 "SUP.spad" 2019574 2019585 2020355 2020508) (-1164 "SUPFRACF.spad" 2018679 2018697 2019564 2019569) (-1163 "SUP2.spad" 2018069 2018082 2018669 2018674) (-1162 "SUMRF.spad" 2017035 2017046 2018059 2018064) (-1161 "SUMFS.spad" 2016668 2016685 2017025 2017030) (-1160 "SULS.spad" 2007207 2007235 2008313 2008742) (-1159 "SUCHTAST.spad" 2006976 2006985 2007197 2007202) (-1158 "SUCH.spad" 2006656 2006671 2006966 2006971) (-1157 "SUBSPACE.spad" 1998663 1998678 2006646 2006651) (-1156 "SUBRESP.spad" 1997823 1997837 1998619 1998624) (-1155 "STTF.spad" 1993922 1993938 1997813 1997818) (-1154 "STTFNC.spad" 1990390 1990406 1993912 1993917) (-1153 "STTAYLOR.spad" 1982788 1982799 1990271 1990276) (-1152 "STRTBL.spad" 1981293 1981310 1981442 1981469) (-1151 "STRING.spad" 1980702 1980711 1980716 1980743) (-1150 "STRICAT.spad" 1980490 1980499 1980670 1980697) (-1149 "STREAM.spad" 1977348 1977359 1980015 1980030) (-1148 "STREAM3.spad" 1976893 1976908 1977338 1977343) (-1147 "STREAM2.spad" 1975961 1975974 1976883 1976888) (-1146 "STREAM1.spad" 1975665 1975676 1975951 1975956) (-1145 "STINPROD.spad" 1974571 1974587 1975655 1975660) (-1144 "STEP.spad" 1973772 1973781 1974561 1974566) (-1143 "STBL.spad" 1972298 1972326 1972465 1972480) (-1142 "STAGG.spad" 1971373 1971384 1972288 1972293) (-1141 "STAGG.spad" 1970446 1970459 1971363 1971368) (-1140 "STACK.spad" 1969797 1969808 1970053 1970080) (-1139 "SREGSET.spad" 1967501 1967518 1969443 1969470) (-1138 "SRDCMPK.spad" 1966046 1966066 1967491 1967496) (-1137 "SRAGG.spad" 1961143 1961152 1966014 1966041) (-1136 "SRAGG.spad" 1956260 1956271 1961133 1961138) (-1135 "SQMATRIX.spad" 1953876 1953894 1954792 1954879) (-1134 "SPLTREE.spad" 1948428 1948441 1953312 1953339) (-1133 "SPLNODE.spad" 1945016 1945029 1948418 1948423) (-1132 "SPFCAT.spad" 1943793 1943802 1945006 1945011) (-1131 "SPECOUT.spad" 1942343 1942352 1943783 1943788) (-1130 "SPADXPT.spad" 1934482 1934491 1942333 1942338) (-1129 "spad-parser.spad" 1933947 1933956 1934472 1934477) (-1128 "SPADAST.spad" 1933648 1933657 1933937 1933942) (-1127 "SPACEC.spad" 1917661 1917672 1933638 1933643) (-1126 "SPACE3.spad" 1917437 1917448 1917651 1917656) (-1125 "SORTPAK.spad" 1916982 1916995 1917393 1917398) (-1124 "SOLVETRA.spad" 1914739 1914750 1916972 1916977) (-1123 "SOLVESER.spad" 1913259 1913270 1914729 1914734) (-1122 "SOLVERAD.spad" 1909269 1909280 1913249 1913254) (-1121 "SOLVEFOR.spad" 1907689 1907707 1909259 1909264) (-1120 "SNTSCAT.spad" 1907289 1907306 1907657 1907684) (-1119 "SMTS.spad" 1905549 1905575 1906854 1906951) (-1118 "SMP.spad" 1902988 1903008 1903378 1903505) (-1117 "SMITH.spad" 1901831 1901856 1902978 1902983) (-1116 "SMATCAT.spad" 1899941 1899971 1901775 1901826) (-1115 "SMATCAT.spad" 1897983 1898015 1899819 1899824) (-1114 "SKAGG.spad" 1896944 1896955 1897951 1897978) (-1113 "SINT.spad" 1895770 1895779 1896810 1896939) (-1112 "SIMPAN.spad" 1895498 1895507 1895760 1895765) (-1111 "SIG.spad" 1894826 1894835 1895488 1895493) (-1110 "SIGNRF.spad" 1893934 1893945 1894816 1894821) (-1109 "SIGNEF.spad" 1893203 1893220 1893924 1893929) (-1108 "SIGAST.spad" 1892584 1892593 1893193 1893198) (-1107 "SHP.spad" 1890502 1890517 1892540 1892545) (-1106 "SHDP.spad" 1880213 1880240 1880722 1880853) (-1105 "SGROUP.spad" 1879821 1879830 1880203 1880208) (-1104 "SGROUP.spad" 1879427 1879438 1879811 1879816) (-1103 "SGCF.spad" 1872308 1872317 1879417 1879422) (-1102 "SFRTCAT.spad" 1871236 1871253 1872276 1872303) (-1101 "SFRGCD.spad" 1870299 1870319 1871226 1871231) (-1100 "SFQCMPK.spad" 1864936 1864956 1870289 1870294) (-1099 "SFORT.spad" 1864371 1864385 1864926 1864931) (-1098 "SEXOF.spad" 1864214 1864254 1864361 1864366) (-1097 "SEX.spad" 1864106 1864115 1864204 1864209) (-1096 "SEXCAT.spad" 1861657 1861697 1864096 1864101) (-1095 "SET.spad" 1859957 1859968 1861078 1861117) (-1094 "SETMN.spad" 1858391 1858408 1859947 1859952) (-1093 "SETCAT.spad" 1857876 1857885 1858381 1858386) (-1092 "SETCAT.spad" 1857359 1857370 1857866 1857871) (-1091 "SETAGG.spad" 1853880 1853891 1857339 1857354) (-1090 "SETAGG.spad" 1850409 1850422 1853870 1853875) (-1089 "SEQAST.spad" 1850112 1850121 1850399 1850404) (-1088 "SEGXCAT.spad" 1849234 1849247 1850102 1850107) (-1087 "SEG.spad" 1849047 1849058 1849153 1849158) (-1086 "SEGCAT.spad" 1847954 1847965 1849037 1849042) (-1085 "SEGBIND.spad" 1847026 1847037 1847909 1847914) (-1084 "SEGBIND2.spad" 1846722 1846735 1847016 1847021) (-1083 "SEGAST.spad" 1846436 1846445 1846712 1846717) (-1082 "SEG2.spad" 1845861 1845874 1846392 1846397) (-1081 "SDVAR.spad" 1845137 1845148 1845851 1845856) (-1080 "SDPOL.spad" 1842527 1842538 1842818 1842945) (-1079 "SCPKG.spad" 1840606 1840617 1842517 1842522) (-1078 "SCOPE.spad" 1839751 1839760 1840596 1840601) (-1077 "SCACHE.spad" 1838433 1838444 1839741 1839746) (-1076 "SASTCAT.spad" 1838342 1838351 1838423 1838428) (-1075 "SAOS.spad" 1838214 1838223 1838332 1838337) (-1074 "SAERFFC.spad" 1837927 1837947 1838204 1838209) (-1073 "SAE.spad" 1836102 1836118 1836713 1836848) (-1072 "SAEFACT.spad" 1835803 1835823 1836092 1836097) (-1071 "RURPK.spad" 1833444 1833460 1835793 1835798) (-1070 "RULESET.spad" 1832885 1832909 1833434 1833439) (-1069 "RULE.spad" 1831089 1831113 1832875 1832880) (-1068 "RULECOLD.spad" 1830941 1830954 1831079 1831084) (-1067 "RSTRCAST.spad" 1830658 1830667 1830931 1830936) (-1066 "RSETGCD.spad" 1827036 1827056 1830648 1830653) (-1065 "RSETCAT.spad" 1816820 1816837 1827004 1827031) (-1064 "RSETCAT.spad" 1806624 1806643 1816810 1816815) (-1063 "RSDCMPK.spad" 1805076 1805096 1806614 1806619) (-1062 "RRCC.spad" 1803460 1803490 1805066 1805071) (-1061 "RRCC.spad" 1801842 1801874 1803450 1803455) (-1060 "RPTAST.spad" 1801544 1801553 1801832 1801837) (-1059 "RPOLCAT.spad" 1780904 1780919 1801412 1801539) (-1058 "RPOLCAT.spad" 1759978 1759995 1780488 1780493) (-1057 "ROUTINE.spad" 1755841 1755850 1758625 1758652) (-1056 "ROMAN.spad" 1755169 1755178 1755707 1755836) (-1055 "ROIRC.spad" 1754249 1754281 1755159 1755164) (-1054 "RNS.spad" 1753152 1753161 1754151 1754244) (-1053 "RNS.spad" 1752141 1752152 1753142 1753147) (-1052 "RNG.spad" 1751876 1751885 1752131 1752136) (-1051 "RMODULE.spad" 1751514 1751525 1751866 1751871) (-1050 "RMCAT2.spad" 1750922 1750979 1751504 1751509) (-1049 "RMATRIX.spad" 1749746 1749765 1750089 1750128) (-1048 "RMATCAT.spad" 1745279 1745310 1749702 1749741) (-1047 "RMATCAT.spad" 1740702 1740735 1745127 1745132) (-1046 "RINTERP.spad" 1740590 1740610 1740692 1740697) (-1045 "RING.spad" 1740060 1740069 1740570 1740585) (-1044 "RING.spad" 1739538 1739549 1740050 1740055) (-1043 "RIDIST.spad" 1738922 1738931 1739528 1739533) (-1042 "RGCHAIN.spad" 1737501 1737517 1738407 1738434) (-1041 "RGBCSPC.spad" 1737282 1737294 1737491 1737496) (-1040 "RGBCMDL.spad" 1736812 1736824 1737272 1737277) (-1039 "RF.spad" 1734426 1734437 1736802 1736807) (-1038 "RFFACTOR.spad" 1733888 1733899 1734416 1734421) (-1037 "RFFACT.spad" 1733623 1733635 1733878 1733883) (-1036 "RFDIST.spad" 1732611 1732620 1733613 1733618) (-1035 "RETSOL.spad" 1732028 1732041 1732601 1732606) (-1034 "RETRACT.spad" 1731456 1731467 1732018 1732023) (-1033 "RETRACT.spad" 1730882 1730895 1731446 1731451) (-1032 "RETAST.spad" 1730694 1730703 1730872 1730877) (-1031 "RESULT.spad" 1728754 1728763 1729341 1729368) (-1030 "RESRING.spad" 1728101 1728148 1728692 1728749) (-1029 "RESLATC.spad" 1727425 1727436 1728091 1728096) (-1028 "REPSQ.spad" 1727154 1727165 1727415 1727420) (-1027 "REP.spad" 1724706 1724715 1727144 1727149) (-1026 "REPDB.spad" 1724411 1724422 1724696 1724701) (-1025 "REP2.spad" 1713983 1713994 1724253 1724258) (-1024 "REP1.spad" 1707973 1707984 1713933 1713938) (-1023 "REGSET.spad" 1705770 1705787 1707619 1707646) (-1022 "REF.spad" 1705099 1705110 1705725 1705730) (-1021 "REDORDER.spad" 1704275 1704292 1705089 1705094) (-1020 "RECLOS.spad" 1703058 1703078 1703762 1703855) (-1019 "REALSOLV.spad" 1702190 1702199 1703048 1703053) (-1018 "REAL.spad" 1702062 1702071 1702180 1702185) (-1017 "REAL0Q.spad" 1699344 1699359 1702052 1702057) (-1016 "REAL0.spad" 1696172 1696187 1699334 1699339) (-1015 "RDUCEAST.spad" 1695893 1695902 1696162 1696167) (-1014 "RDIV.spad" 1695544 1695569 1695883 1695888) (-1013 "RDIST.spad" 1695107 1695118 1695534 1695539) (-1012 "RDETRS.spad" 1693903 1693921 1695097 1695102) (-1011 "RDETR.spad" 1692010 1692028 1693893 1693898) (-1010 "RDEEFS.spad" 1691083 1691100 1692000 1692005) (-1009 "RDEEF.spad" 1690079 1690096 1691073 1691078) (-1008 "RCFIELD.spad" 1687265 1687274 1689981 1690074) (-1007 "RCFIELD.spad" 1684537 1684548 1687255 1687260) (-1006 "RCAGG.spad" 1682449 1682460 1684527 1684532) (-1005 "RCAGG.spad" 1680288 1680301 1682368 1682373) (-1004 "RATRET.spad" 1679648 1679659 1680278 1680283) (-1003 "RATFACT.spad" 1679340 1679352 1679638 1679643) (-1002 "RANDSRC.spad" 1678659 1678668 1679330 1679335) (-1001 "RADUTIL.spad" 1678413 1678422 1678649 1678654) (-1000 "RADIX.spad" 1675314 1675328 1676880 1676973) (-999 "RADFF.spad" 1673728 1673764 1673846 1674002) (-998 "RADCAT.spad" 1673322 1673330 1673718 1673723) (-997 "RADCAT.spad" 1672914 1672924 1673312 1673317) (-996 "QUEUE.spad" 1672257 1672267 1672521 1672548) (-995 "QUAT.spad" 1670839 1670849 1671181 1671246) (-994 "QUATCT2.spad" 1670458 1670476 1670829 1670834) (-993 "QUATCAT.spad" 1668623 1668633 1670388 1670453) (-992 "QUATCAT.spad" 1666539 1666551 1668306 1668311) (-991 "QUAGG.spad" 1665365 1665375 1666507 1666534) (-990 "QQUTAST.spad" 1665134 1665142 1665355 1665360) (-989 "QFORM.spad" 1664597 1664611 1665124 1665129) (-988 "QFCAT.spad" 1663300 1663310 1664499 1664592) (-987 "QFCAT.spad" 1661594 1661606 1662795 1662800) (-986 "QFCAT2.spad" 1661285 1661301 1661584 1661589) (-985 "QEQUAT.spad" 1660842 1660850 1661275 1661280) (-984 "QCMPACK.spad" 1655589 1655608 1660832 1660837) (-983 "QALGSET.spad" 1651664 1651696 1655503 1655508) (-982 "QALGSET2.spad" 1649660 1649678 1651654 1651659) (-981 "PWFFINTB.spad" 1646970 1646991 1649650 1649655) (-980 "PUSHVAR.spad" 1646299 1646318 1646960 1646965) (-979 "PTRANFN.spad" 1642425 1642435 1646289 1646294) (-978 "PTPACK.spad" 1639513 1639523 1642415 1642420) (-977 "PTFUNC2.spad" 1639334 1639348 1639503 1639508) (-976 "PTCAT.spad" 1638583 1638593 1639302 1639329) (-975 "PSQFR.spad" 1637890 1637914 1638573 1638578) (-974 "PSEUDLIN.spad" 1636748 1636758 1637880 1637885) (-973 "PSETPK.spad" 1622181 1622197 1636626 1636631) (-972 "PSETCAT.spad" 1616101 1616124 1622161 1622176) (-971 "PSETCAT.spad" 1609995 1610020 1616057 1616062) (-970 "PSCURVE.spad" 1608978 1608986 1609985 1609990) (-969 "PSCAT.spad" 1607745 1607774 1608876 1608973) (-968 "PSCAT.spad" 1606602 1606633 1607735 1607740) (-967 "PRTITION.spad" 1605547 1605555 1606592 1606597) (-966 "PRTDAST.spad" 1605266 1605274 1605537 1605542) (-965 "PRS.spad" 1594828 1594845 1605222 1605227) (-964 "PRQAGG.spad" 1594259 1594269 1594796 1594823) (-963 "PROPLOG.spad" 1593662 1593670 1594249 1594254) (-962 "PROPFRML.spad" 1591580 1591591 1593652 1593657) (-961 "PROPERTY.spad" 1591074 1591082 1591570 1591575) (-960 "PRODUCT.spad" 1588754 1588766 1589040 1589095) (-959 "PR.spad" 1587140 1587152 1587845 1587972) (-958 "PRINT.spad" 1586892 1586900 1587130 1587135) (-957 "PRIMES.spad" 1585143 1585153 1586882 1586887) (-956 "PRIMELT.spad" 1583124 1583138 1585133 1585138) (-955 "PRIMCAT.spad" 1582747 1582755 1583114 1583119) (-954 "PRIMARR.spad" 1581752 1581762 1581930 1581957) (-953 "PRIMARR2.spad" 1580475 1580487 1581742 1581747) (-952 "PREASSOC.spad" 1579847 1579859 1580465 1580470) (-951 "PPCURVE.spad" 1578984 1578992 1579837 1579842) (-950 "PORTNUM.spad" 1578759 1578767 1578974 1578979) (-949 "POLYROOT.spad" 1577588 1577610 1578715 1578720) (-948 "POLY.spad" 1574885 1574895 1575402 1575529) (-947 "POLYLIFT.spad" 1574146 1574169 1574875 1574880) (-946 "POLYCATQ.spad" 1572248 1572270 1574136 1574141) (-945 "POLYCAT.spad" 1565654 1565675 1572116 1572243) (-944 "POLYCAT.spad" 1558362 1558385 1564826 1564831) (-943 "POLY2UP.spad" 1557810 1557824 1558352 1558357) (-942 "POLY2.spad" 1557405 1557417 1557800 1557805) (-941 "POLUTIL.spad" 1556346 1556375 1557361 1557366) (-940 "POLTOPOL.spad" 1555094 1555109 1556336 1556341) (-939 "POINT.spad" 1553933 1553943 1554020 1554047) (-938 "PNTHEORY.spad" 1550599 1550607 1553923 1553928) (-937 "PMTOOLS.spad" 1549356 1549370 1550589 1550594) (-936 "PMSYM.spad" 1548901 1548911 1549346 1549351) (-935 "PMQFCAT.spad" 1548488 1548502 1548891 1548896) (-934 "PMPRED.spad" 1547957 1547971 1548478 1548483) (-933 "PMPREDFS.spad" 1547401 1547423 1547947 1547952) (-932 "PMPLCAT.spad" 1546471 1546489 1547333 1547338) (-931 "PMLSAGG.spad" 1546052 1546066 1546461 1546466) (-930 "PMKERNEL.spad" 1545619 1545631 1546042 1546047) (-929 "PMINS.spad" 1545195 1545205 1545609 1545614) (-928 "PMFS.spad" 1544768 1544786 1545185 1545190) (-927 "PMDOWN.spad" 1544054 1544068 1544758 1544763) (-926 "PMASS.spad" 1543066 1543074 1544044 1544049) (-925 "PMASSFS.spad" 1542035 1542051 1543056 1543061) (-924 "PLOTTOOL.spad" 1541815 1541823 1542025 1542030) (-923 "PLOT.spad" 1536646 1536654 1541805 1541810) (-922 "PLOT3D.spad" 1533066 1533074 1536636 1536641) (-921 "PLOT1.spad" 1532207 1532217 1533056 1533061) (-920 "PLEQN.spad" 1519423 1519450 1532197 1532202) (-919 "PINTERP.spad" 1519039 1519058 1519413 1519418) (-918 "PINTERPA.spad" 1518821 1518837 1519029 1519034) (-917 "PI.spad" 1518428 1518436 1518795 1518816) (-916 "PID.spad" 1517384 1517392 1518354 1518423) (-915 "PICOERCE.spad" 1517041 1517051 1517374 1517379) (-914 "PGROEB.spad" 1515638 1515652 1517031 1517036) (-913 "PGE.spad" 1506891 1506899 1515628 1515633) (-912 "PGCD.spad" 1505773 1505790 1506881 1506886) (-911 "PFRPAC.spad" 1504916 1504926 1505763 1505768) (-910 "PFR.spad" 1501573 1501583 1504818 1504911) (-909 "PFOTOOLS.spad" 1500831 1500847 1501563 1501568) (-908 "PFOQ.spad" 1500201 1500219 1500821 1500826) (-907 "PFO.spad" 1499620 1499647 1500191 1500196) (-906 "PF.spad" 1499194 1499206 1499425 1499518) (-905 "PFECAT.spad" 1496860 1496868 1499120 1499189) (-904 "PFECAT.spad" 1494554 1494564 1496816 1496821) (-903 "PFBRU.spad" 1492424 1492436 1494544 1494549) (-902 "PFBR.spad" 1489962 1489985 1492414 1492419) (-901 "PERM.spad" 1485643 1485653 1489792 1489807) (-900 "PERMGRP.spad" 1480379 1480389 1485633 1485638) (-899 "PERMCAT.spad" 1478931 1478941 1480359 1480374) (-898 "PERMAN.spad" 1477463 1477477 1478921 1478926) (-897 "PENDTREE.spad" 1476802 1476812 1477092 1477097) (-896 "PDRING.spad" 1475293 1475303 1476782 1476797) (-895 "PDRING.spad" 1473792 1473804 1475283 1475288) (-894 "PDEPROB.spad" 1472807 1472815 1473782 1473787) (-893 "PDEPACK.spad" 1466809 1466817 1472797 1472802) (-892 "PDECOMP.spad" 1466271 1466288 1466799 1466804) (-891 "PDECAT.spad" 1464625 1464633 1466261 1466266) (-890 "PCOMP.spad" 1464476 1464489 1464615 1464620) (-889 "PBWLB.spad" 1463058 1463075 1464466 1464471) (-888 "PATTERN.spad" 1457489 1457499 1463048 1463053) (-887 "PATTERN2.spad" 1457225 1457237 1457479 1457484) (-886 "PATTERN1.spad" 1455527 1455543 1457215 1457220) (-885 "PATRES.spad" 1453074 1453086 1455517 1455522) (-884 "PATRES2.spad" 1452736 1452750 1453064 1453069) (-883 "PATMATCH.spad" 1450893 1450924 1452444 1452449) (-882 "PATMAB.spad" 1450318 1450328 1450883 1450888) (-881 "PATLRES.spad" 1449402 1449416 1450308 1450313) (-880 "PATAB.spad" 1449166 1449176 1449392 1449397) (-879 "PARTPERM.spad" 1446528 1446536 1449156 1449161) (-878 "PARSURF.spad" 1445956 1445984 1446518 1446523) (-877 "PARSU2.spad" 1445751 1445767 1445946 1445951) (-876 "script-parser.spad" 1445271 1445279 1445741 1445746) (-875 "PARSCURV.spad" 1444699 1444727 1445261 1445266) (-874 "PARSC2.spad" 1444488 1444504 1444689 1444694) (-873 "PARPCURV.spad" 1443946 1443974 1444478 1444483) (-872 "PARPC2.spad" 1443735 1443751 1443936 1443941) (-871 "PAN2EXPR.spad" 1443147 1443155 1443725 1443730) (-870 "PALETTE.spad" 1442117 1442125 1443137 1443142) (-869 "PAIR.spad" 1441100 1441113 1441705 1441710) (-868 "PADICRC.spad" 1438430 1438448 1439605 1439698) (-867 "PADICRAT.spad" 1436445 1436457 1436666 1436759) (-866 "PADIC.spad" 1436140 1436152 1436371 1436440) (-865 "PADICCT.spad" 1434681 1434693 1436066 1436135) (-864 "PADEPAC.spad" 1433360 1433379 1434671 1434676) (-863 "PADE.spad" 1432100 1432116 1433350 1433355) (-862 "OWP.spad" 1431340 1431370 1431958 1432025) (-861 "OVERSET.spad" 1430913 1430921 1431330 1431335) (-860 "OVAR.spad" 1430694 1430717 1430903 1430908) (-859 "OUT.spad" 1429778 1429786 1430684 1430689) (-858 "OUTFORM.spad" 1419074 1419082 1429768 1429773) (-857 "OUTBFILE.spad" 1418492 1418500 1419064 1419069) (-856 "OUTBCON.spad" 1417490 1417498 1418482 1418487) (-855 "OUTBCON.spad" 1416486 1416496 1417480 1417485) (-854 "OSI.spad" 1415961 1415969 1416476 1416481) (-853 "OSGROUP.spad" 1415879 1415887 1415951 1415956) (-852 "ORTHPOL.spad" 1414340 1414350 1415796 1415801) (-851 "OREUP.spad" 1413793 1413821 1414020 1414059) (-850 "ORESUP.spad" 1413092 1413116 1413473 1413512) (-849 "OREPCTO.spad" 1410911 1410923 1413012 1413017) (-848 "OREPCAT.spad" 1404968 1404978 1410867 1410906) (-847 "OREPCAT.spad" 1398915 1398927 1404816 1404821) (-846 "ORDSET.spad" 1398081 1398089 1398905 1398910) (-845 "ORDSET.spad" 1397245 1397255 1398071 1398076) (-844 "ORDRING.spad" 1396635 1396643 1397225 1397240) (-843 "ORDRING.spad" 1396033 1396043 1396625 1396630) (-842 "ORDMON.spad" 1395888 1395896 1396023 1396028) (-841 "ORDFUNS.spad" 1395014 1395030 1395878 1395883) (-840 "ORDFIN.spad" 1394834 1394842 1395004 1395009) (-839 "ORDCOMP.spad" 1393299 1393309 1394381 1394410) (-838 "ORDCOMP2.spad" 1392584 1392596 1393289 1393294) (-837 "OPTPROB.spad" 1391222 1391230 1392574 1392579) (-836 "OPTPACK.spad" 1383607 1383615 1391212 1391217) (-835 "OPTCAT.spad" 1381282 1381290 1383597 1383602) (-834 "OPSIG.spad" 1380934 1380942 1381272 1381277) (-833 "OPQUERY.spad" 1380483 1380491 1380924 1380929) (-832 "OP.spad" 1380225 1380235 1380305 1380372) (-831 "OPERCAT.spad" 1379813 1379823 1380215 1380220) (-830 "OPERCAT.spad" 1379399 1379411 1379803 1379808) (-829 "ONECOMP.spad" 1378144 1378154 1378946 1378975) (-828 "ONECOMP2.spad" 1377562 1377574 1378134 1378139) (-827 "OMSERVER.spad" 1376564 1376572 1377552 1377557) (-826 "OMSAGG.spad" 1376352 1376362 1376520 1376559) (-825 "OMPKG.spad" 1374964 1374972 1376342 1376347) (-824 "OM.spad" 1373929 1373937 1374954 1374959) (-823 "OMLO.spad" 1373354 1373366 1373815 1373854) (-822 "OMEXPR.spad" 1373188 1373198 1373344 1373349) (-821 "OMERR.spad" 1372731 1372739 1373178 1373183) (-820 "OMERRK.spad" 1371765 1371773 1372721 1372726) (-819 "OMENC.spad" 1371109 1371117 1371755 1371760) (-818 "OMDEV.spad" 1365398 1365406 1371099 1371104) (-817 "OMCONN.spad" 1364807 1364815 1365388 1365393) (-816 "OINTDOM.spad" 1364570 1364578 1364733 1364802) (-815 "OFMONOID.spad" 1360757 1360767 1364560 1364565) (-814 "ODVAR.spad" 1360018 1360028 1360747 1360752) (-813 "ODR.spad" 1359662 1359688 1359830 1359979) (-812 "ODPOL.spad" 1357008 1357018 1357348 1357475) (-811 "ODP.spad" 1346855 1346875 1347228 1347359) (-810 "ODETOOLS.spad" 1345438 1345457 1346845 1346850) (-809 "ODESYS.spad" 1343088 1343105 1345428 1345433) (-808 "ODERTRIC.spad" 1339029 1339046 1343045 1343050) (-807 "ODERED.spad" 1338416 1338440 1339019 1339024) (-806 "ODERAT.spad" 1335967 1335984 1338406 1338411) (-805 "ODEPRRIC.spad" 1332858 1332880 1335957 1335962) (-804 "ODEPROB.spad" 1332115 1332123 1332848 1332853) (-803 "ODEPRIM.spad" 1329389 1329411 1332105 1332110) (-802 "ODEPAL.spad" 1328765 1328789 1329379 1329384) (-801 "ODEPACK.spad" 1315367 1315375 1328755 1328760) (-800 "ODEINT.spad" 1314798 1314814 1315357 1315362) (-799 "ODEIFTBL.spad" 1312193 1312201 1314788 1314793) (-798 "ODEEF.spad" 1307560 1307576 1312183 1312188) (-797 "ODECONST.spad" 1307079 1307097 1307550 1307555) (-796 "ODECAT.spad" 1305675 1305683 1307069 1307074) (-795 "OCT.spad" 1303813 1303823 1304529 1304568) (-794 "OCTCT2.spad" 1303457 1303478 1303803 1303808) (-793 "OC.spad" 1301231 1301241 1303413 1303452) (-792 "OC.spad" 1298730 1298742 1300914 1300919) (-791 "OCAMON.spad" 1298578 1298586 1298720 1298725) (-790 "OASGP.spad" 1298393 1298401 1298568 1298573) (-789 "OAMONS.spad" 1297913 1297921 1298383 1298388) (-788 "OAMON.spad" 1297774 1297782 1297903 1297908) (-787 "OAGROUP.spad" 1297636 1297644 1297764 1297769) (-786 "NUMTUBE.spad" 1297223 1297239 1297626 1297631) (-785 "NUMQUAD.spad" 1285085 1285093 1297213 1297218) (-784 "NUMODE.spad" 1276221 1276229 1285075 1285080) (-783 "NUMINT.spad" 1273779 1273787 1276211 1276216) (-782 "NUMFMT.spad" 1272619 1272627 1273769 1273774) (-781 "NUMERIC.spad" 1264691 1264701 1272424 1272429) (-780 "NTSCAT.spad" 1263193 1263209 1264659 1264686) (-779 "NTPOLFN.spad" 1262738 1262748 1263110 1263115) (-778 "NSUP.spad" 1255748 1255758 1260288 1260441) (-777 "NSUP2.spad" 1255140 1255152 1255738 1255743) (-776 "NSMP.spad" 1251335 1251354 1251643 1251770) (-775 "NREP.spad" 1249707 1249721 1251325 1251330) (-774 "NPCOEF.spad" 1248953 1248973 1249697 1249702) (-773 "NORMRETR.spad" 1248551 1248590 1248943 1248948) (-772 "NORMPK.spad" 1246453 1246472 1248541 1248546) (-771 "NORMMA.spad" 1246141 1246167 1246443 1246448) (-770 "NONE.spad" 1245882 1245890 1246131 1246136) (-769 "NONE1.spad" 1245558 1245568 1245872 1245877) (-768 "NODE1.spad" 1245027 1245043 1245548 1245553) (-767 "NNI.spad" 1243914 1243922 1245001 1245022) (-766 "NLINSOL.spad" 1242536 1242546 1243904 1243909) (-765 "NIPROB.spad" 1241077 1241085 1242526 1242531) (-764 "NFINTBAS.spad" 1238537 1238554 1241067 1241072) (-763 "NETCLT.spad" 1238511 1238522 1238527 1238532) (-762 "NCODIV.spad" 1236709 1236725 1238501 1238506) (-761 "NCNTFRAC.spad" 1236351 1236365 1236699 1236704) (-760 "NCEP.spad" 1234511 1234525 1236341 1236346) (-759 "NASRING.spad" 1234107 1234115 1234501 1234506) (-758 "NASRING.spad" 1233701 1233711 1234097 1234102) (-757 "NARNG.spad" 1233045 1233053 1233691 1233696) (-756 "NARNG.spad" 1232387 1232397 1233035 1233040) (-755 "NAGSP.spad" 1231460 1231468 1232377 1232382) (-754 "NAGS.spad" 1220985 1220993 1231450 1231455) (-753 "NAGF07.spad" 1219378 1219386 1220975 1220980) (-752 "NAGF04.spad" 1213610 1213618 1219368 1219373) (-751 "NAGF02.spad" 1207419 1207427 1213600 1213605) (-750 "NAGF01.spad" 1203022 1203030 1207409 1207414) (-749 "NAGE04.spad" 1196482 1196490 1203012 1203017) (-748 "NAGE02.spad" 1186824 1186832 1196472 1196477) (-747 "NAGE01.spad" 1182708 1182716 1186814 1186819) (-746 "NAGD03.spad" 1180628 1180636 1182698 1182703) (-745 "NAGD02.spad" 1173159 1173167 1180618 1180623) (-744 "NAGD01.spad" 1167272 1167280 1173149 1173154) (-743 "NAGC06.spad" 1163059 1163067 1167262 1167267) (-742 "NAGC05.spad" 1161528 1161536 1163049 1163054) (-741 "NAGC02.spad" 1160783 1160791 1161518 1161523) (-740 "NAALG.spad" 1160318 1160328 1160751 1160778) (-739 "NAALG.spad" 1159873 1159885 1160308 1160313) (-738 "MULTSQFR.spad" 1156831 1156848 1159863 1159868) (-737 "MULTFACT.spad" 1156214 1156231 1156821 1156826) (-736 "MTSCAT.spad" 1154248 1154269 1156112 1156209) (-735 "MTHING.spad" 1153905 1153915 1154238 1154243) (-734 "MSYSCMD.spad" 1153339 1153347 1153895 1153900) (-733 "MSET.spad" 1151281 1151291 1153045 1153084) (-732 "MSETAGG.spad" 1151126 1151136 1151249 1151276) (-731 "MRING.spad" 1148097 1148109 1150834 1150901) (-730 "MRF2.spad" 1147665 1147679 1148087 1148092) (-729 "MRATFAC.spad" 1147211 1147228 1147655 1147660) (-728 "MPRFF.spad" 1145241 1145260 1147201 1147206) (-727 "MPOLY.spad" 1142676 1142691 1143035 1143162) (-726 "MPCPF.spad" 1141940 1141959 1142666 1142671) (-725 "MPC3.spad" 1141755 1141795 1141930 1141935) (-724 "MPC2.spad" 1141397 1141430 1141745 1141750) (-723 "MONOTOOL.spad" 1139732 1139749 1141387 1141392) (-722 "MONOID.spad" 1139051 1139059 1139722 1139727) (-721 "MONOID.spad" 1138368 1138378 1139041 1139046) (-720 "MONOGEN.spad" 1137114 1137127 1138228 1138363) (-719 "MONOGEN.spad" 1135882 1135897 1136998 1137003) (-718 "MONADWU.spad" 1133896 1133904 1135872 1135877) (-717 "MONADWU.spad" 1131908 1131918 1133886 1133891) (-716 "MONAD.spad" 1131052 1131060 1131898 1131903) (-715 "MONAD.spad" 1130194 1130204 1131042 1131047) (-714 "MOEBIUS.spad" 1128880 1128894 1130174 1130189) (-713 "MODULE.spad" 1128750 1128760 1128848 1128875) (-712 "MODULE.spad" 1128640 1128652 1128740 1128745) (-711 "MODRING.spad" 1127971 1128010 1128620 1128635) (-710 "MODOP.spad" 1126630 1126642 1127793 1127860) (-709 "MODMONOM.spad" 1126359 1126377 1126620 1126625) (-708 "MODMON.spad" 1123118 1123134 1123837 1123990) (-707 "MODFIELD.spad" 1122476 1122515 1123020 1123113) (-706 "MMLFORM.spad" 1121336 1121344 1122466 1122471) (-705 "MMAP.spad" 1121076 1121110 1121326 1121331) (-704 "MLO.spad" 1119503 1119513 1121032 1121071) (-703 "MLIFT.spad" 1118075 1118092 1119493 1119498) (-702 "MKUCFUNC.spad" 1117608 1117626 1118065 1118070) (-701 "MKRECORD.spad" 1117210 1117223 1117598 1117603) (-700 "MKFUNC.spad" 1116591 1116601 1117200 1117205) (-699 "MKFLCFN.spad" 1115547 1115557 1116581 1116586) (-698 "MKCHSET.spad" 1115412 1115422 1115537 1115542) (-697 "MKBCFUNC.spad" 1114897 1114915 1115402 1115407) (-696 "MINT.spad" 1114336 1114344 1114799 1114892) (-695 "MHROWRED.spad" 1112837 1112847 1114326 1114331) (-694 "MFLOAT.spad" 1111353 1111361 1112727 1112832) (-693 "MFINFACT.spad" 1110753 1110775 1111343 1111348) (-692 "MESH.spad" 1108485 1108493 1110743 1110748) (-691 "MDDFACT.spad" 1106678 1106688 1108475 1108480) (-690 "MDAGG.spad" 1105965 1105975 1106658 1106673) (-689 "MCMPLX.spad" 1101939 1101947 1102553 1102754) (-688 "MCDEN.spad" 1101147 1101159 1101929 1101934) (-687 "MCALCFN.spad" 1098249 1098275 1101137 1101142) (-686 "MAYBE.spad" 1097533 1097544 1098239 1098244) (-685 "MATSTOR.spad" 1094809 1094819 1097523 1097528) (-684 "MATRIX.spad" 1093513 1093523 1093997 1094024) (-683 "MATLIN.spad" 1090839 1090863 1093397 1093402) (-682 "MATCAT.spad" 1082424 1082446 1090807 1090834) (-681 "MATCAT.spad" 1073881 1073905 1082266 1082271) (-680 "MATCAT2.spad" 1073149 1073197 1073871 1073876) (-679 "MAPPKG3.spad" 1072048 1072062 1073139 1073144) (-678 "MAPPKG2.spad" 1071382 1071394 1072038 1072043) (-677 "MAPPKG1.spad" 1070200 1070210 1071372 1071377) (-676 "MAPPAST.spad" 1069513 1069521 1070190 1070195) (-675 "MAPHACK3.spad" 1069321 1069335 1069503 1069508) (-674 "MAPHACK2.spad" 1069086 1069098 1069311 1069316) (-673 "MAPHACK1.spad" 1068716 1068726 1069076 1069081) (-672 "MAGMA.spad" 1066506 1066523 1068706 1068711) (-671 "MACROAST.spad" 1066085 1066093 1066496 1066501) (-670 "M3D.spad" 1063781 1063791 1065463 1065468) (-669 "LZSTAGG.spad" 1061009 1061019 1063771 1063776) (-668 "LZSTAGG.spad" 1058235 1058247 1060999 1061004) (-667 "LWORD.spad" 1054940 1054957 1058225 1058230) (-666 "LSTAST.spad" 1054724 1054732 1054930 1054935) (-665 "LSQM.spad" 1052950 1052964 1053348 1053399) (-664 "LSPP.spad" 1052483 1052500 1052940 1052945) (-663 "LSMP.spad" 1051323 1051351 1052473 1052478) (-662 "LSMP1.spad" 1049127 1049141 1051313 1051318) (-661 "LSAGG.spad" 1048796 1048806 1049095 1049122) (-660 "LSAGG.spad" 1048485 1048497 1048786 1048791) (-659 "LPOLY.spad" 1047439 1047458 1048341 1048410) (-658 "LPEFRAC.spad" 1046696 1046706 1047429 1047434) (-657 "LO.spad" 1046097 1046111 1046630 1046657) (-656 "LOGIC.spad" 1045699 1045707 1046087 1046092) (-655 "LOGIC.spad" 1045299 1045309 1045689 1045694) (-654 "LODOOPS.spad" 1044217 1044229 1045289 1045294) (-653 "LODO.spad" 1043601 1043617 1043897 1043936) (-652 "LODOF.spad" 1042645 1042662 1043558 1043563) (-651 "LODOCAT.spad" 1041303 1041313 1042601 1042640) (-650 "LODOCAT.spad" 1039959 1039971 1041259 1041264) (-649 "LODO2.spad" 1039232 1039244 1039639 1039678) (-648 "LODO1.spad" 1038632 1038642 1038912 1038951) (-647 "LODEEF.spad" 1037404 1037422 1038622 1038627) (-646 "LNAGG.spad" 1033206 1033216 1037394 1037399) (-645 "LNAGG.spad" 1028972 1028984 1033162 1033167) (-644 "LMOPS.spad" 1025708 1025725 1028962 1028967) (-643 "LMODULE.spad" 1025350 1025360 1025698 1025703) (-642 "LMDICT.spad" 1024633 1024643 1024901 1024928) (-641 "LITERAL.spad" 1024539 1024550 1024623 1024628) (-640 "LIST.spad" 1022257 1022267 1023686 1023713) (-639 "LIST3.spad" 1021548 1021562 1022247 1022252) (-638 "LIST2.spad" 1020188 1020200 1021538 1021543) (-637 "LIST2MAP.spad" 1017065 1017077 1020178 1020183) (-636 "LINEXP.spad" 1016497 1016507 1017045 1017060) (-635 "LINDEP.spad" 1015274 1015286 1016409 1016414) (-634 "LIMITRF.spad" 1013188 1013198 1015264 1015269) (-633 "LIMITPS.spad" 1012071 1012084 1013178 1013183) (-632 "LIE.spad" 1010085 1010097 1011361 1011506) (-631 "LIECAT.spad" 1009561 1009571 1010011 1010080) (-630 "LIECAT.spad" 1009065 1009077 1009517 1009522) (-629 "LIB.spad" 1007113 1007121 1007724 1007739) (-628 "LGROBP.spad" 1004466 1004485 1007103 1007108) (-627 "LF.spad" 1003385 1003401 1004456 1004461) (-626 "LFCAT.spad" 1002404 1002412 1003375 1003380) (-625 "LEXTRIPK.spad" 997907 997922 1002394 1002399) (-624 "LEXP.spad" 995910 995937 997887 997902) (-623 "LETAST.spad" 995609 995617 995900 995905) (-622 "LEADCDET.spad" 993993 994010 995599 995604) (-621 "LAZM3PK.spad" 992697 992719 993983 993988) (-620 "LAUPOL.spad" 991386 991399 992290 992359) (-619 "LAPLACE.spad" 990959 990975 991376 991381) (-618 "LA.spad" 990399 990413 990881 990920) (-617 "LALG.spad" 990175 990185 990379 990394) (-616 "LALG.spad" 989959 989971 990165 990170) (-615 "KVTFROM.spad" 989694 989704 989949 989954) (-614 "KTVLOGIC.spad" 989117 989125 989684 989689) (-613 "KRCFROM.spad" 988855 988865 989107 989112) (-612 "KOVACIC.spad" 987568 987585 988845 988850) (-611 "KONVERT.spad" 987290 987300 987558 987563) (-610 "KOERCE.spad" 987027 987037 987280 987285) (-609 "KERNEL.spad" 985562 985572 986811 986816) (-608 "KERNEL2.spad" 985265 985277 985552 985557) (-607 "KDAGG.spad" 984368 984390 985245 985260) (-606 "KDAGG.spad" 983479 983503 984358 984363) (-605 "KAFILE.spad" 982442 982458 982677 982704) (-604 "JORDAN.spad" 980269 980281 981732 981877) (-603 "JOINAST.spad" 979963 979971 980259 980264) (-602 "JAVACODE.spad" 979829 979837 979953 979958) (-601 "IXAGG.spad" 977952 977976 979819 979824) (-600 "IXAGG.spad" 975930 975956 977799 977804) (-599 "IVECTOR.spad" 974701 974716 974856 974883) (-598 "ITUPLE.spad" 973846 973856 974691 974696) (-597 "ITRIGMNP.spad" 972657 972676 973836 973841) (-596 "ITFUN3.spad" 972151 972165 972647 972652) (-595 "ITFUN2.spad" 971881 971893 972141 972146) (-594 "ITAYLOR.spad" 969673 969688 971717 971842) (-593 "ISUPS.spad" 962084 962099 968647 968744) (-592 "ISUMP.spad" 961581 961597 962074 962079) (-591 "ISTRING.spad" 960584 960597 960750 960777) (-590 "ISAST.spad" 960303 960311 960574 960579) (-589 "IRURPK.spad" 959016 959035 960293 960298) (-588 "IRSN.spad" 956976 956984 959006 959011) (-587 "IRRF2F.spad" 955451 955461 956932 956937) (-586 "IRREDFFX.spad" 955052 955063 955441 955446) (-585 "IROOT.spad" 953383 953393 955042 955047) (-584 "IR.spad" 951172 951186 953238 953265) (-583 "IR2.spad" 950192 950208 951162 951167) (-582 "IR2F.spad" 949392 949408 950182 950187) (-581 "IPRNTPK.spad" 949152 949160 949382 949387) (-580 "IPF.spad" 948717 948729 948957 949050) (-579 "IPADIC.spad" 948478 948504 948643 948712) (-578 "IP4ADDR.spad" 948035 948043 948468 948473) (-577 "IOMODE.spad" 947656 947664 948025 948030) (-576 "IOBFILE.spad" 947017 947025 947646 947651) (-575 "IOBCON.spad" 946882 946890 947007 947012) (-574 "INVLAPLA.spad" 946527 946543 946872 946877) (-573 "INTTR.spad" 939773 939790 946517 946522) (-572 "INTTOOLS.spad" 937484 937500 939347 939352) (-571 "INTSLPE.spad" 936790 936798 937474 937479) (-570 "INTRVL.spad" 936356 936366 936704 936785) (-569 "INTRF.spad" 934720 934734 936346 936351) (-568 "INTRET.spad" 934152 934162 934710 934715) (-567 "INTRAT.spad" 932827 932844 934142 934147) (-566 "INTPM.spad" 931190 931206 932470 932475) (-565 "INTPAF.spad" 928958 928976 931122 931127) (-564 "INTPACK.spad" 919268 919276 928948 928953) (-563 "INT.spad" 918629 918637 919122 919263) (-562 "INTHERTR.spad" 917895 917912 918619 918624) (-561 "INTHERAL.spad" 917561 917585 917885 917890) (-560 "INTHEORY.spad" 913974 913982 917551 917556) (-559 "INTG0.spad" 907437 907455 913906 913911) (-558 "INTFTBL.spad" 901466 901474 907427 907432) (-557 "INTFACT.spad" 900525 900535 901456 901461) (-556 "INTEF.spad" 898840 898856 900515 900520) (-555 "INTDOM.spad" 897455 897463 898766 898835) (-554 "INTDOM.spad" 896132 896142 897445 897450) (-553 "INTCAT.spad" 894385 894395 896046 896127) (-552 "INTBIT.spad" 893888 893896 894375 894380) (-551 "INTALG.spad" 893070 893097 893878 893883) (-550 "INTAF.spad" 892562 892578 893060 893065) (-549 "INTABL.spad" 891080 891111 891243 891270) (-548 "INT8.spad" 890960 890968 891070 891075) (-547 "INT32.spad" 890839 890847 890950 890955) (-546 "INT16.spad" 890718 890726 890829 890834) (-545 "INS.spad" 888185 888193 890620 890713) (-544 "INS.spad" 885738 885748 888175 888180) (-543 "INPSIGN.spad" 885172 885185 885728 885733) (-542 "INPRODPF.spad" 884238 884257 885162 885167) (-541 "INPRODFF.spad" 883296 883320 884228 884233) (-540 "INNMFACT.spad" 882267 882284 883286 883291) (-539 "INMODGCD.spad" 881751 881781 882257 882262) (-538 "INFSP.spad" 880036 880058 881741 881746) (-537 "INFPROD0.spad" 879086 879105 880026 880031) (-536 "INFORM.spad" 876247 876255 879076 879081) (-535 "INFORM1.spad" 875872 875882 876237 876242) (-534 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diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase
index 9c3dd555..f7e35655 100644
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155755) ((-31 . -609) 155721) ((-50 . -1051) T) ((-250 . -721) 155631) ((-249 . -721) 155541) ((-1201 . -1092) T) ((-664 . -23) T) ((-579 . -1051) T) ((-517 . -1051) T) ((-378 . -1050) 155506) ((-321 . -111) 155481) ((-73 . -382) T) ((-73 . -394) T) ((-1019 . -38) 155418) ((-688 . -399) 155400) ((-99 . -102) T) ((-706 . -1092) T) ((-998 . -144) 155372) ((-998 . -146) 155344) ((-378 . -111) 155300) ((-318 . -1211) 155279) ((-473 . -997) 155245) ((-353 . -38) 155210) ((-40 . -369) 155182) ((-868 . -609) 155054) ((-127 . -125) 155038) ((-121 . -125) 155022) ((-831 . -1050) 154992) ((-828 . -21) 154944) ((-822 . -1050) 154928) ((-828 . -25) 154880) ((-318 . -554) 154831) ((-516 . -612) 154812) ((-562 . -823) T) ((-239 . -1207) T) ((-1029 . -612) 154781) ((-831 . -111) 154746) ((-822 . -111) 154725) ((-1240 . -609) 154707) ((-1219 . -609) 154689) ((-1219 . -610) 154360) ((-1164 . -904) 154339) ((-1117 . -904) 154318) ((-48 . -38) 154283) ((-1278 . -1104) T) ((-598 . -609) 154195) ((-598 . 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153098) ((-326 . -513) 153031) ((-495 . -285) 153008) ((-378 . -242) T) ((-378 . -232) T) ((-831 . -1044) T) ((-822 . -1044) T) ((-707 . -944) 152977) ((-695 . -845) T) ((-473 . -609) 152959) ((-822 . -232) 152938) ((-133 . -845) T) ((-652 . -1092) T) ((-1180 . -600) 152917) ((-548 . -1183) 152896) ((-335 . -1092) T) ((-318 . -362) 152875) ((-406 . -146) 152854) ((-406 . -144) 152833) ((-959 . -1104) 152732) ((-239 . -895) 152664) ((-810 . -1104) 152574) ((-648 . -847) 152558) ((-478 . -600) 152537) ((-548 . -107) 152487) ((-999 . -376) 152469) ((-999 . -337) 152451) ((-97 . -1092) T) ((-959 . -23) 152262) ((-476 . -21) T) ((-476 . -25) T) ((-810 . -23) 152132) ((-1168 . -609) 152114) ((-59 . -19) 152098) ((-1168 . -610) 152020) ((-1164 . -721) T) ((-1117 . -721) T) ((-515 . -19) 152004) ((-495 . -19) 151988) ((-59 . -600) 151965) ((-1079 . -1092) T) ((-896 . -102) 151943) ((-849 . -721) T) ((-777 . -1092) T) ((-515 . -600) 151920) ((-495 . -600) 151897) ((-775 . -1092) T) ((-775 . 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-609) 148772) ((-378 . -790) T) ((-222 . -1092) T) ((-378 . -787) T) ((-224 . -789) T) ((-224 . -786) T) ((-59 . -610) 148733) ((-59 . -609) 148645) ((-224 . -721) T) ((-515 . -610) 148606) ((-515 . -609) 148518) ((-496 . -609) 148450) ((-495 . -610) 148411) ((-495 . -609) 148323) ((-1072 . -362) 148274) ((-40 . -410) 148251) ((-77 . -1207) T) ((-866 . -904) NIL) ((-358 . -328) 148235) ((-358 . -362) T) ((-352 . -328) 148219) ((-352 . -362) T) ((-344 . -328) 148203) ((-344 . -362) T) ((-315 . -283) 148182) ((-108 . -362) T) ((-70 . -1207) T) ((-1220 . -337) 148134) ((-866 . -642) 148079) ((-1220 . -376) 148031) ((-959 . -130) 147886) ((-810 . -130) 147756) ((-953 . -645) 147740) ((-1079 . -171) 147651) ((-953 . -372) 147635) ((-1055 . -789) T) ((-1055 . -786) T) ((-867 . -612) 147533) ((-777 . -171) 147424) ((-775 . -171) 147335) ((-811 . -47) 147297) ((-1055 . -721) T) ((-326 . -488) 147281) ((-947 . -721) T) ((-453 . -171) 147192) ((-244 . -285) 147169) ((-1269 . -308) 147107) ((-480 . -721) T) ((-1248 . -895) 147020) ((-1241 . -895) 146926) ((-1240 . -1050) 146761) ((-1220 . -895) 146594) ((-1219 . -1050) 146402) ((-1201 . -289) 146381) ((-1175 . -367) T) ((-1174 . -367) T) ((-1138 . -150) 146365) ((-1112 . -102) T) ((-1110 . -1092) T) ((-1072 . -23) T) ((-1067 . -102) T) ((-922 . -950) T) ((-732 . -308) 146303) ((-75 . -1207) T) ((-30 . -950) T) ((-168 . -904) 146256) ((-658 . -381) 146228) ((-112 . -839) T) ((-1 . -609) 146210) ((-1072 . -1104) T) ((-128 . -645) 146192) ((-50 . -616) 146176) ((-998 . -408) 146148) ((-592 . -895) 146061) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 146043) ((-867 . -1044) T) ((-828 . -845) 146022) ((-81 . -1207) T) ((-706 . -289) T) ((-40 . -1051) T) ((-579 . -171) T) ((-517 . -171) T) ((-510 . -609) 146004) ((-168 . -642) 145914) ((-506 . -609) 145896) ((-350 . -146) 145878) ((-350 . -144) T) ((-358 . -1104) T) ((-352 . -1104) T) ((-344 . -1104) T) ((-999 . -306) T) ((-909 . -306) T) ((-867 . -242) T) ((-108 . -1104) T) 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143948) ((-865 . -1051) T) ((-222 . -616) 143925) ((-326 . -285) 143902) ((-473 . -111) 143723) ((-1240 . -1044) T) ((-1219 . -1044) T) ((-811 . -376) 143707) ((-168 . -721) T) ((-648 . -102) T) ((-1240 . -242) 143686) ((-1240 . -232) 143638) ((-1219 . -232) 143543) ((-1219 . -242) 143522) ((-998 . -401) NIL) ((-664 . -635) 143470) ((-315 . -38) 143380) ((-312 . -38) 143309) ((-69 . -609) 143291) ((-318 . -492) 143257) ((-1180 . -287) 143236) ((-1214 . -845) T) ((-1105 . -1104) 143146) ((-83 . -1207) T) ((-61 . -609) 143128) ((-478 . -287) 143107) ((-1271 . -1033) 143084) ((-1156 . -1092) T) ((-1105 . -23) 142954) ((-811 . -895) 142890) ((-1229 . -721) T) ((-1094 . -1207) T) ((-473 . -612) 142716) ((-1079 . -289) 142647) ((-961 . -1092) T) ((-888 . -102) T) ((-777 . -289) 142558) ((-326 . -19) 142542) ((-59 . -287) 142519) ((-775 . -289) 142450) ((-850 . -721) T) ((-117 . -843) NIL) ((-515 . -287) 142427) ((-326 . -600) 142404) ((-495 . -287) 142381) ((-453 . -289) 142312) ((-1030 . -308) 142163) ((-675 . -489) 142144) ((-569 . -721) T) ((-670 . -489) 142125) ((-675 . -609) 142075) ((-670 . -609) 142041) ((-656 . -609) 142023) ((-477 . -489) 142004) ((-477 . -609) 141970) ((-244 . -610) 141931) ((-244 . -489) 141908) ((-137 . -489) 141889) ((-136 . -489) 141870) ((-132 . -489) 141851) ((-244 . -609) 141743) ((-212 . -102) T) ((-137 . -609) 141709) ((-136 . -609) 141675) ((-132 . -609) 141641) ((-1139 . -34) T) ((-938 . -1207) T) ((-342 . -712) 141586) ((-664 . -25) T) ((-664 . -21) T) ((-1168 . -612) 141567) ((-473 . -1044) T) ((-631 . -416) 141532) ((-603 . -416) 141497) ((-1112 . -1143) T) ((-579 . -289) T) ((-517 . -289) T) ((-1241 . -306) 141476) ((-473 . -232) 141428) ((-473 . -242) 141407) ((-1220 . -306) 141386) ((-1220 . -1017) NIL) ((-1072 . -130) T) ((-867 . -790) 141365) ((-143 . -102) T) ((-40 . -1092) T) ((-867 . -787) 141344) ((-639 . -1005) 141328) ((-578 . -1051) T) ((-562 . -1051) T) ((-494 . -1051) T) ((-406 . -451) T) ((-358 . -130) T) ((-315 . -399) 141312) ((-312 . -399) 141273) ((-352 . -130) T) ((-344 . -130) T) ((-1173 . -1092) T) ((-1112 . -38) 141260) ((-1086 . -609) 141227) ((-108 . -130) T) ((-949 . -1092) T) ((-916 . -1092) T) ((-766 . -1092) T) ((-666 . -1092) T) ((-695 . -146) T) ((-116 . -146) T) ((-1278 . -21) T) ((-1278 . -25) T) ((-1276 . -21) T) ((-1276 . -25) T) ((-658 . -1050) 141211) ((-530 . -845) T) ((-499 . -845) T) ((-354 . -1050) 141163) ((-351 . -1050) 141115) ((-343 . -1050) 141067) ((-250 . -1207) T) ((-249 . -1207) T) ((-263 . -1050) 140910) ((-246 . -1050) 140753) ((-658 . -111) 140732) ((-546 . -839) T) ((-354 . -111) 140670) ((-351 . -111) 140608) ((-343 . -111) 140546) ((-263 . -111) 140375) ((-246 . -111) 140204) ((-812 . -1211) 140183) ((-619 . -410) 140167) ((-44 . -21) T) ((-44 . -25) T) ((-810 . -635) 140073) ((-812 . -554) 140052) ((-250 . -1033) 139879) ((-249 . -1033) 139706) ((-126 . -119) 139690) ((-905 . -1050) 139655) ((-707 . -102) T) ((-693 . -1051) T) ((-535 . -614) 139558) 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137425) ((-354 . -242) T) ((-351 . -232) 137404) ((-351 . -242) T) ((-343 . -232) 137383) ((-343 . -242) T) ((-246 . -325) 137340) ((-263 . -325) 137312) ((-263 . -232) 137291) ((-1148 . -150) 137275) ((-250 . -895) 137207) ((-249 . -895) 137139) ((-1074 . -845) T) ((-413 . -1104) T) ((-1048 . -23) T) ((-905 . -1044) T) ((-321 . -642) 137121) ((-1019 . -843) T) ((-1201 . -997) 137087) ((-1165 . -915) 137066) ((-1159 . -915) 137045) ((-1159 . -815) NIL) ((-905 . -242) T) ((-812 . -362) 137024) ((-384 . -23) T) ((-127 . -1092) 137002) ((-121 . -1092) 136980) ((-905 . -232) T) ((-128 . -34) T) ((-378 . -642) 136945) ((-865 . -712) 136932) ((-1041 . -150) 136897) ((-40 . -171) T) ((-688 . -410) 136879) ((-707 . -308) 136866) ((-831 . -642) 136826) ((-822 . -642) 136800) ((-318 . -25) T) ((-318 . -21) T) ((-652 . -285) 136779) ((-578 . -1092) T) ((-562 . -1092) T) ((-494 . -1092) T) ((-244 . -287) 136756) ((-312 . -230) 136717) ((-1164 . -881) NIL) ((-55 . -1092) T) ((-1117 . -881) 136576) 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-25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -554) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -612) 134753) ((-137 . -612) 134734) ((-136 . -612) 134715) ((-132 . -612) 134696) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1051) T) ((-578 . -171) T) ((-562 . -171) T) ((-494 . -171) T) ((-652 . -609) 134678) ((-732 . -731) 134662) ((-335 . -609) 134644) ((-68 . -382) T) ((-68 . -394) T) ((-1094 . -107) 134628) ((-1055 . -881) 134610) ((-947 . -881) 134535) ((-647 . -1104) T) ((-619 . -712) 134522) ((-480 . -881) NIL) ((-1138 . -102) T) ((-1086 . -614) 134506) ((-1055 . -1033) 134488) ((-97 . -609) 134470) ((-476 . -146) T) ((-947 . -1033) 134350) ((-117 . -712) 134295) ((-647 . -23) T) ((-480 . -1033) 134171) ((-1079 . -610) NIL) ((-1079 . -609) 134153) ((-777 . -610) NIL) ((-777 . -609) 134114) ((-775 . -610) 133748) ((-775 . -609) 133662) ((-1105 . -635) 133568) ((-460 . -609) 133550) ((-453 . -609) 133532) ((-453 . -610) 133393) ((-1030 . -228) 133339) ((-867 . -904) 133318) ((-126 . -34) T) ((-812 . -130) T) ((-643 . -609) 133300) ((-576 . -102) T) ((-354 . -1275) 133284) ((-351 . -1275) 133268) ((-343 . -1275) 133252) ((-127 . -513) 133185) ((-121 . -513) 133118) ((-510 . -787) T) ((-510 . -790) T) ((-509 . -789) T) ((-103 . -308) 133056) ((-221 . -102) 133034) ((-688 . -1092) T) ((-693 . -171) T) ((-867 . -642) 132986) ((-65 . -383) T) ((-274 . -609) 132968) ((-65 . -394) T) ((-947 . -376) 132952) ((-865 . -289) T) ((-50 . -609) 132934) ((-994 . -38) 132882) ((-579 . -609) 132864) ((-480 . -376) 132848) ((-579 . -610) 132830) ((-517 . -609) 132812) ((-905 . -1275) 132799) ((-866 . -1207) T) ((-695 . -451) T) ((-494 . -513) 132765) ((-486 . -362) T) ((-354 . -367) 132744) ((-351 . -367) 132723) ((-343 . -367) 132702) ((-709 . -721) T) ((-216 . -362) T) ((-116 . -451) T) ((-1279 . -1270) 132686) ((-866 . -879) 132663) ((-866 . -881) NIL) ((-959 . -845) 132562) ((-810 . -845) 132513) ((-648 . -650) 132497) ((-1193 . -34) T) ((-170 . -609) 132479) ((-1105 . -21) 132389) ((-1105 . -25) 132240) ((-866 . -1033) 132217) ((-947 . -895) 132198) ((-1229 . -47) 132175) ((-905 . -367) T) ((-59 . -645) 132159) ((-515 . -645) 132143) ((-480 . -895) 132120) ((-71 . -440) T) ((-71 . -394) T) ((-495 . -645) 132104) ((-59 . -372) 132088) ((-619 . -171) T) ((-515 . -372) 132072) ((-495 . -372) 132056) ((-822 . -703) 132040) ((-1164 . -306) 132019) ((-1170 . -130) T) ((-117 . -171) T) ((-1138 . -308) 131957) ((-168 . -1207) T) ((-631 . -739) 131941) ((-603 . -739) 131925) ((-1268 . -130) T) ((-1241 . -915) 131904) ((-1220 . -915) 131883) ((-1220 . -815) NIL) ((-688 . -712) 131833) ((-1219 . -904) 131786) ((-1019 . -1092) T) ((-866 . -376) 131763) ((-866 . -337) 131740) ((-900 . -1104) T) ((-168 . -879) 131724) ((-168 . -881) 131649) ((-486 . -1104) T) ((-353 . -1092) T) ((-216 . -1104) T) ((-76 . -440) T) ((-76 . -394) T) ((-168 . -1033) 131545) ((-318 . -845) T) ((-1256 . -513) 131478) ((-1240 . -642) 131375) ((-1219 . -642) 131245) 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-895) 129927) ((-693 . -289) T) ((-688 . -171) T) ((-706 . -111) 129883) ((-1284 . -1051) T) ((-1229 . -376) 129867) ((-417 . -1211) 129845) ((-1110 . -609) 129827) ((-312 . -843) NIL) ((-417 . -554) T) ((-224 . -306) T) ((-1219 . -786) 129780) ((-1219 . -789) 129733) ((-1240 . -721) T) ((-1219 . -721) T) ((-48 . -712) 129698) ((-224 . -1017) T) ((-350 . -1263) 129675) ((-1242 . -410) 129641) ((-713 . -721) T) ((-1229 . -895) 129584) ((-1201 . -612) 129466) ((-112 . -609) 129448) ((-112 . -610) 129430) ((-713 . -472) T) ((-706 . -612) 129380) ((-481 . -21) 129290) ((-127 . -488) 129274) ((-121 . -488) 129258) ((-481 . -25) 129109) ((-619 . -289) T) ((-583 . -1050) 129084) ((-436 . -1092) T) ((-1055 . -306) T) ((-117 . -289) T) ((-1096 . -102) T) ((-998 . -102) T) ((-583 . -111) 129052) ((-1134 . -308) 128990) ((-1201 . -1044) T) ((-1055 . -1017) T) ((-66 . -1207) T) ((-1048 . -25) T) ((-1048 . -21) T) ((-706 . -1044) T) ((-384 . -21) T) ((-384 . -25) T) ((-688 . -513) NIL) ((-1019 . -171) T) ((-706 . -242) T) ((-1055 . -544) T) ((-505 . -102) T) ((-501 . -102) T) ((-353 . -171) T) ((-342 . -609) 128972) ((-393 . -609) 128954) ((-473 . -721) T) ((-1112 . -843) T) ((-887 . -1033) 128922) ((-108 . -845) T) ((-652 . -1050) 128906) ((-486 . -130) T) ((-1242 . -1051) T) ((-216 . -130) T) ((-1148 . -102) 128884) ((-99 . -1092) T) ((-244 . -660) 128868) ((-244 . -645) 128852) ((-652 . -111) 128831) ((-583 . -612) 128815) ((-315 . -410) 128799) ((-244 . -372) 128783) ((-1151 . -234) 128730) ((-994 . -230) 128714) ((-74 . -1207) T) ((-48 . -171) T) ((-695 . -386) T) ((-695 . -142) T) ((-1279 . -102) T) ((-1187 . -612) 128696) ((-1079 . -1050) 128539) ((-263 . -904) 128518) ((-246 . -904) 128497) ((-777 . -1050) 128320) ((-775 . -1050) 128163) ((-604 . -1207) T) ((-1156 . -609) 128145) ((-1079 . -111) 127974) ((-1041 . -102) T) ((-474 . -1207) T) ((-460 . -1050) 127945) ((-453 . -1050) 127788) ((-658 . -642) 127772) ((-866 . -306) T) ((-777 . -111) 127581) ((-775 . -111) 127410) ((-354 . -642) 127362) ((-351 . -642) 127314) ((-343 . -642) 127266) ((-263 . -642) 127191) ((-246 . -642) 127116) ((-1150 . -845) T) ((-1080 . -1033) 127100) ((-460 . -111) 127061) ((-453 . -111) 126890) ((-1068 . -1033) 126867) ((-995 . -34) T) ((-961 . -609) 126849) ((-953 . -1207) T) ((-126 . -1005) 126833) ((-958 . -1104) T) ((-866 . -1017) NIL) ((-730 . -1104) T) ((-710 . -1104) T) ((-652 . -612) 126751) ((-1256 . -488) 126735) ((-1134 . -38) 126695) ((-958 . -23) T) ((-860 . -1092) T) ((-838 . -102) T) ((-812 . -21) T) ((-812 . -25) T) ((-730 . -23) T) ((-710 . -23) T) ((-110 . -655) T) ((-905 . -642) 126660) ((-579 . -1050) 126625) ((-517 . -1050) 126570) ((-226 . -57) 126528) ((-452 . -23) T) ((-406 . -102) T) ((-262 . -102) T) ((-688 . -289) T) ((-861 . -38) 126498) ((-579 . -111) 126454) ((-517 . -111) 126383) ((-1079 . -612) 126119) ((-417 . -1104) T) ((-315 . -1051) 126009) ((-312 . -1051) T) ((-128 . -1207) T) ((-777 . -612) 125757) ((-775 . -612) 125523) ((-652 . -1044) T) ((-1284 . -1092) T) ((-453 . -612) 125308) ((-168 . -306) 125239) ((-417 . -23) T) ((-40 . -609) 125221) ((-40 . -610) 125205) ((-108 . -987) 125187) ((-116 . -864) 125171) ((-643 . -612) 125155) ((-48 . -513) 125121) ((-1193 . -1005) 125105) ((-1173 . -609) 125072) ((-1180 . -34) T) ((-949 . -609) 125038) ((-916 . -609) 125020) ((-1105 . -845) 124971) ((-766 . -609) 124953) ((-666 . -609) 124935) ((-1148 . -308) 124873) ((-478 . -34) T) ((-1084 . -1207) T) ((-476 . -451) T) ((-1133 . -34) T) ((-1079 . -1044) T) ((-50 . -612) 124842) ((-777 . -1044) T) ((-775 . -1044) T) ((-641 . -234) 124826) ((-628 . -234) 124772) ((-579 . -612) 124722) ((-517 . -612) 124652) ((-1229 . -306) 124631) ((-1079 . -325) 124592) ((-453 . -1044) T) ((-1170 . -21) T) ((-1079 . -232) 124571) ((-777 . -325) 124548) ((-777 . -232) T) ((-775 . -325) 124520) ((-726 . -1211) 124499) ((-326 . -645) 124483) ((-1170 . -25) T) ((-59 . -34) T) ((-518 . -34) T) ((-515 . -34) T) ((-453 . -325) 124462) ((-326 . -372) 124446) ((-496 . -34) T) ((-495 . -34) T) ((-998 . -1143) NIL) ((-726 . -554) 124377) ((-631 . -102) T) ((-603 . -102) T) ((-354 . -721) T) ((-351 . -721) T) ((-343 . -721) T) ((-263 . -721) T) ((-246 . -721) T) ((-1041 . -308) 124285) ((-896 . -1092) 124263) ((-50 . -1044) T) ((-1268 . -21) T) ((-1268 . -25) T) ((-1166 . -554) 124242) ((-1165 . -1211) 124221) ((-579 . -1044) T) ((-517 . -1044) T) ((-1159 . -1211) 124200) ((-360 . -1033) 124184) ((-321 . -1033) 124168) ((-1019 . -289) T) ((-378 . -881) 124150) ((-1165 . -554) 124101) ((-1159 . -554) 124052) ((-998 . -38) 123997) ((-794 . -1104) T) ((-905 . -721) T) ((-579 . -242) T) ((-579 . -232) T) ((-517 . -232) T) ((-517 . -242) T) ((-1118 . -554) 123976) ((-353 . -289) T) ((-641 . -689) 123960) ((-378 . -1033) 123920) ((-1112 . -1051) T) ((-103 . -125) 123904) ((-794 . -23) T) ((-1278 . -1273) 123880) ((-1256 . -285) 123857) ((-406 . -308) 123822) ((-1276 . -1273) 123801) ((-1242 . -1092) T) ((-865 . -609) 123783) ((-831 . -1033) 123752) ((-202 . -782) T) ((-201 . -782) T) ((-200 . -782) T) ((-199 . -782) T) ((-198 . -782) T) ((-197 . -782) T) ((-196 . -782) T) ((-195 . -782) T) ((-194 . -782) T) ((-193 . -782) T) ((-546 . -609) 123734) ((-494 . -997) T) ((-273 . -834) T) ((-272 . -834) T) ((-271 . -834) T) ((-270 . -834) T) ((-48 . -289) T) ((-269 . -834) T) ((-268 . -834) T) ((-267 . -834) T) ((-192 . -782) T) ((-608 . -845) T) ((-648 . -410) 123718) ((-222 . -612) 123680) ((-110 . -845) T) ((-647 . -21) T) ((-647 . -25) T) ((-1279 . -38) 123650) ((-117 . -285) 123601) ((-1256 . -19) 123585) ((-1256 . -600) 123562) ((-1269 . -1092) T) ((-1069 . -1092) T) ((-982 . -1092) T) ((-958 . -130) T) ((-732 . -1092) T) ((-730 . -130) T) ((-710 . -130) T) ((-510 . -788) T) ((-406 . -1143) 123540) ((-452 . -130) T) ((-510 . -789) T) ((-222 . -1044) T) ((-293 . -102) 123322) ((-140 . -1092) T) ((-693 . -997) T) ((-91 . -1207) T) ((-127 . -609) 123254) ((-121 . -609) 123186) ((-1284 . -171) T) ((-1165 . -362) 123165) ((-1159 . -362) 123144) ((-315 . -1092) T) ((-417 . -130) T) ((-312 . -1092) T) ((-406 . -38) 123096) ((-1125 . -102) T) ((-1242 . -712) 122988) ((-648 . -1051) T) ((-1127 . -1251) T) ((-318 . -144) 122967) ((-318 . -146) 122946) ((-138 . -1092) T) ((-135 . -1092) T) ((-114 . -1092) T) ((-853 . -102) T) ((-578 . -609) 122928) ((-562 . -610) 122827) ((-562 . -609) 122809) ((-494 . -609) 122791) ((-494 . -610) 122736) ((-484 . -23) T) ((-481 . -845) 122687) ((-486 . -635) 122669) ((-960 . -609) 122651) ((-216 . -635) 122633) ((-224 . -403) T) ((-656 . -642) 122617) ((-55 . -609) 122599) ((-1164 . -915) 122578) ((-726 . -1104) T) ((-350 . -102) T) ((-1206 . -1075) T) ((-1112 . -839) T) ((-813 . -845) T) ((-726 . -23) T) ((-342 . -1050) 122523) ((-1150 . -1149) T) ((-1139 . -107) 122507) ((-1166 . -1104) T) ((-1165 . -1104) T) ((-514 . -1033) 122491) ((-1159 . -1104) T) ((-1118 . -1104) T) ((-342 . -111) 122420) ((-999 . -1211) T) ((-126 . -1207) T) ((-909 . -1211) T) ((-688 . -285) NIL) ((-1257 . -609) 122402) ((-1166 . -23) T) ((-1165 . -23) T) ((-1159 . -23) T) ((-999 . -554) T) ((-1134 . -230) 122386) ((-909 . -554) T) ((-1118 . -23) T) ((-247 . -609) 122368) ((-1067 . -1092) T) ((-794 . -130) T) ((-705 . -609) 122350) ((-315 . -712) 122260) ((-312 . -712) 122189) ((-693 . -609) 122171) ((-693 . -610) 122116) ((-406 . -399) 122100) ((-437 . -1092) T) ((-486 . -25) T) ((-486 . -21) T) ((-1112 . -1092) T) ((-216 . -25) T) ((-216 . -21) T) ((-707 . -410) 122084) ((-709 . -1033) 122053) ((-1256 . -609) 121965) ((-1256 . -610) 121926) ((-1242 . -171) T) ((-244 . -34) T) ((-342 . -612) 121856) ((-393 . -612) 121838) ((-921 . -969) T) ((-1193 . -1207) T) ((-656 . -786) 121817) ((-656 . -789) 121796) ((-397 . -394) T) ((-522 . -102) 121774) ((-1030 . -1092) T) ((-221 . -990) 121758) ((-503 . -102) T) ((-619 . -609) 121740) ((-45 . -845) NIL) ((-619 . -610) 121717) ((-1030 . -606) 121692) ((-896 . -513) 121625) ((-342 . -1044) T) ((-117 . -610) NIL) ((-117 . -609) 121607) ((-867 . -1207) T) ((-664 . -416) 121591) ((-664 . -1115) 121536) ((-499 . -150) 121518) ((-342 . -232) T) ((-342 . -242) T) ((-40 . -1050) 121463) ((-867 . -879) 121447) ((-867 . -881) 121372) ((-707 . -1051) T) ((-688 . -997) NIL) ((-3 . |UnionCategory|) T) ((-1240 . -47) 121342) ((-1219 . -47) 121319) ((-1133 . -1005) 121290) ((-224 . -915) T) ((-40 . -111) 121219) ((-867 . -1033) 121083) ((-1112 . -712) 121070) ((-1097 . -609) 121052) ((-1072 . -146) 121031) ((-1072 . -144) 120982) ((-999 . -362) T) ((-318 . -1195) 120948) ((-378 . -306) T) ((-318 . -1192) 120914) ((-315 . -171) 120893) ((-312 . -171) T) ((-998 . -230) 120870) ((-909 . -362) T) ((-579 . -1275) 120857) ((-517 . -1275) 120834) ((-358 . -146) 120813) ((-358 . -144) 120764) ((-352 . -146) 120743) ((-352 . -144) 120694) ((-604 . -1183) 120670) ((-344 . -146) 120649) ((-344 . -144) 120600) ((-318 . -35) 120566) ((-474 . -1183) 120545) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120511) ((-378 . -1017) T) 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. -1104) T) ((-909 . -1104) T) ((-82 . -609) 119317) ((-40 . -1044) T) ((-865 . -1050) 119304) ((-998 . -348) NIL) ((-867 . -895) 119263) ((-695 . -102) T) ((-966 . -23) T) ((-598 . -1207) T) ((-909 . -23) T) ((-865 . -111) 119248) ((-426 . -1104) T) ((-212 . -1092) T) ((-473 . -47) 119218) ((-133 . -102) T) ((-40 . -232) 119190) ((-40 . -242) T) ((-116 . -102) T) ((-593 . -554) 119169) ((-592 . -554) 119148) ((-688 . -609) 119130) ((-688 . -610) 119038) ((-315 . -513) 119004) ((-312 . -513) 118896) ((-1240 . -1033) 118880) ((-1219 . -1033) 118666) ((-994 . -410) 118650) ((-426 . -23) T) ((-1112 . -171) T) ((-1242 . -289) T) ((-648 . -712) 118620) ((-143 . -1092) T) ((-48 . -997) T) ((-406 . -230) 118604) ((-294 . -234) 118554) ((-866 . -915) T) ((-866 . -815) NIL) ((-865 . -612) 118526) ((-859 . -845) T) ((-1219 . -337) 118496) ((-1219 . -376) 118466) ((-221 . -1113) 118450) ((-1256 . -287) 118427) ((-1201 . -642) 118352) ((-958 . -21) T) ((-958 . -25) T) ((-730 . -21) T) ((-730 . -25) T) ((-710 . -21) T) ((-710 . -25) T) ((-706 . -642) 118317) ((-452 . -21) T) ((-452 . -25) T) ((-338 . -102) T) ((-173 . -102) T) ((-994 . -1051) T) ((-865 . -1044) T) ((-769 . -102) T) ((-1241 . -362) 118296) ((-1240 . -895) 118202) ((-1220 . -362) 118181) ((-1219 . -895) 118032) ((-1019 . -609) 118014) ((-406 . -823) 117967) ((-1166 . -492) 117933) ((-168 . -915) 117864) ((-1165 . -492) 117830) ((-1159 . -492) 117796) ((-707 . -1092) T) ((-1118 . -492) 117762) ((-578 . -1050) 117749) ((-562 . -1050) 117736) ((-494 . -1050) 117701) ((-315 . -289) 117680) ((-312 . -289) T) ((-353 . -609) 117662) ((-417 . -25) T) ((-417 . -21) T) ((-99 . -285) 117641) ((-578 . -111) 117626) ((-562 . -111) 117611) ((-494 . -111) 117567) ((-1168 . -881) 117534) ((-896 . -488) 117518) ((-48 . -609) 117500) ((-48 . -610) 117445) ((-239 . -130) 117315) ((-1229 . -915) 117294) ((-811 . -1211) 117273) ((-387 . -489) 117254) ((-1030 . -513) 117098) ((-387 . -609) 117064) ((-811 . -554) 116995) ((-583 . 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-1270) 116165) ((-766 . -787) T) ((-766 . -790) T) ((-695 . -38) 116152) ((-562 . -232) T) ((-494 . -242) T) ((-494 . -232) T) ((-1142 . -234) 116102) ((-1079 . -904) 116081) ((-116 . -38) 116068) ((-208 . -795) T) ((-207 . -795) T) ((-206 . -795) T) ((-205 . -795) T) ((-867 . -1017) 116046) ((-1269 . -488) 116030) ((-777 . -904) 116009) ((-775 . -904) 115988) ((-1180 . -1207) T) ((-453 . -904) 115967) ((-732 . -488) 115951) ((-1079 . -642) 115876) ((-693 . -612) 115811) ((-777 . -642) 115736) ((-619 . -1050) 115723) ((-478 . -1207) T) ((-342 . -367) T) ((-140 . -488) 115705) ((-775 . -642) 115630) ((-1133 . -1207) T) ((-547 . -845) T) ((-460 . -642) 115601) ((-263 . -881) 115460) ((-246 . -881) NIL) ((-117 . -1050) 115405) ((-453 . -642) 115330) ((-658 . -1033) 115307) ((-619 . -111) 115292) ((-354 . -1033) 115276) ((-351 . -1033) 115260) ((-343 . -1033) 115244) ((-263 . -1033) 115088) ((-246 . -1033) 114964) ((-117 . -111) 114893) ((-59 . -1207) T) ((-518 . -1207) T) ((-515 . -1207) T) ((-496 . -1207) T) ((-495 . -1207) T) ((-436 . -609) 114875) ((-433 . -609) 114857) ((-3 . -102) T) ((-1022 . -1200) 114826) ((-828 . -102) T) ((-683 . -57) 114784) ((-693 . -1044) T) ((-50 . -642) 114758) ((-288 . -451) T) ((-475 . -1200) 114727) ((0 . -102) T) ((-579 . -642) 114692) ((-517 . -642) 114637) ((-49 . -102) T) ((-905 . -1033) 114624) ((-693 . -242) T) ((-1072 . -408) 114603) ((-726 . -635) 114551) ((-994 . -1092) T) ((-707 . -171) 114442) ((-619 . -612) 114337) ((-486 . -987) 114319) ((-263 . -376) 114303) ((-246 . -376) 114287) ((-398 . -1092) T) ((-1021 . -102) 114265) ((-338 . -38) 114249) ((-216 . -987) 114231) ((-117 . -612) 114161) ((-173 . -38) 114093) ((-1240 . -306) 114072) ((-1219 . -306) 114051) ((-652 . -721) T) ((-99 . -609) 114033) ((-1159 . -635) 113985) ((-484 . -25) T) ((-484 . -21) T) ((-1219 . -1017) 113937) ((-619 . -1044) T) ((-378 . -403) T) ((-389 . -102) T) ((-1097 . -614) 113852) ((-263 . -895) 113798) ((-246 . -895) 113775) ((-117 . -1044) T) 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T) ((-344 . -451) T) ((-473 . -306) 113183) ((-1214 . -102) T) ((-312 . -285) 113118) ((-108 . -451) T) ((-79 . -440) T) ((-79 . -394) T) ((-476 . -102) T) ((-685 . -612) 113102) ((-1284 . -609) 113084) ((-1284 . -610) 113066) ((-1072 . -401) 113045) ((-1030 . -488) 112976) ((-562 . -790) T) ((-562 . -787) T) ((-1056 . -234) 112922) ((-358 . -401) 112873) ((-352 . -401) 112824) ((-344 . -401) 112775) ((-1271 . -1104) T) ((-688 . -612) 112710) ((-1271 . -23) T) ((-1258 . -102) T) ((-174 . -609) 112692) ((-1134 . -1051) T) ((-546 . -367) T) ((-664 . -739) 112676) ((-1170 . -144) 112655) ((-1170 . -146) 112634) ((-1138 . -1092) T) ((-1138 . -1064) 112603) ((-69 . -1207) T) ((-1019 . -1050) 112540) ((-861 . -1051) T) ((-239 . -635) 112446) ((-688 . -1044) T) ((-353 . -1050) 112391) ((-61 . -1207) T) ((-1019 . -111) 112307) ((-896 . -609) 112218) ((-688 . -242) T) ((-688 . -232) NIL) ((-838 . -843) 112197) ((-693 . -790) T) ((-693 . -787) T) ((-998 . -410) 112174) ((-353 . -111) 112103) 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. -1044) T) ((-998 . -1051) T) ((-48 . -612) 110771) ((-342 . -642) 110716) ((-617 . -38) 110700) ((-1269 . -609) 110662) ((-1269 . -610) 110623) ((-1069 . -609) 110605) ((-1019 . -242) T) ((-353 . -1044) T) ((-810 . -1263) 110575) ((-250 . -23) T) ((-249 . -23) T) ((-982 . -609) 110557) ((-732 . -610) 110518) ((-732 . -609) 110500) ((-794 . -845) 110479) ((-1151 . -150) 110426) ((-994 . -513) 110338) ((-353 . -232) T) ((-353 . -242) T) ((-387 . -612) 110319) ((-999 . -25) T) ((-140 . -609) 110301) ((-140 . -610) 110260) ((-905 . -306) T) ((-999 . -21) T) ((-966 . -25) T) ((-909 . -21) T) ((-909 . -25) T) ((-426 . -21) T) ((-426 . -25) T) ((-838 . -410) 110244) ((-48 . -1044) T) ((-1278 . -1270) 110228) ((-1276 . -1270) 110212) ((-1030 . -600) 110187) ((-315 . -610) 110048) ((-315 . -609) 110030) ((-312 . -610) NIL) ((-312 . -609) 110012) ((-48 . -242) T) ((-48 . -232) T) ((-648 . -285) 109973) ((-548 . -234) 109923) ((-138 . -609) 109890) ((-135 . -609) 109872) ((-114 . -609) 109854) 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109049) ((-478 . -107) 108999) ((-988 . -23) T) ((-1280 . -38) 108969) ((-1164 . -1104) T) ((-1117 . -1104) T) ((-1055 . -1211) T) ((-310 . -102) T) ((-849 . -1104) T) ((-947 . -1211) 108948) ((-480 . -1211) 108927) ((-726 . -845) 108906) ((-1055 . -554) T) ((-947 . -554) 108837) ((-1164 . -23) T) ((-1117 . -23) T) ((-849 . -23) T) ((-480 . -554) 108768) ((-1134 . -712) 108700) ((-1138 . -513) 108633) ((-1030 . -610) NIL) ((-1030 . -609) 108615) ((-96 . -1075) T) ((-861 . -712) 108585) ((-1201 . -47) 108554) ((-250 . -130) T) ((-249 . -130) T) ((-1096 . -1092) T) ((-998 . -1092) T) ((-62 . -609) 108536) ((-1159 . -845) NIL) ((-1019 . -787) T) ((-1019 . -790) T) ((-1284 . -1050) 108523) ((-1284 . -111) 108508) ((-865 . -642) 108495) ((-1248 . -25) T) ((-1248 . -21) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-1220 . -21) T) ((-1220 . -25) T) ((-1022 . -150) 108479) ((-867 . -815) 108458) ((-867 . -915) T) ((-707 . -285) 108385) ((-593 . -21) T) ((-593 . -25) T) ((-592 . -21) T) ((-40 . -721) T) ((-221 . -513) 108318) ((-592 . -25) T) ((-475 . -150) 108302) ((-462 . -150) 108286) ((-916 . -789) T) ((-916 . -721) T) ((-766 . -788) T) ((-766 . -789) T) ((-505 . -1092) T) ((-501 . -1092) T) ((-766 . -721) T) ((-224 . -362) T) ((-1148 . -1092) 108264) ((-866 . -1211) T) ((-648 . -609) 108246) ((-866 . -554) T) ((-688 . -367) NIL) ((-1284 . -612) 108228) ((-358 . -1263) 108212) ((-664 . -102) T) ((-352 . -1263) 108196) ((-344 . -1263) 108180) ((-1279 . -1092) T) ((-519 . -845) 108159) ((-812 . -451) 108138) ((-1041 . -1092) T) ((-1041 . -1064) 108067) ((-1022 . -971) 108036) ((-814 . -1104) T) ((-998 . -712) 107981) ((-385 . -1104) T) ((-475 . -971) 107950) ((-462 . -971) 107919) ((-110 . -150) 107901) ((-73 . -609) 107883) ((-888 . -609) 107865) ((-1072 . -719) 107844) ((-1284 . -1044) T) ((-811 . -635) 107792) ((-293 . -1051) 107734) ((-168 . -1211) 107639) ((-224 . -1104) T) ((-323 . -23) T) ((-1159 . -987) 107591) ((-838 . -1092) T) ((-1242 . -1050) 107496) ((-1118 . -735) 107475) ((-1240 . -915) 107454) ((-1219 . -915) 107433) ((-865 . -721) T) ((-168 . -554) 107344) ((-578 . -642) 107331) ((-562 . -642) 107318) ((-406 . -1092) T) ((-262 . -1092) T) ((-212 . -609) 107300) ((-494 . -642) 107265) ((-224 . -23) T) ((-1219 . -815) 107218) ((-1278 . -102) T) ((-353 . -1275) 107195) ((-1276 . -102) T) ((-1242 . -111) 107087) ((-143 . -609) 107069) ((-988 . -130) T) ((-44 . -102) T) ((-239 . -845) 107020) ((-1229 . -1211) 106999) ((-103 . -488) 106983) ((-1279 . -712) 106953) ((-1079 . -47) 106914) ((-1055 . -1104) T) ((-947 . -1104) T) ((-127 . -34) T) ((-121 . -34) T) ((-777 . -47) 106891) ((-775 . -47) 106863) ((-1229 . -554) 106774) ((-353 . -367) T) ((-480 . -1104) T) ((-1164 . -130) T) ((-1117 . -130) T) ((-453 . -47) 106753) ((-866 . -362) T) ((-849 . -130) T) ((-151 . -102) T) ((-1055 . -23) T) ((-947 . -23) T) ((-569 . -554) T) ((-811 . -25) T) ((-811 . -21) T) ((-1134 . -513) 106686) ((-589 . -1075) T) ((-583 . -1033) 106670) ((-1242 . -612) 106544) ((-480 . -23) T) ((-350 . -1051) T) ((-1201 . -895) 106525) ((-664 . -308) 106463) ((-1105 . -1263) 106433) ((-693 . -642) 106398) ((-998 . -171) T) ((-958 . -144) 106377) ((-631 . -1092) T) ((-603 . -1092) T) ((-958 . -146) 106356) ((-999 . -845) T) ((-730 . -146) 106335) ((-730 . -144) 106314) ((-966 . -845) T) ((-473 . -915) 106293) ((-315 . -1050) 106203) ((-312 . -1050) 106132) ((-994 . -285) 106090) ((-406 . -712) 106042) ((-695 . -843) T) ((-1242 . -1044) T) ((-315 . -111) 105938) ((-312 . -111) 105851) ((-959 . -102) T) ((-810 . -102) 105641) ((-707 . -610) NIL) ((-707 . -609) 105623) ((-652 . -1033) 105519) ((-1242 . -325) 105463) ((-1030 . -287) 105438) ((-578 . -721) T) ((-562 . -789) T) ((-168 . -362) 105389) ((-562 . -786) T) ((-562 . -721) T) ((-494 . -721) T) ((-1138 . -488) 105373) ((-1079 . -881) NIL) ((-866 . -1104) T) ((-117 . -904) NIL) ((-1278 . -1277) 105349) ((-1276 . -1277) 105328) ((-777 . -881) NIL) ((-775 . -881) 105187) ((-1271 . -25) T) ((-1271 . -21) T) ((-1204 . -102) 105165) ((-1098 . -394) T) ((-619 . -642) 105152) ((-453 . -881) NIL) ((-669 . -102) 105130) ((-1079 . -1033) 104957) ((-866 . -23) T) ((-777 . -1033) 104816) ((-775 . -1033) 104673) ((-117 . -642) 104618) ((-453 . -1033) 104494) ((-315 . -612) 104058) ((-312 . -612) 103941) ((-643 . -1033) 103925) ((-623 . -102) T) ((-221 . -488) 103909) ((-1256 . -34) T) ((-135 . -612) 103893) ((-631 . -712) 103877) ((-603 . -712) 103861) ((-664 . -38) 103821) ((-318 . -102) T) ((-85 . -609) 103803) ((-50 . -1033) 103787) ((-1112 . -1050) 103774) ((-1079 . -376) 103758) ((-777 . -376) 103742) ((-60 . -57) 103704) ((-693 . -789) T) ((-693 . -786) T) ((-579 . -1033) 103691) ((-517 . -1033) 103668) ((-693 . -721) T) ((-323 . -130) T) ((-315 . -1044) 103558) ((-312 . -1044) T) ((-168 . -1104) T) ((-775 . -376) 103542) ((-45 . -150) 103492) ((-999 . -987) 103474) ((-453 . -376) 103458) ((-406 . -171) T) ((-315 . -242) 103437) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1092) 103219) ((-224 . -130) T) ((-1112 . -111) 103204) ((-168 . -23) T) ((-794 . -146) 103183) ((-794 . -144) 103162) ((-250 . -635) 103068) ((-249 . -635) 102974) ((-318 . -283) 102940) ((-1148 . -513) 102873) ((-1125 . -1092) T) ((-224 . -1053) T) ((-810 . -308) 102811) ((-1079 . -895) 102746) ((-777 . -895) 102689) ((-775 . -895) 102673) ((-1278 . -38) 102643) ((-1276 . -38) 102613) ((-1229 . -1104) T) ((-850 . -1104) T) ((-453 . -895) 102590) ((-853 . -1092) T) ((-1229 . -23) T) ((-1112 . -612) 102562) ((-569 . -1104) T) ((-850 . -23) T) ((-619 . -721) T) ((-354 . -915) T) ((-351 . -915) T) ((-288 . -102) T) ((-343 . -915) T) ((-1055 . -130) T) ((-965 . -1075) T) ((-947 . -130) T) ((-117 . -789) NIL) ((-117 . -786) NIL) ((-117 . -721) T) ((-688 . -904) NIL) ((-1041 . -513) 102463) ((-480 . -130) T) ((-569 . -23) T) ((-669 . -308) 102401) ((-631 . -756) T) ((-603 . -756) T) ((-1220 . -845) NIL) ((-998 . -289) T) ((-250 . -21) T) ((-688 . -642) 102351) ((-350 . -1092) T) ((-250 . -25) T) 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-787) T) ((-695 . -1092) T) ((-576 . -609) 99437) ((-378 . -362) T) ((-168 . -492) 99415) ((-221 . -609) 99347) ((-133 . -1092) T) ((-116 . -1092) T) ((-48 . -721) T) ((-1041 . -488) 99312) ((-140 . -424) 99294) ((-140 . -367) T) ((-1022 . -102) T) ((-511 . -508) 99273) ((-707 . -612) 99029) ((-475 . -102) T) ((-462 . -102) T) ((-1029 . -1104) T) ((-1173 . -1033) 98964) ((-1166 . -35) 98930) ((-1166 . -95) 98896) ((-1166 . -1195) 98862) ((-1166 . -1192) 98828) ((-1150 . -308) NIL) ((-89 . -395) T) ((-89 . -394) T) ((-1072 . -1143) 98807) ((-1165 . -1192) 98773) ((-1165 . -1195) 98739) ((-1029 . -23) T) ((-1165 . -95) 98705) ((-569 . -492) T) ((-1165 . -35) 98671) ((-1159 . -1192) 98637) ((-1159 . -1195) 98603) ((-1159 . -95) 98569) ((-360 . -1104) T) ((-358 . -1143) 98548) ((-352 . -1143) 98527) ((-344 . -1143) 98506) ((-1159 . -35) 98472) ((-1118 . -35) 98438) ((-1118 . -95) 98404) ((-108 . -1143) T) ((-1118 . -1195) 98370) ((-828 . -1051) 98349) ((-641 . -308) 98287) ((-628 . -308) 98138) ((-1118 . -1192) 98104) ((-707 . -1044) T) ((-1055 . -635) 98086) ((-1072 . -38) 97954) ((-947 . -635) 97902) ((-999 . -146) T) ((-999 . -144) NIL) ((-378 . -1104) T) ((-323 . -25) T) ((-321 . -23) T) ((-938 . -845) 97881) ((-707 . -325) 97858) ((-480 . -635) 97806) ((-40 . -1033) 97694) ((-707 . -232) T) ((-695 . -712) 97681) ((-338 . -1092) T) ((-173 . -1092) T) ((-330 . -845) T) ((-417 . -451) 97631) ((-378 . -23) T) ((-358 . -38) 97596) ((-352 . -38) 97561) ((-344 . -38) 97526) ((-80 . -440) T) ((-80 . -394) T) ((-224 . -25) T) ((-224 . -21) T) ((-831 . -1104) T) ((-108 . -38) 97476) ((-822 . -1104) T) ((-769 . -1092) T) ((-116 . -712) 97463) ((-666 . -1033) 97447) ((-608 . -102) T) ((-831 . -23) T) ((-822 . -23) T) ((-1148 . -285) 97424) ((-1105 . -308) 97362) ((-1094 . -234) 97346) ((-64 . -395) T) ((-64 . -394) T) ((-110 . -102) T) ((-40 . -376) 97323) ((-96 . -102) T) ((-647 . -847) 97307) ((-1127 . -1075) T) ((-1055 . -21) T) ((-1055 . -25) T) ((-810 . -230) 97276) 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-21) T) ((-813 . -102) T) ((-413 . -102) T) ((-384 . -102) T) ((-110 . -308) NIL) ((-226 . -102) 95745) ((-127 . -1207) T) ((-121 . -1207) T) ((-1029 . -130) T) ((-664 . -366) 95729) ((-994 . -1044) T) ((-1229 . -635) 95677) ((-1096 . -609) 95659) ((-998 . -609) 95641) ((-514 . -23) T) ((-509 . -23) T) ((-342 . -306) T) ((-507 . -23) T) ((-321 . -130) T) ((-3 . -1092) T) ((-998 . -610) 95625) ((-994 . -242) 95604) ((-994 . -232) 95583) ((-1284 . -721) T) ((-1248 . -144) 95562) ((-828 . -1092) T) ((-1248 . -146) 95541) ((-1241 . -146) 95520) ((-1241 . -144) 95499) ((-1240 . -1211) 95478) ((-1220 . -144) 95385) ((-1220 . -146) 95292) ((-1219 . -1211) 95271) ((-378 . -130) T) ((-562 . -881) 95253) ((0 . -1092) T) ((-173 . -171) T) ((-168 . -21) T) ((-168 . -25) T) ((-49 . -1092) T) ((-1242 . -642) 95158) ((-1240 . -554) 95109) ((-709 . -1104) T) ((-1219 . -554) 95060) ((-562 . -1033) 95042) ((-592 . -146) 95021) ((-592 . -144) 95000) ((-494 . -1033) 94943) ((-1127 . -1129) T) ((-87 . -383) T) ((-87 . -394) T) ((-867 . -362) T) ((-831 . -130) T) ((-822 . -130) T) ((-709 . -23) T) ((-505 . -609) 94909) ((-501 . -609) 94891) ((-1280 . -1051) T) ((-378 . -1053) T) ((-1021 . -1092) 94869) ((-55 . -1033) 94851) ((-896 . -34) T) ((-481 . -308) 94789) ((-589 . -102) T) ((-1148 . -610) 94750) ((-1148 . -609) 94682) ((-1164 . -845) 94661) ((-45 . -102) T) ((-1117 . -845) 94640) ((-812 . -102) T) ((-1229 . -25) T) ((-1229 . -21) T) ((-850 . -25) T) ((-44 . -366) 94624) ((-850 . -21) T) ((-726 . -451) 94575) ((-1279 . -609) 94557) ((-1048 . -308) 94495) ((-665 . -1075) T) ((-602 . -1075) T) ((-389 . -1092) T) ((-569 . -25) T) ((-569 . -21) T) ((-179 . -1075) T) ((-160 . -1075) T) ((-155 . -1075) T) ((-153 . -1075) T) ((-617 . -1092) T) ((-693 . -881) 94477) ((-1256 . -1207) T) ((-226 . -308) 94415) ((-143 . -367) T) ((-1041 . -610) 94357) ((-1041 . -609) 94300) ((-312 . -904) NIL) ((-1214 . -839) T) ((-693 . -1033) 94245) ((-706 . -915) T) ((-473 . -1211) 94224) ((-1165 . -451) 94203) ((-1159 . -451) 94182) ((-329 . -102) T) ((-867 . -1104) T) ((-315 . -642) 94003) ((-312 . -642) 93932) ((-473 . -554) 93883) ((-338 . -513) 93849) ((-548 . -150) 93799) ((-40 . -306) T) ((-838 . -609) 93781) ((-695 . -289) T) ((-867 . -23) T) ((-378 . -492) T) ((-1072 . -230) 93751) ((-511 . -102) T) ((-406 . -610) 93558) ((-406 . -609) 93540) ((-262 . -609) 93522) ((-116 . -289) T) ((-1242 . -721) T) ((-1240 . -362) 93501) ((-1219 . -362) 93480) ((-1269 . -34) T) ((-1214 . -1092) T) ((-117 . -1207) T) ((-108 . -230) 93462) ((-1170 . -102) T) ((-476 . -1092) T) ((-522 . -488) 93446) ((-732 . -34) T) ((-481 . -38) 93416) ((-140 . -34) T) ((-117 . -879) 93393) ((-117 . -881) NIL) ((-619 . -1033) 93276) ((-639 . -845) 93255) ((-1268 . -102) T) ((-294 . -102) T) ((-707 . -367) 93234) ((-117 . -1033) 93211) ((-389 . -712) 93195) ((-617 . -712) 93179) ((-45 . -308) 92983) ((-811 . -144) 92962) ((-811 . -146) 92941) ((-1279 . -381) 92920) ((-814 . -845) T) ((-1258 . -1092) T) 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-895) 91878) ((-1280 . -1092) T) ((-380 . -1092) T) ((-1206 . -1092) T) ((-1105 . -230) 91847) ((-82 . -1207) T) ((-1055 . -845) T) ((-947 . -845) 91826) ((-117 . -895) NIL) ((-777 . -915) 91805) ((-708 . -845) T) ((-530 . -1092) T) ((-499 . -1092) T) ((-354 . -1211) T) ((-351 . -1211) T) ((-343 . -1211) T) ((-263 . -1211) 91784) ((-246 . -1211) 91763) ((-532 . -855) T) ((-480 . -845) 91742) ((-1150 . -823) T) ((-1134 . -1050) 91726) ((-389 . -756) T) ((-688 . -1207) T) ((-685 . -1033) 91710) ((-354 . -554) T) ((-351 . -554) T) ((-343 . -554) T) ((-263 . -554) 91641) ((-246 . -554) 91572) ((-524 . -1075) T) ((-1134 . -111) 91551) ((-452 . -739) 91521) ((-861 . -1050) 91491) ((-812 . -38) 91433) ((-688 . -879) 91415) ((-688 . -881) 91397) ((-294 . -308) 91201) ((-905 . -1211) T) ((-664 . -410) 91185) ((-861 . -111) 91150) ((-688 . -1033) 91095) ((-999 . -451) T) ((-905 . -554) T) ((-532 . -609) 91077) ((-579 . -915) T) ((-473 . -1104) T) ((-517 . -915) T) ((-1148 . -287) 91054) ((-909 . -451) T) ((-65 . -609) 91036) ((-628 . -228) 90982) ((-473 . -23) T) ((-1112 . -789) T) ((-867 . -130) T) ((-1112 . -786) T) ((-1271 . -1273) 90961) ((-1112 . -721) T) ((-648 . -642) 90935) ((-293 . -609) 90676) ((-1134 . -612) 90594) ((-1030 . -34) T) ((-810 . -843) 90573) ((-578 . -306) T) ((-562 . -306) T) ((-494 . -306) T) ((-1280 . -712) 90543) ((-688 . -376) 90525) ((-688 . -337) 90507) ((-476 . -171) T) ((-380 . -712) 90477) ((-861 . -612) 90412) ((-866 . -845) NIL) ((-562 . -1017) T) ((-494 . -1017) T) ((-1125 . -609) 90394) ((-1105 . -237) 90373) ((-213 . -102) T) ((-1142 . -102) T) ((-71 . -609) 90355) ((-1134 . -1044) T) ((-1170 . -38) 90252) ((-853 . -609) 90234) ((-562 . -544) T) ((-664 . -1051) T) ((-726 . -944) 90187) ((-1134 . -232) 90166) ((-1074 . -1092) T) ((-1029 . -25) T) ((-1029 . -21) T) ((-998 . -1050) 90111) ((-900 . -102) T) ((-861 . -1044) T) ((-688 . -895) NIL) ((-354 . -328) 90095) ((-354 . -362) T) ((-351 . -328) 90079) ((-351 . -362) T) ((-343 . -328) 90063) ((-343 . -362) T) ((-486 . -102) T) ((-1268 . -38) 90033) ((-545 . -845) T) ((-522 . -681) 89983) ((-216 . -102) T) ((-1019 . -1033) 89863) ((-998 . -111) 89792) ((-1166 . -968) 89761) ((-1165 . -968) 89723) ((-519 . -150) 89707) ((-1072 . -369) 89686) ((-350 . -609) 89668) ((-321 . -21) T) ((-353 . -1033) 89645) ((-321 . -25) T) ((-1159 . -968) 89614) ((-1118 . -968) 89581) ((-76 . -609) 89563) ((-693 . -306) T) ((-168 . -845) 89542) ((-129 . -839) T) ((-905 . -362) T) ((-378 . -25) T) ((-378 . -21) T) ((-905 . -328) 89529) ((-86 . -609) 89511) ((-693 . -1017) T) ((-671 . -845) T) ((-1240 . -130) T) ((-1219 . -130) T) ((-896 . -1005) 89495) ((-831 . -21) T) ((-48 . -1033) 89438) ((-831 . -25) T) ((-822 . -25) T) ((-822 . -21) T) ((-1278 . -1051) T) ((-547 . -102) T) ((-1276 . -1051) T) ((-648 . -721) T) ((-1096 . -614) 89341) ((-998 . -612) 89271) ((-1279 . -1050) 89255) ((-1229 . -845) 89234) ((-810 . -410) 89203) ((-103 . -119) 89187) ((-129 . -1092) T) ((-52 . -1092) T) 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86504) ((-1105 . -843) 86483) ((-769 . -609) 86465) ((-128 . -845) T) ((-604 . -234) 86412) ((-474 . -234) 86362) ((-1278 . -712) 86332) ((-48 . -306) T) ((-1276 . -712) 86302) ((-65 . -612) 86231) ((-959 . -1092) T) ((-810 . -1092) 86021) ((-311 . -102) T) ((-896 . -1207) T) ((-48 . -1017) T) ((-1219 . -635) 85929) ((-683 . -102) 85907) ((-44 . -712) 85891) ((-548 . -102) T) ((-293 . -612) 85822) ((-67 . -382) T) ((-67 . -394) T) ((-656 . -23) T) ((-664 . -756) T) ((-1204 . -1092) 85800) ((-350 . -1050) 85745) ((-669 . -1092) 85723) ((-1055 . -146) T) ((-947 . -146) 85702) ((-947 . -144) 85681) ((-794 . -102) T) ((-151 . -712) 85665) ((-480 . -146) 85644) ((-480 . -144) 85623) ((-350 . -111) 85552) ((-1072 . -1051) T) ((-321 . -845) 85531) ((-1248 . -968) 85500) ((-623 . -1092) T) ((-1241 . -968) 85462) ((-510 . -130) T) ((-506 . -130) T) ((-294 . -228) 85412) ((-358 . -1051) T) ((-352 . -1051) T) ((-344 . -1051) T) ((-293 . -1044) 85354) ((-1220 . -968) 85323) ((-378 . -845) T) 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. -242) T) ((-312 . -1207) T) ((-288 . -1092) T) ((-1172 . -609) 84444) ((-706 . -1211) T) ((-1148 . -645) 84428) ((-1201 . -554) 84407) ((-706 . -554) T) ((-315 . -879) 84391) ((-315 . -881) 84316) ((-312 . -879) 84277) ((-312 . -881) NIL) ((-794 . -308) 84242) ((-318 . -712) 84083) ((-323 . -322) 84060) ((-484 . -102) T) ((-473 . -25) T) ((-473 . -21) T) ((-417 . -38) 84034) ((-315 . -1033) 83697) ((-224 . -1192) T) ((-224 . -1195) T) ((-3 . -609) 83679) ((-312 . -1033) 83609) ((-2 . -1092) T) ((-2 . |RecordCategory|) T) ((-828 . -609) 83591) ((-1105 . -1051) 83521) ((-578 . -915) T) ((-562 . -815) T) ((-562 . -915) T) ((-494 . -915) T) ((-135 . -1033) 83505) ((-224 . -95) T) ((-75 . -440) T) ((-75 . -394) T) ((0 . -609) 83487) ((-168 . -146) 83466) ((-168 . -144) 83417) ((-224 . -35) T) ((-49 . -609) 83399) ((-476 . -1051) T) ((-486 . -230) 83381) ((-483 . -963) 83365) ((-481 . -843) 83344) ((-216 . -230) 83326) ((-81 . -440) T) ((-81 . -394) T) ((-1138 . -34) T) ((-810 . -171) 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. -308) 79098) ((-499 . -609) 79080) ((-499 . -610) 79062) ((-1206 . -609) 79028) ((-1159 . -1143) NIL) ((-1022 . -1064) 78997) ((-1022 . -1092) T) ((-999 . -102) T) ((-966 . -102) T) ((-909 . -102) T) ((-888 . -1033) 78974) ((-1134 . -721) T) ((-998 . -642) 78919) ((-475 . -1092) T) ((-462 . -1092) T) ((-583 . -23) T) ((-569 . -35) T) ((-569 . -95) T) ((-426 . -102) T) ((-1056 . -228) 78865) ((-1166 . -38) 78762) ((-861 . -721) T) ((-688 . -915) T) ((-510 . -25) T) ((-506 . -21) T) ((-506 . -25) T) ((-1165 . -38) 78603) ((-338 . -1044) T) ((-1159 . -38) 78399) ((-1072 . -171) T) ((-173 . -1044) T) ((-1118 . -38) 78296) ((-707 . -47) 78273) ((-358 . -171) T) ((-352 . -171) T) ((-518 . -57) 78247) ((-496 . -57) 78197) ((-350 . -1275) 78174) ((-224 . -451) T) ((-318 . -289) 78125) ((-344 . -171) T) ((-173 . -242) T) ((-1219 . -845) 78024) ((-108 . -171) T) ((-867 . -987) 78008) ((-652 . -1104) T) ((-579 . -362) T) ((-579 . -328) 77995) ((-517 . -328) 77972) ((-517 . -362) T) ((-315 . 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-308) NIL) ((-810 . -488) 77147) ((-353 . -915) T) ((-1148 . -34) T) ((-406 . -642) 77099) ((-50 . -23) T) ((-706 . -130) T) ((-707 . -1033) 76979) ((-579 . -23) T) ((-108 . -513) NIL) ((-517 . -23) T) ((-168 . -408) 76950) ((-1132 . -1092) T) ((-1271 . -1270) 76934) ((-695 . -790) T) ((-695 . -787) T) ((-1112 . -306) T) ((-378 . -146) T) ((-279 . -609) 76916) ((-1219 . -987) 76886) ((-48 . -915) T) ((-669 . -488) 76870) ((-250 . -1263) 76840) ((-249 . -1263) 76810) ((-1168 . -845) T) ((-1105 . -171) 76789) ((-1112 . -1017) T) ((-1041 . -34) T) ((-831 . -146) 76768) ((-831 . -144) 76747) ((-732 . -107) 76731) ((-608 . -131) T) ((-481 . -1092) 76521) ((-1170 . -1051) T) ((-866 . -451) T) ((-85 . -1207) T) ((-239 . -38) 76491) ((-140 . -107) 76473) ((-707 . -376) 76457) ((-828 . -612) 76325) ((-1112 . -544) T) ((-577 . -102) T) ((-129 . -489) 76307) ((-389 . -1050) 76291) ((-1279 . -721) T) ((-1164 . -944) 76260) ((-129 . -609) 76227) ((-52 . -609) 76209) ((-1117 . -944) 76176) ((-647 . -410) 76160) ((-1268 . -1051) T) ((-617 . -1050) 76144) ((-656 . -25) T) ((-656 . -21) T) ((-1150 . -513) NIL) ((-1248 . -102) T) ((-1241 . -102) T) ((-389 . -111) 76123) ((-221 . -253) 76107) ((-1220 . -102) T) ((-1048 . -1092) T) ((-999 . -1143) T) ((-1048 . -1047) 76047) ((-813 . -1092) T) ((-342 . -1211) T) ((-631 . -642) 76031) ((-617 . -111) 76010) ((-603 . -642) 75994) ((-593 . -102) T) ((-310 . -489) 75975) ((-583 . -130) T) ((-592 . -102) T) ((-413 . -1092) T) ((-384 . -1092) T) ((-310 . -609) 75941) ((-226 . -1092) 75919) ((-641 . -513) 75852) ((-628 . -513) 75696) ((-828 . -1044) 75675) ((-639 . -150) 75659) ((-342 . -554) T) ((-707 . -895) 75602) ((-548 . -228) 75552) ((-1248 . -283) 75518) ((-1072 . -289) 75469) ((-486 . -843) T) ((-222 . -1104) T) ((-1241 . -283) 75435) ((-1220 . -283) 75401) ((-999 . -38) 75351) ((-216 . -843) T) ((-1201 . -492) 75317) ((-909 . -38) 75269) ((-838 . -789) 75248) ((-838 . -786) 75227) ((-838 . -721) 75206) ((-358 . -289) T) ((-352 . -289) T) ((-344 . -289) T) ((-168 . -451) 75137) ((-426 . -38) 75121) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -789) 75100) ((-406 . -786) 75079) ((-406 . -721) T) ((-499 . -287) 75054) ((-476 . -1050) 75019) ((-652 . -130) T) ((-617 . -612) 74988) ((-1105 . -513) 74921) ((-335 . -130) T) ((-168 . -401) 74900) ((-481 . -712) 74842) ((-810 . -285) 74819) ((-476 . -111) 74775) ((-647 . -1051) T) ((-1229 . -451) 74706) ((-1267 . -1075) T) ((-1266 . -1075) T) ((-1079 . -130) T) ((-1048 . -712) 74648) ((-263 . -845) 74627) ((-246 . -845) 74606) ((-777 . -130) T) ((-775 . -130) T) ((-569 . -451) T) ((-1022 . -513) 74539) ((-617 . -1044) T) ((-589 . -1092) T) ((-532 . -172) T) ((-460 . -130) T) ((-453 . -130) T) ((-45 . -1092) T) ((-384 . -712) 74509) ((-812 . -1092) T) ((-475 . -513) 74442) ((-462 . -513) 74375) ((-452 . -366) 74345) ((-45 . -606) 74324) ((-315 . -301) T) ((-476 . -612) 74274) ((-664 . -609) 74236) ((-59 . -845) 74215) ((-1220 . -308) 74100) ((-999 . -399) 74082) ((-810 . -600) 74059) ((-515 . -845) 74038) ((-495 . -845) 74017) ((-40 . -1211) T) ((-994 . -1033) 73913) ((-50 . -130) T) ((-579 . -130) T) ((-517 . -130) T) ((-293 . -642) 73773) ((-342 . -328) 73750) ((-342 . -362) T) ((-321 . -322) 73727) ((-318 . -285) 73712) ((-40 . -554) T) ((-378 . -1192) T) ((-378 . -1195) T) ((-1030 . -1183) 73687) ((-1180 . -234) 73637) ((-1159 . -230) 73589) ((-329 . -1092) T) ((-378 . -95) T) ((-378 . -35) T) ((-1030 . -107) 73535) ((-476 . -1044) T) ((-478 . -234) 73485) ((-1151 . -488) 73419) ((-1280 . -1050) 73403) ((-380 . -1050) 73387) ((-476 . -242) T) ((-811 . -102) T) ((-709 . -146) 73366) ((-709 . -144) 73345) ((-483 . -488) 73329) ((-484 . -334) 73298) ((-1280 . -111) 73277) ((-511 . -1092) T) ((-481 . -171) 73256) ((-994 . -376) 73240) ((-412 . -102) T) ((-380 . -111) 73219) ((-994 . -337) 73203) ((-278 . -978) 73187) ((-277 . -978) 73171) ((-1278 . -609) 73153) ((-1276 . -609) 73135) ((-110 . -513) NIL) ((-1164 . -1232) 73119) ((-849 . -847) 73103) ((-1170 . 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. -130) T) ((-603 . -130) T) ((-353 . -451) T) ((-239 . -367) 17123) ((-378 . -171) T) ((-1240 . -1051) T) ((-1219 . -1051) T) ((-224 . -997) T) ((-811 . -612) 16860) ((-693 . -386) T) ((-417 . -721) T) ((-695 . -1211) T) ((-1134 . -635) 16808) ((-578 . -864) 16792) ((-1271 . -1050) 16776) ((-1151 . -1183) 16752) ((-695 . -554) T) ((-126 . -1092) 16730) ((-709 . -1092) T) ((-481 . -895) 16662) ((-248 . -1092) T) ((-186 . -1092) T) ((-652 . -38) 16632) ((-353 . -401) T) ((-315 . -146) 16611) ((-315 . -144) 16590) ((-128 . -513) NIL) ((-116 . -554) T) ((-312 . -146) 16546) ((-312 . -144) 16502) ((-48 . -451) T) ((-161 . -1092) T) ((-156 . -1092) T) ((-1151 . -107) 16449) ((-777 . -1143) 16427) ((-683 . -34) T) ((-1271 . -111) 16406) ((-548 . -34) T) ((-483 . -107) 16390) ((-250 . -287) 16367) ((-249 . -287) 16344) ((-866 . -285) 16295) ((-45 . -1207) T) ((-1213 . -839) T) ((-811 . -1044) T) ((-1170 . -47) 16272) ((-811 . -325) 16234) ((-1079 . -38) 16083) ((-811 . -232) 16062) ((-777 . 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-882) 136597) ((-129 . -846) T) ((-1165 . -1034) 136477) ((-1118 . -1034) 136360) ((-183 . -610) 136342) ((-850 . -1034) 136238) ((-778 . -286) 136165) ((-813 . -1105) T) ((-1030 . -722) T) ((-599 . -646) 136149) ((-1042 . -972) 136078) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1144) 136056) ((-689 . -1052) T) ((-599 . -373) 136040) ((-351 . -452) T) ((-343 . -290) T) ((-1258 . -1093) T) ((-248 . -1093) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1093) T) ((-694 . -1093) T) ((-361 . -473) T) ((-1202 . -610) 136022) ((-1165 . -377) 136006) ((-1118 . -377) 135990) ((-1020 . -411) 135952) ((-141 . -229) 135934) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -610) 135916) ((-708 . -38) 135745) ((-1257 . -1255) 135729) ((-351 . -402) T) ((-1257 . -1093) 135679) ((-579 . -713) 135666) ((-563 . -713) 135653) ((-495 . -713) 135618) ((-316 . -626) 135597) ((-832 . -722) T) ((-823 . -722) T) ((-640 . -1208) T) ((-1073 . 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133360) ((-868 . -905) 133339) ((-126 . -34) T) ((-813 . -131) T) ((-644 . -610) 133321) ((-577 . -102) T) ((-355 . -1276) 133305) ((-352 . -1276) 133289) ((-344 . -1276) 133273) ((-127 . -514) 133206) ((-121 . -514) 133139) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133077) ((-222 . -102) 133055) ((-689 . -1093) T) ((-694 . -172) T) ((-868 . -643) 133007) ((-65 . -384) T) ((-275 . -610) 132989) ((-65 . -395) T) ((-948 . -377) 132973) ((-866 . -290) T) ((-50 . -610) 132955) ((-995 . -38) 132903) ((-580 . -610) 132885) ((-481 . -377) 132869) ((-580 . -611) 132851) ((-518 . -610) 132833) ((-906 . -1276) 132820) ((-867 . -1208) T) ((-696 . -452) T) ((-495 . -514) 132786) ((-487 . -363) T) ((-355 . -368) 132765) ((-352 . -368) 132744) ((-344 . -368) 132723) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1280 . -1271) 132707) ((-867 . -880) 132684) ((-867 . -882) NIL) ((-960 . -846) 132583) ((-811 . -846) 132534) ((-649 . -651) 132518) ((-1194 . -34) T) 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NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -610) 128993) ((-394 . -610) 128975) ((-474 . -722) T) ((-1113 . -844) T) ((-888 . -1034) 128943) ((-108 . -846) T) ((-653 . -1051) 128927) ((-487 . -131) T) ((-1243 . -1052) T) ((-217 . -131) T) ((-1149 . -102) 128905) ((-99 . -1093) T) ((-245 . -661) 128889) ((-245 . -646) 128873) ((-653 . -111) 128852) ((-584 . -613) 128836) ((-316 . -411) 128820) ((-245 . -373) 128804) ((-1152 . -235) 128751) ((-995 . -231) 128735) ((-74 . -1208) T) ((-48 . -172) T) ((-696 . -387) T) ((-696 . -143) T) ((-1280 . -102) T) ((-1188 . -613) 128717) ((-1080 . -1051) 128560) ((-264 . -905) 128539) ((-247 . -905) 128518) ((-778 . -1051) 128341) ((-776 . -1051) 128184) ((-605 . -1208) T) ((-1157 . -610) 128166) ((-1080 . -111) 127995) ((-1042 . -102) T) ((-475 . -1208) T) ((-461 . -1051) 127966) ((-454 . -1051) 127809) ((-659 . -643) 127793) ((-867 . -307) T) ((-778 . -111) 127602) 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125544) ((-653 . -1045) T) ((-1285 . -1093) T) ((-454 . -613) 125329) ((-169 . -307) 125260) ((-418 . -23) T) ((-40 . -610) 125242) ((-40 . -611) 125226) ((-108 . -988) 125208) ((-116 . -865) 125192) ((-644 . -613) 125176) ((-48 . -514) 125142) ((-1194 . -1006) 125126) ((-1174 . -610) 125093) ((-1181 . -34) T) ((-950 . -610) 125059) ((-917 . -610) 125041) ((-1106 . -846) 124992) ((-767 . -610) 124974) ((-667 . -610) 124956) ((-1149 . -309) 124894) ((-479 . -34) T) ((-1085 . -1208) T) ((-477 . -452) T) ((-1134 . -34) T) ((-1080 . -1045) T) ((-50 . -613) 124863) ((-778 . -1045) T) ((-776 . -1045) T) ((-642 . -235) 124847) ((-629 . -235) 124793) ((-580 . -613) 124743) ((-518 . -613) 124673) ((-1230 . -307) 124652) ((-1080 . -326) 124613) ((-454 . -1045) T) ((-1171 . -21) T) ((-1080 . -233) 124592) ((-778 . -326) 124569) ((-778 . -233) T) ((-776 . -326) 124541) ((-727 . -1212) 124520) ((-327 . -646) 124504) ((-1171 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124483) ((-327 . -373) 124467) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1144) NIL) ((-727 . -555) 124398) ((-632 . -102) T) ((-604 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124306) ((-897 . -1093) 124284) ((-50 . -1045) T) ((-1269 . -21) T) ((-1269 . -25) T) ((-1167 . -555) 124263) ((-1166 . -1212) 124242) ((-580 . -1045) T) ((-518 . -1045) T) ((-1160 . -1212) 124221) ((-361 . -1034) 124205) ((-322 . -1034) 124189) ((-1020 . -290) T) ((-379 . -882) 124171) ((-1166 . -555) 124122) ((-1160 . -555) 124073) ((-999 . -38) 124018) ((-795 . -1105) T) ((-906 . -722) T) ((-580 . -243) T) ((-580 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1119 . -555) 123997) ((-354 . -290) T) ((-642 . -690) 123981) ((-379 . -1034) 123941) ((-1113 . -1052) T) ((-103 . -125) 123925) ((-795 . -23) T) ((-1279 . -1274) 123901) ((-1257 . -286) 123878) ((-407 . -309) 123843) ((-1277 . -1274) 123822) ((-1243 . -1093) T) ((-866 . -610) 123804) ((-832 . -1034) 123773) ((-203 . -783) T) ((-202 . -783) T) ((-201 . -783) T) ((-200 . -783) T) ((-199 . -783) T) ((-198 . -783) T) ((-197 . -783) T) ((-196 . -783) T) ((-195 . -783) T) ((-194 . -783) T) ((-547 . -610) 123755) ((-495 . -998) T) ((-274 . -835) T) ((-273 . -835) T) ((-272 . -835) T) ((-271 . -835) T) ((-48 . -290) T) ((-270 . -835) T) ((-269 . -835) T) ((-268 . -835) T) ((-193 . -783) T) ((-609 . -846) T) ((-649 . -411) 123739) ((-223 . -613) 123701) ((-110 . -846) T) ((-648 . -21) T) ((-648 . -25) T) ((-1280 . -38) 123671) ((-117 . -286) 123622) ((-1257 . -19) 123606) ((-1257 . -601) 123583) ((-1270 . -1093) T) ((-1070 . -1093) T) ((-983 . -1093) T) ((-959 . -131) T) ((-733 . -1093) T) ((-731 . -131) T) ((-711 . -131) T) ((-511 . -789) T) ((-407 . -1144) 123561) ((-453 . -131) T) ((-511 . -790) T) ((-223 . -1045) T) ((-294 . -102) 123343) ((-141 . -1093) T) ((-694 . -998) T) ((-91 . -1208) T) ((-127 . -610) 123275) ((-121 . -610) 123207) ((-1285 . -172) T) 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T) ((-689 . -286) NIL) ((-1258 . -610) 122423) ((-1167 . -23) T) ((-1166 . -23) T) ((-1160 . -23) T) ((-1000 . -555) T) ((-1135 . -231) 122407) ((-910 . -555) T) ((-1119 . -23) T) ((-248 . -610) 122389) ((-1068 . -1093) T) ((-795 . -131) T) ((-706 . -610) 122371) ((-316 . -713) 122281) ((-313 . -713) 122210) ((-694 . -610) 122192) ((-694 . -611) 122137) ((-407 . -400) 122121) ((-438 . -1093) T) ((-487 . -25) T) ((-487 . -21) T) ((-1113 . -1093) T) ((-217 . -25) T) ((-217 . -21) T) ((-708 . -411) 122105) ((-710 . -1034) 122074) ((-1257 . -610) 121986) ((-1257 . -611) 121947) ((-1243 . -172) T) ((-245 . -34) T) ((-343 . -613) 121877) ((-394 . -613) 121859) ((-922 . -970) T) ((-1194 . -1208) T) ((-657 . -787) 121838) ((-657 . -790) 121817) ((-398 . -395) T) ((-523 . -102) 121795) ((-1031 . -1093) T) ((-222 . -991) 121779) ((-504 . -102) T) ((-620 . -610) 121761) ((-45 . -846) NIL) ((-620 . -611) 121738) ((-1031 . -607) 121713) ((-897 . -514) 121646) ((-343 . -1045) T) ((-117 . -611) NIL) 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119356) ((-1000 . -1105) T) ((-910 . -1105) T) ((-82 . -610) 119338) ((-40 . -1045) T) ((-866 . -1051) 119325) ((-999 . -349) NIL) ((-868 . -896) 119284) ((-696 . -102) T) ((-967 . -23) T) ((-599 . -1208) T) ((-910 . -23) T) ((-866 . -111) 119269) ((-427 . -1105) T) ((-213 . -1093) T) ((-474 . -47) 119239) ((-134 . -102) T) ((-40 . -233) 119211) ((-40 . -243) T) ((-116 . -102) T) ((-594 . -555) 119190) ((-593 . -555) 119169) ((-689 . -610) 119151) ((-689 . -611) 119059) ((-316 . -514) 119025) ((-313 . -514) 118917) ((-1241 . -1034) 118901) ((-1220 . -1034) 118687) ((-995 . -411) 118671) ((-427 . -23) T) ((-1113 . -172) T) ((-1243 . -290) T) ((-649 . -713) 118641) ((-144 . -1093) T) ((-48 . -998) T) ((-407 . -231) 118625) ((-295 . -235) 118575) ((-867 . -916) T) ((-867 . -816) NIL) ((-866 . -613) 118547) ((-860 . -846) T) ((-1220 . -338) 118517) ((-1220 . -377) 118487) ((-222 . -1114) 118471) ((-1257 . -288) 118448) ((-1202 . -643) 118373) ((-959 . -21) T) ((-959 . -25) T) ((-731 . -21) 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. -1208) T) ((-497 . -1208) T) ((-496 . -1208) T) ((-437 . -610) 114896) ((-434 . -610) 114878) ((-3 . -102) T) ((-1023 . -1201) 114847) ((-829 . -102) T) ((-684 . -57) 114805) ((-694 . -1045) T) ((-50 . -643) 114779) ((-289 . -452) T) ((-476 . -1201) 114748) ((0 . -102) T) ((-580 . -643) 114713) ((-518 . -643) 114658) ((-49 . -102) T) ((-906 . -1034) 114645) ((-694 . -243) T) ((-1073 . -409) 114624) ((-727 . -636) 114572) ((-995 . -1093) T) ((-708 . -172) 114463) ((-620 . -613) 114358) ((-487 . -988) 114340) ((-264 . -377) 114324) ((-247 . -377) 114308) ((-399 . -1093) T) ((-1022 . -102) 114286) ((-339 . -38) 114270) ((-217 . -988) 114252) ((-117 . -613) 114182) ((-174 . -38) 114114) ((-1241 . -307) 114093) ((-1220 . -307) 114072) ((-653 . -722) T) ((-99 . -610) 114054) ((-1160 . -636) 114006) ((-485 . -25) T) ((-485 . -21) T) ((-1220 . -1018) 113958) ((-620 . -1045) T) ((-379 . -404) T) ((-390 . -102) T) ((-1098 . -615) 113873) ((-264 . -896) 113819) ((-247 . -896) 113796) ((-117 . 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. -309) 100429) ((-570 . -131) T) ((-618 . -844) 100408) ((-1149 . -489) 100392) ((-1143 . -151) 100342) ((-1139 . -610) 100304) ((-1139 . -611) 100265) ((-1020 . -787) T) ((-1020 . -790) T) ((-1020 . -722) T) ((-708 . -1051) 100088) ((-484 . -309) 100026) ((-453 . -417) 99996) ((-351 . -172) T) ((-289 . -38) 99983) ((-274 . -102) T) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-343 . -1034) 99960) ((-268 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-203 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-354 . -722) T) ((-708 . -111) 99769) ((-665 . -231) 99753) ((-580 . -307) T) ((-518 . -307) T) ((-294 . -514) 99702) ((-108 . -309) NIL) ((-72 . -395) T) ((-1106 . -102) 99492) ((-829 . -411) 99476) ((-1113 . -791) T) 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. -309) 98159) ((-1119 . -1193) 98125) ((-708 . -1045) T) ((-1056 . -636) 98107) ((-1073 . -38) 97975) ((-948 . -636) 97923) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1105) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97902) ((-708 . -326) 97879) ((-481 . -636) 97827) ((-40 . -1034) 97715) ((-708 . -233) T) ((-696 . -713) 97702) ((-339 . -1093) T) ((-174 . -1093) T) ((-331 . -846) T) ((-418 . -452) 97652) ((-379 . -23) T) ((-359 . -38) 97617) ((-353 . -38) 97582) ((-345 . -38) 97547) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1105) T) ((-108 . -38) 97497) ((-823 . -1105) T) ((-770 . -1093) T) ((-116 . -713) 97484) ((-667 . -1034) 97468) ((-609 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1149 . -286) 97445) ((-1106 . -309) 97383) ((-1095 . -235) 97367) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97344) ((-96 . -102) T) ((-648 . -848) 97328) ((-1128 . -1076) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97297) ((-948 . -25) T) ((-948 . -21) T) ((-618 . -1052) T) ((-1113 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 97235) ((-885 . -610) 97217) ((-881 . -610) 97199) ((-251 . -846) 97150) ((-250 . -846) 97101) ((-523 . -514) 97034) ((-867 . -636) 97011) ((-476 . -309) 96949) ((-463 . -309) 96887) ((-351 . -290) T) ((-1149 . -1245) 96871) ((-1135 . -610) 96833) ((-1135 . -611) 96794) ((-1133 . -102) T) ((-995 . -1051) 96690) ((-40 . -896) 96642) ((-1149 . -601) 96619) ((-1285 . -643) 96606) ((-862 . -490) 96583) ((-1057 . -151) 96529) ((-868 . -1212) T) ((-995 . -111) 96411) ((-339 . -713) 96395) ((-862 . -610) 96357) ((-174 . -713) 96289) ((-407 . -286) 96247) ((-868 . -555) T) ((-108 . -400) 96229) ((-84 . -384) T) ((-84 . -395) T) ((-696 . -172) T) ((-614 . -610) 96211) ((-99 . -722) T) ((-482 . -102) 96001) ((-99 . -473) T) ((-116 . -172) T) ((-1106 . -38) 95971) ((-169 . -636) 95919) ((-1049 . -102) T) ((-995 . -613) 95809) ((-867 . -25) T) ((-811 . -238) 95788) 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91075) ((-910 . -452) T) ((-65 . -610) 91057) ((-629 . -229) 91003) ((-474 . -23) T) ((-1113 . -790) T) ((-868 . -131) T) ((-1113 . -787) T) ((-1272 . -1274) 90982) ((-1113 . -722) T) ((-649 . -643) 90956) ((-294 . -610) 90697) ((-1135 . -613) 90615) ((-1031 . -34) T) ((-811 . -844) 90594) ((-579 . -307) T) ((-563 . -307) T) ((-495 . -307) T) ((-1281 . -713) 90564) ((-689 . -377) 90546) ((-689 . -338) 90528) ((-477 . -172) T) ((-381 . -713) 90498) ((-862 . -613) 90433) ((-867 . -846) NIL) ((-563 . -1018) T) ((-495 . -1018) T) ((-1126 . -610) 90415) ((-1106 . -238) 90394) ((-214 . -102) T) ((-1143 . -102) T) ((-71 . -610) 90376) ((-1135 . -1045) T) ((-1171 . -38) 90273) ((-854 . -610) 90255) ((-563 . -545) T) ((-665 . -1052) T) ((-727 . -945) 90208) ((-1135 . -233) 90187) ((-1075 . -1093) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 90132) ((-901 . -102) T) ((-862 . -1045) T) ((-689 . -896) NIL) ((-355 . -329) 90116) ((-355 . -363) T) ((-352 . -329) 90100) ((-352 . -363) T) 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-290) T) ((-1280 . -1045) T) ((-1213 . -102) T) ((-1057 . -102) T) ((-839 . -613) 88135) ((-500 . -514) NIL) ((-698 . -102) T) ((-482 . -238) 88114) ((-407 . -613) 88012) ((-1165 . -145) 87991) ((-1165 . -147) 87970) ((-1118 . -147) 87949) ((-1118 . -145) 87928) ((-632 . -1051) 87912) ((-604 . -1051) 87896) ((-665 . -1093) T) ((-665 . -1048) 87836) ((-1167 . -1248) 87820) ((-1167 . -1235) 87797) ((-487 . -1144) T) ((-1166 . -1240) 87758) ((-1166 . -1235) 87728) ((-1166 . -1238) 87712) ((-217 . -1144) T) ((-343 . -916) T) ((-814 . -266) 87696) ((-632 . -111) 87675) ((-604 . -111) 87654) ((-1160 . -1219) 87615) ((-839 . -1045) 87594) ((-1160 . -1235) 87571) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1160 . -1217) 87555) ((-407 . -1045) T) ((-319 . -1052) T) ((-689 . -307) T) ((-108 . -844) T) ((-708 . -722) T) ((-407 . -243) T) ((-407 . -233) 87534) ((-487 . -38) 87484) ((-217 . -38) 87434) ((-474 . -493) 87400) ((-1151 . 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-172) 83326) ((-727 . -102) T) ((-1022 . -610) 83293) ((-500 . -286) 83268) ((-316 . -377) 83237) ((-313 . -377) 83198) ((-313 . -338) 83159) ((-1078 . -610) 83141) ((-812 . -945) 83088) ((-657 . -131) T) ((-1230 . -145) 83067) ((-1230 . -147) 83046) ((-1167 . -102) T) ((-1166 . -102) T) ((-1160 . -102) T) ((-1152 . -1093) T) ((-1119 . -102) T) ((-222 . -34) T) ((-289 . -713) 83033) ((-1152 . -607) 83009) ((-591 . -309) NIL) ((-484 . -1093) 82987) ((-390 . -610) 82969) ((-510 . -846) T) ((-1143 . -229) 82919) ((-1249 . -1248) 82903) ((-1249 . -1235) 82880) ((-1242 . -1240) 82841) ((-1242 . -1235) 82811) ((-1242 . -1238) 82795) ((-1221 . -1219) 82756) ((-1221 . -1235) 82733) ((-618 . -610) 82715) ((-1221 . -1217) 82699) ((-694 . -916) T) ((-1167 . -284) 82665) ((-1166 . -284) 82631) ((-1160 . -284) 82597) ((-1073 . -1093) T) ((-1055 . -1093) T) ((-48 . -302) T) ((-316 . -896) 82563) ((-313 . -896) NIL) ((-1055 . -1062) 82542) ((-1113 . -882) 82524) ((-795 . -38) 82508) ((-264 . -636) 82456) ((-247 . -636) 82404) ((-696 . -1051) 82391) ((-593 . -1235) 82368) ((-1119 . -284) 82334) ((-319 . -172) 82265) ((-359 . -1093) T) ((-353 . -1093) T) ((-345 . -1093) T) ((-500 . -19) 82247) ((-1113 . -1034) 82229) ((-1095 . -151) 82213) ((-108 . -1093) T) ((-116 . -1051) 82200) ((-707 . -363) T) ((-500 . -601) 82175) ((-696 . -111) 82160) ((-436 . -102) T) ((-45 . -1142) 82110) ((-116 . -111) 82095) ((-632 . -716) T) ((-604 . -716) T) ((-811 . -514) 82028) ((-1031 . -1208) T) ((-939 . -151) 82012) ((-1215 . -610) 81994) ((-1165 . -452) 81925) ((-1159 . -1093) T) ((-1151 . -1093) T) ((-525 . -102) T) ((-520 . -102) 81875) ((-1135 . -643) 81849) ((-1118 . -452) 81800) ((-1080 . -1212) 81779) ((-778 . -1212) 81758) ((-776 . -1212) 81737) ((-62 . -1208) T) ((-477 . -610) 81689) ((-477 . -611) 81611) ((-1080 . -555) 81542) ((-990 . -1093) T) ((-778 . -555) 81453) ((-776 . -555) 81384) ((-482 . -411) 81353) ((-620 . -916) 81332) ((-454 . -1212) 81311) ((-727 . -309) 81298) ((-696 . 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. -23) T) ((-767 . -1105) T) ((-563 . -1212) T) ((-495 . -1212) T) ((-319 . -610) 70466) ((-1000 . -231) 70448) ((-169 . -166) 70432) ((-579 . -555) T) ((-563 . -555) T) ((-495 . -555) T) ((-767 . -23) T) ((-1241 . -147) 70411) ((-1152 . -601) 70387) ((-1241 . -145) 70366) ((-1023 . -489) 70350) ((-1220 . -145) 70275) ((-1220 . -147) 70200) ((-1272 . -1278) 70179) ((-476 . -489) 70163) ((-463 . -489) 70147) ((-523 . -34) T) ((-648 . -713) 70117) ((-112 . -963) T) ((-657 . -846) 70096) ((-1171 . -172) 70047) ((-365 . -102) T) ((-240 . -238) 70026) ((-251 . -102) T) ((-250 . -102) T) ((-1230 . -945) 69995) ((-245 . -846) 69974) ((-812 . -38) 69823) ((-45 . -514) 69615) ((-1151 . -286) 69590) ((-214 . -1093) T) ((-1143 . -1093) T) ((-1143 . -607) 69569) ((-584 . -25) T) ((-584 . -21) T) ((-1095 . -309) 69507) ((-959 . -411) 69491) ((-694 . -1212) T) ((-629 . -286) 69466) ((-1080 . -636) 69414) ((-778 . -636) 69362) ((-776 . -636) 69310) ((-343 . -131) T) ((-289 . -610) 69292) ((-901 . 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-1051) 68847) ((-517 . -1076) T) ((-461 . -25) T) ((-117 . -555) T) ((-461 . -21) T) ((-454 . -25) T) ((-454 . -21) T) ((-1279 . -1051) 68831) ((-1135 . -1034) 68727) ((-813 . -290) 68706) ((-1277 . -1051) 68690) ((-819 . -1093) T) ((-1241 . -1193) 68656) ((-962 . -963) T) ((-665 . -111) 68635) ((-295 . -514) 68427) ((-1241 . -1196) 68393) ((-1241 . -95) 68359) ((-1224 . -102) 68337) ((-251 . -309) 68275) ((-250 . -309) 68213) ((-1221 . -231) 68165) ((-1152 . -611) NIL) ((-1152 . -610) 68147) ((-1220 . -1193) 68113) ((-1220 . -1196) 68079) ((-1215 . -368) T) ((-96 . -93) T) ((-1213 . -840) T) ((-1135 . -377) 68063) ((-1113 . -816) T) ((-1113 . -916) T) ((-1106 . -601) 68040) ((-1073 . -611) 68024) ((-484 . -610) 67956) ((-811 . -288) 67933) ((-605 . -151) 67880) ((-418 . -1052) T) ((-487 . -713) 67830) ((-482 . -489) 67814) ((-327 . -846) 67793) ((-339 . -643) 67767) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67717) ((-169 . -720) 67688) ((-174 . -643) 67620) ((-580 . -21) T) 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. -1093) T) ((-316 . -1193) 12842) ((-316 . -1196) 12821) ((-1157 . -102) T) ((-316 . -955) 12800) ((-134 . -1105) T) ((-116 . -1105) T) ((-599 . -1255) 12784) ((-696 . -23) T) ((-599 . -1093) 12734) ((-316 . -95) 12713) ((-91 . -514) 12646) ((-174 . -363) T) ((-251 . -613) 12376) ((-250 . -613) 12106) ((-316 . -35) 12085) ((-605 . -489) 12019) ((-134 . -23) T) ((-116 . -23) T) ((-962 . -102) T) ((-714 . -1093) T) ((-475 . -489) 11956) ((-407 . -636) 11904) ((-648 . -1034) 11800) ((-954 . -489) 11784) ((-355 . -1052) T) ((-352 . -1052) T) ((-344 . -1052) T) ((-264 . -1052) T) ((-247 . -1052) T) ((-867 . -611) NIL) ((-867 . -610) 11766) ((-1268 . -490) 11747) ((-1267 . -490) 11728) ((-1280 . -21) T) ((-1268 . -610) 11694) ((-1267 . -610) 11660) ((-570 . -998) T) ((-727 . -722) T) ((-1280 . -25) T) ((-251 . -1045) 11590) ((-250 . -1045) 11520) ((-72 . -1208) T) ((-251 . -233) 11472) ((-250 . -233) 11424) ((-40 . -102) T) ((-906 . -1052) T) ((-128 . -489) 11406) ((-1174 . -102) T) ((-1167 . -722) T) ((-1166 . -722) T) ((-1160 . -722) T) ((-1160 . -787) NIL) ((-1160 . -790) NIL) ((-950 . -102) T) ((-917 . -102) T) ((-1119 . -722) T) ((-767 . -102) T) ((-667 . -102) T) ((-546 . -610) 11388) ((-474 . -1093) T) ((-339 . -1105) T) ((-174 . -1105) T) ((-319 . -916) 11367) ((-1241 . -713) 11208) ((-868 . -172) T) ((-1220 . -713) 11022) ((-839 . -21) 10974) ((-839 . -25) 10926) ((-245 . -1142) 10910) ((-126 . -514) 10843) ((-407 . -25) T) ((-407 . -21) T) ((-339 . -23) T) ((-169 . -611) 10609) ((-169 . -610) 10591) ((-174 . -23) T) ((-640 . -288) 10568) ((-520 . -34) T) ((-894 . -610) 10550) ((-89 . -1208) T) ((-837 . -610) 10532) ((-804 . -610) 10514) ((-765 . -610) 10496) ((-672 . -610) 10478) ((-240 . -643) 10326) ((-1169 . -1093) T) ((-1165 . -1051) 10149) ((-1143 . -1208) T) ((-1118 . -1051) 9992) ((-850 . -1051) 9976) ((-1224 . -615) 9960) ((-1165 . -111) 9769) ((-1118 . -111) 9598) ((-850 . -111) 9577) ((-1230 . -611) NIL) ((-1230 . -610) 9559) ((-343 . -1144) T) ((-851 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-286) 7868) ((-116 . -131) T) ((-477 . -1212) T) ((-605 . -601) 7844) ((-475 . -601) 7823) ((-336 . -335) 7792) ((-536 . -1093) T) ((-477 . -555) T) ((-1165 . -1045) T) ((-1118 . -1045) T) ((-850 . -1045) T) ((-240 . -787) 7771) ((-240 . -790) 7722) ((-240 . -789) 7701) ((-1165 . -326) 7678) ((-240 . -722) 7588) ((-954 . -19) 7572) ((-487 . -377) 7554) ((-487 . -338) 7536) ((-1118 . -326) 7508) ((-354 . -1264) 7485) ((-217 . -377) 7467) ((-217 . -338) 7449) ((-954 . -601) 7426) ((-1165 . -233) T) ((-659 . -1093) T) ((-641 . -1093) T) ((-1253 . -1093) T) ((-1181 . -1093) T) ((-1080 . -253) 7363) ((-355 . -1093) T) ((-352 . -1093) T) ((-344 . -1093) T) ((-264 . -1093) T) ((-247 . -1093) T) ((-84 . -1208) T) ((-127 . -102) 7341) ((-121 . -102) 7319) ((-1181 . -607) 7298) ((-479 . -1093) T) ((-1134 . -1093) T) ((-479 . -607) 7277) ((-251 . -791) 7228) ((-251 . -788) 7179) ((-250 . -791) 7130) ((-40 . -1144) NIL) ((-250 . -788) 7081) ((-1108 . -613) 7062) ((-128 . -19) 7044) ((-1073 . -916) 6995) ((-1000 . -790) T) ((-1000 . -787) T) ((-1000 . -722) T) ((-967 . -790) T) ((-128 . -601) 6970) ((-910 . -722) T) ((-91 . -489) 6954) ((-487 . -896) NIL) ((-906 . -1093) T) ((-225 . -1051) 6919) ((-868 . -290) T) ((-217 . -896) NIL) ((-829 . -1105) 6898) ((-59 . -1093) 6848) ((-519 . -1093) 6826) ((-516 . -1093) 6776) ((-497 . -1093) 6754) ((-496 . -1093) 6704) ((-579 . -102) T) ((-563 . -102) T) ((-495 . -102) T) ((-474 . -172) 6635) ((-359 . -916) T) ((-353 . -916) T) ((-345 . -916) T) ((-225 . -111) 6591) ((-829 . -23) 6543) ((-427 . -722) T) ((-108 . -916) T) ((-40 . -38) 6488) ((-108 . -816) T) ((-580 . -349) T) ((-518 . -349) T) ((-1220 . -514) 6348) ((-316 . -452) 6327) ((-313 . -452) T) ((-888 . -610) 6309) ((-832 . -286) 6288) ((-339 . -131) T) ((-174 . -131) T) ((-294 . -25) 6152) ((-294 . -21) 6035) ((-45 . -1184) 6014) ((-66 . -610) 5996) ((-55 . -102) T) ((-599 . -514) 5929) ((-45 . -107) 5879) ((-815 . -613) 5863) ((-1095 . -425) 5847) ((-1095 . -368) 5826) ((-386 . -613) 5810) ((-324 . -613) 5794) ((-1057 . -1208) T) ((-1056 . -1051) 5781) ((-948 . -1051) 5624) ((-1258 . -102) T) ((-1257 . -102) 5574) ((-1056 . -111) 5559) ((-481 . -1051) 5402) ((-659 . -713) 5386) ((-948 . -111) 5215) ((-225 . -613) 5165) ((-477 . -363) T) ((-355 . -713) 5117) ((-352 . -713) 5069) ((-344 . -713) 5021) ((-264 . -713) 4870) ((-247 . -713) 4719) ((-1249 . -643) 4644) ((-1221 . -905) NIL) ((-1089 . -93) T) ((-1083 . -93) T) ((-939 . -646) 4628) ((-1067 . -93) T) ((-481 . -111) 4457) ((-1060 . -93) T) ((-1032 . -93) T) ((-939 . -373) 4441) ((-248 . -102) T) ((-1015 . -93) T) ((-74 . -610) 4423) ((-959 . -47) 4402) ((-706 . -102) T) ((-694 . -102) T) ((-1 . -1093) T) ((-618 . -1105) T) ((-1242 . -643) 4299) ((-623 . -93) T) ((-1189 . -610) 4281) ((-1081 . -610) 4263) ((-126 . -489) 4247) ((-483 . -93) T) ((-1069 . -610) 4229) ((-390 . -23) T) ((-87 . -1208) T) ((-218 . -93) T) ((-1221 . -643) 4081) ((-906 . -713) 4046) ((-618 . -23) T) ((-605 . -610) 4028) ((-605 . -611) NIL) ((-475 . -611) NIL) ((-475 . -610) 4010) ((-511 . -1093) T) ((-507 . -1093) T) ((-351 . -25) T) ((-351 . -21) T) ((-127 . -309) 3948) ((-121 . -309) 3886) ((-594 . -643) 3873) ((-225 . -1045) T) ((-593 . -643) 3798) ((-379 . -998) T) ((-225 . -243) T) ((-225 . -233) T) ((-1056 . -613) 3770) ((-1056 . -615) 3751) ((-954 . -611) 3712) ((-954 . -610) 3624) ((-948 . -613) 3413) ((-866 . -38) 3400) ((-709 . -613) 3350) ((-1241 . -290) 3301) ((-1220 . -290) 3252) ((-481 . -613) 3037) ((-1113 . -452) T) ((-502 . -846) T) ((-316 . -1132) 3016) ((-995 . -147) 2995) ((-995 . -145) 2974) ((-495 . -309) 2961) ((-295 . -1184) 2940) ((-1176 . -610) 2922) ((-1175 . -610) 2904) ((-867 . -1051) 2849) ((-477 . -1105) T) ((-139 . -831) 2831) ((-620 . -102) T) ((-1194 . -489) 2815) ((-251 . -368) 2794) ((-250 . -368) 2773) ((-1056 . -1045) T) ((-295 . -107) 2723) ((-130 . -610) 2705) ((-128 . -611) NIL) ((-128 . -610) 2671) ((-117 . -102) T) ((-948 . -1045) T) ((-867 . -111) 2600) ((-477 . -23) T) ((-481 . -1045) T) ((-1056 . -233) T) ((-948 . -326) 2569) ((-481 . -326) 2526) ((-355 . -172) T) ((-352 . -172) T) ((-344 . -172) T) ((-264 . -172) 2437) ((-247 . -172) 2348) ((-959 . -1034) 2244) ((-517 . -490) 2225) ((-731 . -1034) 2196) ((-517 . -610) 2162) ((-1098 . -102) T) ((-1085 . -610) 2129) ((-1030 . -610) 2111) ((-1270 . -151) 2095) ((-1268 . -613) 2076) ((-1262 . -610) 2058) ((-1249 . -722) T) ((-1242 . -722) T) ((-1221 . -787) NIL) ((-1221 . -790) NIL) ((-169 . -1051) 1968) ((-906 . -172) T) ((-867 . -613) 1898) ((-1221 . -722) T) ((-1267 . -613) 1879) ((-999 . -342) 1853) ((-996 . -514) 1786) ((-839 . -846) 1765) ((-563 . -1144) T) ((-474 . -290) 1716) ((-594 . -722) T) ((-361 . -610) 1698) ((-322 . -610) 1680) ((-418 . -1034) 1576) ((-593 . -722) T) ((-407 . -846) 1527) ((-169 . -111) 1423) ((-829 . -131) 1375) ((-733 . -151) 1359) ((-1257 . -309) 1297) ((-487 . -307) T) ((-379 . -610) 1264) ((-520 . -1006) 1248) ((-379 . -611) 1162) ((-217 . -307) T) ((-141 . -151) 1144) ((-710 . -286) 1123) ((-487 . -1018) T) ((-579 . -38) 1110) ((-563 . -38) 1097) ((-495 . -38) 1062) ((-217 . -1018) T) ((-867 . -1045) T) ((-832 . -610) 1044) ((-823 . -610) 1026) ((-821 . -610) 1008) ((-812 . -905) 987) ((-1281 . -1105) T) ((-1230 . -1051) 810) ((-851 . -1051) 794) ((-867 . -243) T) ((-867 . -233) NIL) ((-684 . -1208) T) ((-1281 . -23) T) ((-812 . -643) 719) ((-549 . -1208) T) ((-418 . -338) 703) ((-570 . -1051) 690) ((-1230 . -111) 499) ((-696 . -636) 481) ((-851 . -111) 460) ((-381 . -23) T) ((-169 . -613) 238) ((-1181 . -514) 30) ((-657 . -1093) T) ((-676 . -1093) T) ((-671 . -1093) T)) \ No newline at end of file
diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase
index 5f51ab94..eae6de58 100644
--- a/src/share/algebra/compress.daase
+++ b/src/share/algebra/compress.daase
@@ -1,6 +1,6 @@
-(30 . 3442698062)
-(4406 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
+(30 . 3443021569)
+(4410 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain|
ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join|
|ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&|
|OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup|
@@ -33,22 +33,22 @@
|BinaryRecursiveAggregate&| |BinaryRecursiveAggregate|
|BrillhartTests| |BinarySearchTree| |BitAggregate&| |BitAggregate|
|BinaryTreeCategory&| |BinaryTreeCategory| |BinaryTournament|
- |BinaryTree| |ByteBuffer| |Byte| |CancellationAbelianMonoid|
- |CachableSet| |CapsuleAst| |CardinalNumber|
- |CartesianTensorFunctions2| |CartesianTensor| |CaseAst| |CategoryAst|
- |CategoryConstructor| |Category| |CharacterClass| |CommonDenominator|
- |CombinatorialFunctionCategory| |Character| |CharacteristicNonZero|
- |CharacteristicPolynomialPackage| |CharacteristicZero|
- |ChangeOfVariable| |ComplexIntegerSolveLinearPolynomialEquation|
- |Collection&| |Collection| |CliffordAlgebra|
- |TwoDimensionalPlotClipping| |CollectAst| |ComplexRootPackage|
- |ColonAst| |Color| |CombinatorialFunction|
- |IntegerCombinatoricFunctions| |CombinatorialOpsCategory| |CommaAst|
- |Commutator| |CommonOperators| |CommuteUnivariatePolynomialCategory|
- |ComplexCategory&| |ComplexCategory| |ComplexFactorization|
- |ComplexFunctions2| |Complex| |ComplexPattern|
- |SubSpaceComponentProperty| |CommutativeRing| |Conduit|
- |ContinuedFraction| |Contour| |CoordinateSystems|
+ |BinaryTree| |ByteBuffer| |Byte| |ByteOrder|
+ |CancellationAbelianMonoid| |CachableSet| |CapsuleAst|
+ |CardinalNumber| |CartesianTensorFunctions2| |CartesianTensor|
+ |CaseAst| |CategoryAst| |CategoryConstructor| |Category|
+ |CharacterClass| |CommonDenominator| |CombinatorialFunctionCategory|
+ |Character| |CharacteristicNonZero| |CharacteristicPolynomialPackage|
+ |CharacteristicZero| |ChangeOfVariable|
+ |ComplexIntegerSolveLinearPolynomialEquation| |Collection&|
+ |Collection| |CliffordAlgebra| |TwoDimensionalPlotClipping|
+ |CollectAst| |ComplexRootPackage| |ColonAst| |Color|
+ |CombinatorialFunction| |IntegerCombinatoricFunctions|
+ |CombinatorialOpsCategory| |CommaAst| |Commutator| |CommonOperators|
+ |CommuteUnivariatePolynomialCategory| |ComplexCategory&|
+ |ComplexCategory| |ComplexFactorization| |ComplexFunctions2| |Complex|
+ |ComplexPattern| |SubSpaceComponentProperty| |CommutativeRing|
+ |Conduit| |ContinuedFraction| |Contour| |CoordinateSystems|
|CharacteristicPolynomialInMonogenicalAlgebra| |ComplexPatternMatch|
|CRApackage| |CoerceAst| |ComplexRootFindingPackage|
|CyclicStreamTools| |ConstructorCall| |ConstructorCategory&|
@@ -477,661 +477,661 @@
|XPolynomial| |XPolynomialRing| |XRecursivePolynomial|
|ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage|
|IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping|
- |Record| |Union| |tanintegrate| |cAtanh| |ScanFloatIgnoreSpacesIfCan|
- |alternating| |polynomialZeros| |clearTheFTable|
- |functionIsOscillatory| |denominators| |s14baf| |byte|
- |removeRedundantFactorsInContents| |exponent| |iisqrt3| |truncate|
- |deleteProperty!| |splitLinear| |setPredicates| |dmp2rfi| |totalLex|
- |atanIfCan| |FormatRoman| |cyclic| |iiacsc| |changeNameToObjf|
- |permutationRepresentation| |edf2ef| |radicalEigenvalues|
- |basisOfCenter| |coerceP| |complexZeros| |clearFortranOutputStack|
- |hasoln| |pmintegrate| |int| |lfinfieldint| |cyclicGroup|
- |binaryTournament| |OMReadError?| |forLoop| |outputGeneral| |or?|
- |zeroSetSplitIntoTriangularSystems| |bivariatePolynomials| |fortran|
- |complexRoots| |sturmSequence| |split!| |surface| |generalLambert|
- |fortranLiteral| |SFunction| |setIntersection| |palgint0| |f04atf|
- |prindINFO| |fortranLogical| |complete| |queue| |credPol| |replace|
- |setUnion| |rightScalarTimes!| |increment| |pade| |rightGcd| |f02akf|
- |f02adf| |removeRoughlyRedundantFactorsInContents| |laplace| |points|
- |fullDisplay| |apply| |makeViewport2D| |dimensions| |plus!|
- |partialDenominators| |predicates| |frobenius| |rk4| |currentEnv|
- |mapExpon| |nil| |f02fjf| |e02ahf| |removeSinSq| |numberOfOperations|
- |setAttributeButtonStep| |lambert| |monomial| |LazardQuotient2|
- |getIdentifier| |close!| |s17dlf| |size| |palglimint| |triangSolve|
- |call| |fractRagits| |ideal| |setFieldInfo| |multivariate| |OMbindTCP|
- |meatAxe| |perfectSqrt| |setlast!| |nthFractionalTerm| |sort|
- |spherical| |pointSizeDefault| |kovacic| |rootProduct| |baseRDEsys|
- |variables| |imagI| |sh| |clipWithRanges| |constantLeft| |approximate|
- |function| |calcRanges| |createLowComplexityNormalBasis|
- |removeRedundantFactorsInPols| |iidprod| |nary?| |df2fi|
- |completeEval| |mathieu23| |id| |rationalPower| |complex|
- |viewWriteAvailable| |qelt| |first| |alternatingGroup| |distance|
- |standardBasisOfCyclicSubmodule| |rootOfIrreduciblePoly| |palglimint0|
- |s13acf| |linear| |genericLeftDiscriminant| |transform| |rootsOf|
- |bivariateSLPEBR| |eval| |rest| |qsetelt| |sizeLess?| |cubic| |Aleph|
- |thetaCoord| |leftZero| |remainder| |curryRight| |table| |biRank|
- |equality| |substitute| |random| |xRange| |close| |OMopenString|
- |startPolynomial| |eq?| |saturate| |factor1| |polynomial| |rCoord|
- |pToHdmp| |new| |removeDuplicates| |point| |gcdprim| |yRange|
- |semiResultantEuclidean1| |nthRootIfCan| |obj|
- |eisensteinIrreducible?| |distdfact| |musserTrials| |rightUnits|
- |taylor| |quasiComponent| |search| |compdegd| |log2| |remove|
- |bandedHessian| |continuedFraction| |zRange| |display|
- |semiDegreeSubResultantEuclidean| |cache| |script| BY |critT|
- |leftFactorIfCan| |expextendedint| |laurent| |principal?|
- |OMputEndApp| |balancedBinaryTree| |map!| |plenaryPower| |normalized?|
- |rst| |tanQ| |setLabelValue| |constant| |list?| |puiseux| |smith|
- |tower| |operator| |series| |last| |capacity| |style| |qsetelt!|
- |polyRicDE| |po| |makeResult| |irreducibleFactor| |e01bgf|
- |setScreenResolution3D| |inverseColeman| |assoc| |getlo|
- |antiCommutative?| |OMgetAtp| |notOperand| |just| |keys| |tex|
- |createNormalPoly| |monicRightDivide| |inv| |hitherPlane| |delete!|
- |e02ajf| |integral| |OMParseError?| |middle| |tanNa| |freeOf?|
- |ground?| |genericRightTrace| |trapezoidalo| |tubePointsDefault|
- |rk4a| |OMputAtp| |someBasis| |Lazard2| |input| |LyndonWordsList|
- |explogs2trigs| |mapCoef| |cAtan| |ground| |inputBinaryFile| |s21bdf|
- |removeSuperfluousCases| |min| |library| |complexElementary| |d01aqf|
- |scan| |makeSUP| |sumOfKthPowerDivisors| |e01saf| |reseed|
- |leadingMonomial| |OMputString| |s17agf| |complexNumeric| |lcm|
- |f02abf| |Is| |acsch| |characteristic| |currentScope|
- |associatedEquations| |writeByte!| |member?| |leadingCoefficient|
- |qualifier| |rules| |setEmpty!| |basisOfMiddleNucleus| |totalDegree|
- |jordanAdmissible?| |denominator| |insert!| |kernels|
- |leftRegularRepresentation| |btwFact| |primitiveMonomials|
- |algebraicSort| |sign| |fTable| |left| |ran| |append| |imagi| |sup|
- |mindeg| |resize| |diag| |c06ekf| |f04mcf| |super| |reductum| |fmecg|
- |univariate| |right| |sPol| |coerceL| |gcd| |set| |newTypeLists|
- |linearPart| |divideExponents| |isobaric?| |squareFreePrim| |gradient|
- |shade| |false| |hclf| |readUInt16!| |writeLine!| |contractSolve|
- |useSingleFactorBound| |genericPosition| |minordet| |besselI|
- |overbar| |sum| |minPoints| |bsolve| |invmultisect| |powerSum|
- |headReduce| |yCoordinates| |moebiusMu| |OMputObject| |mainContent|
- |factor| |leftDiscriminant| |explicitlyEmpty?| |retractable?|
- |simplifyPower| |idealSimplify| |bfKeys| |outputSpacing| |vark| |sqrt|
- |initiallyReduced?| |nthExpon| |fractRadix| |lazyPremWithDefault|
- |unitsColorDefault| |countRealRootsMultiple| |leftDivide| |ipow|
- |createPrimitiveElement| |tryFunctionalDecomposition| |numeric|
- |f07aef| |real| |OMgetFloat| |slash| |conjugate| |check| |lp| |empty|
- |imagK| |numerators| |radical| |cTanh| |f02aff| |aromberg| |imag|
- |triangulate| |ptree| |primintegrate| |lazyResidueClass| |multiple?|
- |dflist| |zoom| |directProduct| |d01apf| |OMsupportsSymbol?| |symbol?|
- |df2st| |completeHermite| |reduceLODE| |module| |showSummary| |iprint|
- |d03edf| |s21bcf| |vedf2vef| |shufflein| |term| |inf| |recip|
- |sinh2csch| |OMcloseConn| |e02dcf| |curve| |maxrank| |deref| |exp1|
- |brace| |composites| |inconsistent?| |quadratic?| |sorted?| |setPoly|
- |componentUpperBound| |hash| |sechIfCan| |eigenvectors|
- |linkToFortran| |showAttributes| |f02aaf| |wholeRagits| |destruct|
- |unrankImproperPartitions1| |rationalPoint?| |multiEuclidean| |parts|
- |solveLinear| |show| |count| |viewDeltaXDefault| |d02bhf| |f02awf|
- |PDESolve| |elementary| |symbol| |shiftRight| |iilog| |ranges| =
- |writeUInt8!| |OMgetSymbol| |createGenericMatrix| |crest| |cotIfCan|
- |limit| |pointData| |algDsolve| |ratDsolve| |expression|
- |oneDimensionalArray| |fi2df| |monomialIntegrate| |viewZoomDefault|
- |trace| UTS2UP |lo| |listYoungTableaus| |diagonal?|
- |factorsOfCyclicGroupSize| |leadingCoefficientRicDE|
- |tableForDiscreteLogarithm| |host| |integer| |sylvesterMatrix|
- |weights| |binomThmExpt| < |exquo| |zerosOf| |powern| |incr|
- |rewriteSetByReducingWithParticularGenerators| |mat| |top!| |newReduc|
- |computeCycleEntry| > |trunc| |OMunhandledSymbol| |div| |normal?|
- |nthr| |setnext!| |isPlus| |f07fef| |rdregime| |iicsc| |OMgetString|
- |mkIntegral| GF2FG <= |OMclose| |quo| |complexIntegrate| |infRittWu?|
- |rombergo| |normalForm| |palgextint0| |getBadValues| |whatInfinity|
- |parent| |parabolic| |cSin| >= |label| |radix| |chvar| |rotatey|
- |zeroDimPrime?| |leftMult| |nullary?| |measure| |heapSort|
- |minRowIndex| |lazyPseudoQuotient| |rem| |setStatus!| |endSubProgram|
- |ignore?| |primitivePart!| |basisOfLeftNucleus| |d01amf| |findBinding|
- |countRealRoots| |getProperties| |predicate| |iiacoth|
- |euclideanGroebner| |associatorDependence| |extendedIntegrate|
- |sizePascalTriangle| |cAsin| |tubeRadius| |s18def| |hermite|
- |generalizedInverse| |degreeSubResultant| |powerAssociative?|
- |infinityNorm| |inRadical?| |bitCoef| + |redPol| |mainMonomials|
- |splitSquarefree| |rarrow| |split| |child| |tube| |primitive?|
- |compiledFunction| |OMmakeConn| - |light| |minIndex|
- |quasiAlgebraicSet| |BumInSepFFE| |bounds| |monicDecomposeIfCan|
- |expenseOfEvaluation| |mainExpression| |leastPower| |d03faf| |sqfree|
- / |ode1| |e02dff| |f04mbf| |fortranComplex| |selectFiniteRoutines|
- |resetNew| |cycleElt| |linGenPos| |cCsc| |monomials| |conditionP|
- |f07fdf| |nextLatticePermutation| |addBadValue| |monicModulo|
- |constructor| |iiatan| |pointLists| |toseInvertibleSet|
- |expressIdealMember| |graphs| |bezoutResultant| |readInt32!|
- |externalList| |rightLcm| |maxPoints| |nor| |optpair| |gcdcofact|
- |makeSeries| |returnTypeOf| |cSec| |fortranLinkerArgs| |option|
- |linearAssociatedLog| |nthRoot| |resultantReduitEuclidean|
- |replaceKthElement| |patternMatchTimes| |resultantEuclidean|
- |noKaratsuba| |clipPointsDefault| |branchIfCan| |dequeue!| |digamma|
- |intcompBasis| |lazyEvaluate| |elRow1!| |numericalIntegration|
- |OMputBVar| |evaluateInverse| |normalise| |ramified?| |getZechTable|
- |subTriSet?| |randnum| |mapmult| |parameters| |nothing|
- |mapMatrixIfCan| |exponents| |indiceSubResultantEuclidean|
- |OMreadFile| |sub| |dimensionOfIrreducibleRepresentation|
- |clipSurface| |adjoint| |OMconnOutDevice| |lighting| |maxIndex|
- |numberOfVariables| |binarySearchTree| |dictionary| |divisor|
- |leftQuotient| |twist| |chebyshevT| |minimalPolynomial|
- |GospersMethod| |hasSolution?| |permutation| |viewDeltaYDefault|
- |lift| |insertRoot!| |rightRemainder| |lowerCase?| |movedPoints|
- |wordInStrongGenerators| |reverseLex| |solveInField| |string?|
- |setTex!| |exponential| |csc2sin| |reduce| |reify| |realEigenvalues|
- |space| |inverseLaplace| |s17def| |usingTable?| |associatedSystem|
- |collect| |find| |drawComplexVectorField| |unitCanonical| |outputList|
- |rightTrim| |exprToGenUPS| |tanIfCan| |zeroMatrix| |d02raf|
- |algebraicCoefficients?| |OMUnknownSymbol?| |linearlyDependent?|
- |swapRows!| |positiveSolve| |squareFreePart| |scale| |leftTrim|
- |setsubMatrix!| |defineProperty| |sylvesterSequence| |startTable!|
- |normalizedAssociate| |npcoef| |gbasis| |index?| |getStream|
- |leftExtendedGcd| |complexLimit| |characteristicSerie| |eigenvalues|
- |order| |expintegrate| |s18dcf| |antisymmetric?| |internalAugment|
- |dihedral| |maximumExponent| |ScanFloatIgnoreSpaces| |airyBi|
- |subNode?| |makeViewport3D| |nonSingularModel| |addMatchRestricted|
- |leadingSupport| |firstNumer| |makeMulti| |birth| |showArrayValues|
- |OMputInteger| RF2UTS |exprToUPS| |c06ebf| |HermiteIntegrate|
- |structuralConstants| |c06gsf| |minset| |extendedResultant| |primes|
- |evenlambert| |OMreadStr| |unprotectedRemoveRedundantFactors|
- |anfactor| |extractIndex| |moduleSum| |moreAlgebraic?| |minColIndex|
- |expandTrigProducts| |semiSubResultantGcdEuclidean1| |startStats!|
- |li| |upperCase| |leftRank| |subResultantGcd| |belong?|
- |rewriteIdealWithRemainder| |extract!| |sncndn| |s17akf| |axes|
- |outputFloating| |outputAsScript| |euclideanSize| |messagePrint|
- |deepCopy| |setErrorBound| |elements| |sn| |complexForm| |mulmod|
- |cRationalPower| |outlineRender| |midpoint| |indicialEquations|
- |setLegalFortranSourceExtensions| |extendedSubResultantGcd|
- |squareTop| |charthRoot| |trailingCoefficient| |symmetricPower|
- |numberOfComputedEntries| |initials| |multiplyCoefficients|
- |selectPDERoutines| |factorGroebnerBasis| |f04asf| |binomial|
- |iterationVar| |rroot| |reciprocalPolynomial| |shallowExpand|
- |asechIfCan| |stoseInternalLastSubResultant| |f01qef| |OMgetInteger|
- |mainValue| |inspect| |e04jaf| |cap| |e04dgf| |computeCycleLength|
- |createPrimitivePoly| |fortranCharacter| |SturmHabicht|
- |showClipRegion| |closeComponent| |hi| |backOldPos| |genericRightNorm|
- |real?| |exprToXXP| |s20adf| |createPrimitiveNormalPoly| |cAcos|
- |squareFreeFactors| |subCase?| |infinite?| |asinIfCan| |mapUp!|
- |possiblyInfinite?| |evenInfiniteProduct| |changeName|
- |jacobiIdentity?| |OMputEndBVar| |orthonormalBasis| |realSolve|
- |taylorRep| |leadingExponent| |att2Result| |charpol| |lyndon?|
- |viewpoint| |commutator| |withPredicates| |bivariate?| |byteBuffer|
- |rischDE| |showTheIFTable| |padicallyExpand| |linearAssociatedOrder|
- |aspFilename| |members| |padicFraction| |stopTableGcd!|
- |brillhartTrials| |rightPower| |permutations| |kroneckerDelta|
- |squareMatrix| |OMgetApp| |resultantnaif| |palgextint| |cCoth|
- |pushup| |minGbasis| |f01brf| |nonQsign| |arbitrary| |normalize|
- |matrixGcd| |d01alf| |antisymmetricTensors| |invertIfCan| |zCoord|
- |polygamma| |range| |basisOfLeftAnnihilator| |normalDenom|
- |setMaxPoints| |Hausdorff| |test| |setEpilogue!|
- |showIntensityFunctions| |composite| |toScale| |cAcsc| |corrPoly|
- |simplifyExp| |cSinh| |e02adf| |commonDenominator| |s14abf|
- |changeVar| |cyclicEntries| |generate| |subMatrix|
- |halfExtendedResultant2| |roughUnitIdeal?| |iicot| |mapSolve| |rank|
- |e02bdf| |ListOfTerms| |htrigs| |applyRules| |prefix| |dmpToHdmp|
- |patternVariable| |collectUnder| |extension| |removeSinhSq|
- |roughSubIdeal?| |primeFrobenius| |OMputVariable| |cardinality|
- |setProperties!| |completeHensel| |e02gaf| |factorset| |depth|
- |diagonals| |d02kef| |degreePartition| |OMputEndAtp| |enterPointData|
- |rangePascalTriangle| |outputBinaryFile| |subResultantGcdEuclidean|
- |rightDiscriminant| |content| |consnewpol| |shuffle| |lSpaceBasis|
- |coordinates| |cCsch| |safetyMargin| |column| |collectQuasiMonic|
- |expint| |unitVector| |stoseInvertible?| |selectOrPolynomials|
- |systemSizeIF| |karatsubaDivide| |insertBottom!| |leftRecip|
- |charClass| |iflist2Result| |dimensionsOf| |primlimintfrac|
- |showRegion| |approxSqrt| |null| |rename!| |validExponential|
- |reduceByQuasiMonic| |complexEigenvalues| |paren|
- |identitySquareMatrix| |f01rcf| |clikeUniv| |LowTriBddDenomInv| |not|
- |readLineIfCan!| |optional?| |reducedQPowers| |f04axf| |rowEchelon|
- |dim| |ramifiedAtInfinity?| |rootRadius| |sortConstraints| |digits|
- |and| |quartic| |listOfLists| |imagk| |extractIfCan| |degree| |maxdeg|
- |lowerPolynomial| |e04mbf| |lazyIntegrate| |f01maf| |or|
- |leadingIndex| |OMgetEndBind| |listBranches| |generic| |elseBranch|
- |mappingAst| |cycle| |xor| |prefixRagits| |coefficient| |setRow!|
- |callForm?| |dominantTerm| |f07adf| |unitNormal| |rootPower|
- |processTemplate| |twoFactor| |ptFunc| |case| |weight| |in?| |dark|
- |var1Steps| |identification| |argument| |Vectorise|
- |transcendenceDegree| |Zero| |chebyshevU| |e02bbf| |principalIdeal|
- |inverseIntegralMatrix| |printInfo!| |double?| |scalarTypeOf|
- |approxNthRoot| |One| |viewDefaults| |invmod| |/\\| |makeVariable|
- |f02xef| |wholePart| |paraboloidal| |laguerre| |lquo| |getButtonValue|
- |cSech| |\\/| |screenResolution3D| |perfectNthRoot| |transpose|
- |rationalApproximation| |zeroDimensional?| |logpart| |d01bbf|
- |getProperty| |compactFraction| |collectUpper| |s13aaf|
- |areEquivalent?| |key| |polCase| |coleman| |parseString| |henselFact|
- |equiv?| |leastAffineMultiple| |minPol| |shrinkable| |center|
- |algebraicDecompose| |simpson| |froot| |OMwrite| |cycleEntry|
- |invertibleSet| |filename| |fixedPoints| |patternMatch| |An| |s17adf|
- |palgint| |particularSolution| |setprevious!| |elt| |quoByVar|
- |setProperty| |ratDenom| |seed| |not?| |second| |autoReduced?|
- |pdf2df| |fullPartialFraction| |superscript| |compound?| |resultant|
- |rootPoly| |parse| |third| |solveLinearPolynomialEquationByFractions|
- |cot2trig| |basisOfNucleus| |localAbs| |mapExponents| |getGoodPrime|
- |tubePlot| |entries| |rightFactorCandidate| |c05adf| |dec| |connect|
- |pushNewContour| |updateStatus!| |trapezoidal| |fixedPointExquo|
- |simplifyLog| |shanksDiscLogAlgorithm| |closedCurve| |d01ajf|
- |intermediateResultsIF| |recolor| |moebius| |realElementary| |conjug|
- |infieldIntegrate| |reopen!| |insertMatch| |removeConstantTerm|
- |createMultiplicationMatrix| |setPosition|
- |genericRightMinimalPolynomial| |zeroOf| |lazyVariations| |tab|
- |lieAdmissible?| |leadingTerm| |imaginary| |acosIfCan|
- |wordsForStrongGenerators| |diagonal| |expr| |zag| |complexNormalize|
- |rquo| |OMputEndBind| |expandPower| |signAround| |goodnessOfFit|
- |divideIfCan!| |nodes| |bezoutDiscriminant| |kmax| |iFTable| |cAcoth|
- |clearDenominator| |exprex| |internal?| |principalAncestors|
- |mightHaveRoots| |systemCommand| |kind| |fortranInteger| |e02aef|
- |gderiv| |prepareSubResAlgo| |e02bcf| |OMsupportsCD?| |comparison|
- |maxPoints3D| |op| |inR?| |stiffnessAndStabilityOfODEIF|
- |measure2Result| |midpoints| |cup| |genus| |failed?|
- |mainDefiningPolynomial| |even?| |stack| |OMencodingSGML| |imagE|
- |setPrologue!| |variable| |rightZero| |getConstant| |localUnquote|
- |rightUnit| |outputMeasure| |removeZeroes| |normal|
- |parabolicCylindrical| |rightTrace| |iterators| |hostPlatform|
- |eigenvector| |readBytes!| |bitTruth| |harmonic| |ReduceOrder|
- |makingStats?| |iiabs| |e02akf| |inverse| |index| |OMputApp|
- |cylindrical| |semicolonSeparate| |factorByRecursion|
- |factorSquareFreeByRecursion| |regime| |totalfract| |alphanumeric?|
- |cyclic?| |rspace| |doubleFloatFormat| |setLength!| |nextSublist|
- |debug3D| |stoseInvertible?reg| |lfextlimint| |redpps|
- |numberOfDivisors| |lexico| |wholeRadix| |setMinPoints3D|
- |loadNativeModule| |quatern| |rischDEsys| |alphanumeric|
- |oddInfiniteProduct| |mapGen| |union| |axesColorDefault| |errorInfo|
- |wrregime| |pair| |integralLastSubResultant| |bat| |knownInfBasis|
- |iisqrt2| |logIfCan| |buildSyntax| |doubleRank| |yellow| |unmakeSUP|
- |goto| |commutativeEquality| |block| |iiGamma| |elRow2!| |whileLoop|
- |prinpolINFO| |genericLeftNorm| |compBound| |element?| |leftLcm|
- |upperCase?| |getGraph| |colorFunction| |eyeDistance| |explimitedint|
- |term?| |symmetricGroup| |fixedPoint| |constDsolve| |factorSFBRlcUnit|
- |varselect| |e02baf| |hdmpToDmp| |double|
- |noncommutativeJordanAlgebra?| |complexExpand| |value| |numFunEvals|
- |palgintegrate| |setCondition!| |interReduce| |dAndcExp|
- |derivationCoordinates| |radicalSimplify| |putColorInfo| |expt|
- |leadingIdeal| |nextPrimitivePoly| |janko2| |s18adf|
- |rationalFunction| |edf2fi| |mathieu11| |partialNumerators| |nullary|
- |currentSubProgram| |logical?| |c06fqf| |conditionsForIdempotents|
- |f02bbf| |pushuconst| |physicalLength| |gramschmidt| |e01bhf|
- |fractionPart| |multiset| |blankSeparate| |removeSquaresIfCan|
- |recoverAfterFail| |userOrdered?| |convergents| |pushdterm|
- |genericRightTraceForm| |symmetricDifference| |push!| |mirror|
- |listLoops| |leftOne| |reduceBasisAtInfinity| |numberOfPrimitivePoly|
- |e04naf| |primitivePart| |perfectNthPower?| |internalLastSubResultant|
- |color| |Gamma| |setVariableOrder| |associator| |acotIfCan| |rule|
- |concat!| |getVariableOrder| |readUInt32!| |minimumExponent| |unparse|
- |f04arf| |say| |combineFeatureCompatibility| |divisors|
- |binaryFunction| |stFunc1| |recur| |rk4qc| |polyRDE| |declare!|
- |gcdPolynomial| |RemainderList| |graphStates| |numericalOptimization|
- |localIntegralBasis| |chiSquare1| |rootOf| |testDim| |quadraticForm|
- |genericRightDiscriminant| |fortranTypeOf| |hMonic| |setleaves!|
- |e01daf| |pointPlot| |setref| |nand| |lineColorDefault|
- |leftRankPolynomial| |generic?| |xn| |scaleRoots| |adaptive?|
- |incrementKthElement| |numFunEvals3D| |pr2dmp| |csubst| |upperCase!|
- |sin2csc| |normalElement| |RittWuCompare|
- |purelyAlgebraicLeadingMonomial?| |tan2trig| |subSet|
- |antiAssociative?| |repeating| |stiffnessAndStabilityFactor|
- |integralBasis| |linearDependence| |se2rfi| |overset?|
- |createLowComplexityTable| |drawComplex| |nthFlag| |doubleComplex?|
- |tanhIfCan| |inputOutputBinaryFile| |void| |reset| |initiallyReduce|
- |extractPoint| |prologue| |solveLinearPolynomialEquation| |formula|
- |factors| |clip| |lyndon| |isConnected?| |viewThetaDefault|
- |readByte!| |front| |aQuartic| |leftTrace| |solid| |elliptic?|
- |writeInt8!| |segment| |uncouplingMatrices| |stripCommentsAndBlanks|
- |write| |lastSubResultant| |reverse!| |uniform| |enterInCache|
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- |univariatePolynomialsGcds| |removeRoughlyRedundantFactorsInPols|
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- |fortranDouble| |name| |bfEntry| |removeZero| |deriv| |coth2trigh|
- |intPatternMatch| |d02bbf| |infix| |crushedSet| |ode| |datalist|
- |c06fpf| |body| |lintgcd| |listRepresentation| |topFortranOutputStack|
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- |fortranLiteralLine| |algebraicVariables| |e04fdf| |firstDenom|
- |curryLeft| |determinant| ** |halfExtendedResultant1|
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- |modularFactor| |f01rdf| |exp| |var2Steps| |makeTerm| |arguments|
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- |alternative?| |fixedDivisor| |central?| |numberOfChildren| |#|
- |lazyPrem| |currentCategoryFrame| |leftNorm| |nextPartition| |ode2|
- |rational?| |primPartElseUnitCanonical| |OMgetEndAttr| |generators|
- |leftUnits| |ricDsolve| |exactQuotient!| |iicos| |leftTraceMatrix|
- |compose| |outputForm| |dom| |fill!| |row| |multMonom| |incrementBy|
- |lprop| |laurentIfCan| |constantIfCan| |squareFreePolynomial|
- |genericLeftMinimalPolynomial| |triangularSystems| |singular?|
- |prime?| |iifact| |realEigenvectors| |rubiksGroup| |expand|
- |radicalEigenvectors| |linears| |part?| |frst| |s17dhf| |droot| |node|
- |push| |OMputEndError| |filterWhile| |univariateSolve| |simplify|
- |shiftLeft| |elem?| |reducedDiscriminant| |prinshINFO| |const|
- |discreteLog| |symmetricRemainder| |aLinear| |filterUntil| |e01sff|
- |extensionDegree| |lookup| |outputArgs| |anticoord| |leftGcd|
- |mapDown!| |swap| |factorOfDegree| |select| |d01akf| |schema| |c06gqf|
- |rightExactQuotient| |c02agf| |parametric?| |title| |bezoutMatrix|
- |clearTable!| |divergence| |options| |cAcot| |OMgetAttr| |elColumn2!|
- |e01bff| |sequences| |bits| |polyred| |pile| |radicalEigenvector|
- |iExquo| |infLex?| |prepareDecompose| |bumptab| |increase| |operation|
- |euclideanNormalForm| |totalGroebner| |accuracyIF|
- |factorSquareFreePolynomial| |bombieriNorm| |cExp| |s17ahf|
- |supDimElseRittWu?| |e| |initial| |OMserve| |UpTriBddDenomInv|
- |cycleLength| |string| |setProperties| |bumprow| |nextPrime|
- |univariatePolynomial| |symbolTableOf| |monicCompleteDecompose|
- |setFormula!| |plusInfinity| |prinb| |directSum| |insertTop!|
- |KrullNumber| |build| |evaluate| |separant| |cyclotomic|
- |partialFraction| |generalizedContinuumHypothesisAssumed?| |iipow|
- |minusInfinity| |makeRecord| |enumerate| |minimize| |constant?|
- |pointColorDefault| |symFunc| |stronglyReduce| |OMencodingBinary|
- |asinhIfCan| |flexible?| |numberOfMonomials| |gethi| |safeCeiling|
- |basisOfRightAnnihilator| |s19aaf| |vspace| |rischNormalize|
- |permanent| |redPo| |ceiling| |multisect| |setProperty!| |cycles|
- |mainVariable| |length| |OMread| |children| |dmpToP|
- |generalTwoFactor| |e02bef| |linear?| |jacobian| |exQuo| |generalSqFr|
- |stoseInvertible?sqfreg| |scripts| |pushucoef| |makeYoungTableau|
- |swap!| |oddlambert| |nthExponent| |factorFraction| |cycleSplit!|
- |tValues| |sqfrFactor| |multiplyExponents| |position!| |implies| |low|
- |resetVariableOrder| |interpolate| |numberOfComponents|
- |generalInfiniteProduct| |constantOpIfCan| |lieAlgebra?|
- |zeroSetSplit| |mapUnivariate| |removeRedundantFactors|
- |zeroDimPrimary?| |findCycle| |ffactor| |ddFact| |diff| |equation|
- |type| |acscIfCan| |characteristicPolynomial| |partitions|
- |trigs2explogs| |f02axf| |errorKind| |boundOfCauchy| |arrayStack|
- |back| |singleFactorBound| |subNodeOf?| |integer?|
- |nativeModuleExtension| |relerror| |latex| |width|
- |lastSubResultantEuclidean| UP2UTS |decimal| |pmComplexintegrate|
- |pack!| |specialTrigs| |toroidal| |returns| |packageCall|
- |firstUncouplingMatrix| |iiasech| |factorAndSplit| |OMgetEndBVar|
- |rightQuotient| |differentialVariables| |horizConcat| |e01sef|
- |viewPosDefault| |list| |power!| |normInvertible?| |decreasePrecision|
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- |lazyPquo| |addPointLast| |OMUnknownCD?| |car| |remove!| |init|
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- |deepExpand| |monic?| |cdr| |nonLinearPart| |setchildren!| |arg1|
- |figureUnits| |explicitlyFinite?| |readUInt8!| |roman| |groebgen|
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- |solveLinearPolynomialEquationByRecursion| |lepol| |symbolIfCan|
- |arg2| |delta| |head| |decompose| |extendedint| |s18aef| |mvar|
- |innerSolve1| |ksec| |preprocess| |llprop| |showAll?| |pop!|
- |showTheSymbolTable| |f02aef| |polygon?| |redmat| |equivOperands|
- |wordInGenerators| |expIfCan| |option?| |nextPrimitiveNormalPoly|
- |conditions| |optional| |fglmIfCan| |restorePrecision| |UnVectorise|
- |algebraic?| |rename| |mathieu12| |pleskenSplit|
- |mainCharacterization| |sin?| |squareFree| |match| |rightOne| |write!|
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- |divideIfCan| |move| |groebnerIdeal| |factorSquareFree| |properties|
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- |badValues| |socf2socdf| |groebnerFactorize| |fillPascalTriangle|
- |lllp| |hdmpToP| |translate| |monomRDEsys| |irreducibleFactors|
- |nullSpace| |screenResolution| |lazyPseudoDivide| |suffix?|
- |LyndonCoordinates| |transcendent?| |c05pbf| |nextItem| |bubbleSort!|
- |coord| |myDegree| |removeCoshSq| |repeatUntilLoop| |reduction|
- |lambda| |factorials| |problemPoints| |pattern| |leftUnit|
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- |complexNumericIfCan| |startTableGcd!| |parametersOf| |prefix?|
- |solid?| |leftMinimalPolynomial| |leftFactor| |monicDivide| |randomR|
- |setright!| |rational| |negative?| |delay| |noLinearFactor?|
- |viewSizeDefault| |iicoth| |f02bjf| |createNormalElement| |hex|
- SEGMENT |create| |makeSketch| |branchPoint?| |positiveRemainder|
- |OMputEndObject| |bit?| |floor| |sech2cosh| |magnitude| |rdHack1|
- |difference| |removeRoughlyRedundantFactorsInPol| |diophantineSystem|
- |iroot| |resultantEuclideannaif| |unary?| |exptMod| |mkPrim|
- |cscIfCan| |graphImage| |nsqfree| |message| |basisOfCentroid|
- |critMTonD1| |solve| |postfix| |changeThreshhold| |var1StepsDefault|
- |OMgetBind| |viewport2D| |stirling2| |sequence| |rotatex| |cCos|
- |OMputEndAttr| |OMsend| |constantRight| |commutative?| |subHeight|
- |s18aff| |trim| |optAttributes| |sdf2lst| |tRange| |asecIfCan|
- |basisOfLeftNucloid| |cyclotomicDecomposition| |sinhIfCan| |product|
- |rationalIfCan| |asimpson| |getSyntaxFormsFromFile| |represents|
- |physicalLength!| |infix?| |wronskianMatrix| |sinhcosh|
- |tryFunctionalDecomposition?| |OMputBind| |removeDuplicates!|
- |interpret| |bat1| |strongGenerators| |variable?| |neglist|
- |quadraticNorm| |mask| |binaryTree| |region| |modTree| |dfRange|
- |csch2sinh| |modularGcdPrimitive| |makeFloatFunction| |subset?|
- |critpOrder| |getDatabase| |homogeneous?| |createIrreduciblePoly|
- |headAst| |realZeros| |rightTraceMatrix| |mantissa| |categoryFrame|
- |OMgetEndAtp| |cons| |airyAi| |splitConstant| |singRicDE|
- |stopMusserTrials| |over| |fixPredicate| |traverse|
- |exprHasAlgebraicWeight| |OMgetObject| |resultantReduit| |retract|
- |limitPlus| |OMputAttr| |atanhIfCan| |error| |factorsOfDegree| |imagJ|
- |updatD| |stoseLastSubResultant| |coefficients| |xCoord|
- |partialQuotients| |andOperands| |finite?| |getMatch| |arity| |assert|
- |stoseInvertibleSetsqfreg| |mapUnivariateIfCan| |high| |ord| |status|
- |bright| |numberOfImproperPartitions| |s17aef| |OMsetEncoding|
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- |sparsityIF| |numericIfCan| |implies?| |mr| |readInt8!| |dn|
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- |createMultiplicationTable| |differentiate| |imagj| |hue|
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- |repSq| OR |categories| |symmetricProduct| |lazy?| ~= |lfunc|
- |functionIsContinuousAtEndPoints| |iiasinh| |taylorQuoByVar|
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- |HenselLift| |connectTo| |coerce| |toseLastSubResultant|
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- |bindings| |universe| |subPolSet?| |f01ref| |denom| |pdct| |trueEqual|
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- |lastSubResultantElseSplit| |s01eaf| |rectangularMatrix| |fintegrate|
- |symmetric?| |tan| |notelem| |pi| |extractSplittingLeaf| |unit?|
- |merge| |iiacot| |primintfldpoly| |coerceS| |yCoord| |cot| |continue|
- |internalZeroSetSplit| |reducedForm| |pointColorPalette| |infinity|
- |OMgetEndError| |divisorCascade| |hexDigit| |lyndonIfCan| |pastel|
- |mainCoefficients| |sec| |setOrder| |showTheFTable| |headRemainder|
- |possiblyNewVariety?| |augment| |useNagFunctions| |nextNormalPoly|
- |isAbsolutelyIrreducible?| |cCosh| |csc| |bag| |eof?| |geometric|
- |virtualDegree| |pointColor| |totalDifferential| |inc| |bracket|
- |asin| |readable?| |kernel| |romberg| |coerceImages| |Frobenius|
- |lowerCase!| |s17ajf| |less?| |ravel| |unaryFunction|
- |symmetricTensors| |acos| |map| |number?| * |draw| |univcase|
- |coHeight| |submod| |lazyPseudoRemainder| |hspace|
- |semiResultantEuclidean2| |reshape| |OMgetEndObject|
- |OMencodingUnknown| |atan| |equiv| |ef2edf| |basicSet| |intersect|
- |seriesSolve| |setScreenResolution| |more?| |monomRDE| |weighted|
- |acot| |setOfMinN| |stronglyReduced?| |integerIfCan| |iiasec|
- |innerSolve| |resetAttributeButtons| |resetBadValues| |asec| |char|
- |var2StepsDefault| |exprHasWeightCosWXorSinWX| |coefChoose| |node?|
- |solve1| |rightDivide| |ParCondList| |printInfo| |reindex| |orbits|
- |acsc| |terms| |prolateSpheroidal| |Ei| |makeObject| |setelt| |pol|
- |cosSinInfo| |rootKerSimp| |stoseIntegralLastSubResultant|
- |subResultantChain| |sinh| |cyclicParents| |convert| |derivative|
- |complexSolve| |upDateBranches| |basisOfRightNucloid|
- |basisOfRightNucleus| |critMonD1| |d01gaf| |update| |safeFloor|
- |iisech| |roughBase?| |copy| |coef| |expenseOfEvaluationIF|
- |bringDown| |nil?| |cos2sec| |showTheRoutinesTable|
- |rewriteSetWithReduction| |makeEq| |testModulus|
- |rewriteIdealWithHeadRemainder| |closed?| |zeroDim?| |badNum|
- |extractTop!| |bothWays| |s17acf| |float| |f04maf| |cyclicSubmodule|
- |complementaryBasis| |innerEigenvectors| |weierstrass| |edf2df|
- |nullity| |showTypeInOutput| |d01fcf| |coordinate| |autoCoerce|
- |iiexp| |semiIndiceSubResultantEuclidean| |contains?| |computeBasis|
- |s17dgf| |failed| |fortranCompilerName| |pascalTriangle|
- |removeSuperfluousQuasiComponents| |typeLists|
- |generalizedEigenvector| |s21baf| |lfextendedint| |OMreceive|
- |vectorise| |match?| |position| |branchPointAtInfinity?| |copy!|
- |algebraicOf| |linearlyDependentOverZ?| |isExpt| |wreath|
- |halfExtendedSubResultantGcd2| |f01qdf| |mapdiv| |OMopenFile|
- |rightRecip| |selectNonFiniteRoutines| |key?| |argumentList!|
- |legendreP| |quasiMonicPolynomials| |leastMonomial| |cyclicCopy|
- |minPoints3D| |groebner?| |presuper| |besselJ| |impliesOperands|
- |numberOfIrreduciblePoly| |character?| |basis| |LyndonBasis| |sincos|
- |primeFactor| |largest| |pseudoRemainder| |exponentialOrder|
- |listOfMonoms| |createThreeSpace| |d02gaf| |atom?|
- |invertibleElseSplit?| |OMgetError| |graphCurves| |exponential1|
- |getMeasure| |external?| |c02aff| |associative?| |unit| |bottom!|
- |comp| |matrixConcat3D| GE |rootDirectory| |extend| |binary| |lhs|
- |intensity| |readInt16!| |modularGcd| |flexibleArray| |psolve|
- |antiCommutator| |zero?| GT |doubleDisc| |loopPoints|
- |integralCoordinates| |rhs| |univariatePolynomials| |sumOfDivisors|
- |extendIfCan| |clipBoolean| |integralMatrix| |next| |rowEchelonLocal|
- LE |getMultiplicationTable| |dimension| |critBonD| |traceMatrix|
- |df2ef| |uniform01| |d03eef| |subQuasiComponent?| |univariate?| LT
- |fibonacci| |f04qaf| |stirling1| |primextendedint| |s19abf|
- |startTableInvSet!| |createNormalPrimitivePoly| |e02def| |polar|
- |setelt!| |degreeSubResultantEuclidean| |imports| |lagrange| |cLog|
- |norm| |operators| |variationOfParameters| |log| |one?|
- |bipolarCylindrical| |scalarMatrix| |triangular?| |leftRemainder|
- |setAdaptive3D| |setValue!| |fracPart| |sts2stst|
- |regularRepresentation| |repeating?| |tableau| |tubePoints| |unknown|
- |semiResultantEuclideannaif| |LazardQuotient| |allRootsOf| |nil|
- |infinite| |arbitraryExponent| |approximate| |complex|
- |shallowMutable| |canonical| |noetherian| |central|
+ |Record| |Union| |e04naf| |oddlambert| |listOfMonoms|
+ |monicRightDivide| |integral?| |processTemplate|
+ |constantCoefficientRicDE| |factorsOfDegree| |LazardQuotient2|
+ |nthExponent| |primitivePart| |createThreeSpace| |hitherPlane| |keys|
+ |routines| |twoFactor| |selectAndPolynomials| |imagJ|
+ |pushFortranOutputStack| |fortranComplex| |perfectNthPower?| |acsch|
+ |factorFraction| |d02gaf| |delete!| |ptFunc| |phiCoord| |tracePowMod|
+ |updatD| |popFortranOutputStack| |selectFiniteRoutines|
+ |internalLastSubResultant| |cycleSplit!| |atom?| |e02ajf| GE |weight|
+ |exactQuotient| |OMgetEndApp| |stoseLastSubResultant| |resetNew|
+ |tValues| |color| |next| |invertibleElseSplit?| |integral| GT
+ |coefficients| |putGraph| |cycleElt| |sqfrFactor| |Gamma| |OMgetError|
+ |iisin| |OMParseError?| LE |composite| |xCoord|
+ |selectIntegrationRoutines| |linGenPos| |setVariableOrder|
+ |multiplyExponents| |graphCurves| |toScale| |middle| |c06eaf| LT
+ |partialQuotients| |mesh?| |cCsc| |position!| |associator|
+ |exponential1| |tanNa| |cAcsc| |numberOfCycles| |pToDmp| |andOperands|
+ |monomials| |changeNameToObjf| |nil| |getMeasure| |freeOf?|
+ |internalIntegrate0| |corrPoly| |basisOfCommutingElements| |finite?|
+ |conditionP| |elem?| |factorByRecursion| |permutationRepresentation|
+ |external?| |genericRightTrace| |cAcsch| |simplifyExp| |dequeue|
+ |getMatch| |f07fdf| |factorSquareFreeByRecursion|
+ |reducedDiscriminant| |edf2ef| |c02aff| |cSinh| |trapezoidalo|
+ |condition| |karatsuba| |arity| |direction| |nextLatticePermutation|
+ |prinshINFO| |regime| |radicalEigenvalues| |associative?|
+ |approximate| |tubePointsDefault| |graeffe| |e02adf| |level| |comment|
+ |addBadValue| |const| |totalfract| |basisOfCenter| |complex| |unit|
+ |rk4a| |and?| |commonDenominator| |OMconnectTCP| |negative?| |eq|
+ |monicModulo| |alphanumeric?| |discreteLog| |coerceP| |bottom!|
+ |OMputAtp| |goodPoint| |s14abf| |delay| |open?| |iter| |iiatan|
+ |symmetricRemainder| |cyclic?| |complexZeros| |matrixConcat3D|
+ |noLinearFactor?| |someBasis| |clearTheIFTable| |changeVar| |refine|
+ |close| |pointLists| |rspace| |aLinear| |clearFortranOutputStack|
+ |Lazard2| |generalPosition| |cyclicEntries| |deleteRoutine!|
+ |viewSizeDefault| |toseInvertibleSet| |e01sff| |doubleFloatFormat|
+ |coefChoose| |hasoln| |curveColorPalette| |LyndonWordsList| |remove|
+ |iicoth| |subMatrix| |nextNormalPrimitivePoly| |display| BY
+ |expressIdealMember| |setLength!| |extensionDegree| |pmintegrate|
+ |node?| |explogs2trigs| |lifting1| |halfExtendedResultant2| |f02bjf|
+ |setClosed| |graphs| |lookup| |nextSublist| |solve1| |int| |mapCoef|
+ |last| |Si| |roughUnitIdeal?| |createNormalElement| |viewWriteDefault|
+ |bezoutResultant| |outputArgs| |debug3D| |lfinfieldint| |rightDivide|
+ |assoc| |cAtan| |iicot| |leftPower| |subtractIfCan| |hex| |readInt32!|
+ |anticoord| |ParCondList| |stoseInvertible?reg| |cyclicGroup|
+ |dimensions| |inputBinaryFile| |singularAtInfinity?| |mapSolve|
+ |solveid| |create| |binaryTournament| |externalList| |lfextlimint|
+ |leftGcd| |reindex| |plus!| |makeSketch| |rootBound| |function|
+ |s21bdf| |e02bdf| |SturmHabichtSequence| |input| |/\\| |mapDown!|
+ |rightLcm| |id| |redpps| |orbits| |OMReadError?| |branchPoint?|
+ |relationsIdeal| |removeSuperfluousCases| |ListOfTerms| |whitePoint|
+ |library| |\\/| |maxPoints| |swap| |numberOfDivisors| |forLoop|
+ |terms| |eval| |complexElementary| |htrigs| |setfirst!|
+ |positiveRemainder| |coth2tanh| |nor| |prolateSpheroidal|
+ |tanintegrate| |factorOfDegree| |lexico| |outputGeneral| |table|
+ |applyRules| |d01aqf| |output| |compile| |torsion?| |domainOf|
+ |OMputEndObject| |cAtanh| |Ei| |optpair| |d01akf| |wholeRadix| |or?|
+ |new| |scan| |c06fuf| |dmpToHdmp| |bit?| |primitiveElement| |obj|
+ |gcdcofact| |pol| |setMinPoints3D| |schema| |search|
+ |zeroSetSplitIntoTriangularSystems| |has?| |makeSUP|
+ |absolutelyIrreducible?| |patternVariable| |floor| |set| |cache|
+ |dilog| |makeSeries| |c06gqf| |quatern| |cosSinInfo|
+ |bivariatePolynomials| |sumOfKthPowerDivisors| |collectUnder|
+ |univariatePolynomialsGcds| |exportedOperators| |sech2cosh| |sin|
+ |returnTypeOf| |rightExactQuotient| |rischDEsys| |rootKerSimp|
+ |complexRoots| |e01saf| |extension|
+ |removeRoughlyRedundantFactorsInPols| |limitedIntegrate| |magnitude|
+ |cos| |cSec| |alphanumeric| |c02agf| |stoseIntegralLastSubResultant|
+ |sturmSequence| |reseed| |contours| |removeSinhSq| |mapBivariate|
+ |rdHack1| |tan| |fortranLinkerArgs| |parametric?| |oddInfiniteProduct|
+ |subResultantChain| |split!| |OMputString| |roughSubIdeal?| |cross|
+ |ip4Address| |difference| |cot| |linearAssociatedLog| |bezoutMatrix|
+ |mapGen| |cyclicParents| |surface| |ldf2lst| |primeFrobenius| |s17agf|
+ |removeRoughlyRedundantFactorsInPol| |splitNodeOf!|
+ |removeRedundantFactorsInContents| |sort| |sec| |derivative| |nthRoot|
+ |clearTable!| |axesColorDefault| |delta| |generalLambert| |pow|
+ |f02abf| |lowerCase| |OMputVariable| |exponent| |diophantineSystem|
+ |csc| |resultantReduitEuclidean| |divergence| |errorInfo|
+ |complexSolve| |fortranLiteral| |Is| |cardinality| |makeCos| |iroot|
+ |binding| |asin| |replaceKthElement| |cAcot| |wrregime| |SFunction|
+ |upDateBranches| |setProperties!| |true| |characteristic| |f02wef| ~=
+ |lexGroebner| |resultantEuclideannaif| |acos| |basisOfRightNucloid|
+ |patternMatchTimes| |OMgetAttr| |integralLastSubResultant| |palgint0|
+ |left| |unary?| |fortranDouble| |currentScope| |completeHensel|
+ |random| |baseRDE| |coerce| |hash| |atan| |basisOfRightNucleus|
+ |resultantEuclidean| |elColumn2!| |bat| |f04atf| |right|
+ |associatedEquations| |bfEntry| |exptMod| |e02gaf| |trivialIdeal?|
+ |construct| |show| |count| |acot| |noKaratsuba| |knownInfBasis|
+ |e01bff| |critMonD1| |prindINFO| |factorset| |writeByte!| =
+ |removeZero| |mkPrim| |subresultantSequence| |asec|
+ |clipPointsDefault| |iisqrt2| |sequences| |fortranLogical| |d01gaf|
+ |deriv| |member?| |diagonals| |setMinPoints| |cscIfCan| |trace| |bits|
+ |acsc| |safeFloor| |branchIfCan| |lambda| |logIfCan| |triangSolve|
+ |complete| |d02kef| |qualifier| < |coth2trigh| |graphImage| |maxrow|
+ |sinh| |dequeue!| |polyred| |buildSyntax| |iisech| |degreePartition|
+ |setEmpty!| |intPatternMatch| > |nsqfree| |d02ejf| |cosh| |digamma|
+ |doubleRank| |pile| |roughBase?| |fractRagits| |basisOfMiddleNucleus|
+ |d02bbf| |OMputEndAtp| <= |basisOfCentroid| |selectsecond| |tanh|
+ |intcompBasis| |yellow| |radicalEigenvector| |expenseOfEvaluationIF|
+ |ideal| |max| >= |totalDegree| |infix| |enterPointData| |critMTonD1|
+ |idealiserMatrix| |coth| |lazyEvaluate| |iExquo| |unmakeSUP|
+ |bringDown| |jordanAdmissible?| |rangePascalTriangle| |crushedSet|
+ |iitanh| |solve| |sech| |showSummary| |elRow1!| |goto| |infLex?|
+ |nil?| |cn| |denominator| |outputBinaryFile| |ode| |postfix|
+ |stoseInvertibleSetreg| |csch| |numericalIntegration|
+ |commutativeEquality| |prepareDecompose| |cos2sec| |c06fpf| |insert!|
+ |subResultantGcdEuclidean| + |rootNormalize| |changeThreshhold|
+ |asinh| |showAttributes| |OMputBVar| |block| |bumptab|
+ |showTheRoutinesTable| |leftRegularRepresentation| |rightDiscriminant|
+ |lintgcd| - |scopes| |var1StepsDefault| |acosh| |evaluateInverse|
+ |increase| |iiGamma| |rewriteSetWithReduction| |btwFact|
+ |listRepresentation| |content| / |unitNormalize| |OMgetBind| |atanh|
+ |normalise| |euclideanNormalForm| |elRow2!| |makeEq|
+ |topFortranOutputStack| |algebraicSort| |consnewpol| |isPower|
+ |setelt| |viewport2D| |acoth| |ramified?| |whileLoop| |totalGroebner|
+ |testModulus| |parents| |sign| |shuffle| |maxRowIndex| |numberOfHues|
+ |stirling2| |asech| |getZechTable| |accuracyIF| |prinpolINFO|
+ |rewriteIdealWithHeadRemainder| |lSpaceBasis| |fTable| |sequence|
+ |complexEigenvectors| |purelyAlgebraic?| |copy| |arg1| |subTriSet?|
+ |genericLeftNorm| |factorSquareFreePolynomial| |closed?| |ran| |isOp|
+ |coordinates| |rotatex| |lflimitedint| |multiple| |arg2| |randnum|
+ |bombieriNorm| |compBound| |zeroDim?| |raisePolynomial| |imagi|
+ |cCsch| |label| |outputFixed| |cCos| |applyQuote| |mapmult| |element?|
+ |cExp| |badNum| |nilFactor| |sup| |safetyMargin| |cAsech|
+ |OMputEndAttr| |autoCoerce| |mapMatrixIfCan| |conditions| |s17ahf|
+ |leftLcm| |extractTop!| |removeIrreducibleRedundantFactors| |column|
+ |OMsend| |numberOfComposites| |exponents| |match| |upperCase?|
+ |supDimElseRittWu?| |sizeLess?| |bothWays| |result| |outputList|
+ |sinIfCan| |collectQuasiMonic| |symmetricSquare| |constantRight|
+ |ruleset| |indiceSubResultantEuclidean| |OMserve| |getGraph| |s17acf|
+ |cubic| |properties| |expint| |deepestTail| |commutative?| |square?|
+ |replace| |OMreadFile| |colorFunction| |UpTriBddDenomInv| |f04maf|
+ |Aleph| |translate| |fortranLiteralLine| |unitVector|
+ |leadingBasisTerm| |subHeight| |rightScalarTimes!| |cycleLength|
+ |eyeDistance| |cyclicSubmodule| |thetaCoord| |stoseInvertible?|
+ |algebraicVariables| |s18aff| |red| |rotatey| |suchThat|
+ |setProperties| |explimitedint| |complementaryBasis| |leftZero|
+ |e04fdf| |selectOrPolynomials| |completeSmith| |trim| |zeroDimPrime?|
+ |term?| |bumprow| |innerEigenvectors| |remainder| |systemSizeIF|
+ |option| |firstDenom| |optAttributes| |coerceListOfPairs| |leftMult|
+ |symmetricGroup| |nextPrime| |weierstrass| |curryRight| |sdf2lst|
+ |changeWeightLevel| |nullary?| |fixedPoint| |univariatePolynomial|
+ |edf2df| |biRank| |infinite?| |stoseSquareFreePart| |nthCoef| |tRange|
+ |measure| |constDsolve| |symbolTableOf| |nullity| |equality|
+ |mergeDifference| |asinIfCan| |checkPrecision| |asecIfCan|
+ |primPartElseUnitCanonical!| |heapSort| |factorSFBRlcUnit|
+ |monicCompleteDecompose| |showTypeInOutput| |OMopenString| |mapUp!|
+ |mesh| |basisOfLeftNucloid| |printingInfo?| |minRowIndex| |d01fcf|
+ |startPolynomial| |computeInt| |perfectSqrt| |possiblyInfinite?|
+ |cyclotomicDecomposition| |minrank| |lazyPseudoQuotient| |bytes|
+ |OMputEndBind| |coordinate| |rightTrim| |eq?| |critM|
+ |evenInfiniteProduct| |interpret| |sinhIfCan| |headReduced?|
+ |setStatus!| |isList| |expandPower| |iiexp| |leftTrim| |saturate|
+ |changeName| |addmod| |besselK| |product| |endSubProgram| |signAround|
+ |qinterval| |semiIndiceSubResultantEuclidean| |factor1|
+ |jacobiIdentity?| |minimumDegree| |ignore?| |goodnessOfFit| |ParCond|
+ |contains?| |rCoord| |getCode| |OMputEndBVar| |write!|
+ |primlimitedint| |retract| |tower| |primitivePart!| |divideIfCan!|
+ |definingEquations| |computeBasis| |stop| |pToHdmp| |s18acf|
+ |orthonormalBasis| |extractBottom!| |invertible?| |basisOfLeftNucleus|
+ |nodes| |expandLog| |s17dgf| |gcdprim| |iiacsch| |realSolve|
+ |rationalPoints| |normalizeIfCan| |d01amf| |bezoutDiscriminant|
+ |useEisensteinCriterion| |semiResultantEuclidean1| |quickSort|
+ |taylorRep| |assign| |euler| |findBinding| |kmax| |perspective|
+ |hexDigit| |directory| |nthRootIfCan| |leadingExponent| |mix|
+ |inverseIntegralMatrixAtInfinity| |chiSquare| |decrease|
+ |countRealRoots| |continue| |iFTable| |lyndonIfCan|
+ |eisensteinIrreducible?| |att2Result| |diagonalMatrix| |entry?|
+ |cosIfCan| |getProperties| |complexNumeric| |cAcoth| |pquo| |pastel|
+ |distdfact| |charpol| |gcdPrimitive| |exteriorDifferential|
+ |extractClosed| |iiacoth| |hasHi| |clearDenominator|
+ |mainCoefficients| |musserTrials| |categories| |lyndon?| |f01qcf|
+ |generalizedEigenvectors| |associates?| |kernels| |alternative?|
+ |euclideanGroebner| |exprex| |retractIfCan| |setOrder| |rightUnits|
+ |iteratedInitials| |viewpoint| |jordanAlgebra?| |signatureAst|
+ |associatorDependence| |univariate| |fixedDivisor| |internal?|
+ |showTheFTable| |numer| |quasiComponent| |integralRepresents|
+ |commutator| |meshFun2Var| |divideIfCan| |extendedIntegrate|
+ |principalAncestors| |central?| |headRemainder| |compdegd| |denom|
+ |withPredicates| |printTypes| |e01sbf| |move| |sizePascalTriangle|
+ |null| |mightHaveRoots| |numberOfChildren| |mapExpon|
+ |possiblyNewVariety?| |log2| |bivariate?| |subscript| |groebnerIdeal|
+ |prod| |fortranInteger| |cAsin| |f02fjf| |lazyPrem| |factor| |augment|
+ |not| |generate| SEGMENT |bandedHessian| |pi| |byteBuffer|
+ |rightAlternative?| |oddintegers| |factorSquareFree| |tubeRadius|
+ |sqrt| |e02aef| |currentCategoryFrame| |useNagFunctions| |and|
+ |infinity| |continuedFraction| |rischDE| |leaf?| |cartesian|
+ |mainMonomial| |nextNormalPoly| |s18def| |leftNorm| |gderiv|
+ |incrementBy| |or| |semiDegreeSubResultantEuclidean| |showTheIFTable|
+ |powers| |vconcat| |maxColIndex| |prepareSubResAlgo| |hermite|
+ |nextPartition| |isAbsolutelyIrreducible?| |xor| |expand| |critT|
+ |padicallyExpand| |mainSquareFreePart| |finiteBound| |graphState|
+ |node| |convert| |generalizedInverse| |cCosh| |e02bcf| |ode2|
+ |filterWhile| |case| |kernel| |leftFactorIfCan|
+ |linearAssociatedOrder| |randomLC| |localReal?| |genericLeftTrace|
+ |bag| |e02ahf| |OMsupportsCD?| |sum| |rightGcd| |degreeSubResultant|
+ |rational?| |map| |Zero| |filterUntil| |draw| |expextendedint|
+ |hessian| |aspFilename| |irreducible?| |useSingleFactorBound?|
+ |comparison| |powerAssociative?| |eof?| |f02akf|
+ |primPartElseUnitCanonical| |One| |removeSinSq| |select| |principal?|
+ |critB| |members| |badValues| |definingInequation| |infinityNorm|
+ |OMgetEndAttr| |maxPoints3D| |geometric| |port| |OMputEndApp|
+ |padicFraction| |power| |mkcomm| |socf2socdf| |inRadical?| |inR?|
+ |generators| |virtualDegree| |balancedBinaryTree| |lp| |rootSplit|
+ |stopTableGcd!| |groebnerFactorize| |solveLinearlyOverQ| |bitCoef|
+ |stiffnessAndStabilityOfODEIF| |leftUnits| |pointColor| |makeObject|
+ |plenaryPower| |t| |brillhartTrials| |mkAnswer| |fillPascalTriangle|
+ |maxint| |redPol| |setFieldInfo| |assert| |measure2Result| |ricDsolve|
+ |totalDifferential| |normalized?| |rightPower| |bumptab1| |iomode|
+ |lllp| |OMbindTCP| |mainMonomials| |midpoints| |exactQuotient!|
+ |bracket| |elt| |rst| |coef| |permutations| |purelyTranscendental?|
+ |hdmpToP| |discriminant| |splitSquarefree| |cup| |iicos| |readable?|
+ |makeRecord| |tanQ| |kroneckerDelta| LODO2FUN |brillhartIrreducible?|
+ |monomRDEsys| |rarrow| |genus| |leftTraceMatrix| |romberg|
+ |setLabelValue| |component| |squareMatrix| |irreducibleFactors|
+ |nextColeman| |split| |failed?| |compose| |formula| |coerceImages|
+ |lhs| |list?| |OMgetApp| |LiePolyIfCan| |atoms| |nullSpace|
+ |systemCommand| |child| |mainDefiningPolynomial| |outputForm|
+ |Frobenius| |rhs| |smith| |createZechTable| |resultantnaif|
+ |screenResolution| |lex| |tube| |fill!| |even?| |lowerCase!|
+ |operator| |palgextint| |radicalRoots| |linearMatrix|
+ |lazyPseudoDivide| |primitive?| |OMencodingSGML| |row| |s17ajf|
+ |depth| |capacity| |limitedint| |cCoth| |UP2ifCan| |LyndonCoordinates|
+ |compiledFunction| |normal| |equation| |multMonom| |imagE| |nrows|
+ |less?| |style| |ScanArabic| |semiResultantReduitEuclidean| |pushup|
+ |key| |transcendent?| |OMmakeConn| |lprop| |setPrologue!|
+ |unaryFunction| |ncols| |polyRicDE| |minGbasis| |quasiRegular|
+ |c05pbf| |nextsubResultant2| |light| |rightZero| |laurentIfCan|
+ |symmetricTensors| |iisqrt3| |filename| |po| |f01brf|
+ |selectMultiDimensionalRoutines| |nextItem| |printHeader|
+ |getConstant| |minIndex| |code| |constantIfCan| |number?|
+ |singularitiesOf| |makeResult| |not?| |nonQsign| |rotate|
+ |bubbleSort!| |truncate| |quasiAlgebraicSet| |localUnquote|
+ |squareFreePolynomial| |univcase| |radicalOfLeftTraceForm| |arbitrary|
+ |irreducibleFactor| |deleteProperty!| |coord| |nextsousResultant2|
+ |parse| |lift| |BumInSepFFE| |rightUnit|
+ |genericLeftMinimalPolynomial| |coHeight| |dioSolve| |e01bgf|
+ |interval| |normalize| |splitLinear| |myDegree| |reduce| |bounds|
+ |outputMeasure| |triangularSystems| |submod| |matrixGcd|
+ |setScreenResolution3D| |coercePreimagesImages| |divide|
+ |removeCoshSq| |setPredicates| |monicDecomposeIfCan| |singular?|
+ |removeZeroes| |lazyPseudoRemainder| |repeatUntilLoop|
+ |inverseColeman| |d01alf| |sturmVariationsOf| |padecf| |dmp2rfi|
+ |loadNativeModule| |expenseOfEvaluation| |parabolicCylindrical|
+ |prime?| |numberOfOperations| |hspace| |getlo| |reduction| |cTan|
+ |expr| |antisymmetricTensors| |addPoint| |totalLex| |mainExpression|
+ |iifact| |rightTrace| |setAttributeButtonStep|
+ |semiResultantEuclidean2| |antiCommutative?| |unknown| |invertIfCan|
+ |opeval| |factorials| |makeop| |real| |leastPower| |realEigenvectors|
+ |hostPlatform| |OMgetEndObject| |OMgetAtp| |findConstructor| |zCoord|
+ |problemPoints| |selectSumOfSquaresRoutines| |imag| |d03faf|
+ |eigenvector| |rubiksGroup| |OMencodingUnknown| |kind| |notOperand|
+ |trace2PowMod| |polygamma| |leftUnit| |abs| |directProduct| |sqfree|
+ |leaves| |readBytes!| |radicalEigenvectors| |equiv| |range| |op|
+ |variable| |drawCurves| |palgLODE0| |pseudoDivide| |rank| |init|
+ |bitTruth| |ode1| |linears| |f02adf| |ef2edf| |basisOfLeftAnnihilator|
+ |iterators| |qqq| |integralAtInfinity?| |fortranReal| |brace|
+ |harmonic| |e02dff| |substring?|
+ |removeRoughlyRedundantFactorsInContents| |part?| |basicSet|
+ |partialDenominators| |Nul| |normalDenom| |dualSignature| |getOrder|
+ |destruct| |f04mbf| |frst| |ReduceOrder| |intersect| |iiacos|
+ |iiacosh| |predicates| |setMaxPoints| |index| |s15aef| |entry|
+ |s17dhf| |suffix?| |makingStats?| |seriesSolve| |escape|
+ |subResultantsChain| |Hausdorff| |complexNumericIfCan| |atanIfCan|
+ |ranges| |droot| |iiabs| |setScreenResolution| |FormatRoman|
+ |toseSquareFreePart| |setEpilogue!| |startTableGcd!| |closedCurve?|
+ |currentEnv| |writeUInt8!| |push| |e02akf| |prefix?| |more?|
+ |constantOperator| |union| |makeSin| |showIntensityFunctions| |pair|
+ |parametersOf| |monomial| |OMgetSymbol| |OMputEndError| |inverse|
+ |monomRDE| |solid?| |readIfCan!| |lists| |multivariate|
+ |createGenericMatrix| |nothing| |OMputApp| |univariateSolve|
+ |weighted| |algintegrate| |axes| |leftMinimalPolynomial|
+ |genericLeftTraceForm| |variables| |crest| |cylindrical| |simplify|
+ |setOfMinN| |outputFloating| |cyclicEqual?| |digit| |leftFactor|
+ |outputAsFortran| |cotIfCan| |semicolonSeparate| |shiftLeft| |value|
+ |stronglyReduced?| |elliptic| |laplace| |outputAsScript| |times!|
+ |monicDivide| |limit| |integerIfCan| |euclideanSize| |cosh2sech|
+ |points| |iibinom| |randomR| |pdf2ef| |pointData| |particularSolution|
+ |top| |infix?| |iiasec| |getRef| |messagePrint| |setright!| |f2df|
+ |algDsolve| |setprevious!| |supRittWu?| |mask| |innerSolve|
+ |laplacian| |deepCopy| |zeroSquareMatrix| |rational| |taylor|
+ |ratDsolve| |chainSubResultants| |quoByVar| |resetAttributeButtons|
+ |setErrorBound| |getOperator| |parts| |laurent| |oneDimensionalArray|
+ |setProperty| |initializeGroupForWordProblem| |resetBadValues|
+ |leftCharacteristicPolynomial| |elements| |multiEuclideanTree|
+ |drawComplex| |constant| |puiseux| |fi2df| |printInfo| |ratDenom|
+ |firstSubsetGray| |var2StepsDefault| |sn| |hasPredicate?| |nthFlag|
+ |lazyPquo| |monomialIntegrate| |palgRDE0| |seed|
+ |exprHasWeightCosWXorSinWX| |adaptive3D?| |complexForm|
+ |doubleComplex?| |addPointLast| |inv| |viewZoomDefault|
+ |rangeIsFinite| |autoReduced?| |mulmod| |s13adf| |OMUnknownCD?|
+ |tanhIfCan| |ground?| UTS2UP |pdf2df| |primaryDecomp|
+ |highCommonTerms| |taylorQuoByVar| |radPoly| |cRationalPower|
+ |inputOutputBinaryFile| |remove!| |ground| |listYoungTableaus|
+ |generalizedContinuumHypothesisAssumed| |fullPartialFraction|
+ |fprindINFO| |numerator| |leftScalarTimes!| |outlineRender| |inrootof|
+ |initiallyReduce| |leadingMonomial| |diagonal?| |numberOfFactors|
+ |superscript| |generateIrredPoly| |stFuncN| |quoted?| |midpoint|
+ |realRoots| |extractPoint| |leadingCoefficient|
+ |factorsOfCyclicGroupSize| |rules| |compound?| |viewPhiDefault|
+ |simpleBounds?| |algSplitSimple| |status| |indicialEquations|
+ |changeMeasure| |besselY| |prologue| |tableau| |primitiveMonomials|
+ |leadingCoefficientRicDE| |selectPolynomials| |resultant| |iicosh|
+ |HenselLift| |operation| |setLegalFortranSourceExtensions|
+ |radicalSolve| |solveLinearPolynomialEquation| |cycleTail|
+ |tubePoints| |reductum| |tableForDiscreteLogarithm| |rootPoly|
+ |constantKernel| |connectTo| |subspace| |duplicates|
+ |extendedSubResultantGcd| |size?| |factors|
+ |semiResultantEuclideannaif| |host| |modularFactor|
+ |solveLinearPolynomialEquationByFractions| |omError|
+ |toseLastSubResultant| |squareTop| |nthFactor| |clip| |sort!|
+ |LazardQuotient| |sylvesterMatrix| |erf| |f01rdf| |cot2trig|
+ |solveRetract| |slex| |symbolTable| |charthRoot| |mainVariable?|
+ |deepExpand| |lyndon| |allRootsOf| |weights| |basisOfNucleus|
+ |var2Steps| |alphabetic?| |pole?| |trailingCoefficient|
+ |semiLastSubResultantEuclidean| |isConnected?| |monic?| |binomThmExpt|
+ |localAbs| |makeTerm| |curry| |indicialEquation| |symmetricPower|
+ |is?| |nonLinearPart| |viewThetaDefault| |zerosOf| |mapExponents|
+ |s19acf| |hconcat| |roughBasicSet| |fullDisplay|
+ |numberOfComputedEntries| |d01asf| |readByte!| |setchildren!|
+ |select!| |powern| |getGoodPrime| |LagrangeInterpolation| |intChoose|
+ |ptree| |makeViewport2D| |acoshIfCan| |initials| |figureUnits| |front|
+ |cyclic| |inc| |rewriteSetByReducingWithParticularGenerators|
+ |tubePlot| |quote| |cyclePartition|
+ |rewriteIdealWithQuasiMonicGenerators| |df2mf| |multiplyCoefficients|
+ |aQuartic| |explicitlyFinite?| |iiacsc| |mat| |entries| |rur|
+ |writable?| |jacobi| |quotientByP| |selectPDERoutines| |leftTrace|
+ |readUInt8!| |top!| |subscriptedVariables| |rightFactorCandidate|
+ |cCot| |indiceSubResultant| |solid| |shiftRoots| |factorGroebnerBasis|
+ |roman| |concat| |newReduc| |setButtonValue| |c05adf| |zeroVector|
+ |prime| |f04asf| |s17dcf| |elliptic?| |groebgen| |computeCycleEntry|
+ |e02zaf| |connect| |d01gbf| |tanSum| |ldf2vmf| |binomial|
+ |oblateSpheroidal| |writeInt8!| |trunc| |useEisensteinCriterion?|
+ |pushNewContour| |mainKernel| |rightCharacteristicPolynomial|
+ |iterationVar| |merge!| |uncouplingMatrices| |groebSolve|
+ |OMunhandledSymbol| |s20acf| |updateStatus!| |overlap| |commaSeparate|
+ |rroot| |tanh2coth| |solveLinearPolynomialEquationByRecursion|
+ |stripCommentsAndBlanks| |normal?| |trapezoidal| |bernoulli|
+ |appendPoint| |c05nbf| |reciprocalPolynomial| |bernoulliB| |lepol|
+ |lastSubResultant| |nthr| |pushdown| |fixedPointExquo| |bipolar|
+ |gcdcofactprim| |shallowExpand| |symbolIfCan| |pseudoQuotient|
+ |reverse!| |optimize| |setnext!| |writeBytes!| |simplifyLog|
+ |factorList| |idealiser| |integralDerivationMatrix| |asechIfCan|
+ |uniform| |head| |signature| |isPlus| |shanksDiscLogAlgorithm|
+ |quasiMonic?| |sayLength| |bitLength| |infieldint|
+ |stoseInternalLastSubResultant| |enterInCache| |decompose| |f07fef|
+ |closedCurve| |argscript| |bindings| |iiatanh| |meshPar1Var| |f01qef|
+ |extendedint| |setvalue!| |s14baf| |rdregime| |makeGraphImage|
+ |d01ajf| |universe| |f04faf| |listexp| |OMgetInteger|
+ |constantToUnaryFunction| |s18aef| |byte| |iicsc|
+ |intermediateResultsIF| |reducedSystem| |acothIfCan| |subPolSet?|
+ |digit?| |cAsinh| |mainValue| |linSolve| |mvar| |OMgetString|
+ |recolor| |insertionSort!| |f01ref| |child?| |delete| |inspect|
+ |mainVariables| |iidsum| |innerSolve1| |mkIntegral| |moebius|
+ |medialSet| |pdct| |clearTheSymbolTable| |functionIsFracPolynomial?|
+ |e04jaf| |ksec| |mindegTerm| GF2FG |realElementary|
+ |listConjugateBases| |trueEqual| |cfirst| |cap| |removeCosSq|
+ |preprocess| |subresultantVector| |functionIsOscillatory| |OMclose|
+ |matrixDimensions| |conjug| |totolex| |rowEchLocal| |getIdentifier|
+ |integralBasisAtInfinity| |e04dgf| |modulus| |llprop| |denominators|
+ |complexIntegrate| |infieldIntegrate| |denomRicDE| |s21bbf| |curve?|
+ |computeCycleLength| |close!| |point?| |abelianGroup| |showAll?|
+ |exquo| |infRittWu?| |reopen!| |conjugates| |overlabel|
+ |inGroundField?| |point| |createPrimitivePoly|
+ |stosePrepareSubResAlgo| |pop!| |separate| |rombergo| |insertMatch|
+ |trigs| |simpsono| |probablyZeroDim?| |fortranCharacter| |rk4f|
+ |OMlistCDs| |showTheSymbolTable| |div| |normalForm| |innerint|
+ |removeConstantTerm| |polarCoordinates| |algint| |presub|
+ |SturmHabicht| FG2F |f02aef| |datalist| |cond| |palgextint0|
+ |createMultiplicationMatrix| |palgRDE| |rightRegularRepresentation|
+ |stopTable!| |series| |chineseRemainder| |showClipRegion|
+ |setTopPredicate| |polygon?| |quo| |getBadValues| |setPosition|
+ |s17aff| |s15adf| |legendre| |companionBlocks| |closeComponent|
+ |iiperm| |redmat| |whatInfinity| |genericRightMinimalPolynomial|
+ |orOperands| |explicitEntries?| |mdeg| |backOldPos| |qPot| |prevPrime|
+ |equivOperands| |parent| |zeroOf| |distribute| |mergeFactors|
+ |identityMatrix| |genericRightNorm| |satisfy?| |copyInto!|
+ |wordInGenerators| |parabolic| |box| |lazyVariations|
+ |certainlySubVariety?| |rootSimp| |lastSubResultantElseSplit| |min|
+ |complement| |numberOfFractionalTerms| |real?| |s17dlf| |expIfCan|
+ |rem| |cSin| |eigenMatrix| |tab| |s01eaf| |unrankImproperPartitions0|
+ |multinomial| |log10| |option?| |exprToXXP| |palglimint| |positive?|
+ |precision| |radix| |lieAdmissible?| |heap| |partition|
+ |rectangularMatrix| |li| |bitand| |s20adf| |SturmHabichtCoefficients|
+ |ratPoly| |nextPrimitiveNormalPoly| |chvar| |leadingTerm|
+ |factorPolynomial| |stopTableInvSet!| |fintegrate| |bitior|
+ |createPrimitiveNormalPoly| |leftExactQuotient| |fglmIfCan|
+ |tensorProduct| |increment| |super| |countable?| |imaginary|
+ |tablePow| |symmetric?| |cAcos| |odd?| |normalizeAtInfinity|
+ |restorePrecision| |pade| |empty| |torsionIfCan| |acosIfCan| |every?|
+ |notelem| |hyperelliptic| |squareFreeFactors| |UnVectorise|
+ |stoseInvertibleSet| |imagK| |printStatement|
+ |wordsForStrongGenerators| |fractionFreeGauss!| |extractSplittingLeaf|
+ |iCompose| |subCase?| |OMputError| |algebraic?| |numerators|
+ |diagonal| |initTable!| |unit?| |OMgetVariable| |rename| |addiag|
+ |cTanh| |contract| |zag| |plotPolar| |merge| |fortranDoubleComplex|
+ |normalizedAssociate| |showFortranOutputStack| |mathieu12| |f02aff| Y
+ |tanAn| |complexNormalize| |iiacot| |octon| |f02ajf| |npcoef|
+ |pleskenSplit| |normalDeriv| |aromberg| |minPoly| |rquo|
+ |primintfldpoly| |halfExtendedSubResultantGcd1| |gbasis|
+ |indicialEquationAtInfinity| |complex?| |mainCharacterization|
+ |triangulate| |drawToScale| |coerceS| F |index?|
+ |linearDependenceOverZ| |sin?| |finiteBasis| |primintegrate|
+ |skewSFunction| |in?| |debug| |yCoord| |unvectorise|
+ |balancedFactorisation| |getStream| |reducedContinuedFraction|
+ |squareFree| |lazyResidueClass| |dark| |mainPrimitivePart| D
+ |logGamma| |internalZeroSetSplit| |zero| |newLine| |leftExtendedGcd|
+ |rightOne| |internalIntegrate| |test| |multiple?| |factorial|
+ |var1Steps| |reducedForm| |printStats!| |cAsec| |complexLimit| |any|
+ |dflist| |identification| |e04gcf| |pointColorPalette| |ocf2ocdf|
+ |And| |OMencodingXML| |characteristicSerie| |implies| |acotIfCan|
+ |zoom| |argument| |mathieu22| |OMgetEndError| |coshIfCan|
+ |eigenvalues| |Or| |null?| |low| |concat!| |prefix| |d01apf|
+ |Vectorise| |unexpand| |divisorCascade| |shallowCopy| |Not|
+ |sumSquares| |order| |getVariableOrder| |resetVariableOrder|
+ |OMsupportsSymbol?| |taylorIfCan| |transcendenceDegree| |expintegrate|
+ |karatsubaOnce| |readUInt32!| |interpolate| |symbol?| |chebyshevU|
+ |splitDenominator| |schwerpunkt| |stoseInvertibleSetsqfreg| **
+ |makeUnit| |s18dcf| |minimumExponent| |numberOfComponents| |df2st|
+ |ellipticCylindrical| |e02bbf| |mapUnivariateIfCan| |green| |e01bef|
+ |antisymmetric?| |unparse| |generalInfiniteProduct| |queue| |lo|
+ |completeHermite| |principalIdeal| |lazyIrreducibleFactors|
+ |denomLODE| |high| |e02daf| |internalAugment| |constantOpIfCan|
+ |f04arf| |ord| |inverseIntegralMatrix| |nextIrreduciblePoly|
+ |reduceLODE| |incr| EQ |credPol| |predicate| |root?| |print| |dim|
+ |dihedral| |ScanRoman| |combineFeatureCompatibility| |lieAlgebra?|
+ |rootDirectory| |module| |resolve| |minus!| |printInfo!|
+ |perfectSquare?| |numberOfImproperPartitions| |maximumExponent|
+ |typeList| |divisors| |zeroSetSplit| |extend| |iprint| |double?|
+ |characteristicSet| |increasePrecision| |s17aef|
+ |ScanFloatIgnoreSpaces| |diagonalProduct| |mapUnivariate|
+ |binaryFunction| |binary| |d03edf| |scalarTypeOf| |rightFactorIfCan|
+ |f02agf| |OMsetEncoding| |airyBi| |revert| |removeRedundantFactors|
+ |stFunc1| |intensity| |s21bcf| |beauzamyBound| |approxNthRoot|
+ |cschIfCan| |getPickedPoints| |shellSort| |subNode?| |name|
+ |zeroDimPrimary?| |recur| |readInt16!| |vedf2vef| |topPredicate|
+ |viewDefaults| |sizeMultiplication| |ridHack1| |d01anf|
+ |makeViewport3D| |body| |rk4qc| |findCycle| |modularGcd| |shufflein|
+ |invmod| |seriesToOutputForm| |weakBiRank| |choosemon| |exp|
+ |category| |nonSingularModel| |setMaxPoints3D| |ffactor| |polyRDE|
+ |flexibleArray| |term| |makeVariable| |laurentRep|
+ |irreducibleRepresentation| |completeEchelonBasis| ~ |domain|
+ |addMatchRestricted| |drawStyle| |ddFact| |gcdPolynomial| |psolve|
+ |parameters| |inf| |f02xef| |definingPolynomial| |sparsityIF|
+ |cothIfCan| |alphabetic| |package| |leadingSupport| |insert| |diff|
+ |RemainderList| |antiCommutator| |recip| |wholePart| |getCurve|
+ |numericIfCan| |semiSubResultantGcdEuclidean2| |open| |identity|
+ |firstNumer| |center| |acscIfCan| |graphStates| |zero?| |paraboloidal|
+ |sinh2csch| |normFactors| |length| |iisec| |implies?| |copies|
+ |makeMulti| |fortran| |characteristicPolynomial|
+ |numericalOptimization| |doubleDisc| |hasTopPredicate?| |OMcloseConn|
+ |hi| |laguerre| |scripts| |readInt8!| |c06ecf| |second| |integers|
+ |birth| |partitions| |localIntegralBasis| |loopPoints| |e02dcf|
+ |duplicates?| |lquo| |dn| |untab| |third| |discriminantEuclidean|
+ |showArrayValues| |trigs2explogs| |chiSquare1| |integralCoordinates|
+ |curve| |getButtonValue| |adaptive| |rightRankPolynomial| |OMputFloat|
+ |operations| |c06gcf| |OMputInteger| |f02axf| |rootOf| |shift|
+ |univariatePolynomials| |maxrank| |cSech| |infiniteProduct|
+ |lfintegrate| |endOfFile?| RF2UTS |quasiRegular?| |testDim|
+ |errorKind| |sumOfDivisors| |deref| |bandedJacobian|
+ |screenResolution3D| |outputAsTex| |cot2tan| |objectOf| |exprToUPS|
+ |boundOfCauchy| |quadraticForm| |extendIfCan| |exp1| |perfectNthRoot|
+ |modifyPoint| |reorder| |checkRur| |c06ebf| |normal01| |arrayStack|
+ |genericRightDiscriminant| |clipBoolean| |quotient| |composites|
+ |squareFreeLexTriangular| |transpose| |LyndonWordsList1| |property|
+ |edf2efi| |HermiteIntegrate| |back| |fortranTypeOf| |integralMatrix|
+ |clearCache| |inconsistent?| |rationalApproximation| |blue|
+ |setImagSteps| |internalSubQuasiComponent?| |structuralConstants|
+ |SturmHabichtMultiple| |singleFactorBound| |hMonic| |rowEchelonLocal|
+ |quadratic?| |lcm| |expPot| |zeroDimensional?| |updatF|
+ |dihedralGroup| |meshPar2Var| |c06gsf| |setleaves!| |subNodeOf?|
+ |getMultiplicationTable| |sorted?| |logpart| |Ci| |components|
+ |relativeApprox| |units| |minset| |quotedOperators| |e01daf|
+ |integer?| |dimension| |unknownEndian| |stack| |append| |setPoly|
+ |read!| |d01bbf| |sumOfSquares| |s14aaf| |extendedResultant|
+ |selectOptimizationRoutines| |pointPlot| |nativeModuleExtension|
+ |critBonD| |littleEndian| |gcd| |componentUpperBound| |getProperty|
+ |f01mcf| |monicLeftDivide| |moduloP| |pomopo!| |comp| |primes|
+ |script| |relerror| |setref| |rightRank| |traceMatrix| |initial|
+ |false| |frobenius| |sechIfCan| |laguerreL| |compactFraction|
+ |bigEndian| |addMatch| |evenlambert| |tubeRadiusDefault| |nand|
+ |latex| |df2ef| |eigenvectors| |rk4| |collectUpper| |changeBase|
+ |hypergeometric0F1| |cPower| |flagFactor| |OMreadStr|
+ |lastSubResultantEuclidean| |lineColorDefault| |uniform01|
+ |linkToFortran| |s13aaf| |readLine!| |atrapezoidal| |plot| |ODESolve|
+ |unprotectedRemoveRedundantFactors| |tex| |leftRankPolynomial| UP2UTS
+ |d03eef| |f02aaf| |linear| |rowEch| |areEquivalent?| |e02ddf|
+ |OMconnInDevice| |conical| |anfactor| |decimal| |generic?|
+ |subQuasiComponent?| |#| |wholeRagits| |polCase| |pair?|
+ |normalizedDivide| |OMgetBVar| |doubleResultant| |extractIndex| |xn|
+ |pmComplexintegrate| |univariate?| |polynomial|
+ |unrankImproperPartitions1| |rightExtendedGcd| |coleman| |makeCrit|
+ |OMgetType| |plusInfinity| |moduleSum| |supersub| |scaleRoots| |pack!|
+ |fibonacci| |dom| |rationalPoint?| |parseString| |hermiteH|
+ |PollardSmallFactor| |float?| |minusInfinity| |moreAlgebraic?|
+ |getOperands| |specialTrigs| |adaptive?| |f04qaf| |multiEuclidean|
+ |ref| |henselFact| |ratpart| |permutationGroup| |toroidal|
+ |computePowers| |minColIndex| |list| |incrementKthElement| |stirling1|
+ |solveLinear| |qroot| |equiv?| |LiePoly| |newSubProgram| |returns|
+ |numberOfNormalPoly| |expandTrigProducts| |car| |numFunEvals3D|
+ |primextendedint| |viewDeltaXDefault| |leastAffineMultiple|
+ |linearPolynomials| |iisinh| |makeprod| |packageCall|
+ |semiSubResultantGcdEuclidean1| |poisson| |cdr| |symbol| |pr2dmp|
+ |s19abf| |d02bhf| |extendedEuclidean| |minPol| |printCode| |Lazard|
+ |setDifference| |aQuadratic| |startStats!| |expression|
+ |firstUncouplingMatrix| |csubst| |startTableInvSet!| |shrinkable|
+ |f02awf| |f04adf| |setrest!| |polygon| |title| |iiasech|
+ |setIntersection| |upperCase| |integrate| |options| |upperCase!|
+ |integer| |createNormalPrimitivePoly| |PDESolve| |inHallBasis?|
+ |algebraicDecompose| |pureLex| |colorDef| |leftRank| |rule|
+ |factorAndSplit| |representationType| |setUnion| |sin2csc| |e02def|
+ |elementary| |say| |c06frf| |simpson| |thenBranch| |returnType!|
+ |type| |qfactor| |normalElement| |subResultantGcd| |OMgetEndBVar|
+ |apply| |polar| |e| |shiftRight| |FormatArabic| |froot| F2FG |isTimes|
+ |belong?| |selectfirst| |string| |rightQuotient| |RittWuCompare|
+ |setelt!| |iilog| |OMwrite| |stFunc2| |summation| |hcrf|
+ |differentialVariables| |rewriteIdealWithRemainder|
+ |scanOneDimSubspaces| |purelyAlgebraicLeadingMonomial?| |size|
+ |degreeSubResultantEuclidean| |curveColor| |cycleEntry|
+ |toseInvertible?| |quadratic| |extract!| |empty?| |horizConcat|
+ |tan2trig| |leader| |imports| |mindeg| |constructor|
+ |rightMinimalPolynomial| |invertibleSet| |createMultiplicationTable|
+ |controlPanel| |exprHasLogarithmicWeights| |sncndn| |e01sef| |subSet|
+ |lagrange| |resize| |polyPart| |fixedPoints| |imagj| |aCubic|
+ |antiAssociative?| |s17akf| |getExplanations| |viewPosDefault| |first|
+ |cLog| |diag| |void| |reset| |f01bsf| |patternMatch| |hue| |epilogue|
+ |power!| |repeating| |rest| |norm| |c06ekf| |An| |round| |reflect|
+ |monicRightFactorIfCan| |sub| |meatAxe| |stiffnessAndStabilityFactor|
+ |substitute| |normInvertible?| |operators| |f04mcf| |numeric| |write|
+ |s17adf| |cycleRagits| |approximants| |exists?|
+ |dimensionOfIrreducibleRepresentation| |removeDuplicates|
+ |decreasePrecision| |integralBasis| |variationOfParameters| |fmecg|
+ |save| |radical| |palgint| |showAllElements| |monomialIntPoly|
+ |modifyPointData| |clipSurface| |linearDependence| |d02cjf| |one?|
+ |sPol| |iicsch| |rightNorm| |adjoint| |fortranCarriageReturn| |se2rfi|
+ |bipolarCylindrical| |width| |call| |coerceL| |curryLeft|
+ |karatsubaDivide| |repSq| |mpsode| |OMconnOutDevice| |lifting|
+ |overset?| |scalarMatrix| |newTypeLists| |insertBottom!| |determinant|
+ |symmetricProduct| |lllip| |lighting| |createLowComplexityTable|
+ |root| |triangular?| |linearPart| |leftRecip| |halfExtendedResultant1|
+ |lazy?| |mathieu24| |maxIndex| |leftRemainder| |divideExponents|
+ |charClass| |cyclotomicFactorization| |lfunc| |rotate!|
+ |numberOfVariables| |setFormula!| |varselect| |setAdaptive3D|
+ |isobaric?| |dec| |iflist2Result| |acschIfCan| |kovacic|
+ |functionIsContinuousAtEndPoints| |nextSubsetGray| |binarySearchTree|
+ |prinb| |e02baf| |setValue!| |squareFreePrim| |cAcosh| |dimensionsOf|
+ |rootProduct| |iiasinh| |flatten| |vertConcat| |setlast!| |dictionary|
+ |directSum| |hdmpToDmp| |fracPart| |gradient| |primlimintfrac|
+ |decomposeFunc| |baseRDEsys| |nthFractionalTerm| |divisor|
+ |insertTop!| |noncommutativeJordanAlgebra?| |optional| |sts2stst|
+ |checkForZero| |shade| |primextintfrac| |showRegion| |imagI|
+ |rationalIfCan| |spherical| |leftQuotient| |complexExpand|
+ |KrullNumber| |regularRepresentation| |approxSqrt| |hclf| |sh|
+ |secIfCan| |asimpson| |monomial?| |pointSizeDefault| |twist| |build|
+ |numFunEvals| |repeating?| |clipWithRanges| |readUInt16!| |rename!|
+ |Beta| |getSyntaxFormsFromFile| |interpretString| |chebyshevT|
+ |palgintegrate| |evaluate| |validExponential| |writeLine!|
+ |represents| |deepestInitial| |constantLeft| |create3Space|
+ |minimalPolynomial| |separant| |setCondition!| |fortranCompilerName|
+ |physicalLength!| |contractSolve| |mainForm| |reduceByQuasiMonic|
+ |calcRanges| |tan2cot| |GospersMethod| |cyclotomic| |interReduce|
+ |pascalTriangle| |createLowComplexityNormalBasis|
+ |useSingleFactorBound| |complexEigenvalues| |enqueue!| |pattern|
+ |wronskianMatrix| |createRandomElement| |hasSolution?| |dAndcExp|
+ |partialFraction| |removeSuperfluousQuasiComponents| |genericPosition|
+ |removeRedundantFactorsInPols| |paren| |nodeOf?| |internalSubPolSet?|
+ |sinhcosh| |permutation| |generalizedContinuumHypothesisAssumed?|
+ |derivationCoordinates| |typeLists| |iidprod| |minordet|
+ |identitySquareMatrix| |rightMult| |tryFunctionalDecomposition?|
+ |c06gbf| |outerProduct| |viewDeltaYDefault| |iipow| |radicalSimplify|
+ |generalizedEigenvector| |nary?| |besselI| |f01rcf| |reduced?|
+ |lexTriangular| |OMputBind| |varList| |insertRoot!| |bright|
+ |putColorInfo| |enumerate| |s21baf| |iitan| |df2fi| |overbar|
+ |message| |clikeUniv| |swapColumns!| |removeDuplicates!|
+ |rightRemainder| |minimize| |expt| |lfextendedint| |completeEval|
+ |minPoints| |leftAlternative?| |LowTriBddDenomInv| |palginfieldint|
+ |bat1| |lowerCase?| |leadingIdeal| |constant?| |OMreceive| |e04ycf|
+ |bsolve| NOT |f04jgf| |readLineIfCan!| |mathieu23| |strongGenerators|
+ |movedPoints| |nextPrimitivePoly| |pointColorDefault| |vectorise|
+ |rationalPower| OR |invmultisect| |optional?| |selectODEIVPRoutines|
+ |variable?| |transcendentalDecompose| |matrix|
+ |wordInStrongGenerators| |janko2| |symFunc| |branchPointAtInfinity?|
+ |powerSum| |neglist| AND |reducedQPowers| |distFact|
+ |getMultiplicationMatrix| |viewWriteAvailable| |mantissa| |reverseLex|
+ |s18adf| |stronglyReduce| |copy!| |doublyTransitive?| |headReduce|
+ |quadraticNorm| |f04axf| |groebner| |alternatingGroup|
+ |OMencodingBinary| |solveInField| |cons| |rationalFunction|
+ |algebraicOf| |binaryTree| |yCoordinates| |showScalarValues|
+ |rowEchelon| |d02gbf| |distance| |string?| |edf2fi| |asinhIfCan|
+ |linearlyDependentOverZ?| |error| |ramifiedAtInfinity?| |moebiusMu|
+ |BasicMethod| |isOpen?| |region| |standardBasisOfCyclicSubmodule|
+ |setTex!| |flexible?| |mathieu11| |isExpt| |modTree| |OMputObject|
+ |rootRadius| |e01baf| |rootOfIrreduciblePoly| |dot| |arguments|
+ |exponential| |partialNumerators| |numberOfMonomials| |wreath|
+ |morphism| |mainContent| |sortConstraints| |normDeriv2| |dfRange|
+ |palglimint0| |vector| |mr| |csc2sin| |gethi| |nullary| |double|
+ |halfExtendedSubResultantGcd2| |leftDiscriminant| |eulerPhi| |digits|
+ |sec2cos| |s13acf| |csch2sinh| |reify| |safeCeiling|
+ |currentSubProgram| |f01qdf| |rotatez| |explicitlyEmpty?|
+ |genericLeftDiscriminant| |quartic| |modularGcdPrimitive| |youngGroup|
+ |basisOfRightAnnihilator| |realEigenvalues| |logical?| |source|
+ |mapdiv| |subst| |transform| |retractable?| |s19adf| |listOfLists|
+ |makeFloatFunction| |setStatus| |plus| |space| |c06fqf| |s19aaf|
+ |OMopenFile| |rootsOf| |simplifyPower| * |separateFactors| |imagk|
+ |subset?| |nlde| |inverseLaplace| |conditionsForIdempotents| |vspace|
+ |rightRecip| |separateDegrees| |idealSimplify| |makeFR| |extractIfCan|
+ |critpOrder| |bivariateSLPEBR| |s17def| |rischNormalize| |f02bbf|
+ |selectNonFiniteRoutines| |bfKeys| |linearAssociatedExp| |degree|
+ |getDatabase| |argumentListOf| |usingTable?| |pushuconst| |permanent|
+ |key?| |outputSpacing| |setColumn!| |maxdeg| |homogeneous?|
+ |setClipValue| |times| |associatedSystem| |redPo| |physicalLength|
+ |target| |argumentList!| |declare!| |vark| |isQuotient|
+ |lowerPolynomial| |prem| |setleft!| |createIrreduciblePoly| |collect|
+ |gramschmidt| |ceiling| |legendreP| |headAst| |initiallyReduced?|
+ |e04mbf| |eulerE| |e02agf| |objects| |differentiate| |find| |e01bhf|
+ |multisect| |quasiMonicPolynomials| |expintfldpoly| |nthExpon|
+ |lazyIntegrate| |tab1| |base| |realZeros| |drawComplexVectorField|
+ |setProperty!| |fractionPart| |leastMonomial| |fractRadix|
+ |integralMatrixAtInfinity| |f01maf| |rightTraceMatrix|
+ |roughEqualIdeals?| |monom| |unitCanonical| |multiset| |cycles|
+ |cyclicCopy| |lazyPremWithDefault| |leadingIndex| |tanh2trigh|
+ |unravel| |categoryFrame| |exprToGenUPS| |blankSeparate|
+ |mainVariable| |minPoints3D| |height| |unitsColorDefault|
+ |OMgetEndBind| |sample| |iiasin| |OMgetEndAtp| |OMread| |tanIfCan|
+ |failed| |removeSquaresIfCan| |ravel| |groebner?|
+ |ScanFloatIgnoreSpacesIfCan| |countRealRootsMultiple| |listBranches|
+ |lazyGintegrate| |airyAi| |addPoint2| |common| |zeroMatrix| |reshape|
+ |recoverAfterFail| |children| |presuper| |segment| |alternating|
+ |leftDivide| |generic| |scripted?| |hexDigit?| |splitConstant| |tree|
+ |d02raf| |dmpToP| |userOrdered?| |besselJ| |ipow| |polynomialZeros|
+ |elseBranch| |OMputSymbol| |clipParametric| |singRicDE| |declare|
+ |algebraicCoefficients?| |convergents| |generalTwoFactor|
+ |impliesOperands| |char| |createPrimitiveElement| |clearTheFTable|
+ |mappingAst| |OMlistSymbols| |setRealSteps| |stopMusserTrials|
+ |pushdterm| |OMUnknownSymbol?| |e02bef| |qelt|
+ |numberOfIrreduciblePoly| |tryFunctionalDecomposition| |cycle|
+ |B1solve| |isMult| |over| |qsetelt| |linearlyDependent?| |tail|
+ |genericRightTraceForm| |linear?| |character?| |f07aef| |palgLODE|
+ |prefixRagits| |orbit| |fixPredicate| |swapRows!| |jacobian| |xRange|
+ |symmetricDifference| |basis| |update| |OMgetFloat| |indices|
+ |coefficient| |leviCivitaSymbol| |traverse| |exQuo| |positiveSolve|
+ |yRange| |push!| |LyndonBasis| |setRow!| |slash| |integerBound|
+ |exprHasAlgebraicWeight| |previous| |setAdaptive| |generator| |zRange|
+ |squareFreePart| |generalSqFr| |mirror| |sincos| |conjugate| |float|
+ |callForm?| |internalInfRittWu?| |OMgetObject| |extractProperty|
+ |map!| |scale| |stoseInvertible?sqfreg| |listLoops| |primeFactor|
+ |check| |superHeight| |dominantTerm| |f2st| |resultantReduit|
+ |qsetelt!| |setsubMatrix!| |leftOne| |pushucoef| |largest| |f07adf|
+ |internalDecompose| |powmod| |limitPlus| |reduceBasisAtInfinity|
+ |defineProperty| |makeYoungTableau| |match?| |position|
+ |pseudoRemainder| |just| |log| |unitNormal| |viewport3D| |OMputAttr|
+ |semiDiscriminantEuclidean| |sylvesterSequence|
+ |numberOfPrimitivePoly| |swap!| |exponentialOrder| |createNormalPoly|
+ |rootPower| |reverse| |any?| |e04ucf| |atanhIfCan| |lambert|
+ |startTable!| |nil| |infinite| |arbitraryExponent| |approximate|
+ |complex| |shallowMutable| |canonical| |noetherian| |central|
|partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed|
|noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation|
|unitsKnown| |canonicalUnitNormal| |multiplicativeValuation|
diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase
index d9c2c341..fb759cd3 100644
--- a/src/share/algebra/interp.daase
+++ b/src/share/algebra/interp.daase
@@ -1,5295 +1,5299 @@
-(3194856 . 3442698085)
-((-1706 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-3737 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-4200 ((|#2| $ (-562) |#2|) NIL) ((|#2| $ (-1223 (-562)) |#2|) 34)) (-2673 (($ $) 59)) (-1954 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-4265 (((-562) (-1 (-112) |#2|) $) 22) (((-562) |#2| $) NIL) (((-562) |#2| $ (-562)) 73)) (-1720 (((-639 |#2|) $) 13)) (-4103 (($ (-1 (-112) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (-1491 (($ (-1 |#2| |#2|) $) 29)) (-4152 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 44)) (-3295 (($ |#2| $ (-562)) NIL) (($ $ $ (-562)) 50)) (-1963 (((-3 |#2| "failed") (-1 (-112) |#2|) $) 24)) (-3008 (((-112) (-1 (-112) |#2|) $) 21)) (-2343 ((|#2| $ (-562) |#2|) NIL) ((|#2| $ (-562)) NIL) (($ $ (-1223 (-562))) 49)) (-2880 (($ $ (-562)) 56) (($ $ (-1223 (-562))) 55)) (-1723 (((-766) (-1 (-112) |#2|) $) 26) (((-766) |#2| $) NIL)) (-2694 (($ $ $ (-562)) 52)) (-4220 (($ $) 51)) (-4064 (($ (-639 |#2|)) 53)) (-2767 (($ $ |#2|) NIL) (($ |#2| $) NIL) (($ $ $) 64) (($ (-639 $)) 62)) (-4053 (((-857) $) 69)) (-2879 (((-112) (-1 (-112) |#2|) $) 20)) (-1733 (((-112) $ $) 72)) (-1761 (((-112) $ $) 75)))
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-NIL
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-(((-19 |#1|) (-139) (-1207)) (T -19))
-NIL
-(-13 (-372 |t#1|) (-10 -7 (-6 -4404)))
-(((-34) . T) ((-102) -4037 (|has| |#1| (-1092)) (|has| |#1| (-845))) ((-609 (-857)) -4037 (|has| |#1| (-1092)) (|has| |#1| (-845)) (|has| |#1| (-609 (-857)))) ((-150 |#1|) . T) ((-610 (-535)) |has| |#1| (-610 (-535))) ((-285 #0=(-562) |#1|) . T) ((-287 #0# |#1|) . T) ((-308 |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((-372 |#1|) . T) ((-488 |#1|) . T) ((-600 #0# |#1|) . T) ((-513 |#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1092))) ((-645 |#1|) . T) ((-845) |has| |#1| (-845)) ((-1092) -4037 (|has| |#1| (-1092)) (|has| |#1| (-845))) ((-1207) . T))
-((-2781 (((-3 $ "failed") $ $) 12)) (-1847 (($ $) NIL) (($ $ $) 9)) (* (($ (-916) $) NIL) (($ (-766) $) 16) (($ (-562) $) 21)))
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-NIL
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NIL
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-NIL
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-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
-NIL
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(NIL) -8 NIL NIL NIL) (-1205 2918808 2919010 2919250 "TWOFACT" 2919631 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1204 2917880 2918217 2918452 "TUPLE" 2918608 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1203 2915571 2916090 2916629 "TUBETOOL" 2917363 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1202 2914420 2914625 2914866 "TUBE" 2915364 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1201 2909184 2913392 2913675 "TS" 2914172 NIL TS (NIL T) -8 NIL NIL NIL) (-1200 2897851 2901943 2902040 "TSETCAT" 2907309 NIL TSETCAT (NIL T T T T) -9 NIL 2908840 NIL) (-1199 2892586 2894183 2896074 "TSETCAT-" 2896079 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1198 2886849 2887695 2888637 "TRMANIP" 2891722 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1197 2886290 2886353 2886516 "TRIMAT" 2886781 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1196 2884086 2884323 2884687 "TRIGMNIP" 2886039 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1195 2883606 2883719 2883749 "TRIGCAT" 2883962 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1194 2883275 2883354 2883495 "TRIGCAT-" 2883500 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1193 2880172 2882133 2882414 "TREE" 2883029 NIL TREE (NIL T) -8 NIL NIL NIL) (-1192 2879446 2879974 2880004 "TRANFUN" 2880039 T TRANFUN (NIL) -9 NIL 2880105 NIL) (-1191 2878725 2878916 2879196 "TRANFUN-" 2879201 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1190 2878529 2878561 2878622 "TOPSP" 2878686 T TOPSP (NIL) -7 NIL NIL NIL) (-1189 2877877 2877992 2878146 "TOOLSIGN" 2878410 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1188 2876538 2877054 2877293 "TEXTFILE" 2877660 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1187 2874477 2874991 2875420 "TEX" 2876131 T TEX (NIL) -8 NIL NIL NIL) (-1186 2874258 2874289 2874361 "TEX1" 2874440 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1185 2873906 2873969 2874059 "TEMUTL" 2874190 T TEMUTL (NIL) -7 NIL NIL NIL) (-1184 2872060 2872340 2872665 "TBCMPPK" 2873629 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1183 2863948 2870220 2870276 "TBAGG" 2870676 NIL TBAGG (NIL T T) -9 NIL 2870887 NIL) (-1182 2859018 2860506 2862260 "TBAGG-" 2862265 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1181 2858402 2858509 2858654 "TANEXP" 2858907 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1180 2851903 2858259 2858352 "TABLE" 2858357 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1179 2851315 2851414 2851552 "TABLEAU" 2851800 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1178 2845923 2847143 2848391 "TABLBUMP" 2850101 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1177 2845351 2845451 2845579 "SYSTEM" 2845817 T SYSTEM (NIL) -7 NIL NIL NIL) (-1176 2841814 2842509 2843292 "SYSSOLP" 2844602 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1175 2840871 2841338 2841451 "SYSNNI" 2841637 NIL SYSNNI (NIL NIL) -8 NIL NIL 2841716) (-1174 2840324 2840729 2840771 "SYSINT" 2840776 NIL SYSINT (NIL NIL) -8 NIL NIL 2840784) (-1173 2836658 2837585 2838301 "SYNTAX" 2839630 T SYNTAX (NIL) -8 NIL NIL NIL) (-1172 2833816 2834418 2835050 "SYMTAB" 2836048 T SYMTAB (NIL) -8 NIL NIL NIL) (-1171 2829065 2829967 2830950 "SYMS" 2832855 T SYMS (NIL) -8 NIL NIL NIL) (-1170 2826337 2828523 2828753 "SYMPOLY" 2828870 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1169 2825854 2825929 2826052 "SYMFUNC" 2826249 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1168 2821906 2823166 2823979 "SYMBOL" 2825063 T SYMBOL (NIL) -8 NIL NIL NIL) (-1167 2815445 2817134 2818854 "SWITCH" 2820208 T SWITCH (NIL) -8 NIL NIL NIL) (-1166 2808715 2814266 2814569 "SUTS" 2815200 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2800816 2807962 2808235 "SUPXS" 2808500 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1164 2792346 2800434 2800560 "SUP" 2800725 NIL SUP (NIL T) -8 NIL NIL NIL) (-1163 2791505 2791632 2791849 "SUPFRACF" 2792214 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1162 2791126 2791185 2791298 "SUP2" 2791440 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1161 2789539 2789813 2790176 "SUMRF" 2790825 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1160 2788853 2788919 2789118 "SUMFS" 2789460 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1159 2772860 2788030 2788281 "SULS" 2788660 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1158 2772489 2772682 2772752 "SUCHTAST" 2772812 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1157 2771811 2772014 2772154 "SUCH" 2772397 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1156 2765705 2766717 2767676 "SUBSPACE" 2770899 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1155 2765135 2765225 2765389 "SUBRESP" 2765593 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1154 2758504 2759800 2761111 "STTF" 2763871 NIL STTF (NIL T) -7 NIL NIL NIL) (-1153 2752677 2753797 2754944 "STTFNC" 2757404 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1152 2743992 2745859 2747653 "STTAYLOR" 2750918 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1151 2737236 2743856 2743939 "STRTBL" 2743944 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1150 2732627 2737191 2737222 "STRING" 2737227 T STRING (NIL) -8 NIL NIL NIL) (-1149 2727515 2732000 2732030 "STRICAT" 2732089 T STRICAT (NIL) -9 NIL 2732151 NIL) (-1148 2720325 2725134 2725745 "STREAM" 2726939 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1147 2719835 2719912 2720056 "STREAM3" 2720242 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1146 2718817 2719000 2719235 "STREAM2" 2719648 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1145 2718505 2718557 2718650 "STREAM1" 2718759 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1144 2717521 2717702 2717933 "STINPROD" 2718321 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1143 2717099 2717283 2717313 "STEP" 2717393 T STEP (NIL) -9 NIL 2717471 NIL) (-1142 2710642 2716998 2717075 "STBL" 2717080 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1141 2705816 2709863 2709906 "STAGG" 2710059 NIL STAGG (NIL T) -9 NIL 2710148 NIL) (-1140 2703518 2704120 2704992 "STAGG-" 2704997 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1139 2701713 2703288 2703380 "STACK" 2703461 NIL STACK (NIL T) -8 NIL NIL NIL) (-1138 2694438 2699854 2700310 "SREGSET" 2701343 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1137 2686864 2688232 2689745 "SRDCMPK" 2693044 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1136 2679831 2684304 2684334 "SRAGG" 2685637 T SRAGG (NIL) -9 NIL 2686245 NIL) (-1135 2678848 2679103 2679482 "SRAGG-" 2679487 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1134 2673343 2677795 2678216 "SQMATRIX" 2678474 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1133 2667092 2670061 2670788 "SPLTREE" 2672688 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1132 2663082 2663748 2664394 "SPLNODE" 2666518 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1131 2662129 2662362 2662392 "SPFCAT" 2662836 T SPFCAT (NIL) -9 NIL NIL NIL) (-1130 2660866 2661076 2661340 "SPECOUT" 2661887 T SPECOUT (NIL) -7 NIL NIL NIL) (-1129 2652518 2654262 2654292 "SPADXPT" 2658684 T SPADXPT (NIL) -9 NIL 2660718 NIL) (-1128 2652279 2652319 2652388 "SPADPRSR" 2652471 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1127 2650462 2652234 2652265 "SPADAST" 2652270 T SPADAST (NIL) -8 NIL NIL NIL) (-1126 2642433 2644180 2644223 "SPACEC" 2648596 NIL SPACEC (NIL T) -9 NIL 2650412 NIL) (-1125 2640604 2642365 2642414 "SPACE3" 2642419 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1124 2639356 2639527 2639818 "SORTPAK" 2640409 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1123 2637406 2637709 2638128 "SOLVETRA" 2639020 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1122 2636417 2636639 2636913 "SOLVESER" 2637179 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1121 2631637 2632518 2633520 "SOLVERAD" 2635469 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1120 2627452 2628061 2628790 "SOLVEFOR" 2631004 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1119 2621749 2626801 2626898 "SNTSCAT" 2626903 NIL SNTSCAT (NIL T T T T) -9 NIL 2626973 NIL) (-1118 2615892 2620072 2620463 "SMTS" 2621439 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1117 2610343 2615780 2615857 "SMP" 2615862 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1116 2608502 2608803 2609201 "SMITH" 2610040 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1115 2601397 2605553 2605656 "SMATCAT" 2607007 NIL SMATCAT (NIL NIL T T T) -9 NIL 2607557 NIL) (-1114 2598337 2599160 2600338 "SMATCAT-" 2600343 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1113 2596050 2597573 2597616 "SKAGG" 2597877 NIL SKAGG (NIL T) -9 NIL 2598012 NIL) (-1112 2592392 2595466 2595661 "SINT" 2595848 T SINT (NIL) -8 NIL NIL 2596021) (-1111 2592164 2592202 2592268 "SIMPAN" 2592348 T SIMPAN (NIL) -7 NIL NIL NIL) (-1110 2591471 2591699 2591839 "SIG" 2592046 T SIG (NIL) -8 NIL NIL NIL) (-1109 2590309 2590530 2590805 "SIGNRF" 2591230 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1108 2589114 2589265 2589556 "SIGNEF" 2590138 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1107 2588447 2588697 2588821 "SIGAST" 2589012 T SIGAST (NIL) -8 NIL NIL NIL) (-1106 2586137 2586591 2587097 "SHP" 2587988 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1105 2580043 2586038 2586114 "SHDP" 2586119 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1104 2579642 2579808 2579838 "SGROUP" 2579931 T SGROUP (NIL) -9 NIL 2579993 NIL) (-1103 2579500 2579526 2579599 "SGROUP-" 2579604 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1102 2576336 2577033 2577756 "SGCF" 2578799 T SGCF (NIL) -7 NIL NIL NIL) (-1101 2570731 2575783 2575880 "SFRTCAT" 2575885 NIL SFRTCAT (NIL T T T T) -9 NIL 2575924 NIL) (-1100 2564155 2565170 2566306 "SFRGCD" 2569714 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1099 2557283 2558354 2559540 "SFQCMPK" 2563088 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1098 2556905 2556994 2557104 "SFORT" 2557224 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1097 2556050 2556745 2556866 "SEXOF" 2556871 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1096 2555184 2555931 2555999 "SEX" 2556004 T SEX (NIL) -8 NIL NIL NIL) (-1095 2550723 2551412 2551507 "SEXCAT" 2554444 NIL SEXCAT (NIL T T T T T) -9 NIL 2555022 NIL) (-1094 2547903 2550657 2550705 "SET" 2550710 NIL SET (NIL T) -8 NIL NIL NIL) (-1093 2546154 2546616 2546921 "SETMN" 2547644 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1092 2545760 2545886 2545916 "SETCAT" 2546033 T SETCAT (NIL) -9 NIL 2546118 NIL) (-1091 2545540 2545592 2545691 "SETCAT-" 2545696 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1090 2541927 2544001 2544044 "SETAGG" 2544914 NIL SETAGG (NIL T) -9 NIL 2545254 NIL) (-1089 2541385 2541501 2541738 "SETAGG-" 2541743 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1088 2540855 2541081 2541182 "SEQAST" 2541306 T SEQAST (NIL) -8 NIL NIL NIL) (-1087 2540054 2540348 2540409 "SEGXCAT" 2540695 NIL SEGXCAT (NIL T T) -9 NIL 2540815 NIL) (-1086 2539110 2539720 2539902 "SEG" 2539907 NIL SEG (NIL T) -8 NIL NIL NIL) (-1085 2538089 2538303 2538346 "SEGCAT" 2538868 NIL SEGCAT (NIL T) -9 NIL 2539089 NIL) (-1084 2537138 2537468 2537668 "SEGBIND" 2537924 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1083 2536759 2536818 2536931 "SEGBIND2" 2537073 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1082 2536360 2536560 2536637 "SEGAST" 2536704 T SEGAST (NIL) -8 NIL NIL NIL) (-1081 2535579 2535705 2535909 "SEG2" 2536204 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1080 2535016 2535514 2535561 "SDVAR" 2535566 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1079 2527306 2534786 2534916 "SDPOL" 2534921 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1078 2525899 2526165 2526484 "SCPKG" 2527021 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1077 2525035 2525215 2525415 "SCOPE" 2525721 T SCOPE (NIL) -8 NIL NIL NIL) (-1076 2524256 2524389 2524568 "SCACHE" 2524890 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1075 2523928 2524088 2524118 "SASTCAT" 2524123 T SASTCAT (NIL) -9 NIL 2524136 NIL) (-1074 2523442 2523763 2523839 "SAOS" 2523874 T SAOS (NIL) -8 NIL NIL NIL) (-1073 2523007 2523042 2523215 "SAERFFC" 2523401 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1072 2516981 2522904 2522984 "SAE" 2522989 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1071 2516574 2516609 2516768 "SAEFACT" 2516940 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1070 2514895 2515209 2515610 "RURPK" 2516240 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1069 2513531 2513810 2514122 "RULESET" 2514729 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1068 2510718 2511221 2511686 "RULE" 2513212 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1067 2510357 2510512 2510595 "RULECOLD" 2510670 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1066 2509855 2510074 2510168 "RSTRCAST" 2510285 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1065 2504704 2505498 2506418 "RSETGCD" 2509054 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1064 2493961 2499013 2499110 "RSETCAT" 2503229 NIL RSETCAT (NIL T T T T) -9 NIL 2504326 NIL) (-1063 2491888 2492427 2493251 "RSETCAT-" 2493256 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1062 2484275 2485650 2487170 "RSDCMPK" 2490487 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1061 2482280 2482721 2482795 "RRCC" 2483881 NIL RRCC (NIL T T) -9 NIL 2484225 NIL) (-1060 2481631 2481805 2482084 "RRCC-" 2482089 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1059 2481101 2481327 2481428 "RPTAST" 2481552 T RPTAST (NIL) -8 NIL NIL NIL) (-1058 2455107 2464694 2464761 "RPOLCAT" 2475425 NIL RPOLCAT (NIL T T T) -9 NIL 2478584 NIL) (-1057 2446607 2448945 2452067 "RPOLCAT-" 2452072 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1056 2437654 2444818 2445300 "ROUTINE" 2446147 T ROUTINE (NIL) -8 NIL NIL NIL) (-1055 2434487 2437280 2437420 "ROMAN" 2437536 T ROMAN (NIL) -8 NIL NIL NIL) (-1054 2432762 2433347 2433607 "ROIRC" 2434292 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1053 2429155 2431398 2431428 "RNS" 2431732 T RNS (NIL) -9 NIL 2432005 NIL) (-1052 2427664 2428047 2428581 "RNS-" 2428656 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1051 2427113 2427495 2427525 "RNG" 2427530 T RNG (NIL) -9 NIL 2427551 NIL) (-1050 2426505 2426867 2426910 "RMODULE" 2426972 NIL RMODULE (NIL T) -9 NIL 2427014 NIL) (-1049 2425341 2425435 2425771 "RMCAT2" 2426406 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1048 2422218 2424687 2424984 "RMATRIX" 2425103 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1047 2415160 2417394 2417509 "RMATCAT" 2420868 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2421850 NIL) (-1046 2414535 2414682 2414989 "RMATCAT-" 2414994 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1045 2414102 2414177 2414305 "RINTERP" 2414454 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1044 2413235 2413755 2413785 "RING" 2413841 T RING (NIL) -9 NIL 2413927 NIL) (-1043 2413027 2413071 2413168 "RING-" 2413173 NIL RING- (NIL T) -8 NIL NIL NIL) (-1042 2411868 2412105 2412363 "RIDIST" 2412791 T RIDIST (NIL) -7 NIL NIL NIL) (-1041 2403184 2411336 2411542 "RGCHAIN" 2411716 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1040 2402560 2402940 2402981 "RGBCSPC" 2403039 NIL RGBCSPC (NIL T) -9 NIL 2403091 NIL) (-1039 2401744 2402099 2402140 "RGBCMDL" 2402372 NIL RGBCMDL (NIL T) -9 NIL 2402486 NIL) (-1038 2398738 2399352 2400022 "RF" 2401108 NIL RF (NIL T) -7 NIL NIL NIL) (-1037 2398384 2398447 2398550 "RFFACTOR" 2398669 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1036 2398109 2398144 2398241 "RFFACT" 2398343 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1035 2396226 2396590 2396972 "RFDIST" 2397749 T RFDIST (NIL) -7 NIL NIL NIL) (-1034 2395679 2395771 2395934 "RETSOL" 2396128 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1033 2395315 2395395 2395438 "RETRACT" 2395571 NIL RETRACT (NIL T) -9 NIL 2395658 NIL) (-1032 2395164 2395189 2395276 "RETRACT-" 2395281 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1031 2394793 2394986 2395056 "RETAST" 2395116 T RETAST (NIL) -8 NIL NIL NIL) (-1030 2387647 2394446 2394573 "RESULT" 2394688 T RESULT (NIL) -8 NIL NIL NIL) (-1029 2386273 2386916 2387115 "RESRING" 2387550 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1028 2385909 2385958 2386056 "RESLATC" 2386210 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1027 2385615 2385649 2385756 "REPSQ" 2385868 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1026 2383037 2383617 2384219 "REP" 2385035 T REP (NIL) -7 NIL NIL NIL) (-1025 2382735 2382769 2382880 "REPDB" 2382996 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1024 2376645 2378024 2379247 "REP2" 2381547 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1023 2373022 2373703 2374511 "REP1" 2375872 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1022 2365748 2371163 2371619 "REGSET" 2372652 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1021 2364561 2364896 2365146 "REF" 2365533 NIL REF (NIL T) -8 NIL NIL NIL) (-1020 2363938 2364041 2364208 "REDORDER" 2364445 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1019 2359943 2363151 2363378 "RECLOS" 2363766 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1018 2358995 2359176 2359391 "REALSOLV" 2359750 T REALSOLV (NIL) -7 NIL NIL NIL) (-1017 2358841 2358882 2358912 "REAL" 2358917 T REAL (NIL) -9 NIL 2358952 NIL) (-1016 2355324 2356126 2357010 "REAL0Q" 2358006 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1015 2350925 2351913 2352974 "REAL0" 2354305 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1014 2350423 2350642 2350736 "RDUCEAST" 2350853 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1013 2349828 2349900 2350107 "RDIV" 2350345 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1012 2348896 2349070 2349283 "RDIST" 2349650 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1011 2347493 2347780 2348152 "RDETRS" 2348604 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1010 2345305 2345759 2346297 "RDETR" 2347035 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1009 2343916 2344194 2344598 "RDEEFS" 2345021 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1008 2342411 2342717 2343149 "RDEEF" 2343604 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1007 2336672 2339547 2339577 "RCFIELD" 2340872 T RCFIELD (NIL) -9 NIL 2341602 NIL) (-1006 2334736 2335240 2335936 "RCFIELD-" 2336011 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) 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2230939 2231760 "PSETCAT-" 2231765 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-969 2229654 2229819 2229847 "PSCURVE" 2230115 T PSCURVE (NIL) -9 NIL 2230282 NIL) (-968 2226010 2227492 2227557 "PSCAT" 2228401 NIL PSCAT (NIL T T T) -9 NIL 2228641 NIL) (-967 2225073 2225289 2225689 "PSCAT-" 2225694 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-966 2223805 2224438 2224643 "PRTITION" 2224888 T PRTITION (NIL) -8 NIL NIL NIL) (-965 2223307 2223526 2223618 "PRTDAST" 2223733 T PRTDAST (NIL) -8 NIL NIL NIL) (-964 2212405 2214611 2216799 "PRS" 2221169 NIL PRS (NIL T T) -7 NIL NIL NIL) (-963 2210263 2211755 2211795 "PRQAGG" 2211978 NIL PRQAGG (NIL T) -9 NIL 2212080 NIL) (-962 2209649 2209878 2209906 "PROPLOG" 2210091 T PROPLOG (NIL) -9 NIL 2210213 NIL) (-961 2206819 2207463 2207927 "PROPFRML" 2209217 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-960 2206279 2206389 2206519 "PROPERTY" 2206709 T PROPERTY (NIL) -8 NIL NIL NIL) (-959 2200364 2204445 2205265 "PRODUCT" 2205505 NIL PRODUCT (NIL T T) -8 NIL NIL 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2135996 2136064 2136158 "PLOTTOOL" 2136267 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-922 2130618 2131807 2132955 "PLOT" 2134868 T PLOT (NIL) -8 NIL NIL NIL) (-921 2126432 2127466 2128387 "PLOT3D" 2129717 T PLOT3D (NIL) -8 NIL NIL NIL) (-920 2125344 2125521 2125756 "PLOT1" 2126236 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-919 2100738 2105410 2110261 "PLEQN" 2120610 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-918 2100056 2100178 2100358 "PINTERP" 2100603 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-917 2099749 2099796 2099899 "PINTERPA" 2100003 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-916 2098997 2099518 2099605 "PI" 2099645 T PI (NIL) -8 NIL NIL 2099712) (-915 2097394 2098335 2098363 "PID" 2098545 T PID (NIL) -9 NIL 2098679 NIL) (-914 2097119 2097156 2097244 "PICOERCE" 2097351 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-913 2096439 2096578 2096754 "PGROEB" 2096975 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-912 2092026 2092840 2093745 "PGE" 2095554 T PGE (NIL) -7 NIL NIL NIL) (-911 2090150 2090396 2090762 "PGCD" 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2023323 2023363 2023430 "PARSER" 2023512 T PARSER (NIL) -7 NIL NIL NIL) (-874 2022944 2023007 2023109 "PARSCURV" 2023254 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-873 2022576 2022633 2022742 "PARSC2" 2022881 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-872 2022215 2022273 2022370 "PARPCURV" 2022512 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-871 2021847 2021904 2022013 "PARPC2" 2022152 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-870 2021367 2021453 2021572 "PAN2EXPR" 2021748 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-869 2020173 2020488 2020716 "PALETTE" 2021159 T PALETTE (NIL) -8 NIL NIL NIL) (-868 2018641 2019178 2019538 "PAIR" 2019859 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-867 2012547 2017900 2018094 "PADICRC" 2018496 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-866 2005811 2011893 2012077 "PADICRAT" 2012395 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-865 2004161 2005748 2005793 "PADIC" 2005798 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-864 2001371 2002901 2002941 "PADICCT" 2003522 NIL PADICCT (NIL NIL) -9 NIL 2003804 NIL) (-863 2000328 2000528 2000796 "PADEPAC" 2001158 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-862 1999540 1999673 1999879 "PADE" 2000190 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-861 1997962 1998748 1999028 "OWP" 1999344 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-860 1997482 1997668 1997765 "OVERSET" 1997885 T OVERSET (NIL) -8 NIL NIL NIL) (-859 1996555 1997087 1997259 "OVAR" 1997350 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-858 1995819 1995940 1996101 "OUT" 1996414 T OUT (NIL) -7 NIL NIL NIL) (-857 1984726 1986928 1989128 "OUTFORM" 1993639 T OUTFORM (NIL) -8 NIL NIL NIL) (-856 1984062 1984323 1984450 "OUTBFILE" 1984619 T OUTBFILE (NIL) -8 NIL NIL NIL) (-855 1983369 1983534 1983562 "OUTBCON" 1983880 T OUTBCON (NIL) -9 NIL 1984046 NIL) (-854 1982970 1983082 1983239 "OUTBCON-" 1983244 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-853 1982378 1982699 1982788 "OSI" 1982901 T OSI (NIL) -8 NIL NIL NIL) (-852 1981934 1982246 1982274 "OSGROUP" 1982279 T OSGROUP (NIL) -9 NIL 1982301 NIL) (-851 1980679 1980906 1981191 "ORTHPOL" 1981681 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-850 1978265 1980514 1980635 "OREUP" 1980640 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-849 1975703 1977956 1978083 "ORESUP" 1978207 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-848 1973231 1973731 1974292 "OREPCTO" 1975192 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-847 1967055 1969222 1969263 "OREPCAT" 1971611 NIL OREPCAT (NIL T) -9 NIL 1972715 NIL) (-846 1964202 1964984 1966042 "OREPCAT-" 1966047 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-845 1963379 1963651 1963679 "ORDSET" 1963988 T ORDSET (NIL) -9 NIL 1964152 NIL) (-844 1962898 1963020 1963213 "ORDSET-" 1963218 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-843 1961532 1962289 1962317 "ORDRING" 1962519 T ORDRING (NIL) -9 NIL 1962644 NIL) (-842 1961177 1961271 1961415 "ORDRING-" 1961420 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-841 1960583 1961020 1961048 "ORDMON" 1961053 T ORDMON (NIL) -9 NIL 1961074 NIL) (-840 1959745 1959892 1960087 "ORDFUNS" 1960432 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-839 1959109 1959502 1959530 "ORDFIN" 1959595 T ORDFIN (NIL) -9 NIL 1959669 NIL) (-838 1955701 1957695 1958104 "ORDCOMP" 1958733 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-837 1954967 1955094 1955280 "ORDCOMP2" 1955561 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1951575 1952458 1953272 "OPTPROB" 1954173 T OPTPROB (NIL) -8 NIL NIL NIL) (-835 1948377 1949016 1949720 "OPTPACK" 1950891 T OPTPACK (NIL) -7 NIL NIL NIL) (-834 1946090 1946830 1946858 "OPTCAT" 1947677 T OPTCAT (NIL) -9 NIL 1948327 NIL) (-833 1945533 1945767 1945872 "OPSIG" 1946005 T OPSIG (NIL) -8 NIL NIL NIL) (-832 1945301 1945340 1945406 "OPQUERY" 1945487 T OPQUERY (NIL) -7 NIL NIL NIL) (-831 1942467 1943612 1944116 "OP" 1944830 NIL OP (NIL T) -8 NIL NIL NIL) (-830 1942002 1942173 1942214 "OPERCAT" 1942349 NIL OPERCAT (NIL T) -9 NIL 1942417 NIL) (-829 1941848 1941875 1941961 "OPERCAT-" 1941966 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-828 1938693 1940645 1941014 "ONECOMP" 1941512 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-827 1937998 1938113 1938287 "ONECOMP2" 1938565 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-826 1937417 1937523 1937653 "OMSERVER" 1937888 T OMSERVER (NIL) -7 NIL NIL NIL) (-825 1934305 1936857 1936897 "OMSAGG" 1936958 NIL OMSAGG (NIL T) -9 NIL 1937022 NIL) (-824 1932928 1933191 1933473 "OMPKG" 1934043 T OMPKG (NIL) -7 NIL NIL NIL) (-823 1932358 1932461 1932489 "OM" 1932788 T OM (NIL) -9 NIL NIL NIL) (-822 1930940 1931907 1932076 "OMLO" 1932239 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-821 1929865 1930012 1930239 "OMEXPR" 1930766 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-820 1929183 1929411 1929547 "OMERR" 1929749 T OMERR (NIL) -8 NIL NIL NIL) (-819 1928361 1928604 1928764 "OMERRK" 1929043 T OMERRK (NIL) -8 NIL NIL NIL) (-818 1927839 1928038 1928146 "OMENC" 1928273 T OMENC (NIL) -8 NIL NIL NIL) (-817 1921734 1922919 1924090 "OMDEV" 1926688 T OMDEV (NIL) -8 NIL NIL NIL) (-816 1920803 1920974 1921168 "OMCONN" 1921560 T OMCONN (NIL) -8 NIL NIL NIL) (-815 1919424 1920366 1920394 "OINTDOM" 1920399 T OINTDOM (NIL) -9 NIL 1920420 NIL) (-814 1915230 1916414 1917130 "OFMONOID" 1918740 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-813 1914668 1915167 1915212 "ODVAR" 1915217 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-812 1912126 1914413 1914568 "ODR" 1914573 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-811 1904470 1911902 1912028 "ODPOL" 1912033 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-810 1898346 1904342 1904447 "ODP" 1904452 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-809 1897112 1897327 1897602 "ODETOOLS" 1898120 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-808 1894081 1894737 1895453 "ODESYS" 1896445 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-807 1888963 1889871 1890896 "ODERTRIC" 1893156 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-806 1888389 1888471 1888665 "ODERED" 1888875 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-805 1885277 1885825 1886502 "ODERAT" 1887812 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-804 1882237 1882701 1883298 "ODEPRRIC" 1884806 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-803 1880207 1880776 1881262 "ODEPROB" 1881771 T ODEPROB (NIL) -8 NIL NIL NIL) (-802 1876729 1877212 1877859 "ODEPRIM" 1879686 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-801 1875978 1876080 1876340 "ODEPAL" 1876621 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-800 1872140 1872931 1873795 "ODEPACK" 1875134 T ODEPACK (NIL) -7 NIL NIL NIL) (-799 1871173 1871280 1871509 "ODEINT" 1872029 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-798 1865274 1866699 1868146 "ODEIFTBL" 1869746 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-797 1860609 1861395 1862354 "ODEEF" 1864433 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-796 1859944 1860033 1860263 "ODECONST" 1860514 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-795 1858095 1858730 1858758 "ODECAT" 1859363 T ODECAT (NIL) -9 NIL 1859894 NIL) (-794 1855002 1857807 1857926 "OCT" 1858008 NIL OCT (NIL T) -8 NIL NIL NIL) (-793 1854640 1854683 1854810 "OCTCT2" 1854953 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-792 1849414 1851814 1851854 "OC" 1852951 NIL OC (NIL T) -9 NIL 1853809 NIL) (-791 1846641 1847389 1848379 "OC-" 1848473 NIL OC- (NIL T T) -8 NIL NIL NIL) (-790 1846019 1846461 1846489 "OCAMON" 1846494 T OCAMON (NIL) -9 NIL 1846515 NIL) (-789 1845576 1845891 1845919 "OASGP" 1845924 T OASGP (NIL) -9 NIL 1845944 NIL) (-788 1844863 1845326 1845354 "OAMONS" 1845394 T OAMONS (NIL) -9 NIL 1845437 NIL) (-787 1844303 1844710 1844738 "OAMON" 1844743 T OAMON (NIL) -9 NIL 1844763 NIL) (-786 1843607 1844099 1844127 "OAGROUP" 1844132 T OAGROUP (NIL) -9 NIL 1844152 NIL) (-785 1843297 1843347 1843435 "NUMTUBE" 1843551 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-784 1836870 1838388 1839924 "NUMQUAD" 1841781 T NUMQUAD (NIL) -7 NIL NIL NIL) (-783 1832626 1833614 1834639 "NUMODE" 1835865 T NUMODE (NIL) -7 NIL NIL NIL) (-782 1830007 1830861 1830889 "NUMINT" 1831812 T NUMINT (NIL) -9 NIL 1832576 NIL) (-781 1828955 1829152 1829370 "NUMFMT" 1829809 T NUMFMT (NIL) -7 NIL NIL NIL) (-780 1815314 1818259 1820791 "NUMERIC" 1826462 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-779 1809711 1814763 1814858 "NTSCAT" 1814863 NIL NTSCAT (NIL T T T T) -9 NIL 1814902 NIL) (-778 1808905 1809070 1809263 "NTPOLFN" 1809550 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-777 1796745 1805730 1806542 "NSUP" 1808126 NIL NSUP (NIL T) -8 NIL NIL NIL) (-776 1796377 1796434 1796543 "NSUP2" 1796682 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-775 1786374 1796151 1796284 "NSMP" 1796289 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-774 1784806 1785107 1785464 "NREP" 1786062 NIL NREP (NIL T) -7 NIL NIL NIL) (-773 1783397 1783649 1784007 "NPCOEF" 1784549 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-772 1782463 1782578 1782794 "NORMRETR" 1783278 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-771 1780504 1780794 1781203 "NORMPK" 1782171 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-770 1780189 1780217 1780341 "NORMMA" 1780470 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-769 1780016 1780146 1780175 "NONE" 1780180 T NONE (NIL) -8 NIL NIL NIL) (-768 1779805 1779834 1779903 "NONE1" 1779980 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-767 1779288 1779350 1779536 "NODE1" 1779737 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-766 1777559 1778382 1778637 "NNI" 1778984 T NNI (NIL) -8 NIL NIL 1779219) (-765 1775979 1776292 1776656 "NLINSOL" 1777227 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-764 1772247 1773215 1774114 "NIPROB" 1775100 T NIPROB (NIL) -8 NIL NIL NIL) (-763 1771004 1771238 1771540 "NFINTBAS" 1772009 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-762 1770178 1770654 1770695 "NETCLT" 1770867 NIL NETCLT (NIL T) -9 NIL 1770949 NIL) (-761 1768886 1769117 1769398 "NCODIV" 1769946 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-760 1768648 1768685 1768760 "NCNTFRAC" 1768843 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-759 1766828 1767192 1767612 "NCEP" 1768273 NIL NCEP (NIL T) -7 NIL NIL NIL) (-758 1765739 1766478 1766506 "NASRING" 1766616 T NASRING (NIL) -9 NIL 1766690 NIL) (-757 1765534 1765578 1765672 "NASRING-" 1765677 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-756 1764687 1765186 1765214 "NARNG" 1765331 T NARNG (NIL) -9 NIL 1765422 NIL) (-755 1764379 1764446 1764580 "NARNG-" 1764585 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-754 1763258 1763465 1763700 "NAGSP" 1764164 T NAGSP (NIL) -7 NIL NIL NIL) (-753 1754530 1756214 1757887 "NAGS" 1761605 T NAGS (NIL) -7 NIL NIL NIL) (-752 1753078 1753386 1753717 "NAGF07" 1754219 T NAGF07 (NIL) -7 NIL NIL NIL) (-751 1747616 1748907 1750214 "NAGF04" 1751791 T NAGF04 (NIL) -7 NIL NIL NIL) (-750 1740584 1742198 1743831 "NAGF02" 1746003 T NAGF02 (NIL) -7 NIL NIL NIL) (-749 1735808 1736908 1738025 "NAGF01" 1739487 T NAGF01 (NIL) -7 NIL NIL NIL) (-748 1729436 1731002 1732587 "NAGE04" 1734243 T NAGE04 (NIL) -7 NIL NIL NIL) (-747 1720605 1722726 1724856 "NAGE02" 1727326 T NAGE02 (NIL) -7 NIL NIL NIL) (-746 1716558 1717505 1718469 "NAGE01" 1719661 T NAGE01 (NIL) -7 NIL NIL NIL) (-745 1714353 1714887 1715445 "NAGD03" 1716020 T NAGD03 (NIL) -7 NIL NIL NIL) (-744 1706103 1708031 1709985 "NAGD02" 1712419 T NAGD02 (NIL) -7 NIL NIL NIL) (-743 1699914 1701339 1702779 "NAGD01" 1704683 T NAGD01 (NIL) -7 NIL NIL NIL) (-742 1696123 1696945 1697782 "NAGC06" 1699097 T NAGC06 (NIL) -7 NIL NIL NIL) (-741 1694588 1694920 1695276 "NAGC05" 1695787 T NAGC05 (NIL) -7 NIL NIL NIL) (-740 1693964 1694083 1694227 "NAGC02" 1694464 T NAGC02 (NIL) -7 NIL NIL NIL) (-739 1693024 1693581 1693621 "NAALG" 1693700 NIL NAALG (NIL T) -9 NIL 1693761 NIL) (-738 1692859 1692888 1692978 "NAALG-" 1692983 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-737 1686809 1687917 1689104 "MULTSQFR" 1691755 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-736 1686128 1686203 1686387 "MULTFACT" 1686721 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-735 1679221 1683091 1683144 "MTSCAT" 1684214 NIL MTSCAT (NIL T T) -9 NIL 1684728 NIL) (-734 1678933 1678987 1679079 "MTHING" 1679161 NIL MTHING (NIL T) -7 NIL NIL NIL) (-733 1678725 1678758 1678818 "MSYSCMD" 1678893 T MSYSCMD (NIL) -7 NIL NIL NIL) (-732 1674837 1677480 1677800 "MSET" 1678438 NIL MSET (NIL T) -8 NIL NIL NIL) (-731 1671932 1674398 1674439 "MSETAGG" 1674444 NIL MSETAGG (NIL T) -9 NIL 1674478 NIL) (-730 1667815 1669311 1670056 "MRING" 1671232 NIL MRING (NIL T T) -8 NIL NIL NIL) (-729 1667381 1667448 1667579 "MRF2" 1667742 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-728 1666999 1667034 1667178 "MRATFAC" 1667340 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-727 1664611 1664906 1665337 "MPRFF" 1666704 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-726 1658671 1664465 1664562 "MPOLY" 1664567 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-725 1658161 1658196 1658404 "MPCPF" 1658630 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-724 1657675 1657718 1657902 "MPC3" 1658112 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1656870 1656951 1657172 "MPC2" 1657590 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1655171 1655508 1655898 "MONOTOOL" 1656530 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-721 1654422 1654713 1654741 "MONOID" 1654960 T MONOID (NIL) -9 NIL 1655107 NIL) (-720 1653968 1654087 1654268 "MONOID-" 1654273 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-719 1644827 1650735 1650794 "MONOGEN" 1651468 NIL MONOGEN (NIL T T) -9 NIL 1651924 NIL) (-718 1642045 1642780 1643780 "MONOGEN-" 1643899 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-717 1640904 1641324 1641352 "MONADWU" 1641744 T MONADWU (NIL) -9 NIL 1641982 NIL) (-716 1640276 1640435 1640683 "MONADWU-" 1640688 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-715 1639661 1639879 1639907 "MONAD" 1640114 T MONAD (NIL) -9 NIL 1640226 NIL) (-714 1639346 1639424 1639556 "MONAD-" 1639561 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-713 1637662 1638259 1638538 "MOEBIUS" 1639099 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-712 1637054 1637432 1637472 "MODULE" 1637477 NIL MODULE (NIL T) -9 NIL 1637503 NIL) (-711 1636622 1636718 1636908 "MODULE-" 1636913 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-710 1634337 1634986 1635313 "MODRING" 1636446 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-709 1631323 1632442 1632963 "MODOP" 1633866 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-708 1629938 1630390 1630667 "MODMONOM" 1631186 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-707 1619745 1628229 1628643 "MODMON" 1629575 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-706 1616936 1618589 1618865 "MODFIELD" 1619620 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1615940 1616217 1616407 "MMLFORM" 1616766 T MMLFORM (NIL) -8 NIL NIL NIL) (-704 1615466 1615509 1615688 "MMAP" 1615891 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-703 1613683 1614416 1614457 "MLO" 1614880 NIL MLO (NIL T) -9 NIL 1615122 NIL) (-702 1611050 1611565 1612167 "MLIFT" 1613164 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-701 1610441 1610525 1610679 "MKUCFUNC" 1610961 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-700 1610040 1610110 1610233 "MKRECORD" 1610364 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-699 1609088 1609249 1609477 "MKFUNC" 1609851 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-698 1608476 1608580 1608736 "MKFLCFN" 1608971 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-697 1608019 1608386 1608445 "MKCHSET" 1608450 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-696 1607296 1607398 1607583 "MKBCFUNC" 1607912 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-695 1604038 1606850 1606986 "MINT" 1607180 T MINT (NIL) -8 NIL NIL NIL) (-694 1602850 1603093 1603370 "MHROWRED" 1603793 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-693 1598276 1601385 1601790 "MFLOAT" 1602465 T MFLOAT (NIL) -8 NIL NIL NIL) (-692 1597633 1597709 1597880 "MFINFACT" 1598188 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-691 1593948 1594796 1595680 "MESH" 1596769 T MESH (NIL) -7 NIL NIL NIL) (-690 1592338 1592650 1593003 "MDDFACT" 1593635 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-689 1589180 1591497 1591538 "MDAGG" 1591793 NIL MDAGG (NIL T) -9 NIL 1591936 NIL) (-688 1578958 1588473 1588680 "MCMPLX" 1588993 T MCMPLX (NIL) -8 NIL NIL NIL) (-687 1578099 1578245 1578445 "MCDEN" 1578807 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-686 1575989 1576259 1576639 "MCALCFN" 1577829 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-685 1574914 1575154 1575387 "MAYBE" 1575795 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-684 1572526 1573049 1573611 "MATSTOR" 1574385 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-683 1568532 1571898 1572146 "MATRIX" 1572311 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-682 1564301 1565005 1565741 "MATLIN" 1567889 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-681 1554455 1557593 1557670 "MATCAT" 1562550 NIL MATCAT (NIL T T T) -9 NIL 1563967 NIL) (-680 1550819 1551832 1553188 "MATCAT-" 1553193 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-679 1549413 1549566 1549899 "MATCAT2" 1550654 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-678 1547525 1547849 1548233 "MAPPKG3" 1549088 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-677 1546506 1546679 1546901 "MAPPKG2" 1547349 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-676 1545005 1545289 1545616 "MAPPKG1" 1546212 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-675 1544111 1544411 1544588 "MAPPAST" 1544848 T MAPPAST (NIL) -8 NIL NIL NIL) (-674 1543722 1543780 1543903 "MAPHACK3" 1544047 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-673 1543314 1543375 1543489 "MAPHACK2" 1543654 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-672 1542752 1542855 1542997 "MAPHACK1" 1543205 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-671 1540858 1541452 1541756 "MAGMA" 1542480 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-670 1540364 1540582 1540673 "MACROAST" 1540787 T MACROAST (NIL) -8 NIL NIL NIL) (-669 1536831 1538603 1539064 "M3D" 1539936 NIL M3D (NIL T) -8 NIL NIL NIL) (-668 1530985 1535200 1535241 "LZSTAGG" 1536023 NIL LZSTAGG (NIL T) -9 NIL 1536318 NIL) (-667 1526959 1528116 1529573 "LZSTAGG-" 1529578 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-666 1524073 1524850 1525337 "LWORD" 1526504 NIL LWORD (NIL T) -8 NIL NIL NIL) (-665 1523676 1523877 1523952 "LSTAST" 1524018 T LSTAST (NIL) -8 NIL NIL NIL) (-664 1516877 1523447 1523581 "LSQM" 1523586 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-663 1516101 1516240 1516468 "LSPP" 1516732 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-662 1513913 1514214 1514670 "LSMP" 1515790 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-661 1510692 1511366 1512096 "LSMP1" 1513215 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-660 1504617 1509859 1509900 "LSAGG" 1509962 NIL LSAGG (NIL T) -9 NIL 1510040 NIL) (-659 1501312 1502236 1503449 "LSAGG-" 1503454 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-658 1498938 1500456 1500705 "LPOLY" 1501107 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-657 1498520 1498605 1498728 "LPEFRAC" 1498847 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-656 1496867 1497614 1497867 "LO" 1498352 NIL LO (NIL T T T) -8 NIL NIL NIL) (-655 1496519 1496631 1496659 "LOGIC" 1496770 T LOGIC (NIL) -9 NIL 1496851 NIL) (-654 1496381 1496404 1496475 "LOGIC-" 1496480 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-653 1495574 1495714 1495907 "LODOOPS" 1496237 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-652 1493032 1495490 1495556 "LODO" 1495561 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-651 1491570 1491805 1492158 "LODOF" 1492779 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-650 1487926 1490323 1490364 "LODOCAT" 1490802 NIL LODOCAT (NIL T) -9 NIL 1491013 NIL) (-649 1487659 1487717 1487844 "LODOCAT-" 1487849 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-648 1485014 1487500 1487618 "LODO2" 1487623 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-647 1482484 1484951 1484996 "LODO1" 1485001 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-646 1481344 1481509 1481821 "LODEEF" 1482307 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-645 1476630 1479474 1479515 "LNAGG" 1480462 NIL LNAGG (NIL T) -9 NIL 1480906 NIL) (-644 1475777 1475991 1476333 "LNAGG-" 1476338 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-643 1471940 1472702 1473341 "LMOPS" 1475192 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-642 1471335 1471697 1471738 "LMODULE" 1471799 NIL LMODULE (NIL T) -9 NIL 1471841 NIL) (-641 1468581 1470980 1471103 "LMDICT" 1471245 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-640 1468307 1468489 1468549 "LITERAL" 1468554 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-639 1461534 1467253 1467551 "LIST" 1468042 NIL LIST (NIL T) -8 NIL NIL NIL) (-638 1461059 1461133 1461272 "LIST3" 1461454 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-637 1460066 1460244 1460472 "LIST2" 1460877 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-636 1458200 1458512 1458911 "LIST2MAP" 1459713 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-635 1456930 1457566 1457607 "LINEXP" 1457862 NIL LINEXP (NIL T) -9 NIL 1458011 NIL) (-634 1455577 1455837 1456134 "LINDEP" 1456682 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-633 1452344 1453063 1453840 "LIMITRF" 1454832 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-632 1450620 1450915 1451331 "LIMITPS" 1452039 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-631 1445075 1450131 1450359 "LIE" 1450441 NIL LIE (NIL T T) -8 NIL NIL NIL) (-630 1444124 1444567 1444607 "LIECAT" 1444747 NIL LIECAT (NIL T) -9 NIL 1444898 NIL) (-629 1443965 1443992 1444080 "LIECAT-" 1444085 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-628 1436577 1443414 1443579 "LIB" 1443820 T LIB (NIL) -8 NIL NIL NIL) (-627 1432214 1433095 1434030 "LGROBP" 1435694 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-626 1430080 1430354 1430716 "LF" 1431935 NIL LF (NIL T T) -7 NIL NIL NIL) (-625 1428920 1429612 1429640 "LFCAT" 1429847 T LFCAT (NIL) -9 NIL 1429986 NIL) (-624 1425824 1426452 1427140 "LEXTRIPK" 1428284 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-623 1422595 1423394 1423897 "LEXP" 1425404 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-622 1422098 1422316 1422408 "LETAST" 1422523 T LETAST (NIL) -8 NIL NIL NIL) (-621 1420496 1420809 1421210 "LEADCDET" 1421780 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-620 1419686 1419760 1419989 "LAZM3PK" 1420417 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-619 1414641 1417763 1418301 "LAUPOL" 1419198 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-618 1414206 1414250 1414418 "LAPLACE" 1414591 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-617 1412180 1413307 1413558 "LA" 1414039 NIL LA (NIL T T T) -8 NIL NIL NIL) (-616 1411261 1411811 1411852 "LALG" 1411914 NIL LALG (NIL T) -9 NIL 1411973 NIL) (-615 1410975 1411034 1411170 "LALG-" 1411175 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-614 1410810 1410834 1410875 "KVTFROM" 1410937 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-613 1409613 1410027 1410256 "KTVLOGIC" 1410601 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-612 1409448 1409472 1409513 "KRCFROM" 1409575 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-611 1408352 1408539 1408838 "KOVACIC" 1409248 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-610 1408187 1408211 1408252 "KONVERT" 1408314 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-609 1408022 1408046 1408087 "KOERCE" 1408149 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-608 1405756 1406516 1406909 "KERNEL" 1407661 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-607 1405258 1405339 1405469 "KERNEL2" 1405670 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-606 1399109 1403797 1403851 "KDAGG" 1404228 NIL KDAGG (NIL T T) -9 NIL 1404434 NIL) (-605 1398638 1398762 1398967 "KDAGG-" 1398972 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-604 1391813 1398299 1398454 "KAFILE" 1398516 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-603 1386268 1391324 1391552 "JORDAN" 1391634 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-602 1385674 1385917 1386038 "JOINAST" 1386167 T JOINAST (NIL) -8 NIL NIL NIL) (-601 1385520 1385579 1385634 "JAVACODE" 1385639 T JAVACODE (NIL) -8 NIL NIL NIL) (-600 1381819 1383725 1383779 "IXAGG" 1384708 NIL IXAGG (NIL T T) -9 NIL 1385167 NIL) (-599 1380738 1381044 1381463 "IXAGG-" 1381468 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-598 1376318 1380660 1380719 "IVECTOR" 1380724 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-597 1375084 1375321 1375587 "ITUPLE" 1376085 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-596 1373520 1373697 1374003 "ITRIGMNP" 1374906 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-595 1372265 1372469 1372752 "ITFUN3" 1373296 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-594 1371897 1371954 1372063 "ITFUN2" 1372202 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-593 1369734 1370759 1371058 "ITAYLOR" 1371631 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-592 1358717 1363871 1365034 "ISUPS" 1368604 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-591 1357821 1357961 1358197 "ISUMP" 1358564 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-590 1353085 1357622 1357701 "ISTRING" 1357774 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-589 1352588 1352806 1352898 "ISAST" 1353013 T ISAST (NIL) -8 NIL NIL NIL) (-588 1351798 1351879 1352095 "IRURPK" 1352502 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-587 1350734 1350935 1351175 "IRSN" 1351578 T IRSN (NIL) -7 NIL NIL NIL) (-586 1348763 1349118 1349554 "IRRF2F" 1350372 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-585 1348510 1348548 1348624 "IRREDFFX" 1348719 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-584 1347125 1347384 1347683 "IROOT" 1348243 NIL IROOT (NIL T) -7 NIL NIL NIL) (-583 1343757 1344809 1345501 "IR" 1346465 NIL IR (NIL T) -8 NIL NIL NIL) (-582 1341370 1341865 1342431 "IR2" 1343235 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-581 1340442 1340555 1340776 "IR2F" 1341253 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-580 1340233 1340267 1340327 "IPRNTPK" 1340402 T IPRNTPK (NIL) -7 NIL NIL NIL) (-579 1336852 1340122 1340191 "IPF" 1340196 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-578 1335215 1336777 1336834 "IPADIC" 1336839 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-577 1334555 1334775 1334905 "IP4ADDR" 1335105 T IP4ADDR (NIL) -8 NIL NIL NIL) (-576 1334055 1334259 1334369 "IOMODE" 1334465 T IOMODE (NIL) -8 NIL NIL NIL) (-575 1333128 1333652 1333779 "IOBFILE" 1333948 T IOBFILE (NIL) -8 NIL NIL NIL) (-574 1332616 1333032 1333060 "IOBCON" 1333065 T IOBCON (NIL) -9 NIL 1333086 NIL) (-573 1332113 1332171 1332361 "INVLAPLA" 1332552 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-572 1321762 1324115 1326501 "INTTR" 1329777 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-571 1318106 1318848 1319712 "INTTOOLS" 1320947 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-570 1317692 1317783 1317900 "INTSLPE" 1318009 T INTSLPE (NIL) -7 NIL NIL NIL) (-569 1315687 1317615 1317674 "INTRVL" 1317679 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-568 1313289 1313801 1314376 "INTRF" 1315172 NIL INTRF (NIL T) -7 NIL NIL NIL) (-567 1312700 1312797 1312939 "INTRET" 1313187 NIL INTRET (NIL T) -7 NIL NIL NIL) (-566 1310697 1311086 1311556 "INTRAT" 1312308 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-565 1307925 1308508 1309134 "INTPM" 1310182 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-564 1304628 1305227 1305972 "INTPAF" 1307311 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-563 1299807 1300769 1301820 "INTPACK" 1303597 T INTPACK (NIL) -7 NIL NIL NIL) (-562 1296719 1299536 1299663 "INT" 1299700 T INT (NIL) -8 NIL NIL NIL) (-561 1295971 1296123 1296331 "INTHERTR" 1296561 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-560 1295410 1295490 1295678 "INTHERAL" 1295885 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-559 1293256 1293699 1294156 "INTHEORY" 1294973 T INTHEORY (NIL) -7 NIL NIL NIL) (-558 1284564 1286185 1287964 "INTG0" 1291608 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-557 1265137 1269927 1274737 "INTFTBL" 1279774 T INTFTBL (NIL) -8 NIL NIL NIL) (-556 1264386 1264524 1264697 "INTFACT" 1264996 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-555 1261771 1262217 1262781 "INTEF" 1263940 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-554 1260238 1260943 1260971 "INTDOM" 1261272 T INTDOM (NIL) -9 NIL 1261479 NIL) (-553 1259607 1259781 1260023 "INTDOM-" 1260028 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-552 1256102 1257991 1258045 "INTCAT" 1258844 NIL INTCAT (NIL T) -9 NIL 1259164 NIL) (-551 1255575 1255677 1255805 "INTBIT" 1255994 T INTBIT (NIL) -7 NIL NIL NIL) (-550 1254246 1254400 1254714 "INTALG" 1255420 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-549 1253703 1253793 1253963 "INTAF" 1254150 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-548 1247157 1253513 1253653 "INTABL" 1253658 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-547 1246617 1247030 1247058 "INT8" 1247063 T INT8 (NIL) -8 NIL NIL 1247071) (-546 1246076 1246489 1246517 "INT32" 1246522 T INT32 (NIL) -8 NIL NIL 1246530) (-545 1245535 1245948 1245976 "INT16" 1245981 T INT16 (NIL) -8 NIL NIL 1245989) (-544 1240550 1243224 1243252 "INS" 1244186 T INS (NIL) -9 NIL 1244851 NIL) (-543 1237790 1238561 1239535 "INS-" 1239608 NIL INS- (NIL T) -8 NIL NIL NIL) (-542 1236565 1236792 1237090 "INPSIGN" 1237543 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-541 1235683 1235800 1235997 "INPRODPF" 1236445 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-540 1234577 1234694 1234931 "INPRODFF" 1235563 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-539 1233577 1233729 1233989 "INNMFACT" 1234413 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-538 1232774 1232871 1233059 "INMODGCD" 1233476 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-537 1231283 1231527 1231851 "INFSP" 1232519 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-536 1230467 1230584 1230767 "INFPROD0" 1231163 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-535 1227349 1228532 1229047 "INFORM" 1229960 T INFORM (NIL) -8 NIL NIL NIL) (-534 1226959 1227019 1227117 "INFORM1" 1227284 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-533 1226482 1226571 1226685 "INFINITY" 1226865 T INFINITY (NIL) -7 NIL NIL NIL) (-532 1225658 1226202 1226303 "INETCLTS" 1226401 T INETCLTS (NIL) -8 NIL NIL NIL) (-531 1224275 1224524 1224845 "INEP" 1225406 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-530 1223551 1224172 1224237 "INDE" 1224242 NIL INDE (NIL T) -8 NIL NIL NIL) (-529 1223115 1223183 1223300 "INCRMAPS" 1223478 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-528 1221933 1222384 1222590 "INBFILE" 1222929 T INBFILE (NIL) -8 NIL NIL NIL) (-527 1217244 1218169 1219113 "INBFF" 1221021 NIL INBFF (NIL T) -7 NIL NIL NIL) (-526 1216152 1216421 1216449 "INBCON" 1216962 T INBCON (NIL) -9 NIL 1217228 NIL) (-525 1215404 1215627 1215903 "INBCON-" 1215908 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-524 1214906 1215125 1215217 "INAST" 1215332 T INAST (NIL) -8 NIL NIL NIL) (-523 1214360 1214585 1214691 "IMPTAST" 1214820 T IMPTAST (NIL) -8 NIL NIL NIL) (-522 1210854 1214204 1214308 "IMATRIX" 1214313 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-521 1209566 1209689 1210004 "IMATQF" 1210710 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-520 1207786 1208013 1208350 "IMATLIN" 1209322 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-519 1202412 1207710 1207768 "ILIST" 1207773 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-518 1200365 1202272 1202385 "IIARRAY2" 1202390 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-517 1195798 1200276 1200340 "IFF" 1200345 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-516 1195172 1195415 1195531 "IFAST" 1195702 T IFAST (NIL) -8 NIL NIL NIL) (-515 1190215 1194464 1194652 "IFARRAY" 1195029 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-514 1189422 1190119 1190192 "IFAMON" 1190197 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-513 1189006 1189071 1189125 "IEVALAB" 1189332 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-512 1188681 1188749 1188909 "IEVALAB-" 1188914 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-511 1188339 1188595 1188658 "IDPO" 1188663 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-510 1187616 1188228 1188303 "IDPOAMS" 1188308 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-509 1186950 1187505 1187580 "IDPOAM" 1187585 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-508 1186035 1186285 1186338 "IDPC" 1186751 NIL IDPC (NIL T T) -9 NIL 1186900 NIL) (-507 1185531 1185927 1186000 "IDPAM" 1186005 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-506 1184934 1185423 1185496 "IDPAG" 1185501 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-505 1184702 1184849 1184899 "IDENT" 1184904 T IDENT (NIL) -8 NIL NIL NIL) (-504 1180957 1181805 1182700 "IDECOMP" 1183859 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-503 1173831 1174880 1175927 "IDEAL" 1179993 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-502 1172995 1173107 1173306 "ICDEN" 1173715 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-501 1172094 1172475 1172622 "ICARD" 1172868 T ICARD (NIL) -8 NIL NIL NIL) (-500 1170154 1170467 1170872 "IBPTOOLS" 1171771 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-499 1165788 1169774 1169887 "IBITS" 1170073 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-498 1162511 1163087 1163782 "IBATOOL" 1165205 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-497 1160291 1160752 1161285 "IBACHIN" 1162046 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-496 1158168 1160137 1160240 "IARRAY2" 1160245 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-495 1154321 1158094 1158151 "IARRAY1" 1158156 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-494 1148315 1152733 1153214 "IAN" 1153860 T IAN (NIL) -8 NIL NIL NIL) (-493 1147826 1147883 1148056 "IALGFACT" 1148252 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-492 1147354 1147467 1147495 "HYPCAT" 1147702 T HYPCAT (NIL) -9 NIL NIL NIL) (-491 1146892 1147009 1147195 "HYPCAT-" 1147200 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-490 1146514 1146687 1146770 "HOSTNAME" 1146829 T HOSTNAME (NIL) -8 NIL NIL NIL) (-489 1146359 1146396 1146437 "HOMOTOP" 1146442 NIL HOMOTOP (NIL T) -9 NIL 1146475 NIL) (-488 1143038 1144369 1144410 "HOAGG" 1145391 NIL HOAGG (NIL T) -9 NIL 1146070 NIL) (-487 1141632 1142031 1142557 "HOAGG-" 1142562 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-486 1135674 1141229 1141377 "HEXADEC" 1141504 T HEXADEC (NIL) -8 NIL NIL NIL) (-485 1134422 1134644 1134907 "HEUGCD" 1135451 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-484 1133525 1134259 1134389 "HELLFDIV" 1134394 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-483 1131753 1133302 1133390 "HEAP" 1133469 NIL HEAP (NIL T) -8 NIL NIL NIL) (-482 1131044 1131305 1131439 "HEADAST" 1131639 T HEADAST (NIL) -8 NIL NIL NIL) (-481 1124964 1130959 1131021 "HDP" 1131026 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-480 1118715 1124599 1124751 "HDMP" 1124865 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-479 1118040 1118179 1118343 "HB" 1118571 T HB (NIL) -7 NIL NIL NIL) (-478 1111537 1117886 1117990 "HASHTBL" 1117995 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-477 1111040 1111258 1111350 "HASAST" 1111465 T HASAST (NIL) -8 NIL NIL NIL) (-476 1108852 1110662 1110844 "HACKPI" 1110878 T HACKPI (NIL) -8 NIL NIL NIL) (-475 1104547 1108705 1108818 "GTSET" 1108823 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-474 1098073 1104425 1104523 "GSTBL" 1104528 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-473 1090386 1097104 1097369 "GSERIES" 1097864 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-472 1089553 1089944 1089972 "GROUP" 1090175 T GROUP (NIL) -9 NIL 1090309 NIL) (-471 1088919 1089078 1089329 "GROUP-" 1089334 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-470 1087288 1087607 1087994 "GROEBSOL" 1088596 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-469 1086228 1086490 1086541 "GRMOD" 1087070 NIL GRMOD (NIL T T) -9 NIL 1087238 NIL) (-468 1085996 1086032 1086160 "GRMOD-" 1086165 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-467 1081322 1082350 1083350 "GRIMAGE" 1085016 T GRIMAGE (NIL) -8 NIL NIL NIL) (-466 1079789 1080049 1080373 "GRDEF" 1081018 T GRDEF (NIL) -7 NIL NIL NIL) (-465 1079233 1079349 1079490 "GRAY" 1079668 T GRAY (NIL) -7 NIL NIL NIL) (-464 1078446 1078826 1078877 "GRALG" 1079030 NIL GRALG (NIL T T) -9 NIL 1079123 NIL) (-463 1078107 1078180 1078343 "GRALG-" 1078348 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-462 1074911 1077692 1077870 "GPOLSET" 1078014 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-461 1074265 1074322 1074580 "GOSPER" 1074848 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-460 1070024 1070703 1071229 "GMODPOL" 1073964 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-459 1069029 1069213 1069451 "GHENSEL" 1069836 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-458 1063080 1063923 1064950 "GENUPS" 1068113 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-457 1062777 1062828 1062917 "GENUFACT" 1063023 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-456 1062189 1062266 1062431 "GENPGCD" 1062695 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-455 1061663 1061698 1061911 "GENMFACT" 1062148 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-454 1060231 1060486 1060793 "GENEEZ" 1061406 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-453 1054144 1059842 1060004 "GDMP" 1060154 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-452 1043521 1047915 1049021 "GCNAALG" 1053127 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-451 1041948 1042776 1042804 "GCDDOM" 1043059 T GCDDOM (NIL) -9 NIL 1043216 NIL) (-450 1041418 1041545 1041760 "GCDDOM-" 1041765 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-449 1040090 1040275 1040579 "GB" 1041197 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-448 1028710 1031036 1033428 "GBINTERN" 1037781 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-447 1026547 1026839 1027260 "GBF" 1028385 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-446 1025328 1025493 1025760 "GBEUCLID" 1026363 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-445 1024677 1024802 1024951 "GAUSSFAC" 1025199 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-444 1023044 1023346 1023660 "GALUTIL" 1024396 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-443 1021352 1021626 1021950 "GALPOLYU" 1022771 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-442 1018717 1019007 1019414 "GALFACTU" 1021049 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-441 1010523 1012022 1013630 "GALFACT" 1017149 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-440 1007911 1008569 1008597 "FVFUN" 1009753 T FVFUN (NIL) -9 NIL 1010473 NIL) (-439 1007177 1007359 1007387 "FVC" 1007678 T FVC (NIL) -9 NIL 1007861 NIL) (-438 1006847 1007002 1007070 "FUNDESC" 1007129 T FUNDESC (NIL) -8 NIL NIL NIL) (-437 1006489 1006644 1006725 "FUNCTION" 1006799 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1004260 1004811 1005277 "FT" 1006043 T FT (NIL) -8 NIL NIL NIL) (-435 1003078 1003561 1003764 "FTEM" 1004077 T FTEM (NIL) -8 NIL NIL NIL) (-434 1001334 1001623 1002027 "FSUPFACT" 1002769 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999731 1000020 1000352 "FST" 1001022 T FST (NIL) -8 NIL NIL NIL) (-432 998902 999008 999203 "FSRED" 999613 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997581 997836 998190 "FSPRMELT" 998617 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994666 995104 995603 "FSPECF" 997144 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976726 985169 985209 "FS" 989057 NIL FS (NIL T) -9 NIL 991346 NIL) (-428 965376 968366 972422 "FS-" 972719 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964890 964944 965121 "FSINT" 965317 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 963217 963883 964186 "FSERIES" 964669 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 962231 962347 962578 "FSCINT" 963097 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 958465 961175 961216 "FSAGG" 961586 NIL FSAGG (NIL T) -9 NIL 961845 NIL) (-423 956227 956828 957624 "FSAGG-" 957719 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 955269 955412 955639 "FSAGG2" 956080 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952924 953203 953757 "FS2UPS" 954987 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 952506 952549 952704 "FS2" 952875 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 951363 951534 951843 "FS2EXPXP" 952331 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950789 950904 951056 "FRUTIL" 951243 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 942244 946284 947642 "FR" 949463 NIL FR (NIL T) -8 NIL NIL NIL) (-416 937319 939962 940002 "FRNAALG" 941398 NIL FRNAALG (NIL T) -9 NIL 942005 NIL) (-415 932997 934068 935343 "FRNAALG-" 936093 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932635 932678 932805 "FRNAAF2" 932948 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 931042 931489 931784 "FRMOD" 932447 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928821 929425 929742 "FRIDEAL" 930833 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 928016 928103 928392 "FRIDEAL2" 928728 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 927149 927563 927604 "FRETRCT" 927609 NIL FRETRCT (NIL T) -9 NIL 927785 NIL) (-409 926261 926492 926843 "FRETRCT-" 926848 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 923473 924649 924708 "FRAMALG" 925590 NIL FRAMALG (NIL T T) -9 NIL 925882 NIL) (-407 921607 922062 922692 "FRAMALG-" 922915 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915565 921082 921358 "FRAC" 921363 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 915201 915258 915365 "FRAC2" 915502 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914837 914894 915001 "FR2" 915138 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 909510 912362 912390 "FPS" 913509 T FPS (NIL) -9 NIL 914066 NIL) (-402 908959 909068 909232 "FPS-" 909378 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 906413 908048 908076 "FPC" 908301 T FPC (NIL) -9 NIL 908443 NIL) (-400 906206 906246 906343 "FPC-" 906348 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 905084 905694 905735 "FPATMAB" 905740 NIL FPATMAB (NIL T) -9 NIL 905892 NIL) (-398 902784 903260 903686 "FPARFRAC" 904721 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 898178 898676 899358 "FORTRAN" 902216 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895894 896394 896933 "FORT" 897659 T FORT (NIL) -7 NIL NIL NIL) (-395 893570 894132 894160 "FORTFN" 895220 T FORTFN (NIL) -9 NIL 895844 NIL) (-394 893334 893384 893412 "FORTCAT" 893471 T FORTCAT (NIL) -9 NIL 893533 NIL) (-393 891467 891950 892340 "FORMULA" 892964 T FORMULA (NIL) -8 NIL NIL NIL) (-392 891255 891285 891354 "FORMULA1" 891431 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890778 890830 891003 "FORDER" 891197 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889874 890038 890231 "FOP" 890605 T FOP (NIL) -7 NIL NIL NIL) (-389 888482 889154 889328 "FNLA" 889756 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 887237 887626 887654 "FNCAT" 888114 T FNCAT (NIL) -9 NIL 888374 NIL) (-387 886803 887196 887224 "FNAME" 887229 T FNAME (NIL) -8 NIL NIL NIL) (-386 885466 886395 886423 "FMTC" 886428 T FMTC (NIL) -9 NIL 886464 NIL) (-385 881828 882989 883618 "FMONOID" 884870 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 881047 881570 881719 "FM" 881724 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 878471 879117 879145 "FMFUN" 880289 T FMFUN (NIL) -9 NIL 880997 NIL) (-382 877740 877921 877949 "FMC" 878239 T FMC (NIL) -9 NIL 878421 NIL) (-381 874934 875768 875822 "FMCAT" 877017 NIL FMCAT (NIL T T) -9 NIL 877512 NIL) (-380 873827 874700 874800 "FM1" 874879 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871601 872017 872511 "FLOATRP" 873378 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 865225 869330 869951 "FLOAT" 871000 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862663 863163 863741 "FLOATCP" 864692 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 861472 862276 862317 "FLINEXP" 862322 NIL FLINEXP (NIL T) -9 NIL 862415 NIL) (-375 860626 860861 861189 "FLINEXP-" 861194 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859702 859846 860070 "FLASORT" 860478 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856919 857761 857813 "FLALG" 859040 NIL FLALG (NIL T T) -9 NIL 859507 NIL) (-372 850703 854405 854446 "FLAGG" 855708 NIL FLAGG (NIL T) -9 NIL 856360 NIL) (-371 849429 849768 850258 "FLAGG-" 850263 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 848471 848614 848841 "FLAGG2" 849282 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 845446 846420 846479 "FINRALG" 847607 NIL FINRALG (NIL T T) -9 NIL 848115 NIL) (-368 844606 844835 845174 "FINRALG-" 845179 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 844012 844225 844253 "FINITE" 844449 T FINITE (NIL) -9 NIL 844556 NIL) (-366 836470 838631 838671 "FINAALG" 842338 NIL FINAALG (NIL T) -9 NIL 843791 NIL) (-365 831811 832852 833996 "FINAALG-" 835375 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 831206 831566 831669 "FILE" 831741 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829890 830202 830256 "FILECAT" 830940 NIL FILECAT (NIL T T) -9 NIL 831156 NIL) (-362 827758 829252 829280 "FIELD" 829320 T FIELD (NIL) -9 NIL 829400 NIL) (-361 826378 826763 827274 "FIELD-" 827279 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 824256 825013 825360 "FGROUP" 826064 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 823346 823510 823730 "FGLMICPK" 824088 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 819213 823271 823328 "FFX" 823333 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818814 818875 819010 "FFSLPE" 819146 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814807 815586 816382 "FFPOLY" 818050 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 814311 814347 814556 "FFPOLY2" 814765 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 810197 814230 814293 "FFP" 814298 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805630 810108 810172 "FF" 810177 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800791 804973 805163 "FFNBX" 805484 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795765 799926 800184 "FFNBP" 800645 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 790433 795049 795260 "FFNB" 795598 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 789265 789463 789778 "FFINTBAS" 790230 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 785493 787672 787700 "FFIELDC" 788320 T FFIELDC (NIL) -9 NIL 788696 NIL) (-347 784156 784526 785023 "FFIELDC-" 785028 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783726 783771 783895 "FFHOM" 784098 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 781424 781908 782425 "FFF" 783241 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 777077 781166 781267 "FFCGX" 781367 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772744 776809 776916 "FFCGP" 777020 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767962 772471 772579 "FFCG" 772680 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749795 758833 758919 "FFCAT" 764084 NIL FFCAT (NIL T T T) -9 NIL 765535 NIL) (-340 744993 746040 747354 "FFCAT-" 748584 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 744404 744447 744682 "FFCAT2" 744944 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733616 737376 738596 "FEXPR" 743256 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732616 733051 733092 "FEVALAB" 733176 NIL FEVALAB (NIL T) -9 NIL 733437 NIL) (-336 731775 731985 732323 "FEVALAB-" 732328 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 730368 731158 731361 "FDIV" 731674 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 727434 728149 728264 "FDIVCAT" 729832 NIL FDIVCAT (NIL T T T T) -9 NIL 730269 NIL) (-333 727196 727223 727393 "FDIVCAT-" 727398 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 726416 726503 726780 "FDIV2" 727103 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 725102 725361 725650 "FCPAK1" 726147 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 724230 724602 724743 "FCOMP" 724993 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707967 711380 714918 "FC" 720712 T FC (NIL) -8 NIL NIL NIL) (-328 700546 704531 704571 "FAXF" 706373 NIL FAXF (NIL T) -9 NIL 707065 NIL) (-327 697825 698480 699305 "FAXF-" 699770 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692925 697201 697377 "FARRAY" 697682 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 688178 690210 690263 "FAMR" 691286 NIL FAMR (NIL T T) -9 NIL 691746 NIL) (-324 687068 687370 687805 "FAMR-" 687810 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 686264 686990 687043 "FAMONOID" 687048 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 684076 684760 684813 "FAMONC" 685754 NIL FAMONC (NIL T T) -9 NIL 686140 NIL) (-321 682768 683830 683967 "FAGROUP" 683972 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680563 680882 681285 "FACUTIL" 682449 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679662 679847 680069 "FACTFUNC" 680373 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 672067 678913 679125 "EXPUPXS" 679518 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669550 670090 670676 "EXPRTUBE" 671501 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665744 666336 667073 "EXPRODE" 668889 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 651118 664399 664827 "EXPR" 665348 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645525 646112 646925 "EXPR2UPS" 650416 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 645161 645218 645325 "EXPR2" 645462 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636566 644293 644590 "EXPEXPAN" 644998 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 636393 636523 636552 "EXIT" 636557 T EXIT (NIL) -8 NIL NIL NIL) (-310 635900 636117 636208 "EXITAST" 636322 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635527 635589 635702 "EVALCYC" 635832 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 635068 635186 635227 "EVALAB" 635397 NIL EVALAB (NIL T) -9 NIL 635501 NIL) (-307 634549 634671 634892 "EVALAB-" 634897 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 632017 633285 633313 "EUCDOM" 633868 T EUCDOM (NIL) -9 NIL 634218 NIL) (-305 630422 630864 631454 "EUCDOM-" 631459 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617962 620720 623470 "ESTOOLS" 627692 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617594 617651 617760 "ESTOOLS2" 617899 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 617345 617387 617467 "ESTOOLS1" 617546 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 611250 612978 613006 "ES" 615774 T ES (NIL) -9 NIL 617183 NIL) (-300 606198 607484 609301 "ES-" 609465 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602573 603333 604113 "ESCONT" 605438 T ESCONT (NIL) -7 NIL NIL NIL) (-298 602318 602350 602432 "ESCONT1" 602535 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601993 602043 602143 "ES2" 602262 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601623 601681 601790 "ES1" 601929 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600839 600968 601144 "ERROR" 601467 T ERROR (NIL) -7 NIL NIL NIL) (-294 594342 600698 600789 "EQTBL" 600794 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586899 589656 591105 "EQ" 592926 NIL -3310 (NIL T) -8 NIL NIL NIL) (-292 586531 586588 586697 "EQ2" 586836 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581823 582869 583962 "EP" 585470 NIL EP (NIL T) -7 NIL NIL NIL) (-290 580405 580706 581023 "ENV" 581526 T ENV (NIL) -8 NIL NIL NIL) (-289 579584 580104 580132 "ENTIRER" 580137 T ENTIRER (NIL) -9 NIL 580183 NIL) (-288 576086 577539 577909 "EMR" 579383 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 575230 575415 575469 "ELTAGG" 575849 NIL ELTAGG (NIL T T) -9 NIL 576060 NIL) (-286 574949 575011 575152 "ELTAGG-" 575157 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574738 574767 574821 "ELTAB" 574905 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573864 574010 574209 "ELFUTS" 574589 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573606 573662 573690 "ELEMFUN" 573795 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 573476 573497 573565 "ELEMFUN-" 573570 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 568367 571576 571617 "ELAGG" 572557 NIL ELAGG (NIL T) -9 NIL 573020 NIL) (-280 566652 567086 567749 "ELAGG-" 567754 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 565309 565589 565884 "ELABEXPR" 566377 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 558175 559976 560803 "EFUPXS" 564585 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551625 553426 554236 "EFULS" 557451 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 549047 549405 549884 "EFSTRUC" 551257 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 538119 539684 541244 "EF" 547562 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 537220 537604 537753 "EAB" 537990 T EAB (NIL) -8 NIL NIL NIL) (-273 536429 537179 537207 "E04UCFA" 537212 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535638 536388 536416 "E04NAFA" 536421 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534847 535597 535625 "E04MBFA" 535630 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 534056 534806 534834 "E04JAFA" 534839 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 533267 534015 534043 "E04GCFA" 534048 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 532478 533226 533254 "E04FDFA" 533259 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531687 532437 532465 "E04DGFA" 532470 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525865 527212 528576 "E04AGNT" 530343 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524571 525051 525091 "DVARCAT" 525566 NIL DVARCAT (NIL T) -9 NIL 525765 NIL) (-264 523775 523987 524301 "DVARCAT-" 524306 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516675 523574 523703 "DSMP" 523708 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 511485 512620 513688 "DROPT" 515627 T DROPT (NIL) -8 NIL NIL NIL) (-261 511150 511209 511307 "DROPT1" 511420 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 506265 507391 508528 "DROPT0" 510033 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504610 504935 505321 "DRAWPT" 505899 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 499197 500120 501199 "DRAW" 503584 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498830 498883 499001 "DRAWHACK" 499138 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497561 497830 498121 "DRAWCX" 498559 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 497077 497145 497296 "DRAWCURV" 497487 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487548 489507 491622 "DRAWCFUN" 494982 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 484361 486243 486284 "DQAGG" 486913 NIL DQAGG (NIL T) -9 NIL 487186 NIL) (-252 472640 479339 479422 "DPOLCAT" 481274 NIL DPOLCAT (NIL T T T T) -9 NIL 481819 NIL) (-251 467479 468825 470783 "DPOLCAT-" 470788 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460634 467340 467438 "DPMO" 467443 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453692 460414 460581 "DPMM" 460586 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 453324 453611 453659 "DOMCTOR" 453664 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452619 452846 452983 "DOMAIN" 453207 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 446370 452254 452406 "DMP" 452520 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445970 446026 446170 "DLP" 446308 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439840 445297 445487 "DLIST" 445812 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436684 438693 438734 "DLAGG" 439284 NIL DLAGG (NIL T) -9 NIL 439514 NIL) (-242 435497 436127 436155 "DIVRING" 436247 T DIVRING (NIL) -9 NIL 436330 NIL) (-241 434734 434924 435224 "DIVRING-" 435229 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432836 433193 433599 "DISPLAY" 434348 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426778 432750 432813 "DIRPROD" 432818 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425626 425829 426094 "DIRPROD2" 426571 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414889 420841 420894 "DIRPCAT" 421304 NIL DIRPCAT (NIL NIL T) -9 NIL 422144 NIL) (-236 412215 412857 413738 "DIRPCAT-" 414075 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411502 411662 411848 "DIOSP" 412049 T DIOSP (NIL) -7 NIL NIL NIL) (-234 408204 410414 410455 "DIOPS" 410889 NIL DIOPS (NIL T) -9 NIL 411118 NIL) (-233 407753 407867 408058 "DIOPS-" 408063 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406645 407239 407267 "DIFRING" 407454 T DIFRING (NIL) -9 NIL 407564 NIL) (-231 406291 406368 406520 "DIFRING-" 406525 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 404096 405334 405375 "DIFEXT" 405738 NIL DIFEXT (NIL T) -9 NIL 406032 NIL) (-229 402381 402809 403475 "DIFEXT-" 403480 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399703 401913 401954 "DIAGG" 401959 NIL DIAGG (NIL T) -9 NIL 401979 NIL) (-227 399087 399244 399496 "DIAGG-" 399501 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394552 398046 398323 "DHMATRIX" 398856 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 390164 391073 392083 "DFSFUN" 393562 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 385280 389095 389407 "DFLOAT" 389872 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383508 383789 384185 "DFINTTLS" 384988 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380573 381529 381929 "DERHAM" 383174 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 378422 380348 380437 "DEQUEUE" 380517 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377637 377770 377966 "DEGRED" 378284 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 374032 374777 375630 "DEFINTRF" 376865 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371559 372028 372627 "DEFINTEF" 373551 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370936 371179 371294 "DEFAST" 371464 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364978 370533 370681 "DECIMAL" 370808 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362490 362948 363454 "DDFACT" 364522 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 362086 362129 362280 "DBLRESP" 362441 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359985 360319 360679 "DBASE" 361853 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 359254 359465 359611 "DATAARY" 359884 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 358387 359213 359241 "D03FAFA" 359246 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357521 358346 358374 "D03EEFA" 358379 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 355471 355937 356426 "D03AGNT" 357052 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354787 355430 355458 "D02EJFA" 355463 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 354103 354746 354774 "D02CJFA" 354779 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 353419 354062 354090 "D02BHFA" 354095 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352735 353378 353406 "D02BBFA" 353411 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345933 347521 349127 "D02AGNT" 351149 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343702 344224 344770 "D01WGTS" 345407 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342797 343661 343689 "D01TRNS" 343694 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341892 342756 342784 "D01GBFA" 342789 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340987 341851 341879 "D01FCFA" 341884 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 340082 340946 340974 "D01ASFA" 340979 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 339177 340041 340069 "D01AQFA" 340074 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 338272 339136 339164 "D01APFA" 339169 T D01APFA (NIL) -8 NIL NIL NIL) (-196 337367 338231 338259 "D01ANFA" 338264 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 336462 337326 337354 "D01AMFA" 337359 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335557 336421 336449 "D01ALFA" 336454 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334652 335516 335544 "D01AKFA" 335549 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333747 334611 334639 "D01AJFA" 334644 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 327044 328595 330156 "D01AGNT" 332206 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 326381 326509 326661 "CYCLOTOM" 326912 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 323116 323829 324556 "CYCLES" 325674 T CYCLES (NIL) -7 NIL NIL NIL) (-188 322428 322562 322733 "CVMP" 322977 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 320199 320457 320833 "CTRIGMNP" 322156 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319690 319990 320064 "CTOR" 320145 T CTOR (NIL) -8 NIL NIL NIL) (-185 319226 319421 319522 "CTORKIND" 319609 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318574 318833 318861 "CTORCAT" 319043 T CTORCAT (NIL) -9 NIL 319156 NIL) (-183 318172 318283 318442 "CTORCAT-" 318447 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317688 317875 317973 "CTORCALL" 318094 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317062 317161 317314 "CSTTOOLS" 317585 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312861 313518 314276 "CRFP" 316374 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312363 312582 312674 "CRCEAST" 312789 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311410 311595 311823 "CRAPACK" 312167 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310794 310895 311099 "CPMATCH" 311286 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310519 310547 310653 "CPIMA" 310760 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306883 307555 308273 "COORDSYS" 309854 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306267 306396 306546 "CONTOUR" 306753 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302193 304270 304762 "CONTFRAC" 305807 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302073 302094 302122 "CONDUIT" 302159 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301246 301766 301794 "COMRING" 301799 T COMRING (NIL) -9 NIL 301851 NIL) (-170 300327 300604 300788 "COMPPROP" 301082 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299988 300023 300151 "COMPLPAT" 300286 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290045 299797 299906 "COMPLEX" 299911 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289681 289738 289845 "COMPLEX2" 289982 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289399 289434 289532 "COMPFACT" 289640 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273572 283792 283832 "COMPCAT" 284836 NIL COMPCAT (NIL T) -9 NIL 286221 NIL) (-164 263088 266011 269638 "COMPCAT-" 269994 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262817 262845 262948 "COMMUPC" 263054 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262612 262645 262704 "COMMONOP" 262778 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262195 262363 262450 "COMM" 262545 T COMM (NIL) -8 NIL NIL NIL) (-160 261799 261999 262074 "COMMAAST" 262140 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261048 261242 261270 "COMBOPC" 261608 T COMBOPC (NIL) -9 NIL 261783 NIL) (-158 259944 260154 260396 "COMBINAT" 260838 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256142 256715 257355 "COMBF" 259366 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254928 255258 255493 "COLOR" 255927 T COLOR (NIL) -8 NIL NIL NIL) (-155 254431 254649 254741 "COLONAST" 254856 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254071 254118 254243 "CMPLXRT" 254378 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253546 253771 253870 "CLLCTAST" 253992 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249048 250076 251156 "CLIP" 252486 T CLIP (NIL) -7 NIL NIL NIL) (-151 247430 248154 248393 "CLIF" 248875 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243652 245576 245617 "CLAGG" 246546 NIL CLAGG (NIL T) -9 NIL 247082 NIL) (-149 242074 242531 243114 "CLAGG-" 243119 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241618 241703 241843 "CINTSLPE" 241983 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239119 239590 240138 "CHVAR" 241146 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238362 238882 238910 "CHARZ" 238915 T CHARZ (NIL) -9 NIL 238930 NIL) (-145 238116 238156 238234 "CHARPOL" 238316 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237243 237796 237824 "CHARNZ" 237871 T CHARNZ (NIL) -9 NIL 237927 NIL) (-143 235232 235933 236268 "CHAR" 236928 T CHAR (NIL) -8 NIL NIL NIL) (-142 234958 235019 235047 "CFCAT" 235158 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234203 234314 234496 "CDEN" 234842 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230195 233356 233636 "CCLASS" 233943 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229502 229645 229808 "CATEGORY" 230052 T -10 (NIL) -8 NIL NIL NIL) (-138 229134 229421 229469 "CATCTOR" 229474 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228608 228834 228933 "CATAST" 229055 T CATAST (NIL) -8 NIL NIL NIL) (-136 228111 228329 228421 "CASEAST" 228536 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223163 224140 224893 "CARTEN" 227414 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222271 222419 222640 "CARTEN2" 223010 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220613 221421 221678 "CARD" 222034 T CARD (NIL) -8 NIL NIL NIL) (-132 220216 220417 220492 "CAPSLAST" 220558 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219588 219916 219944 "CACHSET" 220076 T CACHSET (NIL) -9 NIL 220153 NIL) (-130 219084 219380 219408 "CABMON" 219458 T CABMON (NIL) -9 NIL 219514 NIL) (-129 218107 218630 218766 "BYTE" 218929 T BYTE (NIL) -8 NIL NIL 219045) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL 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3144179 "WEIER" 3144958 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1264 3142437 3142861 3142903 "VSPACE" 3143039 NIL VSPACE (NIL T) -9 NIL 3143113 NIL) (-1263 3142275 3142302 3142393 "VSPACE-" 3142398 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1262 3142083 3142126 3142194 "VOID" 3142229 T VOID (NIL) -8 NIL NIL NIL) (-1261 3140219 3140578 3140984 "VIEW" 3141699 T VIEW (NIL) -7 NIL NIL NIL) (-1260 3136644 3137282 3138019 "VIEWDEF" 3139504 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1259 3125980 3128192 3130365 "VIEW3D" 3134493 T VIEW3D (NIL) -8 NIL NIL NIL) (-1258 3118262 3119891 3121470 "VIEW2D" 3124423 T VIEW2D (NIL) -8 NIL NIL NIL) (-1257 3113666 3118032 3118124 "VECTOR" 3118205 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1256 3112243 3112502 3112820 "VECTOR2" 3113396 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1255 3105770 3110027 3110070 "VECTCAT" 3111063 NIL VECTCAT (NIL T) -9 NIL 3111649 NIL) (-1254 3104784 3105038 3105428 "VECTCAT-" 3105433 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104265 3104435 3104555 "VARIABLE" 3104699 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1252 3104198 3104203 3104233 "UTYPE" 3104238 T UTYPE (NIL) -9 NIL NIL NIL) (-1251 3103028 3103182 3103444 "UTSODETL" 3104024 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1250 3100468 3100928 3101452 "UTSODE" 3102569 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1249 3092344 3098094 3098583 "UTS" 3100037 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3083587 3088911 3088954 "UTSCAT" 3090066 NIL UTSCAT (NIL T) -9 NIL 3090823 NIL) (-1247 3080942 3081657 3082646 "UTSCAT-" 3082651 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1246 3080569 3080612 3080745 "UTS2" 3080893 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1245 3074842 3077407 3077450 "URAGG" 3079520 NIL URAGG (NIL T) -9 NIL 3080243 NIL) (-1244 3071781 3072644 3073767 "URAGG-" 3073772 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1243 3067505 3070395 3070867 "UPXSSING" 3071445 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1242 3059607 3066752 3067025 "UPXS" 3067290 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1241 3052720 3059511 3059583 "UPXSCONS" 3059588 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1240 3042965 3049715 3049777 "UPXSCCA" 3050351 NIL UPXSCCA (NIL T T) -9 NIL 3050584 NIL) (-1239 3042603 3042688 3042862 "UPXSCCA-" 3042867 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1238 3032701 3039224 3039267 "UPXSCAT" 3039915 NIL UPXSCAT (NIL T) -9 NIL 3040523 NIL) (-1237 3032131 3032210 3032389 "UPXS2" 3032616 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1236 3030785 3031038 3031389 "UPSQFREE" 3031874 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1235 3024573 3027587 3027642 "UPSCAT" 3028803 NIL UPSCAT (NIL T T) -9 NIL 3029577 NIL) (-1234 3023777 3023984 3024311 "UPSCAT-" 3024316 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1233 3009627 3017625 3017668 "UPOLYC" 3019769 NIL UPOLYC (NIL T) -9 NIL 3020990 NIL) (-1232 3000956 3003381 3006528 "UPOLYC-" 3006533 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1231 3000583 3000626 3000759 "UPOLYC2" 3000907 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1230 2992157 3000266 3000395 "UP" 3000502 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1229 2991496 2991603 2991767 "UPMP" 2992046 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1228 2991049 2991130 2991269 "UPDIVP" 2991409 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1227 2989617 2989866 2990182 "UPDECOMP" 2990798 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1226 2988852 2988964 2989149 "UPCDEN" 2989501 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1225 2988371 2988440 2988589 "UP2" 2988777 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1224 2986888 2987575 2987852 "UNISEG" 2988129 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1223 2986103 2986230 2986435 "UNISEG2" 2986731 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1222 2985163 2985343 2985569 "UNIFACT" 2985919 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1221 2969130 2984340 2984591 "ULS" 2984970 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1220 2957170 2969034 2969106 "ULSCONS" 2969111 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1219 2939786 2951728 2951790 "ULSCCAT" 2952428 NIL ULSCCAT (NIL T T) -9 NIL 2952716 NIL) (-1218 2938836 2939081 2939469 "ULSCCAT-" 2939474 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1217 2928711 2935148 2935191 "ULSCAT" 2936054 NIL ULSCAT (NIL T) -9 NIL 2936784 NIL) (-1216 2928141 2928220 2928399 "ULS2" 2928626 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1215 2927278 2927753 2927854 "UINT8" 2927965 T UINT8 (NIL) -8 NIL NIL 2928044) (-1214 2926414 2926889 2926990 "UINT32" 2927101 T UINT32 (NIL) -8 NIL NIL 2927180) (-1213 2925550 2926025 2926126 "UINT16" 2926237 T UINT16 (NIL) -8 NIL NIL 2926316) (-1212 2923953 2924876 2924906 "UFD" 2925118 T UFD (NIL) -9 NIL 2925232 NIL) (-1211 2923747 2923793 2923888 "UFD-" 2923893 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1210 2922829 2923012 2923228 "UDVO" 2923553 T UDVO (NIL) -7 NIL NIL NIL) (-1209 2920645 2921054 2921525 "UDPO" 2922393 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1208 2920578 2920583 2920613 "TYPE" 2920618 T TYPE (NIL) -9 NIL NIL NIL) (-1207 2920365 2920533 2920564 "TYPEAST" 2920569 T TYPEAST (NIL) -8 NIL NIL NIL) (-1206 2919336 2919538 2919778 "TWOFACT" 2920159 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1205 2918408 2918745 2918980 "TUPLE" 2919136 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1204 2916099 2916618 2917157 "TUBETOOL" 2917891 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1203 2914948 2915153 2915394 "TUBE" 2915892 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1202 2909712 2913920 2914203 "TS" 2914700 NIL TS (NIL T) -8 NIL NIL NIL) (-1201 2898379 2902471 2902568 "TSETCAT" 2907837 NIL TSETCAT (NIL T T T T) -9 NIL 2909368 NIL) (-1200 2893114 2894711 2896602 "TSETCAT-" 2896607 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1199 2887377 2888223 2889165 "TRMANIP" 2892250 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1198 2886818 2886881 2887044 "TRIMAT" 2887309 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1197 2884614 2884851 2885215 "TRIGMNIP" 2886567 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1196 2884134 2884247 2884277 "TRIGCAT" 2884490 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1195 2883803 2883882 2884023 "TRIGCAT-" 2884028 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1194 2880700 2882661 2882942 "TREE" 2883557 NIL TREE (NIL T) -8 NIL NIL NIL) (-1193 2879974 2880502 2880532 "TRANFUN" 2880567 T TRANFUN (NIL) -9 NIL 2880633 NIL) (-1192 2879253 2879444 2879724 "TRANFUN-" 2879729 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1191 2879057 2879089 2879150 "TOPSP" 2879214 T TOPSP (NIL) -7 NIL NIL NIL) (-1190 2878405 2878520 2878674 "TOOLSIGN" 2878938 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1189 2877066 2877582 2877821 "TEXTFILE" 2878188 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1188 2875005 2875519 2875948 "TEX" 2876659 T TEX (NIL) -8 NIL NIL NIL) (-1187 2874786 2874817 2874889 "TEX1" 2874968 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1186 2874434 2874497 2874587 "TEMUTL" 2874718 T TEMUTL (NIL) -7 NIL NIL NIL) (-1185 2872588 2872868 2873193 "TBCMPPK" 2874157 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1184 2864476 2870748 2870804 "TBAGG" 2871204 NIL TBAGG (NIL T T) -9 NIL 2871415 NIL) (-1183 2859546 2861034 2862788 "TBAGG-" 2862793 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1182 2858930 2859037 2859182 "TANEXP" 2859435 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1181 2852431 2858787 2858880 "TABLE" 2858885 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1180 2851843 2851942 2852080 "TABLEAU" 2852328 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1179 2846451 2847671 2848919 "TABLBUMP" 2850629 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1178 2845879 2845979 2846107 "SYSTEM" 2846345 T SYSTEM (NIL) -7 NIL NIL NIL) (-1177 2842342 2843037 2843820 "SYSSOLP" 2845130 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1176 2841399 2841866 2841979 "SYSNNI" 2842165 NIL SYSNNI (NIL NIL) -8 NIL NIL 2842244) (-1175 2840852 2841257 2841299 "SYSINT" 2841304 NIL SYSINT (NIL NIL) -8 NIL NIL 2841312) (-1174 2837186 2838113 2838829 "SYNTAX" 2840158 T SYNTAX (NIL) -8 NIL NIL NIL) (-1173 2834344 2834946 2835578 "SYMTAB" 2836576 T SYMTAB (NIL) -8 NIL NIL NIL) (-1172 2829593 2830495 2831478 "SYMS" 2833383 T SYMS (NIL) -8 NIL NIL NIL) (-1171 2826865 2829051 2829281 "SYMPOLY" 2829398 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1170 2826382 2826457 2826580 "SYMFUNC" 2826777 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1169 2822434 2823694 2824507 "SYMBOL" 2825591 T SYMBOL (NIL) -8 NIL NIL NIL) (-1168 2815973 2817662 2819382 "SWITCH" 2820736 T SWITCH (NIL) -8 NIL NIL NIL) (-1167 2809243 2814794 2815097 "SUTS" 2815728 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2801344 2808490 2808763 "SUPXS" 2809028 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2792874 2800962 2801088 "SUP" 2801253 NIL SUP (NIL T) -8 NIL NIL NIL) (-1164 2792033 2792160 2792377 "SUPFRACF" 2792742 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1163 2791654 2791713 2791826 "SUP2" 2791968 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1162 2790067 2790341 2790704 "SUMRF" 2791353 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1161 2789381 2789447 2789646 "SUMFS" 2789988 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1160 2773388 2788558 2788809 "SULS" 2789188 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2773017 2773210 2773280 "SUCHTAST" 2773340 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1158 2772339 2772542 2772682 "SUCH" 2772925 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1157 2766233 2767245 2768204 "SUBSPACE" 2771427 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1156 2765663 2765753 2765917 "SUBRESP" 2766121 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1155 2759032 2760328 2761639 "STTF" 2764399 NIL STTF (NIL T) -7 NIL NIL NIL) (-1154 2753205 2754325 2755472 "STTFNC" 2757932 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1153 2744520 2746387 2748181 "STTAYLOR" 2751446 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1152 2737764 2744384 2744467 "STRTBL" 2744472 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1151 2733155 2737719 2737750 "STRING" 2737755 T STRING (NIL) -8 NIL NIL NIL) (-1150 2728043 2732528 2732558 "STRICAT" 2732617 T STRICAT (NIL) -9 NIL 2732679 NIL) (-1149 2720853 2725662 2726273 "STREAM" 2727467 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1148 2720363 2720440 2720584 "STREAM3" 2720770 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1147 2719345 2719528 2719763 "STREAM2" 2720176 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1146 2719033 2719085 2719178 "STREAM1" 2719287 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1145 2718049 2718230 2718461 "STINPROD" 2718849 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1144 2717627 2717811 2717841 "STEP" 2717921 T STEP (NIL) -9 NIL 2717999 NIL) (-1143 2711170 2717526 2717603 "STBL" 2717608 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1142 2706344 2710391 2710434 "STAGG" 2710587 NIL STAGG (NIL T) -9 NIL 2710676 NIL) (-1141 2704046 2704648 2705520 "STAGG-" 2705525 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1140 2702241 2703816 2703908 "STACK" 2703989 NIL STACK (NIL T) -8 NIL NIL NIL) (-1139 2694966 2700382 2700838 "SREGSET" 2701871 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1138 2687392 2688760 2690273 "SRDCMPK" 2693572 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2680359 2684832 2684862 "SRAGG" 2686165 T SRAGG (NIL) -9 NIL 2686773 NIL) (-1136 2679376 2679631 2680010 "SRAGG-" 2680015 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1135 2673871 2678323 2678744 "SQMATRIX" 2679002 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1134 2667620 2670589 2671316 "SPLTREE" 2673216 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1133 2663610 2664276 2664922 "SPLNODE" 2667046 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1132 2662657 2662890 2662920 "SPFCAT" 2663364 T SPFCAT (NIL) -9 NIL NIL NIL) (-1131 2661394 2661604 2661868 "SPECOUT" 2662415 T SPECOUT (NIL) -7 NIL NIL NIL) (-1130 2653046 2654790 2654820 "SPADXPT" 2659212 T SPADXPT (NIL) -9 NIL 2661246 NIL) (-1129 2652807 2652847 2652916 "SPADPRSR" 2652999 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1128 2650990 2652762 2652793 "SPADAST" 2652798 T SPADAST (NIL) -8 NIL NIL NIL) (-1127 2642961 2644708 2644751 "SPACEC" 2649124 NIL SPACEC (NIL T) -9 NIL 2650940 NIL) (-1126 2641132 2642893 2642942 "SPACE3" 2642947 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1125 2639884 2640055 2640346 "SORTPAK" 2640937 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1124 2637934 2638237 2638656 "SOLVETRA" 2639548 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1123 2636945 2637167 2637441 "SOLVESER" 2637707 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1122 2632165 2633046 2634048 "SOLVERAD" 2635997 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1121 2627980 2628589 2629318 "SOLVEFOR" 2631532 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1120 2622277 2627329 2627426 "SNTSCAT" 2627431 NIL SNTSCAT (NIL T T T T) -9 NIL 2627501 NIL) (-1119 2616420 2620600 2620991 "SMTS" 2621967 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1118 2610871 2616308 2616385 "SMP" 2616390 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1117 2609030 2609331 2609729 "SMITH" 2610568 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1116 2601925 2606081 2606184 "SMATCAT" 2607535 NIL SMATCAT (NIL NIL T T T) -9 NIL 2608085 NIL) (-1115 2598865 2599688 2600866 "SMATCAT-" 2600871 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1114 2596578 2598101 2598144 "SKAGG" 2598405 NIL SKAGG (NIL T) -9 NIL 2598540 NIL) (-1113 2592920 2595994 2596189 "SINT" 2596376 T SINT (NIL) -8 NIL NIL 2596549) (-1112 2592692 2592730 2592796 "SIMPAN" 2592876 T SIMPAN (NIL) -7 NIL NIL NIL) (-1111 2591999 2592227 2592367 "SIG" 2592574 T SIG (NIL) -8 NIL NIL NIL) (-1110 2590837 2591058 2591333 "SIGNRF" 2591758 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1109 2589642 2589793 2590084 "SIGNEF" 2590666 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1108 2588975 2589225 2589349 "SIGAST" 2589540 T SIGAST (NIL) -8 NIL NIL NIL) (-1107 2586665 2587119 2587625 "SHP" 2588516 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1106 2580571 2586566 2586642 "SHDP" 2586647 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1105 2580170 2580336 2580366 "SGROUP" 2580459 T SGROUP (NIL) -9 NIL 2580521 NIL) (-1104 2580028 2580054 2580127 "SGROUP-" 2580132 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1103 2576864 2577561 2578284 "SGCF" 2579327 T SGCF (NIL) -7 NIL NIL NIL) (-1102 2571259 2576311 2576408 "SFRTCAT" 2576413 NIL SFRTCAT (NIL T T T T) -9 NIL 2576452 NIL) (-1101 2564683 2565698 2566834 "SFRGCD" 2570242 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1100 2557811 2558882 2560068 "SFQCMPK" 2563616 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2557433 2557522 2557632 "SFORT" 2557752 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1098 2556578 2557273 2557394 "SEXOF" 2557399 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1097 2555712 2556459 2556527 "SEX" 2556532 T SEX (NIL) -8 NIL NIL NIL) (-1096 2551251 2551940 2552035 "SEXCAT" 2554972 NIL SEXCAT (NIL T T T T T) -9 NIL 2555550 NIL) (-1095 2548431 2551185 2551233 "SET" 2551238 NIL SET (NIL T) -8 NIL NIL NIL) (-1094 2546682 2547144 2547449 "SETMN" 2548172 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1093 2546288 2546414 2546444 "SETCAT" 2546561 T SETCAT (NIL) -9 NIL 2546646 NIL) (-1092 2546068 2546120 2546219 "SETCAT-" 2546224 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1091 2542455 2544529 2544572 "SETAGG" 2545442 NIL SETAGG (NIL T) -9 NIL 2545782 NIL) (-1090 2541913 2542029 2542266 "SETAGG-" 2542271 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1089 2541383 2541609 2541710 "SEQAST" 2541834 T SEQAST (NIL) -8 NIL NIL NIL) (-1088 2540582 2540876 2540937 "SEGXCAT" 2541223 NIL SEGXCAT (NIL T T) -9 NIL 2541343 NIL) (-1087 2539638 2540248 2540430 "SEG" 2540435 NIL SEG (NIL T) -8 NIL NIL NIL) (-1086 2538617 2538831 2538874 "SEGCAT" 2539396 NIL SEGCAT (NIL T) -9 NIL 2539617 NIL) (-1085 2537666 2537996 2538196 "SEGBIND" 2538452 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1084 2537287 2537346 2537459 "SEGBIND2" 2537601 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1083 2536888 2537088 2537165 "SEGAST" 2537232 T SEGAST (NIL) -8 NIL NIL NIL) (-1082 2536107 2536233 2536437 "SEG2" 2536732 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1081 2535544 2536042 2536089 "SDVAR" 2536094 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1080 2527834 2535314 2535444 "SDPOL" 2535449 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1079 2526427 2526693 2527012 "SCPKG" 2527549 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1078 2525563 2525743 2525943 "SCOPE" 2526249 T SCOPE (NIL) -8 NIL NIL NIL) (-1077 2524784 2524917 2525096 "SCACHE" 2525418 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1076 2524456 2524616 2524646 "SASTCAT" 2524651 T SASTCAT (NIL) -9 NIL 2524664 NIL) (-1075 2523970 2524291 2524367 "SAOS" 2524402 T SAOS (NIL) -8 NIL NIL NIL) (-1074 2523535 2523570 2523743 "SAERFFC" 2523929 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1073 2517509 2523432 2523512 "SAE" 2523517 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1072 2517102 2517137 2517296 "SAEFACT" 2517468 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1071 2515423 2515737 2516138 "RURPK" 2516768 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1070 2514059 2514338 2514650 "RULESET" 2515257 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1069 2511246 2511749 2512214 "RULE" 2513740 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1068 2510885 2511040 2511123 "RULECOLD" 2511198 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1067 2510383 2510602 2510696 "RSTRCAST" 2510813 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2505232 2506026 2506946 "RSETGCD" 2509582 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2494489 2499541 2499638 "RSETCAT" 2503757 NIL RSETCAT (NIL T T T T) -9 NIL 2504854 NIL) (-1064 2492416 2492955 2493779 "RSETCAT-" 2493784 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2484803 2486178 2487698 "RSDCMPK" 2491015 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2482808 2483249 2483323 "RRCC" 2484409 NIL RRCC (NIL T T) -9 NIL 2484753 NIL) (-1061 2482159 2482333 2482612 "RRCC-" 2482617 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2481629 2481855 2481956 "RPTAST" 2482080 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2455635 2465222 2465289 "RPOLCAT" 2475953 NIL RPOLCAT (NIL T T T) -9 NIL 2479112 NIL) (-1058 2447135 2449473 2452595 "RPOLCAT-" 2452600 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2438182 2445346 2445828 "ROUTINE" 2446675 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2435015 2437808 2437948 "ROMAN" 2438064 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2433290 2433875 2434135 "ROIRC" 2434820 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2429683 2431926 2431956 "RNS" 2432260 T RNS (NIL) -9 NIL 2432533 NIL) (-1053 2428192 2428575 2429109 "RNS-" 2429184 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2427641 2428023 2428053 "RNG" 2428058 T RNG (NIL) -9 NIL 2428079 NIL) (-1051 2427033 2427395 2427438 "RMODULE" 2427500 NIL RMODULE (NIL T) -9 NIL 2427542 NIL) (-1050 2425869 2425963 2426299 "RMCAT2" 2426934 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2422746 2425215 2425512 "RMATRIX" 2425631 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2415688 2417922 2418037 "RMATCAT" 2421396 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2422378 NIL) (-1047 2415063 2415210 2415517 "RMATCAT-" 2415522 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2414630 2414705 2414833 "RINTERP" 2414982 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2413763 2414283 2414313 "RING" 2414369 T RING (NIL) -9 NIL 2414455 NIL) (-1044 2413555 2413599 2413696 "RING-" 2413701 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2412396 2412633 2412891 "RIDIST" 2413319 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2403712 2411864 2412070 "RGCHAIN" 2412244 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2403088 2403468 2403509 "RGBCSPC" 2403567 NIL RGBCSPC (NIL T) -9 NIL 2403619 NIL) (-1040 2402272 2402627 2402668 "RGBCMDL" 2402900 NIL RGBCMDL (NIL T) -9 NIL 2403014 NIL) (-1039 2399266 2399880 2400550 "RF" 2401636 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2398912 2398975 2399078 "RFFACTOR" 2399197 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2398637 2398672 2398769 "RFFACT" 2398871 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2396754 2397118 2397500 "RFDIST" 2398277 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2396207 2396299 2396462 "RETSOL" 2396656 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2395843 2395923 2395966 "RETRACT" 2396099 NIL RETRACT (NIL T) -9 NIL 2396186 NIL) (-1033 2395692 2395717 2395804 "RETRACT-" 2395809 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2395321 2395514 2395584 "RETAST" 2395644 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2388175 2394974 2395101 "RESULT" 2395216 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2386801 2387444 2387643 "RESRING" 2388078 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2386437 2386486 2386584 "RESLATC" 2386738 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2386143 2386177 2386284 "REPSQ" 2386396 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2383565 2384145 2384747 "REP" 2385563 T REP (NIL) -7 NIL NIL NIL) (-1026 2383263 2383297 2383408 "REPDB" 2383524 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2377173 2378552 2379775 "REP2" 2382075 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2373550 2374231 2375039 "REP1" 2376400 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2366276 2371691 2372147 "REGSET" 2373180 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2365089 2365424 2365674 "REF" 2366061 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2364466 2364569 2364736 "REDORDER" 2364973 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2360471 2363679 2363906 "RECLOS" 2364294 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2359523 2359704 2359919 "REALSOLV" 2360278 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2359369 2359410 2359440 "REAL" 2359445 T REAL (NIL) -9 NIL 2359480 NIL) (-1017 2355852 2356654 2357538 "REAL0Q" 2358534 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2351453 2352441 2353502 "REAL0" 2354833 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2350951 2351170 2351264 "RDUCEAST" 2351381 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2350356 2350428 2350635 "RDIV" 2350873 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2349424 2349598 2349811 "RDIST" 2350178 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2348021 2348308 2348680 "RDETRS" 2349132 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2345833 2346287 2346825 "RDETR" 2347563 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2344444 2344722 2345126 "RDEEFS" 2345549 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2342939 2343245 2343677 "RDEEF" 2344132 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2337200 2340075 2340105 "RCFIELD" 2341400 T RCFIELD (NIL) -9 NIL 2342130 NIL) (-1007 2335264 2335768 2336464 "RCFIELD-" 2336539 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2331580 2333365 2333408 "RCAGG" 2334492 NIL RCAGG (NIL T) -9 NIL 2334957 NIL) (-1005 2331208 2331302 2331465 "RCAGG-" 2331470 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2330543 2330655 2330820 "RATRET" 2331092 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2330096 2330163 2330284 "RATFACT" 2330471 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2329404 2329524 2329676 "RANDSRC" 2329966 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2329138 2329182 2329255 "RADUTIL" 2329353 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2322291 2327971 2328281 "RADIX" 2328862 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2313948 2322135 2322263 "RADFF" 2322268 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2313600 2313675 2313703 "RADCAT" 2313860 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2313385 2313433 2313530 "RADCAT-" 2313535 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2311536 2313160 2313249 "QUEUE" 2313329 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2308112 2311473 2311518 "QUAT" 2311523 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2307750 2307793 2307920 "QUATCT2" 2308063 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2301497 2304799 2304839 "QUATCAT" 2305619 NIL QUATCAT (NIL T) -9 NIL 2306385 NIL) (-992 2297641 2298678 2300065 "QUATCAT-" 2300159 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2295161 2296725 2296766 "QUAGG" 2297141 NIL QUAGG (NIL T) -9 NIL 2297316 NIL) (-990 2294793 2294986 2295054 "QQUTAST" 2295113 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2293718 2294191 2294363 "QFORM" 2294665 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2284930 2290135 2290175 "QFCAT" 2290833 NIL QFCAT (NIL T) -9 NIL 2291834 NIL) (-987 2280502 2281703 2283294 "QFCAT-" 2283388 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2280140 2280183 2280310 "QFCAT2" 2280453 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2279600 2279710 2279840 "QEQUAT" 2280030 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2272748 2273819 2275003 "QCMPACK" 2278533 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2270324 2270745 2271173 "QALGSET" 2272403 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2269569 2269743 2269975 "QALGSET2" 2270144 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2268260 2268483 2268800 "PWFFINTB" 2269342 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2266442 2266610 2266964 "PUSHVAR" 2268074 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2262360 2263414 2263455 "PTRANFN" 2265339 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2260762 2261053 2261375 "PTPACK" 2262071 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2260394 2260451 2260560 "PTFUNC2" 2260699 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2254921 2259266 2259307 "PTCAT" 2259603 NIL PTCAT (NIL T) -9 NIL 2259756 NIL) (-975 2254579 2254614 2254738 "PSQFR" 2254880 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2253174 2253472 2253806 "PSEUDLIN" 2254277 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2239944 2242308 2244632 "PSETPK" 2250934 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2232988 2235702 2235798 "PSETCAT" 2238819 NIL PSETCAT (NIL T T T T) -9 NIL 2239633 NIL) (-971 2230824 2231458 2232279 "PSETCAT-" 2232284 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2230173 2230338 2230366 "PSCURVE" 2230634 T PSCURVE (NIL) -9 NIL 2230801 NIL) (-969 2226529 2228011 2228076 "PSCAT" 2228920 NIL PSCAT (NIL T T T) -9 NIL 2229160 NIL) (-968 2225592 2225808 2226208 "PSCAT-" 2226213 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2224324 2224957 2225162 "PRTITION" 2225407 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2223826 2224045 2224137 "PRTDAST" 2224252 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2212924 2215130 2217318 "PRS" 2221688 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2210782 2212274 2212314 "PRQAGG" 2212497 NIL PRQAGG (NIL T) -9 NIL 2212599 NIL) (-963 2210168 2210397 2210425 "PROPLOG" 2210610 T PROPLOG (NIL) -9 NIL 2210732 NIL) (-962 2207338 2207982 2208446 "PROPFRML" 2209736 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2206798 2206908 2207038 "PROPERTY" 2207228 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2200883 2204964 2205784 "PRODUCT" 2206024 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2198196 2200341 2200575 "PR" 2200694 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2197992 2198024 2198083 "PRINT" 2198157 T PRINT (NIL) -7 NIL NIL NIL) (-957 2197332 2197449 2197601 "PRIMES" 2197872 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2195397 2195798 2196264 "PRIMELT" 2196911 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2195126 2195175 2195203 "PRIMCAT" 2195327 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2191287 2195064 2195109 "PRIMARR" 2195114 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2190294 2190472 2190700 "PRIMARR2" 2191105 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2189937 2189993 2190104 "PREASSOC" 2190232 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2189412 2189545 2189573 "PPCURVE" 2189778 T PPCURVE (NIL) -9 NIL 2189914 NIL) (-950 2189034 2189207 2189290 "PORTNUM" 2189349 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2186393 2186792 2187384 "POLYROOT" 2188615 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2180338 2185997 2186157 "POLY" 2186266 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2179721 2179779 2180013 "POLYLIFT" 2180274 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2175996 2176445 2177074 "POLYCATQ" 2179266 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2162813 2168171 2168236 "POLYCAT" 2171750 NIL POLYCAT (NIL T T T) -9 NIL 2173678 NIL) (-944 2156263 2158124 2160508 "POLYCAT-" 2160513 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2155850 2155918 2156038 "POLY2UP" 2156189 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2155482 2155539 2155648 "POLY2" 2155787 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2154167 2154406 2154682 "POLUTIL" 2155256 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2152522 2152799 2153130 "POLTOPOL" 2153889 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2148040 2152458 2152504 "POINT" 2152509 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2146227 2146584 2146959 "PNTHEORY" 2147685 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2144646 2144943 2145355 "PMTOOLS" 2145925 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2144239 2144317 2144434 "PMSYM" 2144562 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2143749 2143818 2143992 "PMQFCAT" 2144164 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2143104 2143214 2143370 "PMPRED" 2143626 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2142500 2142586 2142747 "PMPREDFS" 2143005 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2141143 2141351 2141736 "PMPLCAT" 2142262 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2140675 2140754 2140906 "PMLSAGG" 2141058 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2140150 2140226 2140407 "PMKERNEL" 2140593 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2139767 2139842 2139955 "PMINS" 2140069 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2139195 2139264 2139480 "PMFS" 2139692 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2138423 2138541 2138746 "PMDOWN" 2139072 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2137586 2137745 2137927 "PMASS" 2138261 T PMASS (NIL) -7 NIL NIL NIL) (-925 2136860 2136971 2137134 "PMASSFS" 2137472 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2136515 2136583 2136677 "PLOTTOOL" 2136786 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2131137 2132326 2133474 "PLOT" 2135387 T PLOT (NIL) -8 NIL NIL NIL) (-922 2126951 2127985 2128906 "PLOT3D" 2130236 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2125863 2126040 2126275 "PLOT1" 2126755 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2101257 2105929 2110780 "PLEQN" 2121129 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2100575 2100697 2100877 "PINTERP" 2101122 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2100268 2100315 2100418 "PINTERPA" 2100522 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2099516 2100037 2100124 "PI" 2100164 T PI (NIL) -8 NIL NIL 2100231) (-916 2097913 2098854 2098882 "PID" 2099064 T PID (NIL) -9 NIL 2099198 NIL) (-915 2097638 2097675 2097763 "PICOERCE" 2097870 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2096958 2097097 2097273 "PGROEB" 2097494 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2092545 2093359 2094264 "PGE" 2096073 T PGE (NIL) -7 NIL NIL NIL) (-912 2090669 2090915 2091281 "PGCD" 2092262 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2090007 2090110 2090271 "PFRPAC" 2090553 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2086687 2088555 2088908 "PFR" 2089686 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2085076 2085320 2085645 "PFOTOOLS" 2086434 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2083609 2083848 2084199 "PFOQ" 2084833 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2082082 2082294 2082657 "PFO" 2083393 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2078670 2081971 2082040 "PF" 2082045 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2076104 2077341 2077369 "PFECAT" 2077954 T PFECAT (NIL) -9 NIL 2078338 NIL) (-904 2075549 2075703 2075917 "PFECAT-" 2075922 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2074153 2074404 2074705 "PFBRU" 2075298 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2072020 2072371 2072803 "PFBR" 2073804 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2067936 2069396 2070072 "PERM" 2071377 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2063202 2064143 2065013 "PERMGRP" 2067099 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2061334 2062265 2062306 "PERMCAT" 2062752 NIL PERMCAT (NIL T) -9 NIL 2063057 NIL) (-898 2060987 2061028 2061152 "PERMAN" 2061287 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2058523 2060652 2060774 "PENDTREE" 2060898 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2056616 2057350 2057391 "PDRING" 2058048 NIL PDRING (NIL T) -9 NIL 2058334 NIL) (-895 2055719 2055937 2056299 "PDRING-" 2056304 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2052961 2053712 2054380 "PDEPROB" 2055071 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2050508 2051010 2051565 "PDEPACK" 2052426 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2049420 2049610 2049861 "PDECOMP" 2050307 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2047025 2047842 2047870 "PDECAT" 2048657 T PDECAT (NIL) -9 NIL 2049370 NIL) (-890 2046776 2046809 2046899 "PCOMP" 2046986 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2044981 2045577 2045874 "PBWLB" 2046505 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2037486 2039054 2040392 "PATTERN" 2043664 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2037118 2037175 2037284 "PATTERN2" 2037423 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2034875 2035263 2035720 "PATTERN1" 2036707 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2032270 2032824 2033305 "PATRES" 2034440 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2031834 2031901 2032033 "PATRES2" 2032197 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2029717 2030122 2030529 "PATMATCH" 2031501 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2029253 2029436 2029477 "PATMAB" 2029584 NIL PATMAB (NIL T) -9 NIL 2029667 NIL) (-881 2027798 2028107 2028365 "PATLRES" 2029058 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2027344 2027467 2027508 "PATAB" 2027513 NIL PATAB (NIL T) -9 NIL 2027685 NIL) (-879 2024825 2025357 2025930 "PARTPERM" 2026791 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2024446 2024509 2024611 "PARSURF" 2024756 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2024078 2024135 2024244 "PARSU2" 2024383 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2023842 2023882 2023949 "PARSER" 2024031 T PARSER (NIL) -7 NIL NIL NIL) (-875 2023463 2023526 2023628 "PARSCURV" 2023773 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2023095 2023152 2023261 "PARSC2" 2023400 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2022734 2022792 2022889 "PARPCURV" 2023031 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2022366 2022423 2022532 "PARPC2" 2022671 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2021886 2021972 2022091 "PAN2EXPR" 2022267 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2020692 2021007 2021235 "PALETTE" 2021678 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2019160 2019697 2020057 "PAIR" 2020378 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2013066 2018419 2018613 "PADICRC" 2019015 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2006330 2012412 2012596 "PADICRAT" 2012914 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2004680 2006267 2006312 "PADIC" 2006317 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2001890 2003420 2003460 "PADICCT" 2004041 NIL PADICCT (NIL NIL) -9 NIL 2004323 NIL) (-864 2000847 2001047 2001315 "PADEPAC" 2001677 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2000059 2000192 2000398 "PADE" 2000709 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 1998481 1999267 1999547 "OWP" 1999863 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 1998001 1998187 1998284 "OVERSET" 1998404 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1997074 1997606 1997778 "OVAR" 1997869 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1996338 1996459 1996620 "OUT" 1996933 T OUT (NIL) -7 NIL NIL NIL) (-858 1985245 1987447 1989647 "OUTFORM" 1994158 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1984581 1984842 1984969 "OUTBFILE" 1985138 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1983888 1984053 1984081 "OUTBCON" 1984399 T OUTBCON (NIL) -9 NIL 1984565 NIL) (-855 1983489 1983601 1983758 "OUTBCON-" 1983763 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1982897 1983218 1983307 "OSI" 1983420 T OSI (NIL) -8 NIL NIL NIL) (-853 1982453 1982765 1982793 "OSGROUP" 1982798 T OSGROUP (NIL) -9 NIL 1982820 NIL) (-852 1981198 1981425 1981710 "ORTHPOL" 1982200 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1978784 1981033 1981154 "OREUP" 1981159 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976222 1978475 1978602 "ORESUP" 1978726 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1973750 1974250 1974811 "OREPCTO" 1975711 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1967574 1969741 1969782 "OREPCAT" 1972130 NIL OREPCAT (NIL T) -9 NIL 1973234 NIL) (-847 1964721 1965503 1966561 "OREPCAT-" 1966566 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1963898 1964170 1964198 "ORDSET" 1964507 T ORDSET (NIL) -9 NIL 1964671 NIL) (-845 1963417 1963539 1963732 "ORDSET-" 1963737 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1962051 1962808 1962836 "ORDRING" 1963038 T ORDRING (NIL) -9 NIL 1963163 NIL) (-843 1961696 1961790 1961934 "ORDRING-" 1961939 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1961102 1961539 1961567 "ORDMON" 1961572 T ORDMON (NIL) -9 NIL 1961593 NIL) (-841 1960264 1960411 1960606 "ORDFUNS" 1960951 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1959628 1960021 1960049 "ORDFIN" 1960114 T ORDFIN (NIL) -9 NIL 1960188 NIL) (-839 1956220 1958214 1958623 "ORDCOMP" 1959252 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1955486 1955613 1955799 "ORDCOMP2" 1956080 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1952094 1952977 1953791 "OPTPROB" 1954692 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1948896 1949535 1950239 "OPTPACK" 1951410 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1946609 1947349 1947377 "OPTCAT" 1948196 T OPTCAT (NIL) -9 NIL 1948846 NIL) (-834 1946052 1946286 1946391 "OPSIG" 1946524 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1945820 1945859 1945925 "OPQUERY" 1946006 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1942986 1944131 1944635 "OP" 1945349 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1942521 1942692 1942733 "OPERCAT" 1942868 NIL OPERCAT (NIL T) -9 NIL 1942936 NIL) (-830 1942367 1942394 1942480 "OPERCAT-" 1942485 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1939212 1941164 1941533 "ONECOMP" 1942031 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1938517 1938632 1938806 "ONECOMP2" 1939084 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1937936 1938042 1938172 "OMSERVER" 1938407 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1934824 1937376 1937416 "OMSAGG" 1937477 NIL OMSAGG (NIL T) -9 NIL 1937541 NIL) (-825 1933447 1933710 1933992 "OMPKG" 1934562 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1932877 1932980 1933008 "OM" 1933307 T OM (NIL) -9 NIL NIL NIL) (-823 1931459 1932426 1932595 "OMLO" 1932758 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1930384 1930531 1930758 "OMEXPR" 1931285 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1929702 1929930 1930066 "OMERR" 1930268 T OMERR (NIL) -8 NIL NIL NIL) (-820 1928880 1929123 1929283 "OMERRK" 1929562 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1928358 1928557 1928665 "OMENC" 1928792 T OMENC (NIL) -8 NIL NIL NIL) (-818 1922253 1923438 1924609 "OMDEV" 1927207 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1921322 1921493 1921687 "OMCONN" 1922079 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1919943 1920885 1920913 "OINTDOM" 1920918 T OINTDOM (NIL) -9 NIL 1920939 NIL) (-815 1915749 1916933 1917649 "OFMONOID" 1919259 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1915187 1915686 1915731 "ODVAR" 1915736 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1912645 1914932 1915087 "ODR" 1915092 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1904989 1912421 1912547 "ODPOL" 1912552 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1898865 1904861 1904966 "ODP" 1904971 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1897631 1897846 1898121 "ODETOOLS" 1898639 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1894600 1895256 1895972 "ODESYS" 1896964 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1889482 1890390 1891415 "ODERTRIC" 1893675 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1888908 1888990 1889184 "ODERED" 1889394 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1885796 1886344 1887021 "ODERAT" 1888331 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1882756 1883220 1883817 "ODEPRRIC" 1885325 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1880726 1881295 1881781 "ODEPROB" 1882290 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1877248 1877731 1878378 "ODEPRIM" 1880205 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1876497 1876599 1876859 "ODEPAL" 1877140 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1872659 1873450 1874314 "ODEPACK" 1875653 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1871692 1871799 1872028 "ODEINT" 1872548 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1865793 1867218 1868665 "ODEIFTBL" 1870265 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1861128 1861914 1862873 "ODEEF" 1864952 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1860463 1860552 1860782 "ODECONST" 1861033 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1858614 1859249 1859277 "ODECAT" 1859882 T ODECAT (NIL) -9 NIL 1860413 NIL) (-795 1855521 1858326 1858445 "OCT" 1858527 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1855159 1855202 1855329 "OCTCT2" 1855472 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1849933 1852333 1852373 "OC" 1853470 NIL OC (NIL T) -9 NIL 1854328 NIL) (-792 1847160 1847908 1848898 "OC-" 1848992 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1846538 1846980 1847008 "OCAMON" 1847013 T OCAMON (NIL) -9 NIL 1847034 NIL) (-790 1846095 1846410 1846438 "OASGP" 1846443 T OASGP (NIL) -9 NIL 1846463 NIL) (-789 1845382 1845845 1845873 "OAMONS" 1845913 T OAMONS (NIL) -9 NIL 1845956 NIL) (-788 1844822 1845229 1845257 "OAMON" 1845262 T OAMON (NIL) -9 NIL 1845282 NIL) (-787 1844126 1844618 1844646 "OAGROUP" 1844651 T OAGROUP (NIL) -9 NIL 1844671 NIL) (-786 1843816 1843866 1843954 "NUMTUBE" 1844070 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1837389 1838907 1840443 "NUMQUAD" 1842300 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1833145 1834133 1835158 "NUMODE" 1836384 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1830526 1831380 1831408 "NUMINT" 1832331 T NUMINT (NIL) -9 NIL 1833095 NIL) (-782 1829474 1829671 1829889 "NUMFMT" 1830328 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1815833 1818778 1821310 "NUMERIC" 1826981 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1810230 1815282 1815377 "NTSCAT" 1815382 NIL NTSCAT (NIL T T T T) -9 NIL 1815421 NIL) (-779 1809424 1809589 1809782 "NTPOLFN" 1810069 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1797264 1806249 1807061 "NSUP" 1808645 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1796896 1796953 1797062 "NSUP2" 1797201 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1786893 1796670 1796803 "NSMP" 1796808 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1785325 1785626 1785983 "NREP" 1786581 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1783916 1784168 1784526 "NPCOEF" 1785068 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1782982 1783097 1783313 "NORMRETR" 1783797 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1781023 1781313 1781722 "NORMPK" 1782690 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1780708 1780736 1780860 "NORMMA" 1780989 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1780535 1780665 1780694 "NONE" 1780699 T NONE (NIL) -8 NIL NIL NIL) (-769 1780324 1780353 1780422 "NONE1" 1780499 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1779807 1779869 1780055 "NODE1" 1780256 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1778078 1778901 1779156 "NNI" 1779503 T NNI (NIL) -8 NIL NIL 1779738) (-766 1776498 1776811 1777175 "NLINSOL" 1777746 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1772766 1773734 1774633 "NIPROB" 1775619 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1771523 1771757 1772059 "NFINTBAS" 1772528 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1770697 1771173 1771214 "NETCLT" 1771386 NIL NETCLT (NIL T) -9 NIL 1771468 NIL) (-762 1769405 1769636 1769917 "NCODIV" 1770465 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1769167 1769204 1769279 "NCNTFRAC" 1769362 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1767347 1767711 1768131 "NCEP" 1768792 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1766258 1766997 1767025 "NASRING" 1767135 T NASRING (NIL) -9 NIL 1767209 NIL) (-758 1766053 1766097 1766191 "NASRING-" 1766196 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1765206 1765705 1765733 "NARNG" 1765850 T NARNG (NIL) -9 NIL 1765941 NIL) (-756 1764898 1764965 1765099 "NARNG-" 1765104 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1763777 1763984 1764219 "NAGSP" 1764683 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1755049 1756733 1758406 "NAGS" 1762124 T NAGS (NIL) -7 NIL NIL NIL) (-753 1753597 1753905 1754236 "NAGF07" 1754738 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1748135 1749426 1750733 "NAGF04" 1752310 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1741103 1742717 1744350 "NAGF02" 1746522 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1736327 1737427 1738544 "NAGF01" 1740006 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1729955 1731521 1733106 "NAGE04" 1734762 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1721124 1723245 1725375 "NAGE02" 1727845 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1717077 1718024 1718988 "NAGE01" 1720180 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1714872 1715406 1715964 "NAGD03" 1716539 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1706622 1708550 1710504 "NAGD02" 1712938 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1700433 1701858 1703298 "NAGD01" 1705202 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1696642 1697464 1698301 "NAGC06" 1699616 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1695107 1695439 1695795 "NAGC05" 1696306 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1694483 1694602 1694746 "NAGC02" 1694983 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1693543 1694100 1694140 "NAALG" 1694219 NIL NAALG (NIL T) -9 NIL 1694280 NIL) (-739 1693378 1693407 1693497 "NAALG-" 1693502 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1687328 1688436 1689623 "MULTSQFR" 1692274 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1686647 1686722 1686906 "MULTFACT" 1687240 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1679740 1683610 1683663 "MTSCAT" 1684733 NIL MTSCAT (NIL T T) -9 NIL 1685247 NIL) (-735 1679452 1679506 1679598 "MTHING" 1679680 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1679244 1679277 1679337 "MSYSCMD" 1679412 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1675356 1677999 1678319 "MSET" 1678957 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1672451 1674917 1674958 "MSETAGG" 1674963 NIL MSETAGG (NIL T) -9 NIL 1674997 NIL) (-731 1668334 1669830 1670575 "MRING" 1671751 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1667900 1667967 1668098 "MRF2" 1668261 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1667518 1667553 1667697 "MRATFAC" 1667859 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1665130 1665425 1665856 "MPRFF" 1667223 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1659190 1664984 1665081 "MPOLY" 1665086 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1658680 1658715 1658923 "MPCPF" 1659149 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1658194 1658237 1658421 "MPC3" 1658631 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657389 1657470 1657691 "MPC2" 1658109 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1655690 1656027 1656417 "MONOTOOL" 1657049 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1654941 1655232 1655260 "MONOID" 1655479 T MONOID (NIL) -9 NIL 1655626 NIL) (-721 1654487 1654606 1654787 "MONOID-" 1654792 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1645346 1651254 1651313 "MONOGEN" 1651987 NIL MONOGEN (NIL T T) -9 NIL 1652443 NIL) (-719 1642564 1643299 1644299 "MONOGEN-" 1644418 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1641423 1641843 1641871 "MONADWU" 1642263 T MONADWU (NIL) -9 NIL 1642501 NIL) (-717 1640795 1640954 1641202 "MONADWU-" 1641207 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1640180 1640398 1640426 "MONAD" 1640633 T MONAD (NIL) -9 NIL 1640745 NIL) (-715 1639865 1639943 1640075 "MONAD-" 1640080 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1638181 1638778 1639057 "MOEBIUS" 1639618 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1637573 1637951 1637991 "MODULE" 1637996 NIL MODULE (NIL T) -9 NIL 1638022 NIL) (-712 1637141 1637237 1637427 "MODULE-" 1637432 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1634856 1635505 1635832 "MODRING" 1636965 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1631842 1632961 1633482 "MODOP" 1634385 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1630457 1630909 1631186 "MODMONOM" 1631705 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1620264 1628748 1629162 "MODMON" 1630094 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1617455 1619108 1619384 "MODFIELD" 1620139 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1616459 1616736 1616926 "MMLFORM" 1617285 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1615985 1616028 1616207 "MMAP" 1616410 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1614202 1614935 1614976 "MLO" 1615399 NIL MLO (NIL T) -9 NIL 1615641 NIL) (-703 1611569 1612084 1612686 "MLIFT" 1613683 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1610960 1611044 1611198 "MKUCFUNC" 1611480 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1610559 1610629 1610752 "MKRECORD" 1610883 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1609607 1609768 1609996 "MKFUNC" 1610370 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1608995 1609099 1609255 "MKFLCFN" 1609490 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1608538 1608905 1608964 "MKCHSET" 1608969 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-697 1607815 1607917 1608102 "MKBCFUNC" 1608431 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-696 1604557 1607369 1607505 "MINT" 1607699 T MINT (NIL) -8 NIL NIL NIL) (-695 1603369 1603612 1603889 "MHROWRED" 1604312 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-694 1598795 1601904 1602309 "MFLOAT" 1602984 T MFLOAT (NIL) -8 NIL NIL NIL) (-693 1598152 1598228 1598399 "MFINFACT" 1598707 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-692 1594467 1595315 1596199 "MESH" 1597288 T MESH (NIL) -7 NIL NIL NIL) (-691 1592857 1593169 1593522 "MDDFACT" 1594154 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-690 1589699 1592016 1592057 "MDAGG" 1592312 NIL MDAGG (NIL T) -9 NIL 1592455 NIL) (-689 1579477 1588992 1589199 "MCMPLX" 1589512 T MCMPLX (NIL) -8 NIL NIL NIL) (-688 1578618 1578764 1578964 "MCDEN" 1579326 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-687 1576508 1576778 1577158 "MCALCFN" 1578348 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-686 1575433 1575673 1575906 "MAYBE" 1576314 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-685 1573045 1573568 1574130 "MATSTOR" 1574904 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-684 1569051 1572417 1572665 "MATRIX" 1572830 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-683 1564820 1565524 1566260 "MATLIN" 1568408 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-682 1554974 1558112 1558189 "MATCAT" 1563069 NIL MATCAT (NIL T T T) -9 NIL 1564486 NIL) (-681 1551338 1552351 1553707 "MATCAT-" 1553712 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-680 1549932 1550085 1550418 "MATCAT2" 1551173 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-679 1548044 1548368 1548752 "MAPPKG3" 1549607 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-678 1547025 1547198 1547420 "MAPPKG2" 1547868 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-677 1545524 1545808 1546135 "MAPPKG1" 1546731 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-676 1544630 1544930 1545107 "MAPPAST" 1545367 T MAPPAST (NIL) -8 NIL NIL NIL) (-675 1544241 1544299 1544422 "MAPHACK3" 1544566 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-674 1543833 1543894 1544008 "MAPHACK2" 1544173 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-673 1543271 1543374 1543516 "MAPHACK1" 1543724 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-672 1541377 1541971 1542275 "MAGMA" 1542999 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-671 1540883 1541101 1541192 "MACROAST" 1541306 T MACROAST (NIL) -8 NIL NIL NIL) (-670 1537350 1539122 1539583 "M3D" 1540455 NIL M3D (NIL T) -8 NIL NIL NIL) (-669 1531504 1535719 1535760 "LZSTAGG" 1536542 NIL LZSTAGG (NIL T) -9 NIL 1536837 NIL) (-668 1527478 1528635 1530092 "LZSTAGG-" 1530097 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-667 1524592 1525369 1525856 "LWORD" 1527023 NIL LWORD (NIL T) -8 NIL NIL NIL) (-666 1524195 1524396 1524471 "LSTAST" 1524537 T LSTAST (NIL) -8 NIL NIL NIL) (-665 1517396 1523966 1524100 "LSQM" 1524105 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-664 1516620 1516759 1516987 "LSPP" 1517251 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-663 1514432 1514733 1515189 "LSMP" 1516309 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-662 1511211 1511885 1512615 "LSMP1" 1513734 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-661 1505136 1510378 1510419 "LSAGG" 1510481 NIL LSAGG (NIL T) -9 NIL 1510559 NIL) (-660 1501831 1502755 1503968 "LSAGG-" 1503973 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-659 1499457 1500975 1501224 "LPOLY" 1501626 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-658 1499039 1499124 1499247 "LPEFRAC" 1499366 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-657 1497386 1498133 1498386 "LO" 1498871 NIL LO (NIL T T T) -8 NIL NIL NIL) (-656 1497038 1497150 1497178 "LOGIC" 1497289 T LOGIC (NIL) -9 NIL 1497370 NIL) (-655 1496900 1496923 1496994 "LOGIC-" 1496999 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-654 1496093 1496233 1496426 "LODOOPS" 1496756 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-653 1493551 1496009 1496075 "LODO" 1496080 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-652 1492089 1492324 1492677 "LODOF" 1493298 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-651 1488445 1490842 1490883 "LODOCAT" 1491321 NIL LODOCAT (NIL T) -9 NIL 1491532 NIL) (-650 1488178 1488236 1488363 "LODOCAT-" 1488368 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-649 1485533 1488019 1488137 "LODO2" 1488142 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-648 1483003 1485470 1485515 "LODO1" 1485520 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-647 1481863 1482028 1482340 "LODEEF" 1482826 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-646 1477149 1479993 1480034 "LNAGG" 1480981 NIL LNAGG (NIL T) -9 NIL 1481425 NIL) (-645 1476296 1476510 1476852 "LNAGG-" 1476857 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-644 1472459 1473221 1473860 "LMOPS" 1475711 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-643 1471854 1472216 1472257 "LMODULE" 1472318 NIL LMODULE (NIL T) -9 NIL 1472360 NIL) (-642 1469100 1471499 1471622 "LMDICT" 1471764 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-641 1468826 1469008 1469068 "LITERAL" 1469073 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-640 1462053 1467772 1468070 "LIST" 1468561 NIL LIST (NIL T) -8 NIL NIL NIL) (-639 1461578 1461652 1461791 "LIST3" 1461973 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-638 1460585 1460763 1460991 "LIST2" 1461396 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-637 1458719 1459031 1459430 "LIST2MAP" 1460232 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-636 1457449 1458085 1458126 "LINEXP" 1458381 NIL LINEXP (NIL T) -9 NIL 1458530 NIL) (-635 1456096 1456356 1456653 "LINDEP" 1457201 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-634 1452863 1453582 1454359 "LIMITRF" 1455351 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-633 1451139 1451434 1451850 "LIMITPS" 1452558 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-632 1445594 1450650 1450878 "LIE" 1450960 NIL LIE (NIL T T) -8 NIL NIL NIL) (-631 1444643 1445086 1445126 "LIECAT" 1445266 NIL LIECAT (NIL T) -9 NIL 1445417 NIL) (-630 1444484 1444511 1444599 "LIECAT-" 1444604 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-629 1437096 1443933 1444098 "LIB" 1444339 T LIB (NIL) -8 NIL NIL NIL) (-628 1432733 1433614 1434549 "LGROBP" 1436213 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-627 1430599 1430873 1431235 "LF" 1432454 NIL LF (NIL T T) -7 NIL NIL NIL) (-626 1429439 1430131 1430159 "LFCAT" 1430366 T LFCAT (NIL) -9 NIL 1430505 NIL) (-625 1426343 1426971 1427659 "LEXTRIPK" 1428803 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-624 1423114 1423913 1424416 "LEXP" 1425923 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-623 1422617 1422835 1422927 "LETAST" 1423042 T LETAST (NIL) -8 NIL NIL NIL) (-622 1421015 1421328 1421729 "LEADCDET" 1422299 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-621 1420205 1420279 1420508 "LAZM3PK" 1420936 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-620 1415160 1418282 1418820 "LAUPOL" 1419717 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-619 1414725 1414769 1414937 "LAPLACE" 1415110 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-618 1412699 1413826 1414077 "LA" 1414558 NIL LA (NIL T T T) -8 NIL NIL NIL) (-617 1411780 1412330 1412371 "LALG" 1412433 NIL LALG (NIL T) -9 NIL 1412492 NIL) (-616 1411494 1411553 1411689 "LALG-" 1411694 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-615 1411329 1411353 1411394 "KVTFROM" 1411456 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-614 1410132 1410546 1410775 "KTVLOGIC" 1411120 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-613 1409967 1409991 1410032 "KRCFROM" 1410094 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-612 1408871 1409058 1409357 "KOVACIC" 1409767 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-611 1408706 1408730 1408771 "KONVERT" 1408833 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-610 1408541 1408565 1408606 "KOERCE" 1408668 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-609 1406275 1407035 1407428 "KERNEL" 1408180 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-608 1405777 1405858 1405988 "KERNEL2" 1406189 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-607 1399628 1404316 1404370 "KDAGG" 1404747 NIL KDAGG (NIL T T) -9 NIL 1404953 NIL) (-606 1399157 1399281 1399486 "KDAGG-" 1399491 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-605 1392332 1398818 1398973 "KAFILE" 1399035 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-604 1386787 1391843 1392071 "JORDAN" 1392153 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-603 1386193 1386436 1386557 "JOINAST" 1386686 T JOINAST (NIL) -8 NIL NIL NIL) (-602 1386039 1386098 1386153 "JAVACODE" 1386158 T JAVACODE (NIL) -8 NIL NIL NIL) (-601 1382338 1384244 1384298 "IXAGG" 1385227 NIL IXAGG (NIL T T) -9 NIL 1385686 NIL) (-600 1381257 1381563 1381982 "IXAGG-" 1381987 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-599 1376837 1381179 1381238 "IVECTOR" 1381243 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-598 1375603 1375840 1376106 "ITUPLE" 1376604 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-597 1374039 1374216 1374522 "ITRIGMNP" 1375425 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-596 1372784 1372988 1373271 "ITFUN3" 1373815 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-595 1372416 1372473 1372582 "ITFUN2" 1372721 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-594 1370253 1371278 1371577 "ITAYLOR" 1372150 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-593 1359236 1364390 1365553 "ISUPS" 1369123 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-592 1358340 1358480 1358716 "ISUMP" 1359083 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-591 1353604 1358141 1358220 "ISTRING" 1358293 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-590 1353107 1353325 1353417 "ISAST" 1353532 T ISAST (NIL) -8 NIL NIL NIL) (-589 1352317 1352398 1352614 "IRURPK" 1353021 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-588 1351253 1351454 1351694 "IRSN" 1352097 T IRSN (NIL) -7 NIL NIL NIL) (-587 1349282 1349637 1350073 "IRRF2F" 1350891 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-586 1349029 1349067 1349143 "IRREDFFX" 1349238 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-585 1347644 1347903 1348202 "IROOT" 1348762 NIL IROOT (NIL T) -7 NIL NIL NIL) (-584 1344276 1345328 1346020 "IR" 1346984 NIL IR (NIL T) -8 NIL NIL NIL) (-583 1341889 1342384 1342950 "IR2" 1343754 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-582 1340961 1341074 1341295 "IR2F" 1341772 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-581 1340752 1340786 1340846 "IPRNTPK" 1340921 T IPRNTPK (NIL) -7 NIL NIL NIL) (-580 1337371 1340641 1340710 "IPF" 1340715 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-579 1335734 1337296 1337353 "IPADIC" 1337358 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-578 1335074 1335294 1335424 "IP4ADDR" 1335624 T IP4ADDR (NIL) -8 NIL NIL NIL) (-577 1334574 1334778 1334888 "IOMODE" 1334984 T IOMODE (NIL) -8 NIL NIL NIL) (-576 1333647 1334171 1334298 "IOBFILE" 1334467 T IOBFILE (NIL) -8 NIL NIL NIL) (-575 1333135 1333551 1333579 "IOBCON" 1333584 T IOBCON (NIL) -9 NIL 1333605 NIL) (-574 1332632 1332690 1332880 "INVLAPLA" 1333071 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-573 1322281 1324634 1327020 "INTTR" 1330296 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-572 1318625 1319367 1320231 "INTTOOLS" 1321466 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-571 1318211 1318302 1318419 "INTSLPE" 1318528 T INTSLPE (NIL) -7 NIL NIL NIL) (-570 1316206 1318134 1318193 "INTRVL" 1318198 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-569 1313808 1314320 1314895 "INTRF" 1315691 NIL INTRF (NIL T) -7 NIL NIL NIL) (-568 1313219 1313316 1313458 "INTRET" 1313706 NIL INTRET (NIL T) -7 NIL NIL NIL) (-567 1311216 1311605 1312075 "INTRAT" 1312827 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-566 1308444 1309027 1309653 "INTPM" 1310701 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-565 1305147 1305746 1306491 "INTPAF" 1307830 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-564 1300326 1301288 1302339 "INTPACK" 1304116 T INTPACK (NIL) -7 NIL NIL NIL) (-563 1297238 1300055 1300182 "INT" 1300219 T INT (NIL) -8 NIL NIL NIL) (-562 1296490 1296642 1296850 "INTHERTR" 1297080 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-561 1295929 1296009 1296197 "INTHERAL" 1296404 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-560 1293775 1294218 1294675 "INTHEORY" 1295492 T INTHEORY (NIL) -7 NIL NIL NIL) (-559 1285083 1286704 1288483 "INTG0" 1292127 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-558 1265656 1270446 1275256 "INTFTBL" 1280293 T INTFTBL (NIL) -8 NIL NIL NIL) (-557 1264905 1265043 1265216 "INTFACT" 1265515 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-556 1262290 1262736 1263300 "INTEF" 1264459 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-555 1260757 1261462 1261490 "INTDOM" 1261791 T INTDOM (NIL) -9 NIL 1261998 NIL) (-554 1260126 1260300 1260542 "INTDOM-" 1260547 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-553 1256621 1258510 1258564 "INTCAT" 1259363 NIL INTCAT (NIL T) -9 NIL 1259683 NIL) (-552 1256094 1256196 1256324 "INTBIT" 1256513 T INTBIT (NIL) -7 NIL NIL NIL) (-551 1254765 1254919 1255233 "INTALG" 1255939 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-550 1254222 1254312 1254482 "INTAF" 1254669 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-549 1247676 1254032 1254172 "INTABL" 1254177 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-548 1247136 1247549 1247577 "INT8" 1247582 T INT8 (NIL) -8 NIL NIL 1247590) (-547 1246595 1247008 1247036 "INT32" 1247041 T INT32 (NIL) -8 NIL NIL 1247049) (-546 1246054 1246467 1246495 "INT16" 1246500 T INT16 (NIL) -8 NIL NIL 1246508) (-545 1241069 1243743 1243771 "INS" 1244705 T INS (NIL) -9 NIL 1245370 NIL) (-544 1238309 1239080 1240054 "INS-" 1240127 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237084 1237311 1237609 "INPSIGN" 1238062 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1236202 1236319 1236516 "INPRODPF" 1236964 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235096 1235213 1235450 "INPRODFF" 1236082 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234096 1234248 1234508 "INNMFACT" 1234932 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1233293 1233390 1233578 "INMODGCD" 1233995 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1231802 1232046 1232370 "INFSP" 1233038 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1230986 1231103 1231286 "INFPROD0" 1231682 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1227868 1229051 1229566 "INFORM" 1230479 T INFORM (NIL) -8 NIL NIL NIL) (-535 1227478 1227538 1227636 "INFORM1" 1227803 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227001 1227090 1227204 "INFINITY" 1227384 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1226177 1226721 1226822 "INETCLTS" 1226920 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1224794 1225043 1225364 "INEP" 1225925 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224070 1224691 1224756 "INDE" 1224761 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1223634 1223702 1223819 "INCRMAPS" 1223997 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1222452 1222903 1223109 "INBFILE" 1223448 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1217763 1218688 1219632 "INBFF" 1221540 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1216671 1216940 1216968 "INBCON" 1217481 T INBCON (NIL) -9 NIL 1217747 NIL) (-526 1215923 1216146 1216422 "INBCON-" 1216427 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1215425 1215644 1215736 "INAST" 1215851 T INAST (NIL) -8 NIL NIL NIL) (-524 1214879 1215104 1215210 "IMPTAST" 1215339 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1211373 1214723 1214827 "IMATRIX" 1214832 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210085 1210208 1210523 "IMATQF" 1211229 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1208305 1208532 1208869 "IMATLIN" 1209841 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1202931 1208229 1208287 "ILIST" 1208292 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1200884 1202791 1202904 "IIARRAY2" 1202909 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1196317 1200795 1200859 "IFF" 1200864 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1195691 1195934 1196050 "IFAST" 1196221 T IFAST (NIL) -8 NIL NIL NIL) (-516 1190734 1194983 1195171 "IFARRAY" 1195548 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1189941 1190638 1190711 "IFAMON" 1190716 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1189525 1189590 1189644 "IEVALAB" 1189851 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1189200 1189268 1189428 "IEVALAB-" 1189433 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1188858 1189114 1189177 "IDPO" 1189182 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188135 1188747 1188822 "IDPOAMS" 1188827 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1187469 1188024 1188099 "IDPOAM" 1188104 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1186554 1186804 1186857 "IDPC" 1187270 NIL IDPC (NIL T T) -9 NIL 1187419 NIL) (-508 1186050 1186446 1186519 "IDPAM" 1186524 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1185453 1185942 1186015 "IDPAG" 1186020 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1185221 1185368 1185418 "IDENT" 1185423 T IDENT (NIL) -8 NIL NIL NIL) (-505 1181476 1182324 1183219 "IDECOMP" 1184378 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1174350 1175399 1176446 "IDEAL" 1180512 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1173514 1173626 1173825 "ICDEN" 1174234 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1172613 1172994 1173141 "ICARD" 1173387 T ICARD (NIL) -8 NIL NIL NIL) (-501 1170673 1170986 1171391 "IBPTOOLS" 1172290 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1166307 1170293 1170406 "IBITS" 1170592 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163030 1163606 1164301 "IBATOOL" 1165724 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1160810 1161271 1161804 "IBACHIN" 1162565 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1158687 1160656 1160759 "IARRAY2" 1160764 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1154840 1158613 1158670 "IARRAY1" 1158675 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1148834 1153252 1153733 "IAN" 1154379 T IAN (NIL) -8 NIL NIL NIL) (-494 1148345 1148402 1148575 "IALGFACT" 1148771 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1147873 1147986 1148014 "HYPCAT" 1148221 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1147411 1147528 1147714 "HYPCAT-" 1147719 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147033 1147206 1147289 "HOSTNAME" 1147348 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1146878 1146915 1146956 "HOMOTOP" 1146961 NIL HOMOTOP (NIL T) -9 NIL 1146994 NIL) (-489 1143557 1144888 1144929 "HOAGG" 1145910 NIL HOAGG (NIL T) -9 NIL 1146589 NIL) (-488 1142151 1142550 1143076 "HOAGG-" 1143081 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136190 1141746 1141895 "HEXADEC" 1142022 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1134938 1135160 1135423 "HEUGCD" 1135967 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134041 1134775 1134905 "HELLFDIV" 1134910 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1132269 1133818 1133906 "HEAP" 1133985 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1131560 1131821 1131955 "HEADAST" 1132155 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1125480 1131475 1131537 "HDP" 1131542 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119231 1125115 1125267 "HDMP" 1125381 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1118556 1118695 1118859 "HB" 1119087 T HB (NIL) -7 NIL NIL NIL) (-479 1112053 1118402 1118506 "HASHTBL" 1118511 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1111556 1111774 1111866 "HASAST" 1111981 T HASAST (NIL) -8 NIL NIL NIL) (-477 1109369 1111178 1111360 "HACKPI" 1111394 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105064 1109222 1109335 "GTSET" 1109340 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1098590 1104942 1105040 "GSTBL" 1105045 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1090903 1097621 1097886 "GSERIES" 1098381 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090070 1090461 1090489 "GROUP" 1090692 T GROUP (NIL) -9 NIL 1090826 NIL) (-472 1089436 1089595 1089846 "GROUP-" 1089851 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1087805 1088124 1088511 "GROEBSOL" 1089113 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1086745 1087007 1087058 "GRMOD" 1087587 NIL GRMOD (NIL T T) -9 NIL 1087755 NIL) (-469 1086513 1086549 1086677 "GRMOD-" 1086682 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1081839 1082867 1083867 "GRIMAGE" 1085533 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1080306 1080566 1080890 "GRDEF" 1081535 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1079750 1079866 1080007 "GRAY" 1080185 T GRAY (NIL) -7 NIL NIL NIL) (-465 1078963 1079343 1079394 "GRALG" 1079547 NIL GRALG (NIL T T) -9 NIL 1079640 NIL) (-464 1078624 1078697 1078860 "GRALG-" 1078865 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1075428 1078209 1078387 "GPOLSET" 1078531 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1074782 1074839 1075097 "GOSPER" 1075365 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1070541 1071220 1071746 "GMODPOL" 1074481 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1069546 1069730 1069968 "GHENSEL" 1070353 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1063597 1064440 1065467 "GENUPS" 1068630 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1063294 1063345 1063434 "GENUFACT" 1063540 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1062706 1062783 1062948 "GENPGCD" 1063212 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062180 1062215 1062428 "GENMFACT" 1062665 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1060748 1061003 1061310 "GENEEZ" 1061923 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1054661 1060359 1060521 "GDMP" 1060671 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044038 1048432 1049538 "GCNAALG" 1053644 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1042465 1043293 1043321 "GCDDOM" 1043576 T GCDDOM (NIL) -9 NIL 1043733 NIL) (-451 1041935 1042062 1042277 "GCDDOM-" 1042282 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1040607 1040792 1041096 "GB" 1041714 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029227 1031553 1033945 "GBINTERN" 1038298 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027064 1027356 1027777 "GBF" 1028902 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1025845 1026010 1026277 "GBEUCLID" 1026880 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025194 1025319 1025468 "GAUSSFAC" 1025716 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1023561 1023863 1024177 "GALUTIL" 1024913 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1021869 1022143 1022467 "GALPOLYU" 1023288 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019234 1019524 1019931 "GALFACTU" 1021566 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011040 1012539 1014147 "GALFACT" 1017666 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1008428 1009086 1009114 "FVFUN" 1010270 T FVFUN (NIL) -9 NIL 1010990 NIL) (-440 1007694 1007876 1007904 "FVC" 1008195 T FVC (NIL) -9 NIL 1008378 NIL) (-439 1007364 1007519 1007587 "FUNDESC" 1007646 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007006 1007161 1007242 "FUNCTION" 1007316 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1004777 1005328 1005794 "FT" 1006560 T FT (NIL) -8 NIL NIL NIL) (-436 1003595 1004078 1004281 "FTEM" 1004594 T FTEM (NIL) -8 NIL NIL NIL) (-435 1001851 1002140 1002544 "FSUPFACT" 1003286 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000248 1000537 1000869 "FST" 1001539 T FST (NIL) -8 NIL NIL NIL) (-433 999419 999525 999720 "FSRED" 1000130 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998098 998353 998707 "FSPRMELT" 999134 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995183 995621 996120 "FSPECF" 997661 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977243 985686 985726 "FS" 989574 NIL FS (NIL T) -9 NIL 991863 NIL) (-429 965893 968883 972939 "FS-" 973236 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 965407 965461 965638 "FSINT" 965834 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 963734 964400 964703 "FSERIES" 965186 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 962748 962864 963095 "FSCINT" 963614 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 958982 961692 961733 "FSAGG" 962103 NIL FSAGG (NIL T) -9 NIL 962362 NIL) (-424 956744 957345 958141 "FSAGG-" 958236 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 955786 955929 956156 "FSAGG2" 956597 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 953441 953720 954274 "FS2UPS" 955504 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953023 953066 953221 "FS2" 953392 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 951880 952051 952360 "FS2EXPXP" 952848 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951306 951421 951573 "FRUTIL" 951760 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 942761 946801 948159 "FR" 949980 NIL FR (NIL T) -8 NIL NIL NIL) (-417 937836 940479 940519 "FRNAALG" 941915 NIL FRNAALG (NIL T) -9 NIL 942522 NIL) (-416 933514 934585 935860 "FRNAALG-" 936610 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933152 933195 933322 "FRNAAF2" 933465 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 931559 932006 932301 "FRMOD" 932964 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929338 929942 930259 "FRIDEAL" 931350 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 928533 928620 928909 "FRIDEAL2" 929245 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 927666 928080 928121 "FRETRCT" 928126 NIL FRETRCT (NIL T) -9 NIL 928302 NIL) (-410 926778 927009 927360 "FRETRCT-" 927365 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 923990 925166 925225 "FRAMALG" 926107 NIL FRAMALG (NIL T T) -9 NIL 926399 NIL) (-408 922124 922579 923209 "FRAMALG-" 923432 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916082 921599 921875 "FRAC" 921880 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 915718 915775 915882 "FRAC2" 916019 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915354 915411 915518 "FR2" 915655 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910027 912879 912907 "FPS" 914026 T FPS (NIL) -9 NIL 914583 NIL) (-403 909476 909585 909749 "FPS-" 909895 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 906930 908565 908593 "FPC" 908818 T FPC (NIL) -9 NIL 908960 NIL) (-401 906723 906763 906860 "FPC-" 906865 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 905601 906211 906252 "FPATMAB" 906257 NIL FPATMAB (NIL T) -9 NIL 906409 NIL) (-399 903301 903777 904203 "FPARFRAC" 905238 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 898695 899193 899875 "FORTRAN" 902733 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 896411 896911 897450 "FORT" 898176 T FORT (NIL) -7 NIL NIL NIL) (-396 894087 894649 894677 "FORTFN" 895737 T FORTFN (NIL) -9 NIL 896361 NIL) (-395 893851 893901 893929 "FORTCAT" 893988 T FORTCAT (NIL) -9 NIL 894050 NIL) (-394 891984 892467 892857 "FORMULA" 893481 T FORMULA (NIL) -8 NIL NIL NIL) (-393 891772 891802 891871 "FORMULA1" 891948 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891295 891347 891520 "FORDER" 891714 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 890391 890555 890748 "FOP" 891122 T FOP (NIL) -7 NIL NIL NIL) (-390 888999 889671 889845 "FNLA" 890273 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 887754 888143 888171 "FNCAT" 888631 T FNCAT (NIL) -9 NIL 888891 NIL) (-388 887320 887713 887741 "FNAME" 887746 T FNAME (NIL) -8 NIL NIL NIL) (-387 885983 886912 886940 "FMTC" 886945 T FMTC (NIL) -9 NIL 886981 NIL) (-386 882345 883506 884135 "FMONOID" 885387 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 881564 882087 882236 "FM" 882241 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 878988 879634 879662 "FMFUN" 880806 T FMFUN (NIL) -9 NIL 881514 NIL) (-383 878257 878438 878466 "FMC" 878756 T FMC (NIL) -9 NIL 878938 NIL) (-382 875451 876285 876339 "FMCAT" 877534 NIL FMCAT (NIL T T) -9 NIL 878029 NIL) (-381 874344 875217 875317 "FM1" 875396 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872118 872534 873028 "FLOATRP" 873895 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 865742 869847 870468 "FLOAT" 871517 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863180 863680 864258 "FLOATCP" 865209 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 861989 862793 862834 "FLINEXP" 862839 NIL FLINEXP (NIL T) -9 NIL 862932 NIL) (-376 861143 861378 861706 "FLINEXP-" 861711 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860219 860363 860587 "FLASORT" 860995 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 857436 858278 858330 "FLALG" 859557 NIL FLALG (NIL T T) -9 NIL 860024 NIL) (-373 851220 854922 854963 "FLAGG" 856225 NIL FLAGG (NIL T) -9 NIL 856877 NIL) (-372 849946 850285 850775 "FLAGG-" 850780 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 848988 849131 849358 "FLAGG2" 849799 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 845963 846937 846996 "FINRALG" 848124 NIL FINRALG (NIL T T) -9 NIL 848632 NIL) (-369 845123 845352 845691 "FINRALG-" 845696 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 844529 844742 844770 "FINITE" 844966 T FINITE (NIL) -9 NIL 845073 NIL) (-367 836987 839148 839188 "FINAALG" 842855 NIL FINAALG (NIL T) -9 NIL 844308 NIL) (-366 832328 833369 834513 "FINAALG-" 835892 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 831723 832083 832186 "FILE" 832258 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830407 830719 830773 "FILECAT" 831457 NIL FILECAT (NIL T T) -9 NIL 831673 NIL) (-363 828275 829769 829797 "FIELD" 829837 T FIELD (NIL) -9 NIL 829917 NIL) (-362 826895 827280 827791 "FIELD-" 827796 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 824773 825530 825877 "FGROUP" 826581 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 823863 824027 824247 "FGLMICPK" 824605 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 819730 823788 823845 "FFX" 823850 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819331 819392 819527 "FFSLPE" 819663 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815324 816103 816899 "FFPOLY" 818567 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 814828 814864 815073 "FFPOLY2" 815282 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 810714 814747 814810 "FFP" 814815 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806147 810625 810689 "FF" 810694 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801308 805490 805680 "FFNBX" 806001 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796282 800443 800701 "FFNBP" 801162 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 790950 795566 795777 "FFNB" 796115 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 789782 789980 790295 "FFINTBAS" 790747 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786010 788189 788217 "FFIELDC" 788837 T FFIELDC (NIL) -9 NIL 789213 NIL) (-348 784673 785043 785540 "FFIELDC-" 785545 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784243 784288 784412 "FFHOM" 784615 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 781941 782425 782942 "FFF" 783758 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 777594 781683 781784 "FFCGX" 781884 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773261 777326 777433 "FFCGP" 777537 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768479 772988 773096 "FFCG" 773197 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750312 759350 759436 "FFCAT" 764601 NIL FFCAT (NIL T T T) -9 NIL 766052 NIL) (-341 745510 746557 747871 "FFCAT-" 749101 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 744921 744964 745199 "FFCAT2" 745461 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734133 737893 739113 "FEXPR" 743773 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733133 733568 733609 "FEVALAB" 733693 NIL FEVALAB (NIL T) -9 NIL 733954 NIL) (-337 732292 732502 732840 "FEVALAB-" 732845 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 730885 731675 731878 "FDIV" 732191 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 727951 728666 728781 "FDIVCAT" 730349 NIL FDIVCAT (NIL T T T T) -9 NIL 730786 NIL) (-334 727713 727740 727910 "FDIVCAT-" 727915 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 726933 727020 727297 "FDIV2" 727620 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 725619 725878 726167 "FCPAK1" 726664 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 724747 725119 725260 "FCOMP" 725510 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708484 711897 715435 "FC" 721229 T FC (NIL) -8 NIL NIL NIL) (-329 701063 705048 705088 "FAXF" 706890 NIL FAXF (NIL T) -9 NIL 707582 NIL) (-328 698342 698997 699822 "FAXF-" 700287 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693442 697718 697894 "FARRAY" 698199 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 688695 690727 690780 "FAMR" 691803 NIL FAMR (NIL T T) -9 NIL 692263 NIL) (-325 687585 687887 688322 "FAMR-" 688327 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 686781 687507 687560 "FAMONOID" 687565 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684593 685277 685330 "FAMONC" 686271 NIL FAMONC (NIL T T) -9 NIL 686657 NIL) (-322 683285 684347 684484 "FAGROUP" 684489 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681080 681399 681802 "FACUTIL" 682966 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680179 680364 680586 "FACTFUNC" 680890 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672584 679430 679642 "EXPUPXS" 680035 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670067 670607 671193 "EXPRTUBE" 672018 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666261 666853 667590 "EXPRODE" 669406 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651635 664916 665344 "EXPR" 665865 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646042 646629 647442 "EXPR2UPS" 650933 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 645678 645735 645842 "EXPR2" 645979 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637083 644810 645107 "EXPEXPAN" 645515 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 636910 637040 637069 "EXIT" 637074 T EXIT (NIL) -8 NIL NIL NIL) (-311 636417 636634 636725 "EXITAST" 636839 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636044 636106 636219 "EVALCYC" 636349 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635585 635703 635744 "EVALAB" 635914 NIL EVALAB (NIL T) -9 NIL 636018 NIL) (-308 635066 635188 635409 "EVALAB-" 635414 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632534 633802 633830 "EUCDOM" 634385 T EUCDOM (NIL) -9 NIL 634735 NIL) (-306 630939 631381 631971 "EUCDOM-" 631976 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618479 621237 623987 "ESTOOLS" 628209 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618111 618168 618277 "ESTOOLS2" 618416 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 617862 617904 617984 "ESTOOLS1" 618063 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 611767 613495 613523 "ES" 616291 T ES (NIL) -9 NIL 617700 NIL) (-301 606715 608001 609818 "ES-" 609982 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603090 603850 604630 "ESCONT" 605955 T ESCONT (NIL) -7 NIL NIL NIL) (-299 602835 602867 602949 "ESCONT1" 603052 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602510 602560 602660 "ES2" 602779 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602140 602198 602307 "ES1" 602446 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601356 601485 601661 "ERROR" 601984 T ERROR (NIL) -7 NIL NIL NIL) (-295 594859 601215 601306 "EQTBL" 601311 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587416 590173 591622 "EQ" 593443 NIL -3299 (NIL T) -8 NIL NIL NIL) (-293 587048 587105 587214 "EQ2" 587353 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582340 583386 584479 "EP" 585987 NIL EP (NIL T) -7 NIL NIL NIL) (-291 580922 581223 581540 "ENV" 582043 T ENV (NIL) -8 NIL NIL NIL) (-290 580101 580621 580649 "ENTIRER" 580654 T ENTIRER (NIL) -9 NIL 580700 NIL) (-289 576603 578056 578426 "EMR" 579900 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 575747 575932 575986 "ELTAGG" 576366 NIL ELTAGG (NIL T T) -9 NIL 576577 NIL) (-287 575466 575528 575669 "ELTAGG-" 575674 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575255 575284 575338 "ELTAB" 575422 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574381 574527 574726 "ELFUTS" 575106 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574123 574179 574207 "ELEMFUN" 574312 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 573993 574014 574082 "ELEMFUN-" 574087 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 568884 572093 572134 "ELAGG" 573074 NIL ELAGG (NIL T) -9 NIL 573537 NIL) (-281 567169 567603 568266 "ELAGG-" 568271 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 565826 566106 566401 "ELABEXPR" 566894 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 558692 560493 561320 "EFUPXS" 565102 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552142 553943 554753 "EFULS" 557968 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549564 549922 550401 "EFSTRUC" 551774 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538636 540201 541761 "EF" 548079 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 537737 538121 538270 "EAB" 538507 T EAB (NIL) -8 NIL NIL NIL) (-274 536946 537696 537724 "E04UCFA" 537729 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536155 536905 536933 "E04NAFA" 536938 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535364 536114 536142 "E04MBFA" 536147 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534573 535323 535351 "E04JAFA" 535356 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 533784 534532 534560 "E04GCFA" 534565 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 532995 533743 533771 "E04FDFA" 533776 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532204 532954 532982 "E04DGFA" 532987 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526382 527729 529093 "E04AGNT" 530860 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525088 525568 525608 "DVARCAT" 526083 NIL DVARCAT (NIL T) -9 NIL 526282 NIL) (-265 524292 524504 524818 "DVARCAT-" 524823 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517192 524091 524220 "DSMP" 524225 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512002 513137 514205 "DROPT" 516144 T DROPT (NIL) -8 NIL NIL NIL) (-262 511667 511726 511824 "DROPT1" 511937 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 506782 507908 509045 "DROPT0" 510550 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505127 505452 505838 "DRAWPT" 506416 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 499714 500637 501716 "DRAW" 504101 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499347 499400 499518 "DRAWHACK" 499655 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498078 498347 498638 "DRAWCX" 499076 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497594 497662 497813 "DRAWCURV" 498004 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488065 490024 492139 "DRAWCFUN" 495499 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 484878 486760 486801 "DQAGG" 487430 NIL DQAGG (NIL T) -9 NIL 487703 NIL) (-253 473157 479856 479939 "DPOLCAT" 481791 NIL DPOLCAT (NIL T T T T) -9 NIL 482336 NIL) (-252 467996 469342 471300 "DPOLCAT-" 471305 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461151 467857 467955 "DPMO" 467960 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454209 460931 461098 "DPMM" 461103 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 453841 454128 454176 "DOMCTOR" 454181 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453136 453363 453500 "DOMAIN" 453724 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 446887 452771 452923 "DMP" 453037 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446487 446543 446687 "DLP" 446825 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440357 445814 446004 "DLIST" 446329 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437201 439210 439251 "DLAGG" 439801 NIL DLAGG (NIL T) -9 NIL 440031 NIL) (-243 436014 436644 436672 "DIVRING" 436764 T DIVRING (NIL) -9 NIL 436847 NIL) (-242 435251 435441 435741 "DIVRING-" 435746 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433353 433710 434116 "DISPLAY" 434865 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427295 433267 433330 "DIRPROD" 433335 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426143 426346 426611 "DIRPROD2" 427088 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415406 421358 421411 "DIRPCAT" 421821 NIL DIRPCAT (NIL NIL T) -9 NIL 422661 NIL) (-237 412732 413374 414255 "DIRPCAT-" 414592 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412019 412179 412365 "DIOSP" 412566 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408721 410931 410972 "DIOPS" 411406 NIL DIOPS (NIL T) -9 NIL 411635 NIL) (-234 408270 408384 408575 "DIOPS-" 408580 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407162 407756 407784 "DIFRING" 407971 T DIFRING (NIL) -9 NIL 408081 NIL) (-232 406808 406885 407037 "DIFRING-" 407042 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404613 405851 405892 "DIFEXT" 406255 NIL DIFEXT (NIL T) -9 NIL 406549 NIL) (-230 402898 403326 403992 "DIFEXT-" 403997 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400220 402430 402471 "DIAGG" 402476 NIL DIAGG (NIL T) -9 NIL 402496 NIL) (-228 399604 399761 400013 "DIAGG-" 400018 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395069 398563 398840 "DHMATRIX" 399373 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390681 391590 392600 "DFSFUN" 394079 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 385797 389612 389924 "DFLOAT" 390389 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384025 384306 384702 "DFINTTLS" 385505 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381090 382046 382446 "DERHAM" 383691 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 378939 380865 380954 "DEQUEUE" 381034 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378154 378287 378483 "DEGRED" 378801 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374549 375294 376147 "DEFINTRF" 377382 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372076 372545 373144 "DEFINTEF" 374068 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371453 371696 371811 "DEFAST" 371981 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365492 371048 371197 "DECIMAL" 371324 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363004 363462 363968 "DDFACT" 365036 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362600 362643 362794 "DBLRESP" 362955 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360499 360833 361193 "DBASE" 362367 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359768 359979 360125 "DATAARY" 360398 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 358901 359727 359755 "D03FAFA" 359760 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358035 358860 358888 "D03EEFA" 358893 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 355985 356451 356940 "D03AGNT" 357566 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355301 355944 355972 "D02EJFA" 355977 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354617 355260 355288 "D02CJFA" 355293 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 353933 354576 354604 "D02BHFA" 354609 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353249 353892 353920 "D02BBFA" 353925 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346447 348035 349641 "D02AGNT" 351663 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344216 344738 345284 "D01WGTS" 345921 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343311 344175 344203 "D01TRNS" 344208 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342406 343270 343298 "D01GBFA" 343303 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341501 342365 342393 "D01FCFA" 342398 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340596 341460 341488 "D01ASFA" 341493 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339691 340555 340583 "D01AQFA" 340588 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338786 339650 339678 "D01APFA" 339683 T D01APFA (NIL) -8 NIL NIL NIL) (-197 337881 338745 338773 "D01ANFA" 338778 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 336976 337840 337868 "D01AMFA" 337873 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336071 336935 336963 "D01ALFA" 336968 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335166 336030 336058 "D01AKFA" 336063 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334261 335125 335153 "D01AJFA" 335158 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327558 329109 330670 "D01AGNT" 332720 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 326895 327023 327175 "CYCLOTOM" 327426 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323630 324343 325070 "CYCLES" 326188 T CYCLES (NIL) -7 NIL NIL NIL) (-189 322942 323076 323247 "CVMP" 323491 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320713 320971 321347 "CTRIGMNP" 322670 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320204 320504 320578 "CTOR" 320659 T CTOR (NIL) -8 NIL NIL NIL) (-186 319740 319935 320036 "CTORKIND" 320123 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319088 319347 319375 "CTORCAT" 319557 T CTORCAT (NIL) -9 NIL 319670 NIL) (-184 318686 318797 318956 "CTORCAT-" 318961 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318202 318389 318487 "CTORCALL" 318608 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317576 317675 317828 "CSTTOOLS" 318099 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313375 314032 314790 "CRFP" 316888 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 312877 313096 313188 "CRCEAST" 313303 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 311924 312109 312337 "CRAPACK" 312681 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311308 311409 311613 "CPMATCH" 311800 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311033 311061 311167 "CPIMA" 311274 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307397 308069 308787 "COORDSYS" 310368 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 306781 306910 307060 "CONTOUR" 307267 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302707 304784 305276 "CONTFRAC" 306321 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302587 302608 302636 "CONDUIT" 302673 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301760 302280 302308 "COMRING" 302313 T COMRING (NIL) -9 NIL 302365 NIL) (-171 300841 301118 301302 "COMPPROP" 301596 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300502 300537 300665 "COMPLPAT" 300800 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290559 300311 300420 "COMPLEX" 300425 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290195 290252 290359 "COMPLEX2" 290496 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 289913 289948 290046 "COMPFACT" 290154 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274075 284295 284335 "COMPCAT" 285339 NIL COMPCAT (NIL T) -9 NIL 286735 NIL) (-165 263591 266514 270141 "COMPCAT-" 270497 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263320 263348 263451 "COMMUPC" 263557 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263115 263148 263207 "COMMONOP" 263281 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262698 262866 262953 "COMM" 263048 T COMM (NIL) -8 NIL NIL NIL) (-161 262302 262502 262577 "COMMAAST" 262643 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261551 261745 261773 "COMBOPC" 262111 T COMBOPC (NIL) -9 NIL 262286 NIL) (-159 260447 260657 260899 "COMBINAT" 261341 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256645 257218 257858 "COMBF" 259869 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255431 255761 255996 "COLOR" 256430 T COLOR (NIL) -8 NIL NIL NIL) (-156 254934 255152 255244 "COLONAST" 255359 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254574 254621 254746 "CMPLXRT" 254881 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254049 254274 254373 "CLLCTAST" 254495 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249551 250579 251659 "CLIP" 252989 T CLIP (NIL) -7 NIL NIL NIL) (-152 247933 248657 248896 "CLIF" 249378 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244155 246079 246120 "CLAGG" 247049 NIL CLAGG (NIL T) -9 NIL 247585 NIL) (-150 242577 243034 243617 "CLAGG-" 243622 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242121 242206 242346 "CINTSLPE" 242486 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239622 240093 240641 "CHVAR" 241649 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 238865 239385 239413 "CHARZ" 239418 T CHARZ (NIL) -9 NIL 239433 NIL) (-146 238619 238659 238737 "CHARPOL" 238819 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237746 238299 238327 "CHARNZ" 238374 T CHARNZ (NIL) -9 NIL 238430 NIL) (-144 235735 236436 236771 "CHAR" 237431 T CHAR (NIL) -8 NIL NIL NIL) (-143 235461 235522 235550 "CFCAT" 235661 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234706 234817 234999 "CDEN" 235345 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230698 233859 234139 "CCLASS" 234446 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230005 230148 230311 "CATEGORY" 230555 T -10 (NIL) -8 NIL NIL NIL) (-139 229637 229924 229972 "CATCTOR" 229977 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229111 229337 229436 "CATAST" 229558 T CATAST (NIL) -8 NIL NIL NIL) (-137 228614 228832 228924 "CASEAST" 229039 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223666 224643 225396 "CARTEN" 227917 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222774 222922 223143 "CARTEN2" 223513 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221116 221924 222181 "CARD" 222537 T CARD (NIL) -8 NIL NIL NIL) (-133 220719 220920 220995 "CAPSLAST" 221061 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220091 220419 220447 "CACHSET" 220579 T CACHSET (NIL) -9 NIL 220656 NIL) (-131 219587 219883 219911 "CABMON" 219961 T CABMON (NIL) -9 NIL 220017 NIL) (-130 219087 219291 219401 "BYTEORD" 219497 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218110 218633 218769 "BYTE" 218932 T BYTE (NIL) -8 NIL NIL 219048) (-128 213519 217578 217741 "BYTEBUF" 217967 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211076 213211 213318 "BTREE" 213445 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208574 210724 210846 "BTOURN" 210986 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205991 208044 208085 "BTCAT" 208153 NIL BTCAT (NIL T) -9 NIL 208230 NIL) (-124 205658 205738 205887 "BTCAT-" 205892 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200950 204801 204829 "BTAGG" 205051 T BTAGG (NIL) -9 NIL 205212 NIL) (-122 200440 200565 200771 "BTAGG-" 200776 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197484 199718 199933 "BSTREE" 200257 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196622 196748 196932 "BRILL" 197340 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193321 195348 195389 "BRAGG" 196038 NIL BRAGG (NIL T) -9 NIL 196296 NIL) 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NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 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diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase
index cc1eb45f..c3fec088 100644
--- a/src/share/algebra/operation.daase
+++ b/src/share/algebra/operation.daase
@@ -1,3164 +1,2565 @@
-(735629 . 3442698066)
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(-12
(-5 *3
- (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224)))
- (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224))
- (|:| |relerr| (-224))))
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(-5 *2
(-3 (|:| |continuous| "Continuous at the end points")
(|:| |lowerSingular|
@@ -3167,6663 +2568,6672 @@
"There is a singularity at the upper end point")
(|:| |bothSingular| "There are singularities at both end points")
(|:| |notEvaluated| "End point continuity not yet evaluated")))
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(-12
(-5 *3
- (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224)))
- (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224))
- (|:| |relerr| (-224))))
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(-5 *2
(-2
(|:| |endPointContinuity|
@@ -9837,2898 +9247,3245 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1148 (-224)))
+ (-3 (|:| |str| (-1149 (-225)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -2147
+ (|:| -2516
(-3 (|:| |finite| "The range is finite")
(|:| |lowerInfinite| "The bottom of range is infinite")
(|:| |upperInfinite| "The top of range is infinite")
(|:| |bothInfinite|
"Both top and bottom points are infinite")
(|:| |notEvaluated| "Range not yet evaluated")))))
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+ (-12 (|has| *1 (-6 -4407)) (-4 *1 (-601 *4 *3)) (-4 *4 (-1093))
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+ (-4 *4 (-373 *3)) (-4 *5 (-373 *3))))
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+ ((*1 *1 *2)
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+ (-4 *5 (-238 *3 *4)) (-4 *6 (-238 *3 *4)))))
(((*1 *2 *3)
(-12
(-5 *3
@@ -12744,2915 +12501,1294 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1148 (-224)))
+ (-3 (|:| |str| (-1149 (-225)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -2147
+ (|:| -2516
(-3 (|:| |finite| "The range is finite")
(|:| |lowerInfinite| "The bottom of range is infinite")
(|:| |upperInfinite| "The top of range is infinite")
(|:| |bothInfinite|
"Both top and bottom points are infinite")
(|:| |notEvaluated| "Range not yet evaluated")))))
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- (-4 *3 (-1058 *4 *5 *6)))))
-(((*1 *1 *1)
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(((*1 *2 *3)
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(((*1 *1 *2)
(-12
(-5 *2
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+ (-640
+ (-2
+ (|:| -2387
+ (-2 (|:| |xinit| (-225)) (|:| |xend| (-225))
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+ (-12 (-5 *3 (-684 (-169 (-407 (-563)))))
+ (-5 *2
+ (-640
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(((*1 *1 *2)
(-12
(-5 *2
- (-639
+ (-640
(-2
- (|:| -2319
- (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224)))
- (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224))
- (|:| |relerr| (-224))))
- (|:| -2693
+ (|:| -2387
+ (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225)))
+ (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225))
+ (|:| |relerr| (-225))))
+ (|:| -2557
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -15665,10 +13801,10 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1148 (-224)))
+ (-3 (|:| |str| (-1149 (-225)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -2147
+ (|:| -2516
(-3 (|:| |finite| "The range is finite")
(|:| |lowerInfinite|
"The bottom of range is infinite")
@@ -15676,77 +13812,469 @@
(|:| |bothInfinite|
"Both top and bottom points are infinite")
(|:| |notEvaluated| "Range not yet evaluated"))))))))
- (-5 *1 (-557)))))
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+ (-4 *6 (-342 *3 *4 *5)))))
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+(((*1 *2 *1) (-12 (-5 *2 (-1262)) (-5 *1 (-818)))))
+(((*1 *2 *3)
+ (|partial| -12
+ (-5 *3
+ (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225)))
+ (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225))
+ (|:| |relerr| (-225))))
+ (-5 *2
+ (-2
+ (|:| |endPointContinuity|
+ (-3 (|:| |continuous| "Continuous at the end points")
+ (|:| |lowerSingular|
+ "There is a singularity at the lower end point")
+ (|:| |upperSingular|
+ "There is a singularity at the upper end point")
+ (|:| |bothSingular|
+ "There are singularities at both end points")
+ (|:| |notEvaluated|
+ "End point continuity not yet evaluated")))
+ (|:| |singularitiesStream|
+ (-3 (|:| |str| (-1149 (-225)))
+ (|:| |notEvaluated|
+ "Internal singularities not yet evaluated")))
+ (|:| -2516
+ (-3 (|:| |finite| "The range is finite")
+ (|:| |lowerInfinite| "The bottom of range is infinite")
+ (|:| |upperInfinite| "The top of range is infinite")
+ (|:| |bothInfinite|
+ "Both top and bottom points are infinite")
+ (|:| |notEvaluated| "Range not yet evaluated")))))
+ (-5 *1 (-558)))))
+(((*1 *1 *1) (-4 *1 (-35)))
+ ((*1 *2 *2)
+ (-12 (-4 *3 (-13 (-846) (-555))) (-5 *1 (-276 *3 *2))
+ (-4 *2 (-13 (-430 *3) (-998)))))
+ ((*1 *2 *2)
+ (-12 (-4 *3 (-38 (-407 (-563)))) (-4 *4 (-1248 *3))
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+ (-12 (-4 *2 (-363)) (-4 *3 (-789)) (-4 *4 (-846))
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+ (-4 *4 (-373 *2))))
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+ (-12 (-4 *4 (-555))
+ (-5 *2 (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| -3548 *3)))
+ (-5 *1 (-965 *4 *3)) (-4 *3 (-1233 *4)))))
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((*1 *1 *1 *1 *2)
- (-12 (-5 *2 (-562)) (-4 *1 (-281 *3)) (-4 *3 (-1207))))
+ (-12 (-5 *2 (-563)) (-4 *1 (-282 *3)) (-4 *3 (-1208))))
((*1 *1 *2 *1 *3)
- (-12 (-5 *3 (-562)) (-4 *1 (-281 *2)) (-4 *2 (-1207))))
+ (-12 (-5 *3 (-563)) (-4 *1 (-282 *2)) (-4 *2 (-1208))))
((*1 *1 *2)
(-12
(-5 *2
(-2
- (|:| -2319
- (-2 (|:| |var| (-1168)) (|:| |fn| (-315 (-224)))
- (|:| -2147 (-1086 (-838 (-224)))) (|:| |abserr| (-224))
- (|:| |relerr| (-224))))
- (|:| -2693
+ (|:| -2387
+ (-2 (|:| |var| (-1169)) (|:| |fn| (-316 (-225)))
+ (|:| -2516 (-1087 (-839 (-225)))) (|:| |abserr| (-225))
+ (|:| |relerr| (-225))))
+ (|:| -2557
(-2
(|:| |endPointContinuity|
(-3 (|:| |continuous| "Continuous at the end points")
@@ -15759,10 +14287,10 @@
(|:| |notEvaluated|
"End point continuity not yet evaluated")))
(|:| |singularitiesStream|
- (-3 (|:| |str| (-1148 (-224)))
+ (-3 (|:| |str| (-1149 (-225)))
(|:| |notEvaluated|
"Internal singularities not yet evaluated")))
- (|:| -2147
+ (|:| -2516
(-3 (|:| |finite| "The range is finite")
(|:| |lowerInfinite|
"The bottom of range is infinite")
@@ -15770,2596 +14298,4072 @@
(|:| |bothInfinite|
"Both top and bottom points are infinite")
(|:| |notEvaluated| "Range not yet evaluated")))))))
- (-5 *1 (-557))))
+ (-5 *1 (-558))))
((*1 *1 *2 *1 *3)
- (-12 (-5 *3 (-766)) (-4 *1 (-689 *2)) (-4 *2 (-1092))))
+ (-12 (-5 *3 (-767)) (-4 *1 (-690 *2)) (-4 *2 (-1093))))
((*1 *1 *2)
(-12
(-5 *2
(-2
- (|:| -2319
- (-2 (|:| |xinit| (-224)) (|:| |xend| (-224))
- (|:| |fn| (-1256 (-315 (-224)))) (|:| |yinit| (-639 (-224)))
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- (|:| -2693
- (-2 (|:| |stiffness| (-378)) (|:| |stability| (-378))
- (|:| |expense| (-378)) (|:| |accuracy| (-378))
- (|:| |intermediateResults| (-378))))))
- (-5 *1 (-798))))
- ((*1 *2 *3 *4)
- (-12 (-5 *2 (-1261)) (-5 *1 (-1184 *3 *4)) (-4 *3 (-1092))
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- (-12 (-5 *3 (-639 *6)) (-4 *1 (-944 *4 *5 *6)) (-4 *4 (-1044))
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- (-12 (-4 *1 (-855)) (-5 *2 (-685 (-129))) (-5 *3 (-129)))))
-(((*1 *2 *3 *4)
- (-12 (-4 *5 (-362)) (-4 *5 (-554))
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+ (-2 (|:| |xinit| (-225)) (|:| |xend| (-225))
+ (|:| |fn| (-1257 (-316 (-225)))) (|:| |yinit| (-640 (-225)))
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+ (-2 (|:| |stiffness| (-379)) (|:| |stability| (-379))
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+ (-5 *1 (-799))))
+ ((*1 *2 *3 *4)
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+ (-4 *4 (-1093)))))
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+ (-12 (-5 *3 (-563)) (-5 *4 (-1151)) (-5 *5 (-684 (-225)))
+ (-5 *2 (-1031)) (-5 *1 (-743)))))
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(-5 *2
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