diff options
| author | dos-reis <gdr@axiomatics.org> | 2010-07-19 07:27:31 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2010-07-19 07:27:31 +0000 |
| commit | 108ea45edebe23267cc7f4d8620f034fd1b39b81 (patch) | |
| tree | c6041cc375b9ea506df1a897a35d7335dbb0e2fa /src | |
| parent | 08966a5a24823ba5605d9baacebbbb95632842e2 (diff) | |
| download | open-axiom-108ea45edebe23267cc7f4d8620f034fd1b39b81.tar.gz | |
* interp/g-opt.boot ($VMsideEffectFreeOperators): Include
byte relation operators and bitmakst operators.
* interp/g-util.boot: Expand them.
* algebra/data.spad.pamphlet (Byte): Now satisfies Logic. Tidy.
(SystemNonNegativeInteger): Likewise.
* algebra/java.spad.pamphlet (JVMBytecode): Rename from JavaBytecode.
(JVMClassFileAccess): New.
(JVMFieldAccess): Likewise.
(JVMMethodAccess): Likewise.
(JVMConstantTag): Likewise.
(JVMOpcode): Likewise.
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 14 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 12 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 12 | ||||
| -rw-r--r-- | src/algebra/data.spad.pamphlet | 45 | ||||
| -rw-r--r-- | src/algebra/java.spad.pamphlet | 225 | ||||
| -rw-r--r-- | src/interp/g-opt.boot | 15 | ||||
| -rw-r--r-- | src/interp/g-util.boot | 27 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2726 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 4611 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1352 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 10606 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 33160 |
12 files changed, 26579 insertions, 26226 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 8ce51027..55a45813 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,17 @@ +2010-07-19 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * interp/g-opt.boot ($VMsideEffectFreeOperators): Include + byte relation operators and bitmakst operators. + * interp/g-util.boot: Expand them. + * algebra/data.spad.pamphlet (Byte): Now satisfies Logic. Tidy. + (SystemNonNegativeInteger): Likewise. + * algebra/java.spad.pamphlet (JVMBytecode): Rename from JavaBytecode. + (JVMClassFileAccess): New. + (JVMFieldAccess): Likewise. + (JVMMethodAccess): Likewise. + (JVMConstantTag): Likewise. + (JVMOpcode): Likewise. + 2010-07-18 Gabriel Dos Reis <gdr@cs.tamu.edu> * boot/tokens.boot: Add char? as builtin function. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 8577be6d..e2293479 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -537,6 +537,8 @@ $(OUT)/KTVLOGIC.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT) $(OUT)/BYTE.$(FASLEXT) $(OUT)/PROPFUN1.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) $(OUT)/PROPFUN2.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) $(OUT)/DIFEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT) +$(OUT)/BYTE.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/SYSNNI.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) $(OUT)/ORDFIN.$(FASLEXT) axiom_algebra_layer_6 = \ PROPFRML PROPFUN1 AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ @@ -797,7 +799,7 @@ axiom_algebra_layer_15 = \ FRAMALG FRAMALG- MDAGG ODPOL \ PLOT RMCAT2 ROIRC SDPOL \ ULS ULSCONS TUBETOOL UPXSCCA \ - UPXSCCA- JAVACODE POLY BYTEBUF OVERSET \ + UPXSCCA- JVMBCODE POLY BYTEBUF OVERSET \ ULSCCAT ULSCCAT- UTS UTSCAT UTSCAT- axiom_algebra_layer_15_nrlibs = \ @@ -994,7 +996,8 @@ axiom_algebra_layer_user = \ ASP20 ASP30 ASP31 ASP35 ASP41 ASP42 \ ASP74 ASP77 ASP80 ASP29 IRFORM COMPILER \ ITFORM ELABOR TALGOP YDIAGRAM LINELT DBASIS \ - LINFORM LINBASIS + LINFORM LINBASIS JVMOP JVMCFACC JVMFDACC JVMMDACC \ + JVMCSTTG axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) @@ -1081,6 +1084,11 @@ $(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT) $(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \ $(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT) +$(OUT)/JVMOP.$(FASLEXT): $(OUT)/JVMBCODE.$(FASLEXT) +$(OUT)/JVMCFACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/JVMFDACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/JVMMDACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) + .PHONY: all all-algebra mkdir-output-directory all: all-ax diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 06f10433..24d15915 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -521,6 +521,8 @@ $(OUT)/KTVLOGIC.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT) $(OUT)/BYTE.$(FASLEXT) $(OUT)/PROPFUN1.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) $(OUT)/PROPFUN2.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) $(OUT)/DIFEXT.$(FASLEXT): $(OUT)/DSEXT.$(FASLEXT) +$(OUT)/BYTE.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/SYSNNI.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) $(OUT)/ORDFIN.$(FASLEXT) axiom_algebra_layer_6 = \ PROPFRML PROPFUN1 AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ @@ -829,7 +831,7 @@ axiom_algebra_layer_15 = \ FRAMALG FRAMALG- MDAGG ODPOL \ PLOT RMCAT2 ROIRC SDPOL \ ULS ULSCONS TUBETOOL UPXSCCA \ - UPXSCCA- JAVACODE POLY BYTEBUF OVERSET \ + UPXSCCA- JVMBCODE POLY BYTEBUF OVERSET \ ULSCCAT ULSCCAT- UTS UTSCAT UTSCAT- axiom_algebra_layer_15_nrlibs = \ @@ -1073,7 +1075,8 @@ axiom_algebra_layer_user = \ ASP20 ASP30 ASP31 ASP35 ASP41 ASP42 \ ASP74 ASP77 ASP80 ASP29 IRFORM COMPILER \ ITFORM ELABOR TALGOP YDIAGRAM LINELT DBASIS \ - LINFORM LINBASIS + LINFORM LINBASIS JVMOP JVMCFACC JVMFDACC JVMMDACC \ + JVMCSTTG axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) @@ -1160,6 +1163,11 @@ $(OUT)/DBASIS.$(FASLEXT): $(OUT)/ORDFIN.$(FASLEXT) $(OUT)/KVTFROM.$(FASLEXT) $(OUT)/LINFORM.$(FASLEXT): $(OUT)/DBASIS.$(FASLEXT) \ $(OUT)/VSPACE.$(FASLEXT) $(OUT)/LINELT.$(FASLEXT) +$(OUT)/JVMOP.$(FASLEXT): $(OUT)/JVMBCODE.$(FASLEXT) +$(OUT)/JVMCFACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/JVMFDACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) +$(OUT)/JVMMDACC.$(FASLEXT): $(OUT)/LOGIC.$(FASLEXT) + @ \section{Broken Files} diff --git a/src/algebra/data.spad.pamphlet b/src/algebra/data.spad.pamphlet index 81f574cc..39576863 100644 --- a/src/algebra/data.spad.pamphlet +++ b/src/algebra/data.spad.pamphlet @@ -19,13 +19,13 @@ import OutputForm )abbrev domain BYTE Byte ++ Author: Gabriel Dos Reis ++ Date Created: April 19, 2008 -++ Date Last Updated: January 6, 2009 +++ Date Last Updated: July 18, 2010 ++ Basic Operations: byte, bitand, bitor, bitxor ++ Related Constructor: NonNegativeInteger ++ Description: ++ Byte is the datatype of 8-bit sized unsigned integer values. Byte(): Public == Private where - Public == Join(OrderedFinite, HomotopicTo Character) with + Public == Join(OrderedFinite, HomotopicTo Character,Logic) with byte: NonNegativeInteger -> % ++ byte(x) injects the unsigned integer value `v' into ++ the Byte algebra. `v' must be non-negative and less than 256. @@ -36,23 +36,35 @@ Byte(): Public == Private where sample: % ++ \spad{sample} gives a sample datum of type Byte. Private == SubDomain(NonNegativeInteger, #1 < 256) add + import %beq: (%,%) -> Boolean from Foreign Builtin + import %blt: (%,%) -> Boolean from Foreign Builtin + import %bgt: (%,%) -> Boolean from Foreign Builtin + import %ble: (%,%) -> Boolean from Foreign Builtin + import %bge: (%,%) -> Boolean from Foreign Builtin + import %bitand: (%,%) -> % from Foreign Builtin + import %bitior: (%,%) -> % from Foreign Builtin + import %bitnot: % -> % from Foreign Builtin + byte(x: NonNegativeInteger): % == per x sample = 0$Foreign(Builtin) coerce(c: Character) == per ord c coerce(x: %): Character == char rep x - x = y == byteEqual(x,y)$Foreign(Builtin) - x < y == byteLessThan(x,y)$Foreign(Builtin) - x > y == byteGreaterThan(x,y)$Foreign(Builtin) - x <= y == byteLessEqual(x,y)$Foreign(Builtin) - x >= y == byteGreaterEqual(x,y)$Foreign(Builtin) + x = y == %beq(x,y) + x < y == %blt(x,y) + x > y == %bgt(x,y) + x <= y == %ble(x,y) + x >= y == %bge(x,y) min() == per 0 max() == per 255 size() == 256 index n == byte((n - 1) pretend NonNegativeInteger) lookup x == (rep x + 1) pretend PositiveInteger random() == byte random(size())$NonNegativeInteger - bitand(x,y) == bitand(x,y)$Foreign(Builtin) - bitior(x,y) == bitior(x,y)$Foreign(Builtin) + bitand(x,y) == %bitand(x,y) + bitior(x,y) == %bitior(x,y) + x /\ y == bitand(x,y) + x \/ y == bitior(x,y) + ~ x == %bitnot x @ @@ -175,19 +187,26 @@ Int64() == SystemInteger 64 ++ with the hosting operating system, reading/writing external ++ binary format files. SystemNonNegativeInteger(N: PositiveInteger): Public == Private where - Public == OrderedFinite with + Public == Join(OrderedFinite,Logic) with bitand: (%,%) -> % ++ bitand(x,y) returns the bitwise `and' of `x' and `y'. bitior: (%,%) -> % - ++ bitor(x,y) returns the bitwise `inclusive or' of `x' and `y'. + ++ bitior(x,y) returns the bitwise `inclusive or' of `x' and `y'. sample: % ++ \spad{sample} gives a sample datum of type Byte. Private == SubDomain(NonNegativeInteger, length #1 <= N) add + import %bitand: (%,%) -> % from Foreign Builtin + import %bitior: (%,%) -> % from Foreign Builtin + import %bitnot: % -> % from Foreign Builtin + min == per 0 max == per((shift(1,N)-1)::NonNegativeInteger) sample == min - bitand(x,y) == BOOLE(BOOLE_-AND$Foreign(Builtin),x,y)$Foreign(Builtin) - bitior(x,y) == BOOLE(BOOLE_-IOR$Foreign(Builtin),x,y)$Foreign(Builtin) + bitand(x,y) == %bitand(x,y) + bitior(x,y) == %bitior(x,y) + x /\ y == bitand(x,y) + x \/ y == bitior(x,y) + ~ x == %bitnot x @ diff --git a/src/algebra/java.spad.pamphlet b/src/algebra/java.spad.pamphlet index fae7c311..d09d8607 100644 --- a/src/algebra/java.spad.pamphlet +++ b/src/algebra/java.spad.pamphlet @@ -11,16 +11,203 @@ \tableofcontents \eject -\section{The JavaBytecode domain} -<<domain JAVACODE JavaBytecode>>= -)abbrev domain JAVACODE JavaBytecode +\section{Class file access flags} + +<<domain JVMCFACC JVMClassFileAccess>>= +)abbrev domain JVMCFACC JVMClassFileAccess +++ Date Created: July 18, 2008 +++ Data Last Modified: July 18, 2010 +++ Description: JVM class file access bitmask and values. +JVMClassFileAccess(): Public == Private where + Public == Join(SetCategory,Logic) with + jvmPublic: % + ++ The class was declared public, therefore may be accessed + ++ from outside its package + jvmFinal: % + ++ The class was declared final; therefore no derived class allowed. + jvmSuper: % + ++ Instruct the JVM to treat base clss method invokation specially. + jvmInterface: % + ++ The class file represents an interface, not a class. + jvmAbstract: % + ++ The class was declared abstract; therefore object of this class + ++ may not be created. + Private == UInt16 add + jvmPublic == per(16r0001::Rep) + jvmFinal == per(16r0010::Rep) + jvmSuper == per(16r0020::Rep) + jvmInterface == per(16r0200::Rep) + jvmAbstract == per(16r0400::Rep) +@ + +\section{JVM field access flags} + +<<domain JVMFDACC JVMFieldAccess>>= +)abbrev domain JVMFDACC JVMFieldAccess +++ Date Created: July 18, 2008 +++ Data Last Modified: July 18, 2010 +++ Description: +++ JVM class field access bitmask and values. +JVMFieldAccess(): Public == Private where + Public == Join(SetCategory,Logic) with + jvmPublic: % + ++ The field was declared public; therefore mey accessed from + ++ outside its package. + jvmPrivate: % + ++ The field was declared private; threfore can be accessed only + ++ within the defining class. + jvmProtected: % + ++ The field was declared protected; therefore may be accessed + ++ withing derived classes. + jvmStatic: % + ++ The field was declared static. + jvmFinal: % + ++ The field was declared final; therefore may not be modified + ++ after initialization. + jvmVolatile: % + ++ The field was declared volatile. + jvmTransient: % + ++ The field was declared transient. + Private == UInt16 add + jvmPublic == per(16r0001::Rep) + jvmPrivate == per(16r0002::Rep) + jvmProtected == per(16r0004::Rep) + jvmStatic == per(16r0008::Rep) + jvmFinal == per(16r0010::Rep) + jvmVolatile == per(16r0040::Rep) + jvmTransient == per(16r0080::Rep) +@ + + +\section{JVM method access flags} + +<<domain JVMMDACC JVMMethodAccess>>= +)abbrev domain JVMMDACC JVMMethodAccess +)abbrev domain JVMFDACC JVMFieldAccess +++ Date Created: July 18, 2008 +++ Data Last Modified: July 18, 2010 +++ Description: +++ JVM class method access bitmask and values. +JVMMethodAccess(): Public == Private where + Public == Join(SetCategory,Logic) with + jvmPublic: % + ++ The method was declared public; therefore mey accessed from + ++ outside its package. + jvmPrivate: % + ++ The method was declared private; threfore can be accessed only + ++ within the defining class. + jvmProtected: % + ++ The method was declared protected; therefore may be accessed + ++ withing derived classes. + jvmStatic: % + ++ The method was declared static. + jvmFinal: % + ++ The method was declared final; therefore may not be overriden. + ++ in derived classes. + jvmSynchronized: % + ++ The method was declared synchronized. + jvmNative: % + ++ The method was declared native; therefore implemented in a language + ++ other than Java. + jvmAbstract: % + ++ The method was declared abstract; therefore no implementation + ++ is provided. + jvmStrict: % + ++ The method was declared fpstrict; therefore floating-point mode + ++ is FP-strict. + Private == UInt16 add + jvmPublic == per(16r0001::Rep) + jvmPrivate == per(16r0002::Rep) + jvmProtected == per(16r0004::Rep) + jvmStatic == per(16r0008::Rep) + jvmFinal == per(16r0010::Rep) + jvmSynchronized == per(16r0020::Rep) + jvmNative == per(16r0100::Rep) + jvmAbstract == per(16r0400::Rep) + jvmStrict == per(16r0800::Rep) + +@ + +\section{JVM constant pool tags} + +<<domain JVMCSTTG JVMConstantTag>>= +)abbrev domain JVMCSTTG JVMConstantTag +++ Date Created: July 18, 2008 +++ Data Last Modified: July 18, 2010 +++ Description: +++ JVM class file constant pool tags. +JVMConstantTag(): Public == Private where + Public == Join(SetCategory,CoercibleTo Byte) with + jvmUTF8ConstantTag: % + ++ The corresponding constant pool entry is sequence of bytes + ++ representing Java UTF8 string constant. + jvmIntegerConstantTag: % + ++ The corresponding constant pool entry is an integer constant info. + jvmFloatConstantTag: % + ++ The corresponding constant pool entry is a float constant info. + jvmLongConstantTag: % + ++ The corresponding constant pool entry is a long constant info. + jvmDoubleConstantTag: % + ++ The corresponding constant pool entry is a double constant info. + jvmClassConstantTag: % + ++ The corresponding constant pool entry represents a class or + ++ and interface. + jvmStringConstantTag: % + ++ The corresponding constant pool entry is a string constant info. + jvmFieldrefConstantTag: % + ++ The corresponding constant pool entry represents a class field info. + jvmMethodrefConstantTag: % + ++ The correspondong constant pool entry represents a class method info. + jvmInterfaceMethodConstantTag: % + ++ The correspondong constant pool entry represents an interface + ++ method info. + jvmNameAndTypeConstantTag: % + ++ The correspondong constant pool entry represents the name + ++ and type of a field or method info. + Private == Byte add + jvmUTF8ConstantTag == per byte 1 + jvmIntegerConstantTag == per byte 3 + jvmFloatConstantTag == per byte 4 + jvmLongConstantTag == per byte 5 + jvmDoubleConstantTag == per byte 6 + jvmClassConstantTag == per byte 7 + jvmStringConstantTag == per byte 8 + jvmFieldrefConstantTag == per byte 9 + jvmMethodrefConstantTag == per byte 10 + jvmInterfaceMethodConstantTag == per byte 11 + jvmNameAndTypeConstantTag == per byte 12 +@ + + +\section{The JVMBytecode domain} +<<domain JVMBCODE JVMBytecode>>= +)abbrev domain JVMBCODE JVMBytecode ++ Author: Gabriel Dos Reis ++ Date Created: May 08, 2008 -++ Description: This domain defines the datatype for the Java -++ Virtual Machine byte codes. -JavaBytecode(): Public == Private where - Public == Join(CoercibleTo OutputForm, HomotopicTo Byte) - Private == add +++ Data Last Modified: July 18, 2010 +++ Description: +++ This is the datatype for the JVM bytecodes. +JVMBytecode(): Public == Private where + Public == Join(SetCategory, HomotopicTo Byte) + Private == Byte add + coerce(b: Byte): % == + per b + + coerce(x: %): Byte == + rep x +@ + +\section{JVM Opcodes} + +<<domain JVMOP JVMOpcode>>= +)abbrev domain JVMOP JVMOpcode +++ Date Created: July 18, 2008 +++ Data Last Modified: July 18, 2010 +++ Description: +++ This is the datatype for the JVM opcodes. +JVMOpcode(): Public == Private where + Public == Join(SetCategory,HomotopicTo JVMBytecode,HomotopicTo Byte) + Private == JVMBytecode add -- mnemonics equivalent of bytecodes. mnemonics : PrimitiveArray Symbol := [['nop, 'aconst__null, 'iconst__m1, 'iconst__0, 'iconst__1, _ @@ -77,22 +264,17 @@ JavaBytecode(): Public == Private where 'unknownopcode49, 'unknownopcode50, _ 'impldep1, 'impldep2 ]]$PrimitiveArray(Symbol) - Rep == Byte - - coerce(x: Byte): % == - per x - - coerce(x: %): Byte == - rep x - + coerce(x: %): JVMBytecode == rep x + coerce(b: JVMBytecode): % == per b coerce(x: %): OutputForm == mnemonics.(x::Byte::Integer) :: OutputForm + @ \section{License} <<license>>= ---Copyright (C) 2007-2008, Gabriel Dos Reis. +--Copyright (C) 2007-2010, Gabriel Dos Reis. --All rights reserved. -- --Redistribution and use in source and binary forms, with or without @@ -126,7 +308,14 @@ JavaBytecode(): Public == Private where <<*>>= <<license>> -<<domain JAVACODE JavaBytecode>> + +<<domain JVMCFACC JVMClassFileAccess>> +<<domain JVMFDACC JVMFieldAccess>> +<<domain JVMMDACC JVMMethodAccess>> +<<domain JVMCSTTG JVMConstantTag>> +<<domain JVMBCODE JVMBytecode>> +<<domain JVMOP JVMOpcode>> + @ \end{document} diff --git a/src/interp/g-opt.boot b/src/interp/g-opt.boot index 9c4004ed..4d598b05 100644 --- a/src/interp/g-opt.boot +++ b/src/interp/g-opt.boot @@ -473,13 +473,14 @@ $VMsideEffectFreeOperators == MINUSP GREATERP ZEROP ODDP FLOAT_-RADIX FLOAT FLOAT_-SIGN FLOAT_-DIGITS CGREATERP GGREATERP CHAR BOOLE GET BVEC_-GREATER %false %true %and %or %not %peq %ieq %ilt %ile %igt %ige %head %tail %integer? - %imul %iadd %isub %igcd %ilcm %ipow %imin %imax %ieven? %iodd? %iinc - %feq %flt %fle %fgt %fge %fmul %fadd %fsub %fexp %fmin %fmax %float? - %fpow %fdiv %fneg %i2f %fminval %fmaxval %fbase %fprec %ftrunc - %nil %pair? %lconcat %llength %lfirst %lsecond %lthird - %lreverse %lempty? %hash %ismall? %string? %f2s - %ceq %clt %cle %cgt %cge %c2i %i2c %sname - %vref %vlength %before?) + %beq %blt %ble %bgt %bge %bitand %bitior %bitnot + %imul %iadd %isub %igcd %ilcm %ipow %imin %imax %ieven? %iodd? %iinc + %feq %flt %fle %fgt %fge %fmul %fadd %fsub %fexp %fmin %fmax %float? + %fpow %fdiv %fneg %i2f %fminval %fmaxval %fbase %fprec %ftrunc + %nil %pair? %lconcat %llength %lfirst %lsecond %lthird + %lreverse %lempty? %hash %ismall? %string? %f2s + %ceq %clt %cle %cgt %cge %c2i %i2c %sname + %vref %vlength %before?) ++ List of simple VM operators $simpleVMoperators == diff --git a/src/interp/g-util.boot b/src/interp/g-util.boot index c2463dc5..df6628f9 100644 --- a/src/interp/g-util.boot +++ b/src/interp/g-util.boot @@ -244,6 +244,15 @@ expandIlt ['%ilt,x,y] == expandIgt ['%igt,x,y] == expandFlt ['%ilt,y,x] +expandBitand ['%bitand,x,y] == + ['BOOLE,'BOOLE_-AND,expandToVMForm x,expandToVMForm y] + +expandBitior ['%bitior,x,y] == + ['BOOLE,'BOOLE_-IOR,expandToVMForm x,expandToVMForm y] + +expandBitnot ['%bitnot,x] == + ['LOGNOT,expandToVMForm x] + -- Floating point support expandFbase ['%fbase] == @@ -319,6 +328,13 @@ for x in [ ['%c2i, :'CHAR_-CODE], ['%i2c, :'CODE_-CHAR], + -- byte operations + ['%beq, :'byteEqual], + ['%blt, :'byteLessThan], + ['%ble, :'byteLessEqual], + ['%bgt, :'byteGreaterThan], + ['%bge, :'byteGreaterEqual], + -- unary integer operations. ['%iabs, :'ABS], ['%ieven?, :'EVENP], @@ -404,6 +420,9 @@ for x in [ ['%igt, :function expandIgt], ['%ilt, :function expandIlt], ['%ineg, :function expandIneg], + ['%bitand, :function expandBitand], + ['%bitior, :function expandBitior], + ['%bitnot, :function expandBitnot], ['%i2f, :function expandI2f], ['%fbase, :function expandFbase], @@ -417,10 +436,10 @@ for x in [ ['%peq, :function expandPeq], ['%before?, :function expandBefore?], - ["%bind", :function expandBind], - ["%store", :function expandStore], - ["%dynval", :function expandDynval] - ] repeat property(first x,"%Expander") := rest x + ['%bind, :function expandBind], + ['%store, :function expandStore], + ['%dynval, :function expandDynval] + ] repeat property(first x,'%Expander) := rest x ++ Return the expander of a middle-end opcode, or nil if there is none. getOpcodeExpander op == diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index e77bac28..b5dad787 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2296269 . 3487991533) +(2296416 . 3488491117) (-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."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\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(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(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| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|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(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(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . 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(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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|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(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| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|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(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| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4467 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4463 . T) (-4468 . T) (-4462 . T)) +((-4496 . T) (-4494 . T) (-4493 . T) ((-4501 "*") . T) (-4492 . T) (-4497 . T) (-4491 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1985) +(-32 R -2057) ((|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 -1063) (QUOTE (-577))))) +((|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (-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 -4470))) +((|HasAttribute| |#1| (QUOTE -4499))) (-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}."))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . 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"))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . 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 -1985 UP UPUP -1688) +(-40 -2057 UP UPUP -3351) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2811 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2811 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2811 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2811 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2811 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-2811 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) -(-41 R -1985) +((-4492 |has| (-420 |#2|) (-375)) (-4497 |has| (-420 |#2|) (-375)) (-4491 |has| (-420 |#2|) (-375)) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2867 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2867 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2867 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2867 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2867 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -659) (QUOTE (-577)))) (-2867 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) +(-41 R -2057) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -443) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -443) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-318)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) +((-4496 |has| |#1| (-569)) (-4494 . T) (-4493 . T)) ((|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-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."))) -((-4470 . T) (-4471 . T)) -((-2811 (-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|))))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-865))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|))))))) +((-4499 . T) (-4500 . T)) +((-2867 (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|))))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-870))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-375)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (LIST (QUOTE -1068) (QUOTE (-577))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4467 . T)) +((-4496 . 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 -1985) +(-54 |Base| R -2057) ((|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"))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . 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}"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -2668) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -2758) ((|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 -2668) +(-62 -2758) ((|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 -2668) +(-63 -2758) ((|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 -2668) +(-64 -2758) ((|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 -2668) +(-65 -2758) ((|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 -2668) +(-66 -2758) ((|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 -2668) +(-67 -2758) ((|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 -2668) +(-68 -2758) ((|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 -2668) +(-69 -2758) ((|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 -2668) +(-70 -2758) ((|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 -2668) +(-71 -2758) ((|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 -2668) +(-72 -2758) ((|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 -2668) +(-73 -2758) ((|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 -2668) +(-74 -2758) ((|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 @@ -236,55 +236,55 @@ 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 -2668) +(-77 -2758) ((|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 -2668) +(-78 -2758) ((|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 -2668) +(-79 -2758) ((|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 -2668) +(-80 -2758) ((|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 -2668) +(-81 -2758) ((|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 -2668) +(-82 -2758) ((|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 -2668) +(-83 -2758) ((|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 -2668) +(-84 -2758) ((|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 -2668) +(-85 -2758) ((|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 -2668) +(-86 -2758) ((|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 -2668) +(-87 -2758) ((|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 -2668) +(-88 -2758) ((|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 -2668) +(-89 -2758) ((|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 @@ -294,8 +294,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-375)))) (-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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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\"."))) -((-4470 . T)) +((-4499 . 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."))) -((-4470 . T) ((-4472 "*") . T) (-4471 . T) (-4467 . T) (-4465 . T) (-4464 . T) (-4463 . T) (-4468 . T) (-4462 . T) (-4461 . T) (-4460 . T) (-4459 . T) (-4458 . T) (-4466 . T) (-4469 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4457 . T)) +((-4499 . T) ((-4501 "*") . T) (-4500 . T) (-4496 . T) (-4494 . T) (-4493 . T) (-4492 . T) (-4497 . T) (-4491 . T) (-4490 . T) (-4489 . T) (-4488 . T) (-4487 . T) (-4495 . T) (-4498 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4486 . 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}."))) -((-4467 . T)) +((-4496 . 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{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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 (-4472 "*")))) +((|HasAttribute| |#1| (QUOTE (-4501 "*")))) (-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"))) -((-4470 . T)) +((-4499 . 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."))) -((-4471 . T)) +((-4500 . 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2811 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-577) (QUOTE (-937))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1052))) (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870))) (-2867 (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870)))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1182))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1206)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -659) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (|HasCategory| (-577) (QUOTE (-146))))) (-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| (($ (|Identifier|) (|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| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1130))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-870))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-112) (QUOTE (-1130))) (|HasCategory| (-112) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-112) (QUOTE (-102)))) (-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}"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -392,22 +392,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op, p, v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op, p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|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!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op, p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|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| (($ $ (|Identifier|)) "\\spad{assert(op, p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|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|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f, a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|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}."))) NIL NIL -(-116 -1985 UP) +(-116 -2057 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 (-117 |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}."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-118 |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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-117 |#1|) (QUOTE (-932))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-117 |#1|) (QUOTE (-1047))) (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865))) (-2811 (|HasCategory| (-117 |#1|) (QUOTE (-836))) (|HasCategory| (-117 |#1|) (QUOTE (-865)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-1177))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-318))) (|HasCategory| (-117 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-932)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-117 |#1|) (QUOTE (-937))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-148))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-117 |#1|) (QUOTE (-1052))) (|HasCategory| (-117 |#1|) (QUOTE (-841))) (|HasCategory| (-117 |#1|) (QUOTE (-870))) (-2867 (|HasCategory| (-117 |#1|) (QUOTE (-841))) (|HasCategory| (-117 |#1|) (QUOTE (-870)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-1182))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| (-117 |#1|) (QUOTE (-238))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-117 |#1|) (QUOTE (-239))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -527) (QUOTE (-1206)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -117) (|devaluate| |#1|)) (LIST (QUOTE -117) (|devaluate| |#1|)))) (|HasCategory| (-117 |#1|) (QUOTE (-318))) (|HasCategory| (-117 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-117 |#1|) (QUOTE (-937)))) (|HasCategory| (-117 |#1|) (QUOTE (-146))))) (-119 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4471))) +((|HasAttribute| |#1| (QUOTE -4500))) (-120 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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 @@ -418,15 +418,15 @@ NIL NIL (-122 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"))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-123 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-124) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL (-125 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -434,20 +434,20 @@ NIL NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-128 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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129) ((|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.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|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|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-2811 (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-130) (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-130) (QUOTE (-865))) (-2811 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1125))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-2867 (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130))))) (|HasCategory| (-130) (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-130) (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-130) (QUOTE (-870))) (-2867 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1130))) (|HasCategory| (-130) (LIST (QUOTE -320) (QUOTE (-130)))))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|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 @@ -470,13 +470,13 @@ NIL NIL (-135) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4472 "*") . T)) +(((-4501 "*") . T)) NIL -(-136 |minix| -3985 S T$) +(-136 |minix| -3651 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-137 |minix| -3985 R) +(-137 |minix| -3651 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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| $) "\\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 @@ -498,8 +498,8 @@ NIL NIL (-142) ((|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}."))) -((-4470 . T) (-4460 . T) (-4471 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +((-4499 . T) (-4489 . T) (-4500 . T)) +((-2867 (-12 (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-145) (QUOTE (-380))) (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-143 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{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{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 @@ -514,7 +514,7 @@ NIL NIL (-146) ((|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."))) -((-4467 . T)) +((-4496 . T)) NIL (-147 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}."))) @@ -522,9 +522,9 @@ NIL NIL (-148) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4467 . T)) +((-4496 . T)) NIL -(-149 -1985 UP UPUP) +(-149 -2057 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 @@ -535,14 +535,14 @@ NIL (-151 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 -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasAttribute| |#1| (QUOTE -4470))) +((|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasAttribute| |#1| (QUOTE -4499))) (-152 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 (-153 |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."))) -((-4465 . T) (-4464 . T) (-4467 . T)) +((-4494 . T) (-4493 . T) (-4496 . T)) NIL (-154) ((|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."))) @@ -564,7 +564,7 @@ NIL ((|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 -(-159 R -1985) +(-159 R -2057) ((|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 @@ -595,10 +595,10 @@ NIL (-166 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 -((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1027))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4466)) (|HasAttribute| |#2| (QUOTE -4469)) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569)))) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4495)) (|HasAttribute| |#2| (QUOTE -4498)) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569)))) (-167 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})"))) -((-4463 -2811 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-4155 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 -2867 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-937)))) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4495 |has| |#1| (-6 -4495)) (-4498 |has| |#1| (-6 -4498)) (-4225 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-168 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."))) @@ -614,8 +614,8 @@ NIL NIL (-171 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}."))) -((-4463 -2811 (|has| |#1| (-569)) (-12 (|has| |#1| (-318)) (|has| |#1| (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4466 |has| |#1| (-6 -4466)) (-4469 |has| |#1| (-6 -4469)) (-4155 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . 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T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-2867 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-361)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-937))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-937)))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-937))))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1232)))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| |#1| (QUOTE (-1090))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1232)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-375)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-238)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-239))) (-12 (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasAttribute| |#1| (QUOTE -4495)) (|HasAttribute| |#1| (QUOTE -4498)) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206))))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-361))))) (-172 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 @@ -626,7 +626,7 @@ NIL NIL (-174) ((|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."))) -(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-175) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -634,7 +634,7 @@ NIL NIL (-176 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4472 "*") . T) (-4463 . T) (-4468 . T) (-4462 . T) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") . T) (-4492 . T) (-4497 . T) (-4491 . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-177) ((|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| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|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}."))) @@ -651,7 +651,7 @@ NIL (-180 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| (-975 |#2|) (LIST (QUOTE -905) (|devaluate| |#1|)))) +((|HasCategory| (-980 |#2|) (LIST (QUOTE -910) (|devaluate| |#1|)))) (-181 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 @@ -688,7 +688,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-190 R -1985) +(-190 R -2057) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -800,23 +800,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-218 -1985 UP UPUP R) +(-218 -2057 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 -(-219 -1985 FP) +(-219 -2057 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 (-220) ((|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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2811 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-577) (QUOTE (-937))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1052))) (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870))) (-2867 (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870)))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1182))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1206)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -659) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (|HasCategory| (-577) (QUOTE (-146))))) (-221) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-222 R -1985) +(-222 R -2057) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -830,19 +830,19 @@ NIL NIL (-225 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-226 |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}."))) -((-4467 . T)) +((-4496 . T)) NIL -(-227 R -1985) +(-227 R -2057) ((|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 (-228) ((|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}."))) -((-4142 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4215 . T) (-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-229) ((|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{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * 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*\\%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*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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*\\%pi) - J(-v,x))/sin(v*\\%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)}.}"))) @@ -850,19 +850,19 @@ NIL NIL (-230 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}"))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4501 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-231 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 (-232 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."))) -((-4471 . T)) +((-4500 . T)) NIL (-233 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-4467 . T)) +((-4496 . T)) NIL (-234 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -874,7 +874,7 @@ NIL NIL (-236 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-237 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -886,36 +886,36 @@ NIL NIL (-239) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-4467 . T)) +((-4496 . T)) NIL (-240 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 -4470))) +((|HasAttribute| |#1| (QUOTE -4499))) (-241 S) ((|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}."))) -((-4471 . T)) +((-4500 . T)) NIL (-242) ((|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 -(-243 S -3985 R) +(-243 S -3651 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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 (-375))) (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (QUOTE (-865))) (|HasAttribute| |#3| (QUOTE -4467)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1074))) (|HasCategory| |#3| (QUOTE (-1125)))) -(-244 -3985 R) +((|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-814))) (|HasCategory| |#3| (QUOTE (-870))) (|HasAttribute| |#3| (QUOTE -4496)) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (QUOTE (-747))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (QUOTE (-1130)))) +(-244 -3651 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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"))) -((-4464 |has| |#2| (-1074)) (-4465 |has| |#2| (-1074)) (-4467 |has| |#2| (-6 -4467)) (-4470 . T)) +((-4493 |has| |#2| (-1079)) (-4494 |has| |#2| (-1079)) (-4496 |has| |#2| (-6 -4496)) (-4499 . T)) NIL -(-245 -3985 A B) +(-245 -3651 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 -(-246 -3985 R) +(-246 -3651 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."))) -((-4464 |has| |#2| (-1074)) (-4465 |has| |#2| (-1074)) (-4467 |has| |#2| (-6 -4467)) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-380))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809))) (|HasCategory| |#2| (LIST 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(-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-1130)))) (|HasAttribute| |#2| (QUOTE -4496)) (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-1079)))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206))))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))))) (-247) ((|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 @@ -926,7 +926,7 @@ NIL NIL (-249) ((|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}."))) -((-4463 . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-250 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."))) @@ -934,20 +934,20 @@ NIL NIL (-251 S) ((|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}"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-252 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 (-253 R) ((|constructor| (NIL "Category of modules that extend differential rings. \\blankline"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-254 |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"))) -(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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T) (-4493 . T) (-4496 . 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(|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\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| (|DomainConstructor|)) $) "\\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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 ((|HasCategory| |#2| (QUOTE (-239)))) (-261 R S V E) ((|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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL (-262 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}."))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL (-263) ((|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."))) @@ -1019,15 +1019,15 @@ NIL (-272 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-238)))) +((|HasCategory| |#2| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-238)))) (-273 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL (-274 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"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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T) (-4493 . T) (-4496 . 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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}.")) (|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 @@ -1072,11 +1072,11 @@ NIL ((|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 -(-286 R -1985) +(-286 R -2057) ((|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{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 -(-287 R -1985) +(-287 R -2057) ((|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{ki} was rewritten as \\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 @@ -1099,10 +1099,10 @@ NIL (-292 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 (-865))) (|HasCategory| |#2| (QUOTE (-1125)))) +((|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130)))) (-293 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}."))) -((-4471 . T)) +((-4500 . T)) NIL (-294 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}."))) @@ -1123,18 +1123,18 @@ NIL (-298 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 -4471))) +((|HasAttribute| |#1| (QUOTE -4500))) (-299 |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 -(-300 S R |Mod| -2871 -1334 |exactQuo|) +(-300 S R |Mod| -3530 -3771 |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}")) (|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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-301) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4463 . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-302) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1150,21 +1150,21 @@ NIL NIL (-305 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.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102)))) +((-4499 . T) (-4500 . 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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 -(-308 -1985 S) +(-308 -2057 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 -(-309 E -1985) +(-309 E -2057) ((|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 @@ -1179,7 +1179,7 @@ NIL (-312 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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\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 -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1074)))) +((|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1079)))) (-313) ((|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|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| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\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 @@ -1202,7 +1202,7 @@ NIL NIL (-318) ((|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 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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-319 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1212,7 +1212,7 @@ NIL ((|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 -(-321 -1985) +(-321 -2057) ((|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 @@ -1226,8 +1226,8 @@ NIL NIL (-324 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))}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-932))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-1047))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-836))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-865))) (-2811 (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-836))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-865)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-1177))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -1278) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -320) (LIST (QUOTE -1278) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (LIST (QUOTE -297) (LIST (QUOTE -1278) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1278) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-318))) (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-558))) (-12 (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-932))) (|HasCategory| $ (QUOTE (-146)))) (-2811 (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1278 |#1| |#2| |#3| |#4|) (QUOTE (-932))) (|HasCategory| $ (QUOTE (-146)))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1052))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-870))) (-2867 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-870)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-1182))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-238))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-239))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -527) (QUOTE (-1206)) (LIST (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -320) (LIST (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (LIST (QUOTE -297) (LIST (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1283) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-318))) (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-558))) (-12 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| $ (QUOTE (-146)))) (-2867 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (-12 (|HasCategory| (-1283 |#1| |#2| |#3| |#4|) (QUOTE (-937))) (|HasCategory| $ (QUOTE (-146)))))) (-325 R S) ((|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 @@ -1238,9 +1238,9 @@ NIL NIL (-327 R) ((|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."))) -((-4467 -2811 (-12 (|has| |#1| (-569)) (-2811 (|has| |#1| (-1074)) (|has| |#1| (-486)))) (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) -((-2811 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (QUOTE (-1074))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))))) (-2811 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1137)))) (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074)))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))))) (-2811 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1137)))) (-2811 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))))) (-2811 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1074)))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1137))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) -(-328 R -1985) +((-4496 -2867 (-12 (|has| |#1| (-569)) (-2867 (|has| |#1| (-1079)) (|has| |#1| (-486)))) (|has| |#1| (-1079)) (|has| |#1| (-486))) (-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) ((-4501 "*") |has| |#1| (-569)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-569)) (-4491 |has| |#1| (-569))) +((-2867 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-21))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (QUOTE (-1079))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))))) (-2867 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1142)))) (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079)))) (-2867 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079)))) (-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079)))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))))) (-2867 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1142)))) (-2867 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))))) (-2867 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#1| (QUOTE (-1079)))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1142))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (LIST (QUOTE -1068) (QUOTE (-577))))) +(-328 R -2057) ((|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{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + 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 @@ -1250,8 +1250,8 @@ NIL NIL (-330 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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) (-331 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 @@ -1262,8 +1262,8 @@ NIL NIL (-333 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4465 . T) (-4464 . T)) -((|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-808)))) +((-4494 . T) (-4493 . T)) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| (-577) (QUOTE (-813)))) (-334 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * 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| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1271,26 +1271,26 @@ NIL (-335 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-787) (QUOTE (-808)))) +((|HasCategory| (-792) (QUOTE (-813)))) (-336 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL ((|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174)))) (-337 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-338 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."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-339 S -1985) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-339 S -2057) ((|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 (-380)))) -(-340 -1985) +(-340 -2057) ((|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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-341) ((|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."))) @@ -1312,54 +1312,54 @@ NIL ((|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 -(-346 S -1985 UP UPUP R) +(-346 S -2057 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 -(-347 -1985 UP UPUP R) +(-347 -2057 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 -(-348 -1985 UP UPUP R) +(-348 -2057 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-349 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|)))) (-350 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-351 |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{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.}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#3| (LIST (QUOTE -1063) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#3| (LIST (QUOTE -1068) (QUOTE (-391)))) (|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (LIST (QUOTE -1068) (QUOTE (-577))))) (-352 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 -(-353 S -1985 UP UPUP) +(-353 S -2057 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(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 (-380))) (|HasCategory| |#2| (QUOTE (-375)))) -(-354 -1985 UP UPUP) +(-354 -2057 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(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."))) -((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 |has| (-420 |#2|) (-375)) (-4497 |has| (-420 |#2|) (-375)) (-4491 |has| (-420 |#2|) (-375)) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-355 |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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| (-938 |#1|) (QUOTE (-146))) (|HasCategory| (-938 |#1|) (QUOTE (-380)))) (|HasCategory| (-938 |#1|) (QUOTE (-148))) (|HasCategory| (-938 |#1|) (QUOTE (-380))) (|HasCategory| (-938 |#1|) (QUOTE (-146)))) (-356 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-357 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-358 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 @@ -1374,33 +1374,33 @@ NIL NIL (-361) ((|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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-362 R UP -1985) +(-362 R UP -2057) ((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-363 |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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| (-938 |#1|) (QUOTE (-146))) (|HasCategory| (-938 |#1|) (QUOTE (-380)))) (|HasCategory| (-938 |#1|) (QUOTE (-148))) (|HasCategory| (-938 |#1|) (QUOTE (-380))) (|HasCategory| (-938 |#1|) (QUOTE (-146)))) (-364 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-365 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-366 |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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| (-933 |#1|) (QUOTE (-146))) (|HasCategory| (-933 |#1|) (QUOTE (-380)))) (|HasCategory| (-933 |#1|) (QUOTE (-148))) (|HasCategory| (-933 |#1|) (QUOTE (-380))) (|HasCategory| (-933 |#1|) (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| (-938 |#1|) (QUOTE (-146))) (|HasCategory| (-938 |#1|) (QUOTE (-380)))) (|HasCategory| (-938 |#1|) (QUOTE (-148))) (|HasCategory| (-938 |#1|) (QUOTE (-380))) (|HasCategory| (-938 |#1|) (QUOTE (-146)))) (-367 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) -(-368 -1985 GF) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +(-368 -2057 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 @@ -1408,21 +1408,21 @@ NIL ((|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 -(-370 -1985 FP FPP) +(-370 -2057 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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-371 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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-146)))) (-372 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 (-373 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4467 . T)) +((-4496 . T)) NIL (-374 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1430,7 +1430,7 @@ NIL NIL (-375) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-376 |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."))) @@ -1446,7 +1446,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-569)))) (-379 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{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{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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) +((-4496 |has| |#1| (-569)) (-4494 . T) (-4493 . T)) NIL (-380) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1458,7 +1458,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-375)))) (-382 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL (-383 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1467,14 +1467,14 @@ NIL (-384 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125)))) +((|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130)))) (-385 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4470 . T)) +((-4499 . T)) NIL (-386 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4465 . T) (-4464 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4494 . T) (-4493 . T)) NIL (-387 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."))) @@ -1483,7 +1483,7 @@ NIL (-388 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 -654) (QUOTE (-577))))) +((|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577))))) (-389 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 @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|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{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}."))) -((-4453 . T) (-4461 . T) (-4142 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4482 . T) (-4490 . T) (-4215 . T) (-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-392 |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}."))) @@ -1502,11 +1502,11 @@ NIL NIL (-393 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}"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) ((|HasCategory| |#1| (QUOTE (-174)))) (-394 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}."))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-395) ((|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}."))) @@ -1518,8 +1518,8 @@ NIL NIL (-397 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."))) -((-4465 . T) (-4464 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-4494 . T) (-4493 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-398 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) NIL @@ -1527,10 +1527,10 @@ NIL (-399 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-865)))) +((|HasCategory| |#1| (QUOTE (-870)))) (-400) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-401) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1542,13 +1542,13 @@ NIL NIL (-403 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-404) ((|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 -(-405 -1985 UP UPUP R) +(-405 -2057 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 @@ -1572,11 +1572,11 @@ NIL ((|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 -(-411 -2668 |returnType| -1951 |symbols|) +(-411 -2758 |returnType| -2112 |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 -(-412 -1985 UP) +(-412 -2057 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 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.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1590,15 +1590,15 @@ NIL NIL (-415) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-416 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4453)) (|HasAttribute| |#1| (QUOTE -4461))) +((|HasAttribute| |#1| (QUOTE -4482)) (|HasAttribute| |#1| (QUOTE -4490))) (-417) ((|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\"."))) -((-4142 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4215 . T) (-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-418 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."))) @@ -1610,20 +1610,20 @@ NIL NIL (-420 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."))) -((-4457 -12 (|has| |#1| (-6 -4468)) (|has| |#1| (-465)) (|has| |#1| (-6 -4457))) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-836))) (|HasCategory| |#1| (QUOTE (-865)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844))))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-558))) (-12 (|HasAttribute| |#1| (QUOTE -4468)) (|HasAttribute| |#1| (QUOTE -4457)) (|HasCategory| |#1| (QUOTE (-465)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) +((-4486 -12 (|has| |#1| (-6 -4497)) (|has| |#1| (-465)) (|has| |#1| (-6 -4486))) (-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . 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(|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 (-422 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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."))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL (-423 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 -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577))))) +((|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577))))) (-424 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 @@ -1632,14 +1632,14 @@ NIL ((|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 -(-426 R -1985 UP A) +(-426 R -2057 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)}."))) -((-4467 . T)) +((-4496 . T)) NIL -(-427 R -1985 UP A |ibasis|) +(-427 R -2057 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1063) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1068) (|devaluate| |#2|)))) (-428 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1650,12 +1650,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-375)))) (-430 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is 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{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."))) -((-4467 |has| |#1| (-569)) (-4465 . T) (-4464 . T)) +((-4496 |has| |#1| (-569)) (-4494 . T) (-4493 . T)) NIL (-431 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."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -320) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -297) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1246))) (-2811 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1246)))) (|HasCategory| |#1| (QUOTE (-1047))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-465)))) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1206)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -320) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -297) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1251))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-1251)))) (|HasCategory| |#1| (QUOTE (-1052))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-465)))) (-432 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 @@ -1679,40 +1679,40 @@ NIL (-437 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 (-865))) (|HasCategory| |#2| (QUOTE (-380)))) +((|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-380)))) (-438 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4470 . T) (-4460 . T) (-4471 . T)) +((-4499 . T) (-4489 . T) (-4500 . T)) NIL -(-439 R -1985) +(-439 R -2057) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-440 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4457 -12 (|has| |#1| (-6 -4457)) (|has| |#2| (-6 -4457))) (-4464 . T) (-4465 . T) (-4467 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4457)) (|HasAttribute| |#2| (QUOTE -4457)))) -(-441 R -1985) +((-4486 -12 (|has| |#1| (-6 -4486)) (|has| |#2| (-6 -4486))) (-4493 . T) (-4494 . T) (-4496 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4486)) (|HasAttribute| |#2| (QUOTE -4486)))) +(-441 R -2057) ((|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 (-442 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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 -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-1137))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) +((|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-1142))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) (-443 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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) -((-4467 -2811 (|has| |#1| (-1074)) (|has| |#1| (-486))) (-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) ((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-569)) (-4462 |has| |#1| (-569))) +((-4496 -2867 (|has| |#1| (-1079)) (|has| |#1| (-486))) (-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) ((-4501 "*") |has| |#1| (-569)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-569)) (-4491 |has| |#1| (-569))) NIL -(-444 R -1985) +(-444 R -2057) ((|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 -(-445 R -1985) +(-445 R -2057) ((|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{ai = 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{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-446 R -1985) +(-446 R -2057) ((|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 @@ -1720,10 +1720,10 @@ NIL ((|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 -(-448 R -1985 UP) +(-448 R -2057 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 -1063) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-48))))) (-449) ((|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 @@ -1752,7 +1752,7 @@ NIL ((|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 -(-456 R UP -1985) +(-456 R UP -2057) ((|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 @@ -1790,16 +1790,16 @@ NIL NIL (-465) ((|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}."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-466 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"))) -((-4467 |has| (-420 (-975 |#1|)) (-569)) (-4465 . T) (-4464 . T)) -((|HasCategory| (-420 (-975 |#1|)) (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-420 (-975 |#1|)) (QUOTE (-569)))) +((-4496 |has| (-420 (-980 |#1|)) (-569)) (-4494 . T) (-4493 . T)) +((|HasCategory| (-420 (-980 |#1|)) (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-420 (-980 |#1|)) (QUOTE (-569)))) (-467 |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"))) -(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-932))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) +(((-4501 "*") |has| |#2| (-174)) (-4492 |has| |#2| (-569)) (-4497 |has| |#2| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (-2867 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2867 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4497)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-146))))) (-468 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 @@ -1826,7 +1826,7 @@ NIL NIL (-474 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL (-475 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1834,8 +1834,8 @@ NIL NIL (-476 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#4| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) (-477 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 @@ -1864,7 +1864,7 @@ NIL ((|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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-484 |lv| -1985 R) +(-484 |lv| -2057 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1874,23 +1874,23 @@ NIL NIL (-486) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4467 . T)) +((-4496 . T)) NIL (-487 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) (-488 |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."))) -((-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125)))) +((-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130)))) (-489 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)}"))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) (-490) ((|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{pi()} returns the symbolic \\%\\spad{pi}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-491) ((|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'."))) @@ -1898,29 +1898,29 @@ NIL NIL (-492 |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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102)))) (-493) ((|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 (-494 |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.")) 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T)) +((|HasCategory| (-577) (QUOTE (-937))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1052))) (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870))) (-2867 (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870)))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1182))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1206)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -659) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (|HasCategory| (-577) (QUOTE (-146))))) (-501 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 -((|HasAttribute| |#1| (QUOTE -4470)) (|HasAttribute| |#1| (QUOTE -4471)) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) +((|HasAttribute| |#1| (QUOTE -4499)) (|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1956,34 +1956,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-507 -1985 UP |AlExt| |AlPol|) +(-507 -2057 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-508) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| $ (QUOTE (-1074))) (|HasCategory| $ (LIST (QUOTE -1063) (QUOTE (-577))))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| $ (QUOTE (-1079))) (|HasCategory| $ (LIST (QUOTE -1068) (QUOTE (-577))))) (-509 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-510 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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-511 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 -(-512 R UP -1985) +(-512 R UP -2057) ((|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{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\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{mi} is given by \\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{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{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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-513 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-865))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-112) (QUOTE (-1125))) (|HasCategory| (-112) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-112) (QUOTE (-102)))) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1130))) (|HasCategory| (-112) (LIST (QUOTE -320) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-112) (QUOTE (-870))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-112) (QUOTE (-1130))) (|HasCategory| (-112) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-112) (QUOTE (-102)))) (-514 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 @@ -1996,10 +1996,10 @@ NIL ((|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{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{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 -(-517 -1985 |Expon| |VarSet| |DPoly|) +(-517 -2057 |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 -627) (QUOTE (-1201))))) +((|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-1206))))) (-518 |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 @@ -2011,11 +2011,11 @@ NIL (-520 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 -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-521 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 -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-522 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|Pair| |#2| |#1|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\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|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL @@ -2023,15 +2023,15 @@ NIL (-523 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-524 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-525 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125))))) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130))))) (-526 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|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 @@ -2043,39 +2043,39 @@ NIL (-528 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-808)))) +((|HasCategory| |#2| (QUOTE (-813)))) (-529 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}"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-530) ((|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 (-531 |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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((-2811 (|HasCategory| (-594 |#1|) (QUOTE (-146))) (|HasCategory| (-594 |#1|) (QUOTE (-380)))) (|HasCategory| (-594 |#1|) (QUOTE (-148))) (|HasCategory| (-594 |#1|) (QUOTE (-380))) (|HasCategory| (-594 |#1|) (QUOTE (-146)))) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((-2867 (|HasCategory| (-594 |#1|) (QUOTE (-146))) (|HasCategory| (-594 |#1|) (QUOTE (-380)))) (|HasCategory| (-594 |#1|) (QUOTE (-148))) (|HasCategory| (-594 |#1|) (QUOTE (-380))) (|HasCategory| (-594 |#1|) (QUOTE (-146)))) (-532 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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-533 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."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-534 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 -4471))) +((|HasAttribute| |#3| (QUOTE -4500))) (-535 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 -4471))) +((|HasAttribute| |#7| (QUOTE -4500))) (-536 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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4501 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) (-537) ((|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 @@ -2107,8 +2107,8 @@ NIL (-544 |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 -((-12 (|HasCategory| (-787) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125))))) -(-545 K -1985 |Par|) +((-12 (|HasCategory| (-792) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-1130))))) +(-545 K -2057 |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 @@ -2132,7 +2132,7 @@ NIL ((|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 -(-551 K -1985 |Par|) +(-551 K -2057 |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 @@ -2162,7 +2162,7 @@ NIL NIL (-558) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\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."))) -((-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4497 . T) (-4498 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-559) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2182,13 +2182,13 @@ NIL NIL (-563 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102)))) -(-564 R -1985) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102)))) +(-564 R -2057) ((|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 -(-565 R0 -1985 UP UPUP R) +(-565 R0 -2057 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 @@ -2198,7 +2198,7 @@ NIL NIL (-567 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."))) -((-4142 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4215 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-568 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."))) @@ -2206,9 +2206,9 @@ NIL NIL (-569) ((|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."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-570 R -1985) +(-570 R -2057) ((|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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(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 @@ -2220,39 +2220,39 @@ NIL ((|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 -(-573 R -1985 L) +(-573 R -2057 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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 -672) (|devaluate| |#2|)))) +((|HasCategory| |#3| (LIST (QUOTE -677) (|devaluate| |#2|)))) (-574) ((|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 -(-575 -1985 UP UPUP R) +(-575 -2057 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 -(-576 -1985 UP) +(-576 -2057 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 (-577) ((|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."))) -((-4452 . T) (-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4481 . T) (-4487 . T) (-4491 . T) (-4486 . T) (-4497 . T) (-4498 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-578) ((|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 -(-579 R -1985 L) +(-579 R -2057 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,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(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 -672) (|devaluate| |#2|)))) -(-580 R -1985) +((|HasCategory| |#3| (LIST (QUOTE -677) (|devaluate| |#2|)))) +(-580 R -2057) ((|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 -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1164)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-642))))) -(-581 -1985 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1169)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-647))))) +(-581 -2057 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,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(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 @@ -2260,27 +2260,27 @@ NIL ((|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 -(-583 -1985) +(-583 -2057) ((|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, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(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 (-584 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."))) -((-4142 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4215 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-585) ((|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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-586 R -1985) +(-586 R -2057) ((|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 -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-295))) (|HasCategory| |#2| (QUOTE (-642))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-295)))) (|HasCategory| |#1| (QUOTE (-569)))) -(-587 -1985 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-295))) (|HasCategory| |#2| (QUOTE (-647))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-295)))) (|HasCategory| |#1| (QUOTE (-569)))) +(-587 -2057 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' + +/[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(+,[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(+,[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 -(-588 R -1985) +(-588 R -2057) ((|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 @@ -2302,21 +2302,21 @@ NIL NIL (-593 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL (-594 |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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-380)))) (-595) ((|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 -(-596 R -1985) +(-596 R -2057) ((|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 -(-597 E -1985) +(-597 E -2057) ((|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 @@ -2324,10 +2324,10 @@ NIL ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-599 -1985) +(-599 -2057) ((|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}."))) -((-4465 . T) (-4464 . T)) -((|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-1201))))) +((-4494 . T) (-4493 . T)) +((|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-1206))))) (-600 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 @@ -2354,19 +2354,19 @@ NIL NIL (-606 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2811 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-2811 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2867 (|HasCategory| (-145) (LIST (QUOTE -631) (QUOTE (-885)))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130)))) (|HasCategory| (-145) (QUOTE (-870))) (-2867 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-607 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 (-608 |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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|)))) (|HasCategory| (-577) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577)))))) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-577)) (|devaluate| |#1|)))) (|HasCategory| (-577) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-577)))))) (-609 |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}.")) (|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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4472 "*") |has| |#1| (-569)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-569)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-569)))) (-610) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) @@ -2380,7 +2380,7 @@ NIL ((|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 -(-613 R -1985 FG) +(-613 R -2057 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{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{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 @@ -2390,2831 +2390,2851 @@ NIL NIL (-615 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-616 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 -4471)) (|HasCategory| |#2| (QUOTE (-865))) (|HasAttribute| |#1| (QUOTE -4470)) (|HasCategory| |#3| (QUOTE (-1125)))) +((|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-870))) (|HasAttribute| |#1| (QUOTE -4499)) (|HasCategory| |#3| (QUOTE (-1130)))) (-617 |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 (-618) -((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes."))) -NIL -NIL -(-619) ((|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 -(-620 R A) +(-619 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. 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T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) -(-621 |Entry|) +((-4496 -2867 (-2790 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4494 . T) (-4493 . T)) +((-2867 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) +(-620) +((|constructor| (NIL "This is the datatype for the \\spad{JVM} bytecodes."))) +NIL +NIL +(-621) +NIL +NIL +NIL +(-622) +NIL +NIL +NIL +(-623) +NIL +NIL +NIL +(-624) +NIL +NIL +NIL +(-625) +((|constructor| (NIL "This is the datatype for the \\spad{JVM} opcodes."))) +NIL +NIL +(-626 |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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-102)))) -(-622 S |Key| |Entry|) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-870))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-102)))) +(-627 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 -(-623 |Key| |Entry|) +(-628 |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}."))) -((-4471 . T)) +((-4500 . T)) NIL -(-624 R S) +(-629 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 -(-625 S) +(-630 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."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) -(-626 S) +((|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) +(-631 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 -(-627 S) +(-632 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-628 -1985 UP) +(-633 -2057 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 -(-629 S) +(-634 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 -(-630) +(-635) ((|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'")) (|unknown| (($) "the indefinite `unknown'"))) NIL NIL -(-631 S) +(-636 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms \\spad{`s'} into an element of `\\%'."))) NIL NIL -(-632 S R) +(-637 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 -(-633 R) +(-638 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."))) -((-4467 . T)) +((-4496 . T)) NIL -(-634 A R S) +(-639 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}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-864)))) -(-635 R -1985) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-869)))) +(-640 R -2057) ((|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 -(-636 R UP) +(-641 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"))) -((-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4463 . T) (-4467 . T)) -((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) -(-637 R E V P TS ST) +((-4494 . T) (-4493 . T) ((-4501 "*") . T) (-4492 . T) (-4496 . T)) +((|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) +(-642 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 -(-638 OV E Z P) +(-643 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 -(-639) +(-644) ((|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 -(-640 |VarSet| R |Order|) +(-645 |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}}."))) -((-4467 . T)) +((-4496 . T)) NIL -(-641 R |ls|) +(-646 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 -(-642) +(-647) ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-643 R -1985) +(-648 R -2057) ((|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{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\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 -(-644 |lv| -1985) +(-649 |lv| -2057) ((|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 -(-645) +(-650) ((|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}.")) (|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."))) -((-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2438) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-1183) (QUOTE (-865))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 (-52))) (QUOTE (-1125)))) -(-646 S R) +((-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -2727) (QUOTE (-52))))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-1188) (QUOTE (-870))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 (-52))) (QUOTE (-1130)))) +(-651 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-375)))) -(-647 R) +(-652 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4465 . T) (-4464 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4494 . T) (-4493 . T)) NIL -(-648 R A) +(-653 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4467 -2811 (-2700 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4465 . T) (-4464 . T)) -((-2811 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) -(-649 R FE) +((-4496 -2867 (-2790 (|has| |#2| (-379 |#1|)) (|has| |#1| (-569))) (-12 (|has| |#2| (-430 |#1|)) (|has| |#1| (-569)))) (-4494 . T) (-4493 . T)) +((-2867 (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -379) (|devaluate| |#1|)))) +(-654 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 -(-650 R) +(-655 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 -(-651 |vars|) +(-656 |vars|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) NIL NIL -(-652 S R) +(-657 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 -((-2686 (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-375)))) -(-653 K B) +((-2779 (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-375)))) +(-658 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-4465 . T) (-4464 . T)) -((-12 (|HasCategory| (-651 |#2|) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125))))) -(-654 R) +((-4494 . T) (-4493 . T)) +((-12 (|HasCategory| (-656 |#2|) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-1130))))) +(-659 R) ((|constructor| (NIL "An extension of left-module 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}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL -(-655 K B) +(-660 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL -(-656 S) +(-661 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) NIL NIL -(-657 A B) +(-662 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 -(-658 A B) +(-663 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 -(-659 A B C) +(-664 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 -(-660 S) +(-665 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} is the empty list."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-661 T$) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-849))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-666 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-662 S) +(-667 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-663 S) +(-668 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-664 R) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-669 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline"))) NIL NIL -(-665 S E |un|) +(-670 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|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 -(-666 A S) +(-671 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,{}..))}.")) (|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 -4471))) -(-667 S) +((|HasAttribute| |#1| (QUOTE -4500))) +(-672 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,{}..))}.")) (|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 -(-668 R -1985 L) +(-673 R -2057 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 -(-669 A) +(-674 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}}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) -(-670 A M) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) +(-675 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) -(-671 S A) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) +(-676 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-375)))) -(-672 A) +(-677 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}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-673 -1985 UP) +(-678 -2057 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)))) -(-674 A -2202) +(-679 A -1357) ((|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}}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) -(-675 A L) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) +(-680 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 -(-676 S) +(-681 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-677) +(-682) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-678 M R S) +(-683 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}."))) -((-4465 . T) (-4464 . T)) -((|HasCategory| |#1| (QUOTE (-807)))) -(-679 R) +((-4494 . T) (-4493 . T)) +((|HasCategory| |#1| (QUOTE (-812)))) +(-684 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 fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-680 |VarSet| R) +(-685 |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) (-4465 . T) (-4464 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4494 . T) (-4493 . T)) ((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-174)))) -(-681 A S) +(-686 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 -(-682 S) +(-687 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}."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-683 -1985) +(-688 -2057) ((|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 -(-684 -1985 |Row| |Col| M) +(-689 -2057 |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 -(-685 R E OV P) +(-690 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 -(-686 |n| R) +(-691 |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."))) -((-4467 . T) (-4470 . T) (-4464 . T) (-4465 . T)) -((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569))) (-2811 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) -(-687) +((-4496 . T) (-4499 . T) (-4493 . T) (-4494 . T)) +((|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4501 "*"))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569))) (-2867 (|HasAttribute| |#2| (QUOTE (-4501 "*"))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +(-692) ((|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 -(-688 |VarSet|) +(-693 |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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-689 A S) +(-694 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-690 S) +(-695 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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 -(-691 R) +(-696 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 -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-692) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-697) ((|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 -(-693 |VarSet|) +(-698 |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 -(-694 A) +(-699 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 -(-695 A C) +(-700 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 -(-696 A B C) +(-701 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 -(-697) +(-702) ((|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 -(-698 A) +(-703 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 -(-699 A C) +(-704 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 -(-700 A B C) +(-705 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 -(-701 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-706 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 -(-702 S R |Row| |Col|) +(-707 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|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 (-4472 "*"))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569)))) -(-703 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-4501 "*"))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-569)))) +(-708 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| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|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"))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL -(-704 R |Row| |Col| M) +(-709 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 (-375))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569)))) -(-705 R) +(-710 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."))) -((-4470 . T) (-4471 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4472 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-706 R) +((-4499 . T) (-4500 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-318))) (|HasCategory| |#1| (QUOTE (-569))) (|HasAttribute| |#1| (QUOTE (-4501 "*"))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-711 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 -(-707 T$) +(-712 T$) ((|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 -(-708 S -1985 FLAF FLAS) +(-713 S -2057 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}.")) 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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}."))) -((-4471 . T)) +((-4500 . T)) NIL -(-712 U) +(-717 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 -(-713) +(-718) ((|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.")) 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(|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 -(-715) +(-720) ((|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}"))) -((-4142 . T) (-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4215 . T) (-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-716 R) +(-721 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 -(-717) +(-722) ((|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}"))) -((-4469 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4498 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-718 S D1 D2 I) +(-723 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 -(-719 S) +(-724 S) ((|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 -(-720 S) +(-725 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 -(-721 S T$) +(-726 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 -(-722 S -2136 I) +(-727 S -2389 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 -(-723 E OV R P) +(-728 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 -(-724 R) +(-729 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)}.}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-725 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-730 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 -(-726) +(-731) ((|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 -(-727 R |Mod| -2871 -1334 |exactQuo|) +(-732 R |Mod| -3530 -3771 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-728 R |Rep|) +(-733 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-729 IS E |ff|) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4495 |has| |#1| (-375)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-734 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-730 R M) +(-735 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) +((-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-731 R |Mod| -2871 -1334 |exactQuo|) +(-736 R |Mod| -3530 -3771 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4467 . T)) +((-4496 . T)) NIL -(-732 S R) +(-737 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-733 R) +(-738 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL -(-734 -1985) +(-739 -2057) ((|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]]}."))) -((-4467 . T)) +((-4496 . T)) NIL -(-735 S) +(-740 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}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-736) +(-741) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|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 -(-737 S) +(-742 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 -(-738) +(-743) ((|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 -(-739 S R UP) +(-744 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 (-361))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-380)))) -(-740 R UP) +(-745 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."))) -((-4463 |has| |#1| (-375)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 |has| |#1| (-375)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-741 S) +(-746 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 -(-742) +(-747) ((|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 -(-743 -1985 UP) +(-748 -2057 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 -(-744 |VarSet| E1 E2 R S PR PS) +(-749 |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 -(-745 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-750 |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 -(-746 E OV R PPR) +(-751 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 -(-747 |vl| R) +(-752 |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."))) -(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-932))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2811 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-882 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-748 E OV R PRF) +(((-4501 "*") |has| |#2| (-174)) (-4492 |has| |#2| (-569)) (-4497 |has| |#2| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (-2867 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (-2867 (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-569)))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-887 |#1|) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasAttribute| |#2| (QUOTE -4497)) (|HasCategory| |#2| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-753 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-749 E OV R P) +(-754 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-750 R S M) +(-755 R S M) ((|constructor| (NIL "MonoidRingFunctions2 implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-751 R M) +(-756 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-865)))) -(-752 S) +((-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) (-4496 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#2| (QUOTE (-870)))) +(-757 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4460 . T) (-4471 . T)) +((-4489 . T) (-4500 . T)) NIL -(-753 S) +(-758 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}."))) -((-4470 . T) (-4460 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-754) +((-4499 . T) (-4489 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-759) ((|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 -(-755 S) +(-760 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 -(-756 |Coef| |Var|) +(-761 |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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-757 OV E R P) +(-762 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 -(-758 E OV R P) +(-763 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 -(-759 S R) +(-764 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 -(-760 R) +(-765 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}."))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL -(-761) +(-766) ((|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 -(-762) +(-767) ((|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 -(-763) +(-768) ((|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 -(-764) +(-769) ((|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 -(-765) +(-770) ((|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 -(-766) +(-771) ((|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 -(-767) +(-772) ((|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 -(-768) +(-773) ((|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 -(-769) +(-774) ((|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 -(-770) +(-775) ((|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 -(-771) +(-776) ((|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,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,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,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,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 -(-772) +(-777) ((|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 -(-773) +(-778) ((|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 -(-774) +(-779) ((|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 -(-775) +(-780) ((|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 -(-776 S) +(-781 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| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-777) +(-782) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{\\spad{x*}(\\spad{y+z}) = x*y + \\spad{x*z}} \\indented{2}{(x+y)\\spad{*z} = \\spad{x*z} + \\spad{y*z}} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 \\spad{=>} a=0 or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-778 S) +(-783 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative \\spad{rng} which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|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 -(-779) +(-784) ((|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 -(-780 |Par|) +(-785 |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 -(-781 -1985) +(-786 -2057) ((|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 -(-782 P -1985) +(-787 P -2057) ((|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 -(-783 T$) +(-788 T$) NIL NIL NIL -(-784 UP -1985) +(-789 UP -2057) ((|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{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{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{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{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{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{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 -(-785) +(-790) ((|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 -(-786 R) +(-791 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 -(-787) +(-792) ((|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."))) -(((-4472 "*") . T)) +(((-4501 "*") . T)) NIL -(-788 R -1985) +(-793 R -2057) ((|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 -(-789 S) +(-794 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 -(-790) +(-795) ((|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 -(-791 R |PolR| E |PolE|) +(-796 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 -(-792 R E V P TS) +(-797 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 -(-793 -1985 |ExtF| |SUEx| |ExtP| |n|) +(-798 -2057 |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 -(-794 BP E OV R P) +(-799 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 -(-795 |Par|) +(-800 |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 -(-796 R |VarSet|) +(-801 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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206))))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-375))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))) (-2779 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))) (-2779 (|HasCategory| |#1| (QUOTE (-558)))) (-2779 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))) (-2779 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-577))))) (-2779 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-1206)))) (-2779 (|HasCategory| |#1| (LIST (QUOTE -1022) (QUOTE (-577))))))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-802 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 -(-798 R) +(-803 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)}"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1107) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1177))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-799 R) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4495 |has| |#1| (-375)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-1112) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-1182))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-239))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-804 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 -420) (QUOTE (-577)))))) -(-800 R E V P) +(-805 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.}"))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-801 S) +(-806 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 (-569))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1074))) (|HasCategory| |#1| (QUOTE (-174)))) -(-802) +((-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-1079))) (|HasCategory| |#1| (QUOTE (-174)))) +(-807) ((|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 -(-803) +(-808) ((|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 -(-804) +(-809) ((|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 -(-805) +(-810) ((|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 -(-806 |Curve|) +(-811 |Curve|) ((|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 -(-807) +(-812) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering."))) NIL NIL -(-808) +(-813) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-809) +(-814) ((|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| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-810) +(-815) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-811) +(-816) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-812 S R) +(-817 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| ((|#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,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-380)))) -(-813 R) +((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-380)))) +(-818 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-814 -2811 R OS S) +(-819 -2867 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-815 R) +(-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-2811 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1024 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) -(-816) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (-2867 (|HasCategory| (-1029 |#1|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (|HasCategory| (-1029 |#1|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| (-1029 |#1|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1029 |#1|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) +(-821) ((|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 -(-817 R -1985 L) +(-822 R -2057 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{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-818 R -1985) +(-823 R -2057) ((|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 -(-819) +(-824) ((|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 -(-820 R -1985) +(-825 R -2057) ((|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 -(-821) +(-826) ((|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 -(-822 -1985 UP UPUP R) +(-827 -2057 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 -(-823 -1985 UP L LQ) +(-828 -2057 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 -(-824) +(-829) ((|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 -(-825 -1985 UP L LQ) +(-830 -2057 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^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{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{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 ai}} is \\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 -(-826 -1985 UP) +(-831 -2057 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 -(-827 -1985 L UP A LO) +(-832 -2057 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 -(-828 -1985 UP) +(-833 -2057 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{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 ai}} is \\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)))) -(-829 -1985 LO) +(-834 -2057 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 -(-830 -1985 LODO) +(-835 -2057 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(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(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)]}."))) 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T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-839 (-1206)) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-839 (-1206)) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-839 (-1206)) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-839 (-1206)) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-839 (-1206)) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-838 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4472 "*") |has| |#2| (-375)) (-4463 |has| |#2| (-375)) (-4468 |has| |#2| (-375)) (-4462 |has| |#2| (-375)) (-4467 . T) (-4465 . T) (-4464 . T)) +(((-4501 "*") |has| |#2| (-375)) (-4492 |has| |#2| (-375)) (-4497 |has| |#2| (-375)) (-4491 |has| |#2| (-375)) (-4496 . T) (-4494 . T) (-4493 . T)) ((|HasCategory| |#2| (QUOTE (-375)))) -(-834 S) +(-839 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 -(-835 S) +(-840 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** 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}.")) (|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}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|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}."))) NIL -((|HasCategory| |#1| (QUOTE (-865)))) -(-836) +((|HasCategory| |#1| (QUOTE (-870)))) +(-841) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-837) +(-842) ((|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 -(-838) +(-843) ((|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 -(-839) +(-844) ((|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 -(-840) +(-845) ((|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 -(-841) +(-846) ((|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|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-842 R) +(-847 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-843 P R) +(-848 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) ((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-239)))) -(-844) +(-849) ((|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 -(-845) +(-850) ((|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 -(-846 S) +(-851 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4470 . T) (-4460 . T) (-4471 . T)) +((-4499 . T) (-4489 . T) (-4500 . T)) NIL -(-847) +(-852) ((|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 -(-848 R S) +(-853 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 -(-849 R) +(-854 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."))) -((-4467 |has| |#1| (-864))) -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) -(-850 A S) +((-4496 |has| |#1| (-869))) +((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-21))) (-2867 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) +(-855 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.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-851 S) +(-856 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.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-852 R) +(-857 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) +((-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148)))) -(-853) +(-858) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) NIL NIL -(-854) +(-859) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|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 -(-855) +(-860) ((|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 -(-856) +(-861) ((|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 -(-857) +(-862) ((|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 -(-858 R S) +(-863 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 -(-859 R) +(-864 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4467 |has| |#1| (-864))) -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-21))) (-2811 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-864)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (-2811 (|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) -(-860) +((-4496 |has| |#1| (-869))) +((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-21))) (-2867 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-869)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (-2867 (|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-558)))) +(-865) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-861 -3985 S) +(-866 -3651 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-862) +(-867) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-863 S) +(-868 S) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-864) +(-869) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4467 . T)) +((-4496 . T)) NIL -(-865) +(-870) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-866 T$ |f|) +(-871 T$ |f|) ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) -(-867 S) +((|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) +(-872 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-868) +(-873) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-869 S R) +(-874 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174)))) -(-870 R) +(-875 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-871 R C) +(-876 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 (-375))) (|HasCategory| |#1| (QUOTE (-569)))) -(-872 R |sigma| -2630) +(-877 R |sigma| -1797) ((|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."))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) -(-873 |x| R |sigma| -2630) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-375)))) +(-878 |x| R |sigma| -1797) ((|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}."))) -((-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-375)))) -(-874 R) +((-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-375)))) +(-879 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 -420) (QUOTE (-577)))))) -(-875) +(-880) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-876) +(-881) ((|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 -(-877 S) +(-882 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 -(-878) +(-883) ((|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 -(-879) +(-884) ((|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 -(-880) +(-885) ((|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 -(-881) +(-886) ((|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 -(-882 |VariableList|) +(-887 |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 -(-883) +(-888) ((|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 -(-884 R |vl| |wl| |wtlevel|) +(-889 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)"))) -((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) +((-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375)))) -(-885 R PS UP) +(-890 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 -(-886 R |x| |pt|) +(-891 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 -(-887 |p|) +(-892 |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}."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-888 |p|) +(-893 |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)."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-889 |p|) +(-894 |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)."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-888 |#1|) (QUOTE (-932))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-148))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-888 |#1|) (QUOTE (-1047))) (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865))) (-2811 (|HasCategory| (-888 |#1|) (QUOTE (-836))) (|HasCategory| (-888 |#1|) (QUOTE (-865)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-1177))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| (-888 |#1|) (QUOTE (-238))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (QUOTE (-239))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -527) (QUOTE (-1201)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -888) (|devaluate| |#1|)) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| (-888 |#1|) (QUOTE (-318))) (|HasCategory| (-888 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-888 |#1|) (QUOTE (-932)))) (|HasCategory| (-888 |#1|) (QUOTE (-146))))) -(-890 |p| PADIC) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-893 |#1|) (QUOTE (-937))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-893 |#1|) (QUOTE (-146))) (|HasCategory| (-893 |#1|) (QUOTE (-148))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1052))) (|HasCategory| (-893 |#1|) (QUOTE (-841))) (|HasCategory| (-893 |#1|) (QUOTE (-870))) (-2867 (|HasCategory| (-893 |#1|) (QUOTE (-841))) (|HasCategory| (-893 |#1|) (QUOTE (-870)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-893 |#1|) (QUOTE (-1182))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| (-893 |#1|) (QUOTE (-238))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -527) (QUOTE (-1206)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -320) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (LIST (QUOTE -297) (LIST (QUOTE -893) (|devaluate| |#1|)) (LIST (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-318))) (|HasCategory| (-893 |#1|) (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-893 |#1|) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-893 |#1|) (QUOTE (-937)))) (|HasCategory| (-893 |#1|) (QUOTE (-146))))) +(-895 |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)}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-932))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (-2811 (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-932)))) (|HasCategory| |#2| (QUOTE (-146))))) -(-891 S T$) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-870))) (-2867 (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-870)))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1182))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-238))) (|HasCategory| |#2| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -297) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-558))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-937)))) (|HasCategory| |#2| (QUOTE (-146))))) +(-896 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 (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))))) -(-892) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))))) +(-897) ((|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 -(-893) +(-898) ((|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 -(-894) +(-899) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-895 CF1 CF2) +(-900 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-896 |ComponentFunction|) +(-901 |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 -(-897 CF1 CF2) +(-902 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-898 |ComponentFunction|) +(-903 |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 -(-899) +(-904) ((|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 -(-900 CF1 CF2) +(-905 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-901 |ComponentFunction|) +(-906 |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 -(-902) +(-907) ((|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| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-903 R) +(-908 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 -(-904 R S L) +(-909 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 -(-905 S) +(-910 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 -(-906 |Base| |Subject| |Pat|) +(-911 |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 (-2686 (|HasCategory| |#2| (QUOTE (-1074)))) (-2686 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (-12 (|HasCategory| |#2| (QUOTE (-1074))) (-2686 (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201))))) -(-907 R A B) +((-12 (-2779 (|HasCategory| |#2| (QUOTE (-1079)))) (-2779 (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206)))))) (-12 (|HasCategory| |#2| (QUOTE (-1079))) (-2779 (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206)))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206))))) +(-912 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 -(-908 R S) +(-913 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 -(-909 R -2136) +(-914 R -2389) ((|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 -(-910 R S) +(-915 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 -(-911 R) +(-916 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 -(-912 |VarSet|) +(-917 |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 -(-913 UP R) +(-918 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-914 A T$ S) +(-919 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-915 T$ S) +(-920 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-916) +(-921) ((|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 -(-917 UP -1985) +(-922 UP -2057) ((|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 -(-918) +(-923) ((|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 -(-919) +(-924) ((|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 -(-920 R S) +(-925 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL -(-921 S) +(-926 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-4467 . T)) +((-4496 . T)) NIL -(-922 A S) +(-927 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|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}\\spad{-}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)}."))) NIL NIL -(-923 S) +(-928 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|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}\\spad{-}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)}."))) NIL NIL -(-924 S) +(-929 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 (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-925 |n| R) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-930 |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 -(-926 S) +(-931 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}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|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."))) -((-4467 . T)) +((-4496 . T)) NIL -(-927 S) +(-932 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}.")) (|support| (((|Set| |#1|) $) "\\spad{support(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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-928 S) +(-933 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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.")) (|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."))) -((-4467 . T)) -((-2811 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-865)))) -(-929 R E |VarSet| S) +((-4496 . T)) +((-2867 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-870)))) +(-934 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 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 -(-930 R S) +(-935 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 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 -(-931 S) +(-936 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 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 (-146)))) -(-932) +(-937) ((|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 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}."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-933 |p|) +(-938 |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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) ((|HasCategory| $ (QUOTE (-148))) (|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-380)))) -(-934 R0 -1985 UP UPUP R) +(-939 R0 -2057 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 -(-935 UP UPUP R) +(-940 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 -(-936 UP UPUP) +(-941 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 -(-937 R) +(-942 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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-938 R) +(-943 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 -(-939 E OV R P) +(-944 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 -(-940) +(-945) ((|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(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em 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(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em 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(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em 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 ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,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(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,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 -(-941 -1985) +(-946 -2057) ((|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 -(-942 R) +(-947 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 -(-943) +(-948) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-944) +(-949) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4472 "*") . T)) +(((-4501 "*") . T)) NIL -(-945 -1985 P) +(-950 -2057 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-946 |xx| -1985) +(-951 |xx| -2057) ((|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 -(-947 R |Var| |Expon| GR) +(-952 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 -(-948 S) +(-953 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 -(-949) +(-954) ((|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 -(-950) +(-955) ((|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*\\%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 -(-951) +(-956) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-952 R -1985) +(-957 R -2057) ((|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| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-953) +(-958) ((|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|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-954 S A B) +(-959 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 -(-955 S R -1985) +(-960 S R -2057) ((|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 -(-956 I) +(-961 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 -(-957 S E) +(-962 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 -(-958 S R L) +(-963 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 -(-959 S E V R P) +(-964 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 -905) (|devaluate| |#1|)))) -(-960 R -1985 -2136) +((|HasCategory| |#3| (LIST (QUOTE -910) (|devaluate| |#1|)))) +(-965 R -2057 -2389) ((|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 -(-961 -2136) +(-966 -2389) ((|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 -(-962 S R Q) +(-967 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 -(-963 S) +(-968 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 -(-964 S R P) +(-969 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 -(-965) +(-970) ((|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 -(-966 R) +(-971 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-967 |lv| R) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-972 |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 -(-968 |TheField| |ThePols|) +(-973 |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 (-864)))) -(-969 R S) +((|HasCategory| |#1| (QUOTE (-869)))) +(-974 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 -(-970 |x| R) +(-975 |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 -(-971 S R E |VarSet|) +(-976 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 (-932))) (|HasAttribute| |#2| (QUOTE -4468)) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#4| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#4| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#4| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) -(-972 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-937))) (|HasAttribute| |#2| (QUOTE -4497)) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#4| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#4| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#4| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#4| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) +(-977 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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-973 E V R P -1985) +(-978 E V R P -2057) ((|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 -(-974 E |Vars| R P S) +(-979 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 -(-975 R) +(-980 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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1206) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1206) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-1206) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1206) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-1206) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-981 E V R P -2057) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-465)))) -(-977) +(-982) ((|constructor| (NIL "This domain represents network port numbers (notable \\spad{TCP} and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer \\spad{`n'}."))) NIL NIL -(-978) +(-983) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-979 R L) +(-984 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL NIL -(-980 A B) +(-985 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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 -(-981 S) +(-986 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"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-982) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-987) ((|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 -(-983 -1985) +(-988 -2057) ((|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{ai = 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{ai = 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 -(-984 I) +(-989 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 -(-985) +(-990) ((|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 -(-986 R E) +(-991 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}"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4468))) -(-987 A B) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-132)))) (|HasAttribute| |#1| (QUOTE -4497))) +(-992 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) 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(|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-865))))) -(-988) +((-4496 -12 (|has| |#2| (-486)) (|has| |#1| (-486)))) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-870))))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814))))) (-12 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-486)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-486)))) (-12 (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#2| (QUOTE (-747))))) (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-380)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-486))) (|HasCategory| |#2| (QUOTE (-486)))) (-12 (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#2| (QUOTE (-747)))) (-12 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-814))))) (-12 (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#2| (QUOTE (-747)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-132))) (|HasCategory| |#2| (QUOTE (-132)))) (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-870))))) +(-993) ((|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| (($ (|Identifier|) (|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| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-989 T$) +(-994 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-990 T$) +(-995 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} \\spad{++} returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-991 S T$) +(-996 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-992) +(-997) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-993 S) +(-998 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL -(-994 R |polR|) +(-999 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 (-465)))) -(-995) +(-1000) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-996) +(-1001) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\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| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-997 S |Coef| |Expon| |Var|) +(-1002 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 -(-998 |Coef| |Expon| |Var|) +(-1003 |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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-999) +(-1004) ((|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 -(-1000 S R E |VarSet| P) +(-1005 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 (-569)))) -(-1001 R E |VarSet| P) +(-1006 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."))) -((-4470 . T)) +((-4499 . T)) NIL -(-1002 R E V P) +(-1007 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 (-148))) (|HasCategory| |#1| (QUOTE (-318)))) (|HasCategory| |#1| (QUOTE (-465)))) -(-1003 K) +(-1008 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 -(-1004 |VarSet| E RC P) +(-1009 |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 -(-1005 R) +(-1010 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}."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1006 R1 R2) +(-1011 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-1007 R) +(-1012 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 -(-1008 K) +(-1013 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 -(-1009 R E OV PPR) +(-1014 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 -(-1010 K R UP -1985) +(-1015 K R UP -2057) ((|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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\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{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{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1011 |vl| |nv|) +(-1016 |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 -(-1012 R |Var| |Expon| |Dpoly|) +(-1017 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 (-148))) (|HasCategory| |#1| (QUOTE (-318))))) -(-1013 R E V P TS) +(-1018 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 -(-1014) +(-1019) ((|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 -(-1015 A B R S) +(-1020 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 -(-1016 A S) +(-1021 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 (-932))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1047))) (|HasCategory| |#2| (QUOTE (-836))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1177)))) -(-1017 S) +((|HasCategory| |#2| (QUOTE (-937))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1052))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-1182)))) +(-1022 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}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1018 |n| K) +(-1023 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|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 -(-1019) +(-1024) ((|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 -(-1020 S) +(-1025 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."))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL -(-1021 S R) +(-1026 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 (-558))) (|HasCategory| |#2| (QUOTE (-1085))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-301)))) -(-1022 R) +((|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-301)))) +(-1027 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}."))) -((-4463 |has| |#1| (-301)) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 |has| |#1| (-301)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1023 QR R QS S) +(-1028 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 -(-1024 R) +(-1029 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.}"))) -((-4463 |has| |#1| (-301)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1201)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1085))) (|HasCategory| |#1| (QUOTE (-558)))) -(-1025 S) +((-4492 |has| |#1| (-301)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-301))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -527) (QUOTE (-1206)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -297) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-558)))) +(-1030 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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1026 S) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1031 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1027) +(-1032) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1028 -1985 UP UPUP |radicnd| |n|) +(-1033 -2057 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4463 |has| (-420 |#2|) (-375)) (-4468 |has| (-420 |#2|) (-375)) (-4462 |has| (-420 |#2|) (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2811 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2811 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2811 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2811 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2811 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -654) (QUOTE (-577)))) (-2811 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) -(-1029 |bb|) +((-4492 |has| (-420 |#2|) (-375)) (-4497 |has| (-420 |#2|) (-375)) (-4491 |has| (-420 |#2|) (-375)) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-420 |#2|) (QUOTE (-146))) (|HasCategory| (-420 |#2|) (QUOTE (-148))) (|HasCategory| (-420 |#2|) (QUOTE (-361))) (-2867 (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))) (|HasCategory| (-420 |#2|) (QUOTE (-380))) (-2867 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2867 (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (QUOTE (-361)))) (-2867 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-361))))) (-2867 (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -659) (QUOTE (-577)))) (-2867 (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 |#2|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-238))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (QUOTE (-239))) (|HasCategory| (-420 |#2|) (QUOTE (-375)))) (-12 (|HasCategory| (-420 |#2|) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-420 |#2|) (QUOTE (-375))))) +(-1034 |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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-577) (QUOTE (-932))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1047))) (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865))) (-2811 (|HasCategory| (-577) (QUOTE (-836))) (|HasCategory| (-577) (QUOTE (-865)))) (|HasCategory| (-577) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1177))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1201)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -654) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-932)))) (|HasCategory| (-577) (QUOTE (-146))))) -(-1030) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-577) (QUOTE (-937))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-148))) (|HasCategory| (-577) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-1052))) (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870))) (-2867 (|HasCategory| (-577) (QUOTE (-841))) (|HasCategory| (-577) (QUOTE (-870)))) (|HasCategory| (-577) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-1182))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| (-577) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| (-577) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| (-577) (QUOTE (-238))) (|HasCategory| (-577) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| (-577) (QUOTE (-239))) (|HasCategory| (-577) (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| (-577) (LIST (QUOTE -527) (QUOTE (-1206)) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -320) (QUOTE (-577)))) (|HasCategory| (-577) (LIST (QUOTE -297) (QUOTE (-577)) (QUOTE (-577)))) (|HasCategory| (-577) (QUOTE (-318))) (|HasCategory| (-577) (QUOTE (-558))) (|HasCategory| (-577) (LIST (QUOTE -659) (QUOTE (-577)))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-577) (QUOTE (-937)))) (|HasCategory| (-577) (QUOTE (-146))))) +(-1035) ((|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 -(-1031) +(-1036) ((|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 -(-1032 RP) +(-1037 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 -(-1033 S) +(-1038 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 -(-1034 A S) +(-1039 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 -4471)) (|HasCategory| |#2| (QUOTE (-1125)))) -(-1035 S) +((|HasAttribute| |#1| (QUOTE -4500)) (|HasCategory| |#2| (QUOTE (-1130)))) +(-1040 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 -(-1036 S) +(-1041 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 -(-1037) +(-1042) ((|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}}"))) -((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) +((-4492 . T) (-4497 . T) (-4491 . T) (-4494 . T) (-4493 . T) ((-4501 "*") . T) (-4496 . T)) NIL -(-1038 R -1985) +(-1043 R -2057) ((|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 -(-1039 R -1985) +(-1044 R -2057) ((|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 -(-1040 -1985 UP) +(-1045 -2057 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 -(-1041 -1985 UP) +(-1046 -2057 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 -(-1042 S) +(-1047 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 -(-1043 F1 UP UPUP R F2) +(-1048 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 -(-1044) +(-1049) ((|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 -(-1045 |Pol|) +(-1050 |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 -(-1046 |Pol|) +(-1051 |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 -(-1047) +(-1052) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1048) +(-1053) ((|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 -(-1049 |TheField|) +(-1054 |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"))) -((-4463 . T) (-4468 . T) (-4462 . T) (-4465 . T) (-4464 . T) ((-4472 "*") . T) (-4467 . T)) -((-2811 (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1063) (QUOTE (-577))))) -(-1050 -1985 L) +((-4492 . T) (-4497 . T) (-4491 . T) (-4494 . T) (-4493 . T) ((-4501 "*") . T) (-4496 . T)) +((-2867 (|HasCategory| (-420 (-577)) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-420 (-577)) (LIST (QUOTE -1068) (QUOTE (-577))))) +(-1055 -2057 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{fi} must satisfy \\spad{op 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 -(-1051 S) +(-1056 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 (-1125)))) -(-1052 R E V P) +((|HasCategory| |#1| (QUOTE (-1130)))) +(-1057 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."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1053 R) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1058 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(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em 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 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 ai} and {\\em 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 (-4472 "*")))) -(-1054 R) +((|HasAttribute| |#1| (QUOTE (-4501 "*")))) +(-1059 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 (-375))) (|HasCategory| |#1| (QUOTE (-380)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-318)))) -(-1055 S) +(-1060 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 -(-1056) +(-1061) ((|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 -(-1057 S) +(-1062 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 -(-1058 S) +(-1063 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 -(-1059 -1985 |Expon| |VarSet| |FPol| |LFPol|) +(-1064 -2057 |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"))) -(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1060) +(-1065) ((|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.}"))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2438) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102)))) -(-1061) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (QUOTE (-1206))) (LIST (QUOTE |:|) (QUOTE -2727) (QUOTE (-52))))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-1206) (QUOTE (-870))) (|HasCategory| (-52) (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102)))) +(-1066) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1062 A S) +(-1067 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 -(-1063 S) +(-1068 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 -(-1064 Q R) +(-1069 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 -(-1065) +(-1070) ((|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 -(-1066 UP) +(-1071 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 -(-1067 R) +(-1072 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 -(-1068 R) +(-1073 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 -(-1069 T$) +(-1074 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| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1070 T$) +(-1075 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 -(-1071 R |ls|) +(-1076 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}."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-1125))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -796) (|devaluate| |#1|) (LIST (QUOTE -882) (|devaluate| |#2|)))))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-882 |#2|) (QUOTE (-380))) (|HasCategory| (-796 |#1| (-882 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-796 |#1| (-882 |#2|)) (QUOTE (-102)))) -(-1072) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| (-801 |#1| (-887 |#2|)) (QUOTE (-1130))) (|HasCategory| (-801 |#1| (-887 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -801) (|devaluate| |#1|) (LIST (QUOTE -887) (|devaluate| |#2|)))))) (|HasCategory| (-801 |#1| (-887 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-801 |#1| (-887 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| (-887 |#2|) (QUOTE (-380))) (|HasCategory| (-801 |#1| (-887 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-801 |#1| (-887 |#2|)) (QUOTE (-102)))) +(-1077) ((|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 -(-1073 S) +(-1078 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 -(-1074) +(-1079) ((|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."))) -((-4467 . T)) +((-4496 . T)) NIL -(-1075 |xx| -1985) +(-1080 |xx| -2057) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1076 S) +(-1081 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-1077 S |m| |n| R |Row| |Col|) +(-1082 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 (-318))) (|HasCategory| |#4| (QUOTE (-375))) (|HasCategory| |#4| (QUOTE (-569))) (|HasCategory| |#4| (QUOTE (-174)))) -(-1078 |m| |n| R |Row| |Col|) +(-1083 |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"))) -((-4470 . T) (-4465 . T) (-4464 . T)) +((-4499 . T) (-4494 . T) (-4493 . T)) NIL -(-1079 |m| |n| R) +(-1084 |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}."))) -((-4470 . T) (-4465 . T) (-4464 . T)) -((|HasCategory| |#3| (QUOTE (-174))) (-2811 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375)))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1125))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -626) (QUOTE (-880))))) -(-1080 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4499 . T) (-4494 . T) (-4493 . T)) +((|HasCategory| |#3| (QUOTE (-174))) (-2867 (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-375)))) (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (QUOTE (-318))) (|HasCategory| |#3| (QUOTE (-569))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-885))))) +(-1085 |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 -(-1081 R) +(-1086 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"))) NIL NIL -(-1082 S T$) +(-1087 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1125)))) -(-1083) +((|HasCategory| |#1| (QUOTE (-1130)))) +(-1088) ((|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 -(-1084 S) +(-1089 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1085) +(-1090) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1086 |TheField| |ThePolDom|) +(-1091 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1087) +(-1092) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4487 . T) (-4491 . T) (-4486 . T) (-4497 . T) (-4498 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1088) +(-1093) ((|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}"))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (QUOTE (-1201))) (LIST (QUOTE |:|) (QUOTE -2438) (QUOTE (-52))))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1125))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-1125))) (|HasCategory| (-1201) (QUOTE (-865))) (|HasCategory| (-52) (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1201)) (|:| -2438 (-52))) (QUOTE (-102)))) -(-1089 S R E V) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (QUOTE (-1206))) (LIST (QUOTE |:|) (QUOTE -2727) (QUOTE (-52))))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| (-52) (QUOTE (-1130))) (|HasCategory| (-52) (LIST (QUOTE -320) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-1130))) (|HasCategory| (-1206) (QUOTE (-870))) (|HasCategory| (-52) (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102))) (|HasCategory| (-52) (QUOTE (-102)))) (|HasCategory| (-52) (QUOTE (-102))) (|HasCategory| (-52) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1206)) (|:| -2727 (-52))) (QUOTE (-102)))) +(-1094 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1017) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-1201))))) -(-1090 R E V) +((|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1022) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-1206))))) +(-1095 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-1091) +(-1096) ((|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 -(-1092 S |TheField| |ThePols|) +(-1097 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 -(-1093 |TheField| |ThePols|) +(-1098 |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 -(-1094 R E V P TS) +(-1099 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 -(-1095 S R E V P) +(-1100 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,...,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,...,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(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 -(-1096 R E V P) +(-1101 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,...,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,...,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(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}."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1097 R E V P TS) +(-1102 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 -(-1098) +(-1103) ((|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 -(-1099) +(-1104) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1100 |f|) +(-1105 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1101 |Base| R -1985) +(-1106 |Base| R -2057) ((|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 -(-1102 |Base| R -1985) +(-1107 |Base| R -2057) ((|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 -(-1103 R |ls|) +(-1108 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 -(-1104 UP SAE UPA) +(-1109 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 -(-1105 R UP M) +(-1110 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."))) -((-4463 |has| |#1| (-375)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))))) -(-1106 UP SAE UPA) +((-4492 |has| |#1| (-375)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-361))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-361)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-380))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-361))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-361)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206))))) (-12 (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))))) +(-1111 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 -(-1107) +(-1112) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1108) +(-1113) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1109 S) +(-1114 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 -(-1110) +(-1115) ((|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| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of \\spad{`n'} in \\spad{`s'}; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-1111 R) +(-1116 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 -(-1112 R) +(-1117 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"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| (-1113 (-1201)) (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1113 S) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| (-1118 (-1206)) (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| (-1118 (-1206)) (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| (-1118 (-1206)) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| (-1118 (-1206)) (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| (-1118 (-1206)) (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-238))) (|HasCategory| |#1| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1118 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 -(-1114 R S) +(-1119 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 (-864)))) -(-1115) +((|HasCategory| |#1| (QUOTE (-869)))) +(-1120) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1116 R S) +(-1121 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1117 S) +(-1122 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1119 |#1|) (QUOTE (-1125)))) -(-1118 S) +((|HasCategory| (-1124 |#1|) (QUOTE (-1130)))) +(-1123 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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{hi(s)} returns the second endpoint of \\spad{s}. Note: \\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 -(-1119 S) +(-1124 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1125)))) -(-1120 S L) +((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) +(-1125 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 -(-1121) +(-1126) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1122 A S) +(-1127 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1123 S) +(-1128 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4460 . T)) +((-4489 . T)) NIL -(-1124 S) +(-1129 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 -(-1125) +(-1130) ((|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 -(-1126 |m| |n|) +(-1131 |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 -(-1127 S) +(-1132 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)}}"))) -((-4470 . T) (-4460 . T) (-4471 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-1128 |Str| |Sym| |Int| |Flt| |Expr|) +((-4499 . T) (-4489 . T) (-4500 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-380))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-1133 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|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|) $ $) "\\spad{eq(s, t)} is \\spad{true} if \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1129) +(-1134) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1130 |Str| |Sym| |Int| |Flt| |Expr|) +(-1135 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1131 R FS) +(-1136 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 -(-1132 R E V P TS) +(-1137 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 -(-1133 R E V P TS) +(-1138 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 -(-1134 R E V P) +(-1139 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.}"))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1135) +(-1140) ((|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| (|PositiveInteger|)) (|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| (|PositiveInteger|)) (|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| (|PositiveInteger|))) "\\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 pi} in the corresponding double coset. Note: the resulting permutation {\\em 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,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 pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1136 S) +(-1141 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1137) +(-1142) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 -(-1138 |dimtot| |dim1| S) +(-1143 |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}."))) -((-4464 |has| |#3| (-1074)) (-4465 |has| |#3| (-1074)) (-4467 |has| |#3| (-6 -4467)) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-375))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-742))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-809))) (|HasCategory| |#3| (LIST 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(-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (LIST (QUOTE -1068) (QUOTE (-577))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#3| (QUOTE (-1130)))) (|HasAttribute| |#3| (QUOTE -4496)) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1079)))) (-12 (|HasCategory| |#3| (QUOTE (-1079))) (|HasCategory| |#3| (LIST (QUOTE -926) (QUOTE (-1206))))) (|HasCategory| |#3| (QUOTE (-174))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-132))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1130))) (|HasCategory| |#3| (LIST (QUOTE -320) (|devaluate| |#3|))))) +(-1144 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 (-465)))) -(-1140) +(-1145) ((|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 -(-1141 R -1985) +(-1146 R -2057) ((|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 -(-1142 R) +(-1147 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 -(-1143) +(-1148) ((|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 -(-1144) +(-1149) ((|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 -(-1145) +(-1150) ((|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}.")) (|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."))) -((-4458 . T) (-4462 . T) (-4457 . T) (-4468 . T) (-4469 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4487 . T) (-4491 . T) (-4486 . T) (-4497 . T) (-4498 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1146 S) +(-1151 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4470 . T) (-4471 . T)) +((-4499 . T) (-4500 . T)) NIL -(-1147 S |ndim| R |Row| |Col|) +(-1152 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-375))) (|HasAttribute| |#3| (QUOTE (-4472 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) -(-1148 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-375))) (|HasAttribute| |#3| (QUOTE (-4501 "*"))) (|HasCategory| |#3| (QUOTE (-174)))) +(-1153 |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."))) -((-4470 . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4499 . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1149 R |Row| |Col| M) +(-1154 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 -(-1150 R |VarSet|) +(-1155 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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-932))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -905) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -905) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4468)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (-2811 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-932)))) (|HasCategory| |#1| (QUOTE (-146))))) -(-1151 |Coef| |Var| SMP) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-937))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (|HasCategory| |#1| (QUOTE (-465))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-391)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -910) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -910) (QUOTE (-577))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549))))) (|HasCategory| |#1| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4497)) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-937)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1156 |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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) -(-1152 R E V P) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) +(-1157 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}"))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1153 UP -1985) +(-1158 UP -2057) ((|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 -(-1154 R) +(-1159 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 -(-1155 R) +(-1160 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 -(-1156 R) +(-1161 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 -(-1157 S A) +(-1162 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 (-865)))) -(-1158 R) +((|HasCategory| |#1| (QUOTE (-870)))) +(-1163 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 -(-1159 R) +(-1164 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 -(-1160) +(-1165) ((|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 -(-1161) +(-1166) ((|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 -(-1162) +(-1167) ((|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.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst 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.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\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|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|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|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|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 -(-1163) +(-1168) ((|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 -(-1164) +(-1169) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1165 V C) +(-1170 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 -(-1166 V C) +(-1171 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."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))) (-2811 (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125)))) (-2811 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1165) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-1125))))) (|HasCategory| (-1165 |#1| |#2|) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-1165 |#1| |#2|) (QUOTE (-102)))) -(-1167 |ndim| R) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-1170 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1130)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1130))) (-2867 (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1130)))) (-2867 (|HasCategory| (-1170 |#1| |#2|) (LIST (QUOTE -631) (QUOTE (-885)))) (-12 (|HasCategory| (-1170 |#1| |#2|) (LIST (QUOTE -320) (LIST (QUOTE -1170) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-1130))))) (|HasCategory| (-1170 |#1| |#2|) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-1170 |#1| |#2|) (QUOTE (-102)))) +(-1172 |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}."))) -((-4467 . T) (-4459 |has| |#2| (-6 (-4472 "*"))) (-4470 . T) (-4464 . T) (-4465 . T)) -((|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (LIST (QUOTE -923) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1063) (QUOTE (-577)))) (-2811 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -654) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))))) (|HasCategory| |#2| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-375))) (-2811 (|HasAttribute| |#2| (QUOTE (-4472 "*"))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) -(-1168 S) +((-4496 . T) (-4488 |has| |#2| (-6 (-4501 "*"))) (-4499 . T) (-4493 . T) (-4494 . T)) +((|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-238))) (|HasAttribute| |#2| (QUOTE (-4501 "*"))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577)))) (|HasCategory| |#2| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (LIST (QUOTE -1068) (QUOTE (-577)))) (-2867 (-12 (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -659) (QUOTE (-577))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))))) (|HasCategory| |#2| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-318))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-375))) (-2867 (|HasAttribute| |#2| (QUOTE (-4501 "*"))) (|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-174)))) +(-1173 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1169) +(-1174) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1170 R E V P TS) +(-1175 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 -(-1171 R E V P) +(-1176 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."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1172 S) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1177 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}."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1173 A S) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1178 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 -(-1174 S) +(-1179 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 -(-1175 |Key| |Ent| |dent|) +(-1180 |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."))) -((-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125)))) -(-1176) +((-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130)))) +(-1181) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1177) +(-1182) ((|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 -(-1178 |Coef|) +(-1183 |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 -(-1179 S) +(-1184 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 -(-1180 A B) +(-1185 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 -(-1181 A B C) +(-1186 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 -(-1182 S) +(-1187 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."))) -((-4471 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1183) +((-4500 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1188) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2811 (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-145) (QUOTE (-865))) (-2811 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1125))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) -(-1184 |Entry|) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145))))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (-2867 (|HasCategory| (-145) (LIST (QUOTE -631) (QUOTE (-885)))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) (|HasCategory| (-145) (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130)))) (|HasCategory| (-145) (QUOTE (-870))) (-2867 (|HasCategory| (-145) (QUOTE (-102))) (|HasCategory| (-145) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-145) (QUOTE (-102))) (-12 (|HasCategory| (-145) (QUOTE (-1130))) (|HasCategory| (-145) (LIST (QUOTE -320) (QUOTE (-145)))))) +(-1189 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#1|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-1125))) (|HasCategory| (-1183) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 (-1183)) (|:| -2438 |#1|)) (QUOTE (-102)))) -(-1185 A) +((-4499 . 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T)) +((-12 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (QUOTE (-1188))) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#1|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-1130))) (|HasCategory| (-1188) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 (-1188)) (|:| -2727 |#1|)) (QUOTE (-102)))) +(-1190 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 should be invertible.")) (|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,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 (-375))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) -(-1186 |Coef|) +(-1191 |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 -(-1187 |Coef|) +(-1192 |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 -(-1188 R UP) +(-1193 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 (-318)))) -(-1189 |n| R) +(-1194 |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,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,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,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,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,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,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,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,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 -(-1190 S1 S2) +(-1195 S1 S2) ((|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 -(-1191) +(-1196) ((|constructor| (NIL "This domain represents the filter iterator syntax.")) (|predicate| (((|SpadAst|) $) "\\spad{predicate(e)} returns the syntax object for the predicate in the filter iterator syntax `e'."))) NIL NIL -(-1192 |Coef| |var| |cen|) +(-1197 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,x,3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|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.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4472 "*") -2811 (-2700 (|has| |#1| (-375)) (|has| (-1199 |#1| |#2| |#3|) (-836))) (|has| |#1| (-174)) (-2700 (|has| |#1| (-375)) (|has| (-1199 |#1| |#2| |#3|) (-932)))) (-4463 -2811 (-2700 (|has| |#1| (-375)) (|has| (-1199 |#1| |#2| |#3|) (-836))) (|has| |#1| (-569)) (-2700 (|has| |#1| (-375)) (|has| (-1199 |#1| |#2| |#3|) (-932)))) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . 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We may integrate a series when we can divide coefficients by integers."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) -(-1199 |Coef| |var| |cen|) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1204 |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.")) (|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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) -(-1200) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-792)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-792)) (|devaluate| |#1|)))) (|HasCategory| (-792) (QUOTE (-1142))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-792))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-792))))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1205) ((|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 -(-1201) +(-1206) ((|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 -(-1202 R) +(-1207 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{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1203 R) +(-1208 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-6 -4468)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2811 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| (-996) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4468))) -(-1204) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-6 -4497)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-2867 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-465))) (-12 (|HasCategory| (-1001) (QUOTE (-132))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasAttribute| |#1| (QUOTE -4497))) +(-1209) ((|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 -(-1205) +(-1210) ((|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 -(-1206) +(-1211) ((|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}{identifiers,{} 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: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. 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|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if \\spad{`x'} really is an Identifier") (((|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|) (|Identifier|) (|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| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Identifier|) (|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.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier 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'}.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier 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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1207 N) +(-1212 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1208 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| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) +(-1213 N) +((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}."))) NIL NIL -(-1209) +(-1214) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1210 R) +(-1215 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 -(-1211) +(-1216) ((|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} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is 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 -(-1212 S) +(-1217 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 -(-1213 S) +(-1218 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 -(-1214 |Key| |Entry|) +(-1219 |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}"))) -((-4470 . T) (-4471 . T)) -((-12 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4323) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2438) (|devaluate| |#2|)))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1125)))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -627) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1125))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#2| (QUOTE (-1125))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880))))) (-2811 (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| (-2 (|:| -4323 |#1|) (|:| -2438 |#2|)) (QUOTE (-102)))) -(-1215 S) +((-4499 . T) (-4500 . T)) +((-12 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -320) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -4376) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2727) (|devaluate| |#2|)))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1130)))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -632) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1130))) (|HasCategory| |#2| (LIST (QUOTE -320) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#2| (QUOTE (-1130))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885))))) (-2867 (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| (-2 (|:| -4376 |#1|) (|:| -2727 |#2|)) (QUOTE (-102)))) +(-1220 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1216 R) +(-1221 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{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1217 S |Key| |Entry|) +(-1222 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 -(-1218 |Key| |Entry|) +(-1223 |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})}."))) -((-4471 . T)) +((-4500 . T)) NIL -(-1219 |Key| |Entry|) +(-1224 |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 -(-1220) +(-1225) ((|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 -(-1221 S) +(-1226 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 -(-1222) +(-1227) ((|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 -(-1223) +(-1228) ((|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 -(-1224 R) +(-1229 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 -(-1225) +(-1230) ((|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 -(-1226 S) +(-1231 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1227) +(-1232) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1228 S) +(-1233 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1125))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1125)))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-1229 S) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1130))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1130)))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-1234 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1230) +(-1235) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1231 R -1985) +(-1236 R -2057) ((|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 -(-1232 R |Row| |Col| M) +(-1237 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 -(-1233 R -1985) +(-1238 R -2057) ((|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 -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -905) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -627) (LIST (QUOTE -911) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -905) (|devaluate| |#1|))))) -(-1234 S R E V P) +((-12 (|HasCategory| |#1| (LIST (QUOTE -632) (LIST (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -910) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -632) (LIST (QUOTE -916) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -910) (|devaluate| |#1|))))) +(-1239 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 (-380)))) -(-1235 R E V P) +(-1240 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1236 |Coef|) +(-1241 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) -(-1237 |Curve|) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-148))) (|HasCategory| |#1| (QUOTE (-146))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-375)))) +(-1242 |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 -(-1238) +(-1243) ((|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 -(-1239 S) +(-1244 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 (-1125))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) -(-1240 -1985) +((|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) +(-1245 -2057) ((|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 -(-1241) +(-1246) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1242) +(-1247) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1243 S) +(-1248 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 < 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 < 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 (-865)))) -(-1244) +((|HasCategory| |#1| (QUOTE (-870)))) +(-1249) ((|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 -(-1245 S) +(-1250 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 -(-1246) +(-1251) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1247) +(-1252) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1248) +(-1253) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1249) +(-1254) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1250) +(-1255) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1251 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1256 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1252 |Coef|) +(-1257 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1253 S |Coef| UTS) +(-1258 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 (-375)))) -(-1254 |Coef| UTS) +(-1259 |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)}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1255 |Coef| UTS) +(-1260 |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)}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . 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|#3|) (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-174)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (LIST (QUOTE -928) (QUOTE (-1206)))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-238))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-375)))) (-2867 (-12 (|HasCategory| $ (QUOTE (-146))) (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-937))) (|HasCategory| |#1| (QUOTE (-375)))) (-12 (|HasCategory| (-1289 |#1| |#2| |#3|) (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-375)))) (|HasCategory| |#1| (QUOTE (-146))))) +(-1262 ZP) ((|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 -(-1258 R S) +(-1263 R S) ((|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 -((|HasCategory| |#1| (QUOTE (-864)))) -(-1259 S) +((|HasCategory| |#1| (QUOTE (-869)))) +(-1264 S) ((|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 -((|HasCategory| |#1| (QUOTE (-864))) (|HasCategory| |#1| (QUOTE (-1125)))) -(-1260 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-869))) (|HasCategory| |#1| (QUOTE (-1130)))) +(-1265 |x| R |y| S) ((|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 -(-1261 R Q UP) +(-1266 R Q UP) ((|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 -(-1262 R UP) +(-1267 R UP) ((|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 -(-1263 R UP) +(-1268 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 -(-1264 R U) +(-1269 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 -(-1265 |x| R) +(-1270 |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| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-4472 "*") |has| |#2| (-174)) (-4463 |has| |#2| (-569)) (-4466 |has| |#2| (-375)) (-4468 |has| |#2| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . 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(|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1267 S R) +(-1272 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\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 -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1177)))) -(-1268 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375))) (|HasCategory| |#2| (QUOTE (-465))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (QUOTE (-1182)))) +(-1273 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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4466 |has| |#1| (-375)) (-4468 |has| |#1| (-6 -4468)) (-4465 . T) (-4464 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4495 |has| |#1| (-375)) (-4497 |has| |#1| (-6 -4497)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-1269 S |Coef| |Expon|) +(-1274 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}.")) (|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 -921) (QUOTE (-1201)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1137))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3603) (LIST (|devaluate| |#2|) (QUOTE (-1201)))))) -(-1270 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1142))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3709) (LIST (|devaluate| |#2|) (QUOTE (-1206)))))) +(-1275 |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}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1271 RC P) +(-1276 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1272 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1277 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1273 |Coef|) +(-1278 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1274 S |Coef| ULS) +(-1279 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 -(-1275 |Coef| ULS) +(-1280 |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)}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1276 |Coef| ULS) +(-1281 |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)}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) -(-1277 |Coef| |var| |cen|) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) +(-1282 |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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4468 |has| |#1| (-375)) (-4462 |has| |#1| (-375)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1137))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2811 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) -(-1278 R FE |var| |cen|) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4497 |has| |#1| (-375)) (-4491 |has| |#1| (-375)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#1| (QUOTE (-174))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577))) (|devaluate| |#1|)))) (|HasCategory| (-420 (-577)) (QUOTE (-1142))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-2867 (|HasCategory| |#1| (QUOTE (-375))) (|HasCategory| |#1| (QUOTE (-569)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -420) (QUOTE (-577)))))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1283 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))}."))) -(((-4472 "*") |has| (-1277 |#2| |#3| |#4|) (-174)) (-4463 |has| (-1277 |#2| |#3| |#4|) (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) -((|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-174))) (-2811 (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1277 |#2| |#3| |#4|) (LIST (QUOTE -1063) (QUOTE (-577)))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-375))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-465))) (|HasCategory| (-1277 |#2| |#3| |#4|) (QUOTE (-569)))) -(-1279 A S) +(((-4501 "*") |has| (-1282 |#2| |#3| |#4|) (-174)) (-4492 |has| (-1282 |#2| |#3| |#4|) (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| (-1282 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-148))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-174))) (-2867 (|HasCategory| (-1282 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1282 |#2| |#3| |#4|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577)))))) (|HasCategory| (-1282 |#2| |#3| |#4|) (LIST (QUOTE -1068) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| (-1282 |#2| |#3| |#4|) (LIST (QUOTE -1068) (QUOTE (-577)))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-375))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-465))) (|HasCategory| (-1282 |#2| |#3| |#4|) (QUOTE (-569)))) +(-1284 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4471))) -(-1280 S) +((|HasAttribute| |#1| (QUOTE -4500))) +(-1285 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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!| ((|#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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1281 |Coef1| |Coef2| UTS1 UTS2) +(-1286 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1282 S |Coef|) +(-1287 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-1227))) (|HasSignature| |#2| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4129) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1201))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375)))) -(-1283 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#2| (QUOTE (-987))) (|HasCategory| |#2| (QUOTE (-1232))) (|HasSignature| |#2| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1869) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1206))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#2| (QUOTE (-375)))) +(-1288 |Coef|) ((|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."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1284 |Coef| |var| |cen|) +(-1289 |Coef| |var| |cen|) ((|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|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|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))}.}")) (|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}."))) -(((-4472 "*") |has| |#1| (-174)) (-4463 |has| |#1| (-569)) (-4464 . 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2811 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -921) (QUOTE (-1201)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-787)) (|devaluate| |#1|)))) (|HasCategory| (-787) (QUOTE (-1137))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasSignature| |#1| (LIST (QUOTE -3603) (LIST (|devaluate| |#1|) (QUOTE (-1201)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-787))))) (|HasCategory| |#1| (QUOTE (-375))) (-2811 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1227))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -4129) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1201))))) (|HasSignature| |#1| (LIST (QUOTE -3206) (LIST (LIST (QUOTE -660) (QUOTE (-1201))) (|devaluate| |#1|))))))) -(-1285 |Coef| UTS) +(((-4501 "*") |has| |#1| (-174)) (-4492 |has| |#1| (-569)) (-4493 . T) (-4494 . T) (-4496 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasCategory| |#1| (QUOTE (-569))) (-2867 (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-148))) (-12 (|HasCategory| |#1| (LIST (QUOTE -926) (QUOTE (-1206)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-792)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-792)) (|devaluate| |#1|)))) (|HasCategory| (-792) (QUOTE (-1142))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-792))))) (|HasSignature| |#1| (LIST (QUOTE -3709) (LIST (|devaluate| |#1|) (QUOTE (-1206)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-792))))) (|HasCategory| |#1| (QUOTE (-375))) (-2867 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-577)))) (|HasCategory| |#1| (QUOTE (-987))) (|HasCategory| |#1| (QUOTE (-1232))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasSignature| |#1| (LIST (QUOTE -1869) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1206))))) (|HasSignature| |#1| (LIST (QUOTE -3891) (LIST (LIST (QUOTE -665) (QUOTE (-1206))) (|devaluate| |#1|))))))) +(-1290 |Coef| UTS) ((|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 -(-1286 -1985 UP L UTS) +(-1291 -2057 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 (-569)))) -(-1287) +(-1292) ((|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 -(-1288 |sym|) +(-1293 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1289 S R) +(-1294 S R) ((|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 (-1027))) (|HasCategory| |#2| (QUOTE (-1074))) (|HasCategory| |#2| (QUOTE (-742))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1290 R) +((|HasCategory| |#2| (QUOTE (-1032))) (|HasCategory| |#2| (QUOTE (-1079))) (|HasCategory| |#2| (QUOTE (-747))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1295 R) ((|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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4471 . T) (-4470 . T)) +((-4500 . T) (-4499 . T)) NIL -(-1291 A B) +(-1296 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1292 R) +(-1297 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4471 . T) (-4470 . T)) -((-2811 (-12 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2811 (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880))))) (|HasCategory| |#1| (LIST (QUOTE -627) (QUOTE (-549)))) (-2811 (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| |#1| (QUOTE (-865))) (-2811 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125)))) (|HasCategory| (-577) (QUOTE (-865))) (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-742))) (|HasCategory| |#1| (QUOTE (-1074))) (-12 (|HasCategory| |#1| (QUOTE (-1027))) (|HasCategory| |#1| (QUOTE (-1074)))) (|HasCategory| |#1| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1125))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) -(-1293) +((-4500 . T) (-4499 . T)) +((-2867 (-12 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) (-2867 (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885))))) (|HasCategory| |#1| (LIST (QUOTE -632) (QUOTE (-549)))) (-2867 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| |#1| (QUOTE (-870))) (-2867 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130)))) (|HasCategory| (-577) (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-747))) (|HasCategory| |#1| (QUOTE (-1079))) (-12 (|HasCategory| |#1| (QUOTE (-1032))) (|HasCategory| |#1| (QUOTE (-1079)))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1130))) (|HasCategory| |#1| (LIST (QUOTE -320) (|devaluate| |#1|))))) +(-1298) ((|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,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{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\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(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\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 -(-1294) +(-1299) ((|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 -(-1295) +(-1300) ((|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 -(-1296) +(-1301) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(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 -(-1297) +(-1302) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1298 A S) +(-1303 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1299 S) +(-1304 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}."))) -((-4465 . T) (-4464 . T)) +((-4494 . T) (-4493 . T)) NIL -(-1300 R) +(-1305 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 -(-1301 K R UP -1985) +(-1306 K R UP -2057) ((|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{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{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{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{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{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{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1302) +(-1307) ((|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 -(-1303) +(-1308) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1304 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1309 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)"))) -((-4465 |has| |#1| (-174)) (-4464 |has| |#1| (-174)) (-4467 . T)) +((-4494 |has| |#1| (-174)) (-4493 |has| |#1| (-174)) (-4496 . T)) ((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375)))) -(-1305 R E V P) +(-1310 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}}."))) -((-4471 . T) (-4470 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -627) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1125))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -626) (QUOTE (-880)))) (|HasCategory| |#4| (QUOTE (-102)))) -(-1306 R) +((-4500 . T) (-4499 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#4| (LIST (QUOTE -320) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -632) (QUOTE (-549)))) (|HasCategory| |#4| (QUOTE (-1130))) (|HasCategory| |#1| (QUOTE (-569))) (|HasCategory| |#3| (QUOTE (-380))) (|HasCategory| |#4| (LIST (QUOTE -631) (QUOTE (-885)))) (|HasCategory| |#4| (QUOTE (-102)))) +(-1311 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})"))) -((-4464 . T) (-4465 . T) (-4467 . T)) +((-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1307 |vl| R) +(-1312 |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."))) -((-4467 . T) (-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4463))) -(-1308 R |VarSet| XPOLY) +((-4496 . T) (-4492 |has| |#2| (-6 -4492)) (-4494 . T) (-4493 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4492))) +(-1313 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 -(-1309 |vl| R) +(-1314 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) +((-4492 |has| |#2| (-6 -4492)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-1310 S -1985) +(-1315 S -2057) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-380))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-148)))) -(-1311 -1985) +(-1316 -2057) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4462 . T) (-4468 . T) (-4463 . T) ((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +((-4491 . T) (-4497 . T) (-4492 . T) ((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL -(-1312 |VarSet| R) +(-1317 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -733) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasAttribute| |#2| (QUOTE -4463))) -(-1313 |vl| R) +((-4492 |has| |#2| (-6 -4492)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasCategory| |#2| (LIST (QUOTE -738) (LIST (QUOTE -420) (QUOTE (-577))))) (|HasAttribute| |#2| (QUOTE -4492))) +(-1318 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) +((-4492 |has| |#2| (-6 -4492)) (-4494 . T) (-4493 . T) (-4496 . T)) NIL -(-1314 R) +(-1319 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4463 |has| |#1| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4463))) -(-1315 R E) +((-4492 |has| |#1| (-6 -4492)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasAttribute| |#1| (QUOTE -4492))) +(-1320 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4467 . T) (-4468 |has| |#1| (-6 -4468)) (-4463 |has| |#1| (-6 -4463)) (-4465 . T) (-4464 . T)) -((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4467)) (|HasAttribute| |#1| (QUOTE -4468)) (|HasAttribute| |#1| (QUOTE -4463))) -(-1316 |VarSet| R) +((-4496 . T) (-4497 |has| |#1| (-6 -4497)) (-4492 |has| |#1| (-6 -4492)) (-4494 . T) (-4493 . T)) +((|HasCategory| |#1| (QUOTE (-174))) (|HasCategory| |#1| (QUOTE (-375))) (|HasAttribute| |#1| (QUOTE -4496)) (|HasAttribute| |#1| (QUOTE -4497)) (|HasAttribute| |#1| (QUOTE -4492))) +(-1321 |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."))) -((-4463 |has| |#2| (-6 -4463)) (-4465 . T) (-4464 . T) (-4467 . T)) -((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4463))) -(-1317) +((-4492 |has| |#2| (-6 -4492)) (-4494 . T) (-4493 . T) (-4496 . T)) +((|HasCategory| |#2| (QUOTE (-174))) (|HasAttribute| |#2| (QUOTE -4492))) +(-1322) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1318 A) +(-1323 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 -(-1319 R |ls| |ls2|) +(-1324 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 -(-1320 R) +(-1325 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 -(-1321 |p|) +(-1326 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4472 "*") . T) (-4464 . T) (-4465 . T) (-4467 . T)) +(((-4501 "*") . T) (-4493 . T) (-4494 . T) (-4496 . T)) NIL NIL NIL @@ -5232,4 +5252,4 @@ NIL NIL NIL NIL -((-3 NIL 2296249 2296254 2296259 2296264) (-2 NIL 2296229 2296234 2296239 2296244) (-1 NIL 2296209 2296214 2296219 2296224) (0 NIL 2296189 2296194 2296199 2296204) (-1321 "ZMOD.spad" 2295998 2296011 2296127 2296184) (-1320 "ZLINDEP.spad" 2295064 2295075 2295988 2295993) (-1319 "ZDSOLVE.spad" 2285009 2285031 2295054 2295059) (-1318 "YSTREAM.spad" 2284504 2284515 2284999 2285004) (-1317 "YDIAGRAM.spad" 2284138 2284147 2284494 2284499) (-1316 "XRPOLY.spad" 2283358 2283378 2283994 2284063) (-1315 "XPR.spad" 2281153 2281166 2283076 2283175) (-1314 "XPOLY.spad" 2280708 2280719 2281009 2281078) (-1313 "XPOLYC.spad" 2280027 2280043 2280634 2280703) (-1312 "XPBWPOLY.spad" 2278464 2278484 2279807 2279876) (-1311 "XF.spad" 2276927 2276942 2278366 2278459) (-1310 "XF.spad" 2275370 2275387 2276811 2276816) (-1309 "XFALG.spad" 2272418 2272434 2275296 2275365) (-1308 "XEXPPKG.spad" 2271669 2271695 2272408 2272413) (-1307 "XDPOLY.spad" 2271283 2271299 2271525 2271594) (-1306 "XALG.spad" 2270943 2270954 2271239 2271278) (-1305 "WUTSET.spad" 2266746 2266763 2270553 2270580) (-1304 "WP.spad" 2265945 2265989 2266604 2266671) (-1303 "WHILEAST.spad" 2265743 2265752 2265935 2265940) (-1302 "WHEREAST.spad" 2265414 2265423 2265733 2265738) (-1301 "WFFINTBS.spad" 2263077 2263099 2265404 2265409) (-1300 "WEIER.spad" 2261299 2261310 2263067 2263072) (-1299 "VSPACE.spad" 2260972 2260983 2261267 2261294) (-1298 "VSPACE.spad" 2260665 2260678 2260962 2260967) (-1297 "VOID.spad" 2260342 2260351 2260655 2260660) (-1296 "VIEW.spad" 2258022 2258031 2260332 2260337) (-1295 "VIEWDEF.spad" 2253223 2253232 2258012 2258017) (-1294 "VIEW3D.spad" 2237184 2237193 2253213 2253218) (-1293 "VIEW2D.spad" 2225075 2225084 2237174 2237179) (-1292 "VECTOR.spad" 2223596 2223607 2223847 2223874) (-1291 "VECTOR2.spad" 2222235 2222248 2223586 2223591) (-1290 "VECTCAT.spad" 2220139 2220150 2222203 2222230) (-1289 "VECTCAT.spad" 2217850 2217863 2219916 2219921) (-1288 "VARIABLE.spad" 2217630 2217645 2217840 2217845) (-1287 "UTYPE.spad" 2217274 2217283 2217620 2217625) (-1286 "UTSODETL.spad" 2216569 2216593 2217230 2217235) (-1285 "UTSODE.spad" 2214785 2214805 2216559 2216564) (-1284 "UTS.spad" 2209732 2209760 2213252 2213349) (-1283 "UTSCAT.spad" 2207211 2207227 2209630 2209727) (-1282 "UTSCAT.spad" 2204334 2204352 2206755 2206760) (-1281 "UTS2.spad" 2203929 2203964 2204324 2204329) (-1280 "URAGG.spad" 2198602 2198613 2203919 2203924) (-1279 "URAGG.spad" 2193239 2193252 2198558 2198563) (-1278 "UPXSSING.spad" 2190884 2190910 2192320 2192453) (-1277 "UPXS.spad" 2188180 2188208 2189016 2189165) (-1276 "UPXSCONS.spad" 2185939 2185959 2186312 2186461) (-1275 "UPXSCCA.spad" 2184510 2184530 2185785 2185934) (-1274 "UPXSCCA.spad" 2183223 2183245 2184500 2184505) (-1273 "UPXSCAT.spad" 2181812 2181828 2183069 2183218) (-1272 "UPXS2.spad" 2181355 2181408 2181802 2181807) (-1271 "UPSQFREE.spad" 2179769 2179783 2181345 2181350) (-1270 "UPSCAT.spad" 2177556 2177580 2179667 2179764) (-1269 "UPSCAT.spad" 2175049 2175075 2177162 2177167) (-1268 "UPOLYC.spad" 2170089 2170100 2174891 2175044) (-1267 "UPOLYC.spad" 2165021 2165034 2169825 2169830) (-1266 "UPOLYC2.spad" 2164492 2164511 2165011 2165016) (-1265 "UP.spad" 2161598 2161613 2161985 2162138) (-1264 "UPMP.spad" 2160498 2160511 2161588 2161593) (-1263 "UPDIVP.spad" 2160063 2160077 2160488 2160493) (-1262 "UPDECOMP.spad" 2158308 2158322 2160053 2160058) (-1261 "UPCDEN.spad" 2157517 2157533 2158298 2158303) (-1260 "UP2.spad" 2156881 2156902 2157507 2157512) (-1259 "UNISEG.spad" 2156234 2156245 2156800 2156805) (-1258 "UNISEG2.spad" 2155731 2155744 2156190 2156195) (-1257 "UNIFACT.spad" 2154834 2154846 2155721 2155726) (-1256 "ULS.spad" 2144618 2144646 2145563 2145992) (-1255 "ULSCONS.spad" 2135752 2135772 2136122 2136271) (-1254 "ULSCCAT.spad" 2133489 2133509 2135598 2135747) (-1253 "ULSCCAT.spad" 2131334 2131356 2133445 2133450) (-1252 "ULSCAT.spad" 2129566 2129582 2131180 2131329) (-1251 "ULS2.spad" 2129080 2129133 2129556 2129561) (-1250 "UINT8.spad" 2128957 2128966 2129070 2129075) (-1249 "UINT64.spad" 2128833 2128842 2128947 2128952) (-1248 "UINT32.spad" 2128709 2128718 2128823 2128828) (-1247 "UINT16.spad" 2128585 2128594 2128699 2128704) (-1246 "UFD.spad" 2127650 2127659 2128511 2128580) (-1245 "UFD.spad" 2126777 2126788 2127640 2127645) (-1244 "UDVO.spad" 2125658 2125667 2126767 2126772) (-1243 "UDPO.spad" 2123151 2123162 2125614 2125619) (-1242 "TYPE.spad" 2123083 2123092 2123141 2123146) (-1241 "TYPEAST.spad" 2123002 2123011 2123073 2123078) (-1240 "TWOFACT.spad" 2121654 2121669 2122992 2122997) (-1239 "TUPLE.spad" 2121140 2121151 2121553 2121558) (-1238 "TUBETOOL.spad" 2118007 2118016 2121130 2121135) (-1237 "TUBE.spad" 2116654 2116671 2117997 2118002) (-1236 "TS.spad" 2115253 2115269 2116219 2116316) (-1235 "TSETCAT.spad" 2102380 2102397 2115221 2115248) (-1234 "TSETCAT.spad" 2089493 2089512 2102336 2102341) (-1233 "TRMANIP.spad" 2083859 2083876 2089199 2089204) (-1232 "TRIMAT.spad" 2082822 2082847 2083849 2083854) (-1231 "TRIGMNIP.spad" 2081349 2081366 2082812 2082817) (-1230 "TRIGCAT.spad" 2080861 2080870 2081339 2081344) (-1229 "TRIGCAT.spad" 2080371 2080382 2080851 2080856) (-1228 "TREE.spad" 2078829 2078840 2079861 2079888) (-1227 "TRANFUN.spad" 2078668 2078677 2078819 2078824) (-1226 "TRANFUN.spad" 2078505 2078516 2078658 2078663) (-1225 "TOPSP.spad" 2078179 2078188 2078495 2078500) (-1224 "TOOLSIGN.spad" 2077842 2077853 2078169 2078174) (-1223 "TEXTFILE.spad" 2076403 2076412 2077832 2077837) (-1222 "TEX.spad" 2073549 2073558 2076393 2076398) (-1221 "TEX1.spad" 2073105 2073116 2073539 2073544) (-1220 "TEMUTL.spad" 2072660 2072669 2073095 2073100) (-1219 "TBCMPPK.spad" 2070753 2070776 2072650 2072655) (-1218 "TBAGG.spad" 2069803 2069826 2070733 2070748) (-1217 "TBAGG.spad" 2068861 2068886 2069793 2069798) (-1216 "TANEXP.spad" 2068269 2068280 2068851 2068856) (-1215 "TALGOP.spad" 2067993 2068004 2068259 2068264) (-1214 "TABLE.spad" 2065962 2065985 2066232 2066259) (-1213 "TABLEAU.spad" 2065443 2065454 2065952 2065957) (-1212 "TABLBUMP.spad" 2062246 2062257 2065433 2065438) (-1211 "SYSTEM.spad" 2061474 2061483 2062236 2062241) (-1210 "SYSSOLP.spad" 2058957 2058968 2061464 2061469) (-1209 "SYSPTR.spad" 2058856 2058865 2058947 2058952) (-1208 "SYSNNI.spad" 2058038 2058049 2058846 2058851) (-1207 "SYSINT.spad" 2057442 2057453 2058028 2058033) (-1206 "SYNTAX.spad" 2053648 2053657 2057432 2057437) (-1205 "SYMTAB.spad" 2051716 2051725 2053638 2053643) (-1204 "SYMS.spad" 2047739 2047748 2051706 2051711) (-1203 "SYMPOLY.spad" 2046746 2046757 2046828 2046955) (-1202 "SYMFUNC.spad" 2046247 2046258 2046736 2046741) (-1201 "SYMBOL.spad" 2043750 2043759 2046237 2046242) (-1200 "SWITCH.spad" 2040521 2040530 2043740 2043745) (-1199 "SUTS.spad" 2037569 2037597 2038988 2039085) (-1198 "SUPXS.spad" 2034852 2034880 2035701 2035850) (-1197 "SUP.spad" 2031572 2031583 2032345 2032498) (-1196 "SUPFRACF.spad" 2030677 2030695 2031562 2031567) (-1195 "SUP2.spad" 2030069 2030082 2030667 2030672) (-1194 "SUMRF.spad" 2029043 2029054 2030059 2030064) (-1193 "SUMFS.spad" 2028680 2028697 2029033 2029038) (-1192 "SULS.spad" 2018451 2018479 2019409 2019838) (-1191 "SUCHTAST.spad" 2018220 2018229 2018441 2018446) (-1190 "SUCH.spad" 2017902 2017917 2018210 2018215) (-1189 "SUBSPACE.spad" 2010017 2010032 2017892 2017897) (-1188 "SUBRESP.spad" 2009187 2009201 2009973 2009978) (-1187 "STTF.spad" 2005286 2005302 2009177 2009182) (-1186 "STTFNC.spad" 2001754 2001770 2005276 2005281) (-1185 "STTAYLOR.spad" 1994389 1994400 2001635 2001640) (-1184 "STRTBL.spad" 1992440 1992457 1992589 1992616) (-1183 "STRING.spad" 1991227 1991236 1991448 1991475) (-1182 "STREAM.spad" 1988028 1988039 1990635 1990650) (-1181 "STREAM3.spad" 1987601 1987616 1988018 1988023) (-1180 "STREAM2.spad" 1986729 1986742 1987591 1987596) (-1179 "STREAM1.spad" 1986435 1986446 1986719 1986724) (-1178 "STINPROD.spad" 1985371 1985387 1986425 1986430) (-1177 "STEP.spad" 1984572 1984581 1985361 1985366) (-1176 "STEPAST.spad" 1983806 1983815 1984562 1984567) (-1175 "STBL.spad" 1981890 1981918 1982057 1982072) (-1174 "STAGG.spad" 1980965 1980976 1981880 1981885) (-1173 "STAGG.spad" 1980038 1980051 1980955 1980960) (-1172 "STACK.spad" 1979278 1979289 1979528 1979555) (-1171 "SREGSET.spad" 1976946 1976963 1978888 1978915) (-1170 "SRDCMPK.spad" 1975507 1975527 1976936 1976941) (-1169 "SRAGG.spad" 1970650 1970659 1975475 1975502) (-1168 "SRAGG.spad" 1965813 1965824 1970640 1970645) (-1167 "SQMATRIX.spad" 1963356 1963374 1964272 1964359) (-1166 "SPLTREE.spad" 1957752 1957765 1962636 1962663) (-1165 "SPLNODE.spad" 1954340 1954353 1957742 1957747) (-1164 "SPFCAT.spad" 1953149 1953158 1954330 1954335) (-1163 "SPECOUT.spad" 1951701 1951710 1953139 1953144) (-1162 "SPADXPT.spad" 1943296 1943305 1951691 1951696) (-1161 "spad-parser.spad" 1942761 1942770 1943286 1943291) (-1160 "SPADAST.spad" 1942462 1942471 1942751 1942756) (-1159 "SPACEC.spad" 1926661 1926672 1942452 1942457) (-1158 "SPACE3.spad" 1926437 1926448 1926651 1926656) (-1157 "SORTPAK.spad" 1925986 1925999 1926393 1926398) (-1156 "SOLVETRA.spad" 1923749 1923760 1925976 1925981) (-1155 "SOLVESER.spad" 1922277 1922288 1923739 1923744) (-1154 "SOLVERAD.spad" 1918303 1918314 1922267 1922272) (-1153 "SOLVEFOR.spad" 1916765 1916783 1918293 1918298) (-1152 "SNTSCAT.spad" 1916365 1916382 1916733 1916760) (-1151 "SMTS.spad" 1914637 1914663 1915930 1916027) (-1150 "SMP.spad" 1912112 1912132 1912502 1912629) (-1149 "SMITH.spad" 1910957 1910982 1912102 1912107) (-1148 "SMATCAT.spad" 1909067 1909097 1910901 1910952) (-1147 "SMATCAT.spad" 1907109 1907141 1908945 1908950) (-1146 "SKAGG.spad" 1906072 1906083 1907077 1907104) (-1145 "SINT.spad" 1905012 1905021 1905938 1906067) (-1144 "SIMPAN.spad" 1904740 1904749 1905002 1905007) (-1143 "SIG.spad" 1904070 1904079 1904730 1904735) (-1142 "SIGNRF.spad" 1903188 1903199 1904060 1904065) (-1141 "SIGNEF.spad" 1902467 1902484 1903178 1903183) (-1140 "SIGAST.spad" 1901852 1901861 1902457 1902462) (-1139 "SHP.spad" 1899780 1899795 1901808 1901813) (-1138 "SHDP.spad" 1887458 1887485 1887967 1888066) (-1137 "SGROUP.spad" 1887066 1887075 1887448 1887453) (-1136 "SGROUP.spad" 1886672 1886683 1887056 1887061) (-1135 "SGCF.spad" 1879811 1879820 1886662 1886667) (-1134 "SFRTCAT.spad" 1878741 1878758 1879779 1879806) (-1133 "SFRGCD.spad" 1877804 1877824 1878731 1878736) (-1132 "SFQCMPK.spad" 1872441 1872461 1877794 1877799) (-1131 "SFORT.spad" 1871880 1871894 1872431 1872436) (-1130 "SEXOF.spad" 1871723 1871763 1871870 1871875) (-1129 "SEX.spad" 1871615 1871624 1871713 1871718) (-1128 "SEXCAT.spad" 1869387 1869427 1871605 1871610) (-1127 "SET.spad" 1867675 1867686 1868772 1868811) (-1126 "SETMN.spad" 1866125 1866142 1867665 1867670) (-1125 "SETCAT.spad" 1865610 1865619 1866115 1866120) (-1124 "SETCAT.spad" 1865093 1865104 1865600 1865605) (-1123 "SETAGG.spad" 1861642 1861653 1865073 1865088) (-1122 "SETAGG.spad" 1858199 1858212 1861632 1861637) (-1121 "SEQAST.spad" 1857902 1857911 1858189 1858194) (-1120 "SEGXCAT.spad" 1857058 1857071 1857892 1857897) (-1119 "SEG.spad" 1856871 1856882 1856977 1856982) (-1118 "SEGCAT.spad" 1855796 1855807 1856861 1856866) (-1117 "SEGBIND.spad" 1855554 1855565 1855743 1855748) (-1116 "SEGBIND2.spad" 1855252 1855265 1855544 1855549) (-1115 "SEGAST.spad" 1854966 1854975 1855242 1855247) (-1114 "SEG2.spad" 1854401 1854414 1854922 1854927) (-1113 "SDVAR.spad" 1853677 1853688 1854391 1854396) (-1112 "SDPOL.spad" 1851010 1851021 1851301 1851428) (-1111 "SCPKG.spad" 1849099 1849110 1851000 1851005) (-1110 "SCOPE.spad" 1848252 1848261 1849089 1849094) (-1109 "SCACHE.spad" 1846948 1846959 1848242 1848247) (-1108 "SASTCAT.spad" 1846857 1846866 1846938 1846943) (-1107 "SAOS.spad" 1846729 1846738 1846847 1846852) (-1106 "SAERFFC.spad" 1846442 1846462 1846719 1846724) (-1105 "SAE.spad" 1843912 1843928 1844523 1844658) (-1104 "SAEFACT.spad" 1843613 1843633 1843902 1843907) (-1103 "RURPK.spad" 1841272 1841288 1843603 1843608) (-1102 "RULESET.spad" 1840725 1840749 1841262 1841267) (-1101 "RULE.spad" 1838965 1838989 1840715 1840720) (-1100 "RULECOLD.spad" 1838817 1838830 1838955 1838960) (-1099 "RTVALUE.spad" 1838552 1838561 1838807 1838812) (-1098 "RSTRCAST.spad" 1838269 1838278 1838542 1838547) (-1097 "RSETGCD.spad" 1834647 1834667 1838259 1838264) (-1096 "RSETCAT.spad" 1824583 1824600 1834615 1834642) (-1095 "RSETCAT.spad" 1814539 1814558 1824573 1824578) (-1094 "RSDCMPK.spad" 1812991 1813011 1814529 1814534) (-1093 "RRCC.spad" 1811375 1811405 1812981 1812986) (-1092 "RRCC.spad" 1809757 1809789 1811365 1811370) (-1091 "RPTAST.spad" 1809459 1809468 1809747 1809752) (-1090 "RPOLCAT.spad" 1788819 1788834 1809327 1809454) (-1089 "RPOLCAT.spad" 1767892 1767909 1788402 1788407) (-1088 "ROUTINE.spad" 1763313 1763322 1766077 1766104) (-1087 "ROMAN.spad" 1762641 1762650 1763179 1763308) (-1086 "ROIRC.spad" 1761721 1761753 1762631 1762636) (-1085 "RNS.spad" 1760624 1760633 1761623 1761716) (-1084 "RNS.spad" 1759613 1759624 1760614 1760619) (-1083 "RNG.spad" 1759348 1759357 1759603 1759608) (-1082 "RNGBIND.spad" 1758508 1758522 1759303 1759308) (-1081 "RMODULE.spad" 1758273 1758284 1758498 1758503) (-1080 "RMCAT2.spad" 1757693 1757750 1758263 1758268) (-1079 "RMATRIX.spad" 1756481 1756500 1756824 1756863) (-1078 "RMATCAT.spad" 1752060 1752091 1756437 1756476) (-1077 "RMATCAT.spad" 1747529 1747562 1751908 1751913) (-1076 "RLINSET.spad" 1747233 1747244 1747519 1747524) (-1075 "RINTERP.spad" 1747121 1747141 1747223 1747228) (-1074 "RING.spad" 1746591 1746600 1747101 1747116) (-1073 "RING.spad" 1746069 1746080 1746581 1746586) (-1072 "RIDIST.spad" 1745461 1745470 1746059 1746064) (-1071 "RGCHAIN.spad" 1743989 1744005 1744891 1744918) (-1070 "RGBCSPC.spad" 1743770 1743782 1743979 1743984) (-1069 "RGBCMDL.spad" 1743300 1743312 1743760 1743765) (-1068 "RF.spad" 1740942 1740953 1743290 1743295) (-1067 "RFFACTOR.spad" 1740404 1740415 1740932 1740937) (-1066 "RFFACT.spad" 1740139 1740151 1740394 1740399) (-1065 "RFDIST.spad" 1739135 1739144 1740129 1740134) (-1064 "RETSOL.spad" 1738554 1738567 1739125 1739130) (-1063 "RETRACT.spad" 1737982 1737993 1738544 1738549) (-1062 "RETRACT.spad" 1737408 1737421 1737972 1737977) (-1061 "RETAST.spad" 1737220 1737229 1737398 1737403) (-1060 "RESULT.spad" 1734818 1734827 1735405 1735432) (-1059 "RESRING.spad" 1734165 1734212 1734756 1734813) (-1058 "RESLATC.spad" 1733489 1733500 1734155 1734160) (-1057 "REPSQ.spad" 1733220 1733231 1733479 1733484) (-1056 "REP.spad" 1730774 1730783 1733210 1733215) (-1055 "REPDB.spad" 1730481 1730492 1730764 1730769) (-1054 "REP2.spad" 1720139 1720150 1730323 1730328) (-1053 "REP1.spad" 1714335 1714346 1720089 1720094) (-1052 "REGSET.spad" 1712096 1712113 1713945 1713972) (-1051 "REF.spad" 1711431 1711442 1712051 1712056) (-1050 "REDORDER.spad" 1710637 1710654 1711421 1711426) (-1049 "RECLOS.spad" 1709420 1709440 1710124 1710217) (-1048 "REALSOLV.spad" 1708560 1708569 1709410 1709415) (-1047 "REAL.spad" 1708432 1708441 1708550 1708555) (-1046 "REAL0Q.spad" 1705730 1705745 1708422 1708427) (-1045 "REAL0.spad" 1702574 1702589 1705720 1705725) (-1044 "RDUCEAST.spad" 1702295 1702304 1702564 1702569) (-1043 "RDIV.spad" 1701950 1701975 1702285 1702290) (-1042 "RDIST.spad" 1701517 1701528 1701940 1701945) (-1041 "RDETRS.spad" 1700381 1700399 1701507 1701512) (-1040 "RDETR.spad" 1698520 1698538 1700371 1700376) (-1039 "RDEEFS.spad" 1697619 1697636 1698510 1698515) (-1038 "RDEEF.spad" 1696629 1696646 1697609 1697614) (-1037 "RCFIELD.spad" 1693815 1693824 1696531 1696624) (-1036 "RCFIELD.spad" 1691087 1691098 1693805 1693810) (-1035 "RCAGG.spad" 1689015 1689026 1691077 1691082) (-1034 "RCAGG.spad" 1686870 1686883 1688934 1688939) (-1033 "RATRET.spad" 1686230 1686241 1686860 1686865) (-1032 "RATFACT.spad" 1685922 1685934 1686220 1686225) (-1031 "RANDSRC.spad" 1685241 1685250 1685912 1685917) (-1030 "RADUTIL.spad" 1684997 1685006 1685231 1685236) (-1029 "RADIX.spad" 1681821 1681835 1683367 1683460) (-1028 "RADFF.spad" 1679560 1679597 1679679 1679835) (-1027 "RADCAT.spad" 1679155 1679164 1679550 1679555) (-1026 "RADCAT.spad" 1678748 1678759 1679145 1679150) (-1025 "QUEUE.spad" 1677979 1677990 1678238 1678265) (-1024 "QUAT.spad" 1676467 1676478 1676810 1676875) (-1023 "QUATCT2.spad" 1676087 1676106 1676457 1676462) (-1022 "QUATCAT.spad" 1674257 1674268 1676017 1676082) (-1021 "QUATCAT.spad" 1672178 1672191 1673940 1673945) (-1020 "QUAGG.spad" 1671005 1671016 1672146 1672173) (-1019 "QQUTAST.spad" 1670773 1670782 1670995 1671000) (-1018 "QFORM.spad" 1670391 1670406 1670763 1670768) (-1017 "QFCAT.spad" 1669093 1669104 1670293 1670386) (-1016 "QFCAT.spad" 1667386 1667399 1668588 1668593) (-1015 "QFCAT2.spad" 1667078 1667095 1667376 1667381) (-1014 "QEQUAT.spad" 1666636 1666645 1667068 1667073) (-1013 "QCMPACK.spad" 1661382 1661402 1666626 1666631) (-1012 "QALGSET.spad" 1657460 1657493 1661296 1661301) (-1011 "QALGSET2.spad" 1655455 1655474 1657450 1657455) (-1010 "PWFFINTB.spad" 1652870 1652892 1655445 1655450) (-1009 "PUSHVAR.spad" 1652208 1652228 1652860 1652865) (-1008 "PTRANFN.spad" 1648335 1648346 1652198 1652203) (-1007 "PTPACK.spad" 1645422 1645433 1648325 1648330) (-1006 "PTFUNC2.spad" 1645244 1645259 1645412 1645417) (-1005 "PTCAT.spad" 1644498 1644509 1645212 1645239) (-1004 "PSQFR.spad" 1643804 1643829 1644488 1644493) (-1003 "PSEUDLIN.spad" 1642689 1642700 1643794 1643799) (-1002 "PSETPK.spad" 1628121 1628138 1642567 1642572) (-1001 "PSETCAT.spad" 1622040 1622064 1628101 1628116) (-1000 "PSETCAT.spad" 1615933 1615959 1621996 1622001) (-999 "PSCURVE.spad" 1614916 1614924 1615923 1615928) (-998 "PSCAT.spad" 1613699 1613728 1614814 1614911) (-997 "PSCAT.spad" 1612572 1612603 1613689 1613694) (-996 "PRTITION.spad" 1611270 1611278 1612562 1612567) (-995 "PRTDAST.spad" 1610989 1610997 1611260 1611265) (-994 "PRS.spad" 1600551 1600568 1610945 1610950) (-993 "PRQAGG.spad" 1599986 1599996 1600519 1600546) (-992 "PROPLOG.spad" 1599558 1599566 1599976 1599981) (-991 "PROPFUN2.spad" 1599181 1599194 1599548 1599553) (-990 "PROPFUN1.spad" 1598579 1598590 1599171 1599176) (-989 "PROPFRML.spad" 1597147 1597158 1598569 1598574) (-988 "PROPERTY.spad" 1596635 1596643 1597137 1597142) (-987 "PRODUCT.spad" 1594317 1594329 1594601 1594656) (-986 "PR.spad" 1592709 1592721 1593408 1593535) (-985 "PRINT.spad" 1592461 1592469 1592699 1592704) (-984 "PRIMES.spad" 1590714 1590724 1592451 1592456) (-983 "PRIMELT.spad" 1588795 1588809 1590704 1590709) (-982 "PRIMCAT.spad" 1588422 1588430 1588785 1588790) (-981 "PRIMARR.spad" 1587274 1587284 1587452 1587479) (-980 "PRIMARR2.spad" 1586041 1586053 1587264 1587269) (-979 "PREASSOC.spad" 1585423 1585435 1586031 1586036) (-978 "PPCURVE.spad" 1584560 1584568 1585413 1585418) (-977 "PORTNUM.spad" 1584335 1584343 1584550 1584555) (-976 "POLYROOT.spad" 1583184 1583206 1584291 1584296) (-975 "POLY.spad" 1580519 1580529 1581034 1581161) (-974 "POLYLIFT.spad" 1579784 1579807 1580509 1580514) (-973 "POLYCATQ.spad" 1577902 1577924 1579774 1579779) (-972 "POLYCAT.spad" 1571372 1571393 1577770 1577897) (-971 "POLYCAT.spad" 1564180 1564203 1570580 1570585) (-970 "POLY2UP.spad" 1563632 1563646 1564170 1564175) (-969 "POLY2.spad" 1563229 1563241 1563622 1563627) (-968 "POLUTIL.spad" 1562170 1562199 1563185 1563190) (-967 "POLTOPOL.spad" 1560918 1560933 1562160 1562165) (-966 "POINT.spad" 1559603 1559613 1559690 1559717) (-965 "PNTHEORY.spad" 1556305 1556313 1559593 1559598) (-964 "PMTOOLS.spad" 1555080 1555094 1556295 1556300) (-963 "PMSYM.spad" 1554629 1554639 1555070 1555075) (-962 "PMQFCAT.spad" 1554220 1554234 1554619 1554624) (-961 "PMPRED.spad" 1553699 1553713 1554210 1554215) (-960 "PMPREDFS.spad" 1553153 1553175 1553689 1553694) (-959 "PMPLCAT.spad" 1552233 1552251 1553085 1553090) (-958 "PMLSAGG.spad" 1551818 1551832 1552223 1552228) (-957 "PMKERNEL.spad" 1551397 1551409 1551808 1551813) (-956 "PMINS.spad" 1550977 1550987 1551387 1551392) (-955 "PMFS.spad" 1550554 1550572 1550967 1550972) (-954 "PMDOWN.spad" 1549844 1549858 1550544 1550549) (-953 "PMASS.spad" 1548854 1548862 1549834 1549839) (-952 "PMASSFS.spad" 1547821 1547837 1548844 1548849) (-951 "PLOTTOOL.spad" 1547601 1547609 1547811 1547816) (-950 "PLOT.spad" 1542524 1542532 1547591 1547596) (-949 "PLOT3D.spad" 1538988 1538996 1542514 1542519) (-948 "PLOT1.spad" 1538145 1538155 1538978 1538983) (-947 "PLEQN.spad" 1525435 1525462 1538135 1538140) (-946 "PINTERP.spad" 1525057 1525076 1525425 1525430) (-945 "PINTERPA.spad" 1524841 1524857 1525047 1525052) (-944 "PI.spad" 1524450 1524458 1524815 1524836) (-943 "PID.spad" 1523420 1523428 1524376 1524445) (-942 "PICOERCE.spad" 1523077 1523087 1523410 1523415) (-941 "PGROEB.spad" 1521678 1521692 1523067 1523072) (-940 "PGE.spad" 1513295 1513303 1521668 1521673) (-939 "PGCD.spad" 1512185 1512202 1513285 1513290) (-938 "PFRPAC.spad" 1511334 1511344 1512175 1512180) (-937 "PFR.spad" 1507997 1508007 1511236 1511329) (-936 "PFOTOOLS.spad" 1507255 1507271 1507987 1507992) (-935 "PFOQ.spad" 1506625 1506643 1507245 1507250) (-934 "PFO.spad" 1506044 1506071 1506615 1506620) (-933 "PF.spad" 1505618 1505630 1505849 1505942) (-932 "PFECAT.spad" 1503300 1503308 1505544 1505613) (-931 "PFECAT.spad" 1501010 1501020 1503256 1503261) (-930 "PFBRU.spad" 1498898 1498910 1501000 1501005) (-929 "PFBR.spad" 1496458 1496481 1498888 1498893) (-928 "PERM.spad" 1492265 1492275 1496288 1496303) (-927 "PERMGRP.spad" 1487035 1487045 1492255 1492260) (-926 "PERMCAT.spad" 1485696 1485706 1487015 1487030) (-925 "PERMAN.spad" 1484228 1484242 1485686 1485691) (-924 "PENDTREE.spad" 1483452 1483462 1483740 1483745) (-923 "PDSPC.spad" 1482265 1482275 1483442 1483447) (-922 "PDSPC.spad" 1481076 1481088 1482255 1482260) (-921 "PDRING.spad" 1480918 1480928 1481056 1481071) (-920 "PDMOD.spad" 1480734 1480746 1480886 1480913) (-919 "PDEPROB.spad" 1479749 1479757 1480724 1480729) (-918 "PDEPACK.spad" 1473789 1473797 1479739 1479744) (-917 "PDECOMP.spad" 1473259 1473276 1473779 1473784) (-916 "PDECAT.spad" 1471615 1471623 1473249 1473254) (-915 "PDDOM.spad" 1471053 1471066 1471605 1471610) (-914 "PDDOM.spad" 1470489 1470504 1471043 1471048) (-913 "PCOMP.spad" 1470342 1470355 1470479 1470484) (-912 "PBWLB.spad" 1468930 1468947 1470332 1470337) (-911 "PATTERN.spad" 1463469 1463479 1468920 1468925) (-910 "PATTERN2.spad" 1463207 1463219 1463459 1463464) (-909 "PATTERN1.spad" 1461543 1461559 1463197 1463202) (-908 "PATRES.spad" 1459118 1459130 1461533 1461538) (-907 "PATRES2.spad" 1458790 1458804 1459108 1459113) (-906 "PATMATCH.spad" 1456987 1457018 1458498 1458503) (-905 "PATMAB.spad" 1456416 1456426 1456977 1456982) (-904 "PATLRES.spad" 1455502 1455516 1456406 1456411) (-903 "PATAB.spad" 1455266 1455276 1455492 1455497) (-902 "PARTPERM.spad" 1453274 1453282 1455256 1455261) (-901 "PARSURF.spad" 1452708 1452736 1453264 1453269) (-900 "PARSU2.spad" 1452505 1452521 1452698 1452703) (-899 "script-parser.spad" 1452025 1452033 1452495 1452500) (-898 "PARSCURV.spad" 1451459 1451487 1452015 1452020) (-897 "PARSC2.spad" 1451250 1451266 1451449 1451454) (-896 "PARPCURV.spad" 1450712 1450740 1451240 1451245) (-895 "PARPC2.spad" 1450503 1450519 1450702 1450707) (-894 "PARAMAST.spad" 1449631 1449639 1450493 1450498) (-893 "PAN2EXPR.spad" 1449043 1449051 1449621 1449626) (-892 "PALETTE.spad" 1448013 1448021 1449033 1449038) (-891 "PAIR.spad" 1447000 1447013 1447601 1447606) (-890 "PADICRC.spad" 1444241 1444259 1445412 1445505) (-889 "PADICRAT.spad" 1442149 1442161 1442370 1442463) (-888 "PADIC.spad" 1441844 1441856 1442075 1442144) (-887 "PADICCT.spad" 1440393 1440405 1441770 1441839) (-886 "PADEPAC.spad" 1439082 1439101 1440383 1440388) (-885 "PADE.spad" 1437834 1437850 1439072 1439077) (-884 "OWP.spad" 1437074 1437104 1437692 1437759) (-883 "OVERSET.spad" 1436647 1436655 1437064 1437069) (-882 "OVAR.spad" 1436428 1436451 1436637 1436642) (-881 "OUT.spad" 1435514 1435522 1436418 1436423) (-880 "OUTFORM.spad" 1424906 1424914 1435504 1435509) (-879 "OUTBFILE.spad" 1424324 1424332 1424896 1424901) (-878 "OUTBCON.spad" 1423330 1423338 1424314 1424319) (-877 "OUTBCON.spad" 1422334 1422344 1423320 1423325) (-876 "OSI.spad" 1421809 1421817 1422324 1422329) (-875 "OSGROUP.spad" 1421727 1421735 1421799 1421804) (-874 "ORTHPOL.spad" 1420212 1420222 1421644 1421649) (-873 "OREUP.spad" 1419665 1419693 1419892 1419931) (-872 "ORESUP.spad" 1418966 1418990 1419345 1419384) (-871 "OREPCTO.spad" 1416823 1416835 1418886 1418891) (-870 "OREPCAT.spad" 1410970 1410980 1416779 1416818) (-869 "OREPCAT.spad" 1405007 1405019 1410818 1410823) (-868 "ORDTYPE.spad" 1404244 1404252 1404997 1405002) (-867 "ORDTYPE.spad" 1403479 1403489 1404234 1404239) (-866 "ORDSTRCT.spad" 1403252 1403267 1403415 1403420) (-865 "ORDSET.spad" 1402952 1402960 1403242 1403247) (-864 "ORDRING.spad" 1402342 1402350 1402932 1402947) (-863 "ORDRING.spad" 1401740 1401750 1402332 1402337) (-862 "ORDMON.spad" 1401595 1401603 1401730 1401735) (-861 "ORDFUNS.spad" 1400727 1400743 1401585 1401590) (-860 "ORDFIN.spad" 1400547 1400555 1400717 1400722) (-859 "ORDCOMP.spad" 1399012 1399022 1400094 1400123) (-858 "ORDCOMP2.spad" 1398305 1398317 1399002 1399007) (-857 "OPTPROB.spad" 1396943 1396951 1398295 1398300) (-856 "OPTPACK.spad" 1389352 1389360 1396933 1396938) (-855 "OPTCAT.spad" 1387031 1387039 1389342 1389347) (-854 "OPSIG.spad" 1386685 1386693 1387021 1387026) (-853 "OPQUERY.spad" 1386234 1386242 1386675 1386680) (-852 "OP.spad" 1385976 1385986 1386056 1386123) (-851 "OPERCAT.spad" 1385442 1385452 1385966 1385971) (-850 "OPERCAT.spad" 1384906 1384918 1385432 1385437) (-849 "ONECOMP.spad" 1383651 1383661 1384453 1384482) (-848 "ONECOMP2.spad" 1383075 1383087 1383641 1383646) (-847 "OMSERVER.spad" 1382081 1382089 1383065 1383070) (-846 "OMSAGG.spad" 1381869 1381879 1382037 1382076) (-845 "OMPKG.spad" 1380485 1380493 1381859 1381864) (-844 "OM.spad" 1379458 1379466 1380475 1380480) (-843 "OMLO.spad" 1378883 1378895 1379344 1379383) (-842 "OMEXPR.spad" 1378717 1378727 1378873 1378878) (-841 "OMERR.spad" 1378262 1378270 1378707 1378712) (-840 "OMERRK.spad" 1377296 1377304 1378252 1378257) (-839 "OMENC.spad" 1376640 1376648 1377286 1377291) (-838 "OMDEV.spad" 1370949 1370957 1376630 1376635) (-837 "OMCONN.spad" 1370358 1370366 1370939 1370944) (-836 "OINTDOM.spad" 1370121 1370129 1370284 1370353) (-835 "OFMONOID.spad" 1368244 1368254 1370077 1370082) (-834 "ODVAR.spad" 1367505 1367515 1368234 1368239) (-833 "ODR.spad" 1367149 1367175 1367317 1367466) (-832 "ODPOL.spad" 1364438 1364448 1364778 1364905) (-831 "ODP.spad" 1352252 1352272 1352625 1352724) (-830 "ODETOOLS.spad" 1350901 1350920 1352242 1352247) (-829 "ODESYS.spad" 1348595 1348612 1350891 1350896) (-828 "ODERTRIC.spad" 1344604 1344621 1348552 1348557) (-827 "ODERED.spad" 1344003 1344027 1344594 1344599) (-826 "ODERAT.spad" 1341618 1341635 1343993 1343998) (-825 "ODEPRRIC.spad" 1338655 1338677 1341608 1341613) (-824 "ODEPROB.spad" 1337912 1337920 1338645 1338650) (-823 "ODEPRIM.spad" 1335246 1335268 1337902 1337907) (-822 "ODEPAL.spad" 1334632 1334656 1335236 1335241) (-821 "ODEPACK.spad" 1321298 1321306 1334622 1334627) (-820 "ODEINT.spad" 1320733 1320749 1321288 1321293) (-819 "ODEIFTBL.spad" 1318128 1318136 1320723 1320728) (-818 "ODEEF.spad" 1313619 1313635 1318118 1318123) (-817 "ODECONST.spad" 1313156 1313174 1313609 1313614) (-816 "ODECAT.spad" 1311754 1311762 1313146 1313151) (-815 "OCT.spad" 1309890 1309900 1310604 1310643) (-814 "OCTCT2.spad" 1309536 1309557 1309880 1309885) (-813 "OC.spad" 1307332 1307342 1309492 1309531) (-812 "OC.spad" 1304853 1304865 1307015 1307020) (-811 "OCAMON.spad" 1304701 1304709 1304843 1304848) (-810 "OASGP.spad" 1304516 1304524 1304691 1304696) (-809 "OAMONS.spad" 1304038 1304046 1304506 1304511) (-808 "OAMON.spad" 1303899 1303907 1304028 1304033) (-807 "OAGROUP.spad" 1303761 1303769 1303889 1303894) (-806 "NUMTUBE.spad" 1303352 1303368 1303751 1303756) (-805 "NUMQUAD.spad" 1291328 1291336 1303342 1303347) (-804 "NUMODE.spad" 1282682 1282690 1291318 1291323) (-803 "NUMINT.spad" 1280248 1280256 1282672 1282677) (-802 "NUMFMT.spad" 1279088 1279096 1280238 1280243) (-801 "NUMERIC.spad" 1271202 1271212 1278893 1278898) (-800 "NTSCAT.spad" 1269710 1269726 1271170 1271197) (-799 "NTPOLFN.spad" 1269261 1269271 1269627 1269632) (-798 "NSUP.spad" 1262214 1262224 1266754 1266907) (-797 "NSUP2.spad" 1261606 1261618 1262204 1262209) (-796 "NSMP.spad" 1257836 1257855 1258144 1258271) (-795 "NREP.spad" 1256214 1256228 1257826 1257831) (-794 "NPCOEF.spad" 1255460 1255480 1256204 1256209) (-793 "NORMRETR.spad" 1255058 1255097 1255450 1255455) (-792 "NORMPK.spad" 1252960 1252979 1255048 1255053) (-791 "NORMMA.spad" 1252648 1252674 1252950 1252955) (-790 "NONE.spad" 1252389 1252397 1252638 1252643) (-789 "NONE1.spad" 1252065 1252075 1252379 1252384) (-788 "NODE1.spad" 1251552 1251568 1252055 1252060) (-787 "NNI.spad" 1250447 1250455 1251526 1251547) (-786 "NLINSOL.spad" 1249073 1249083 1250437 1250442) (-785 "NIPROB.spad" 1247614 1247622 1249063 1249068) (-784 "NFINTBAS.spad" 1245174 1245191 1247604 1247609) (-783 "NETCLT.spad" 1245148 1245159 1245164 1245169) (-782 "NCODIV.spad" 1243364 1243380 1245138 1245143) (-781 "NCNTFRAC.spad" 1243006 1243020 1243354 1243359) (-780 "NCEP.spad" 1241172 1241186 1242996 1243001) (-779 "NASRING.spad" 1240768 1240776 1241162 1241167) (-778 "NASRING.spad" 1240362 1240372 1240758 1240763) (-777 "NARNG.spad" 1239714 1239722 1240352 1240357) (-776 "NARNG.spad" 1239064 1239074 1239704 1239709) (-775 "NAGSP.spad" 1238141 1238149 1239054 1239059) (-774 "NAGS.spad" 1227802 1227810 1238131 1238136) (-773 "NAGF07.spad" 1226233 1226241 1227792 1227797) (-772 "NAGF04.spad" 1220635 1220643 1226223 1226228) (-771 "NAGF02.spad" 1214704 1214712 1220625 1220630) (-770 "NAGF01.spad" 1210465 1210473 1214694 1214699) (-769 "NAGE04.spad" 1204165 1204173 1210455 1210460) (-768 "NAGE02.spad" 1194825 1194833 1204155 1204160) (-767 "NAGE01.spad" 1190827 1190835 1194815 1194820) (-766 "NAGD03.spad" 1188831 1188839 1190817 1190822) (-765 "NAGD02.spad" 1181578 1181586 1188821 1188826) (-764 "NAGD01.spad" 1175871 1175879 1181568 1181573) (-763 "NAGC06.spad" 1171746 1171754 1175861 1175866) (-762 "NAGC05.spad" 1170247 1170255 1171736 1171741) (-761 "NAGC02.spad" 1169514 1169522 1170237 1170242) (-760 "NAALG.spad" 1169055 1169065 1169482 1169509) (-759 "NAALG.spad" 1168616 1168628 1169045 1169050) (-758 "MULTSQFR.spad" 1165574 1165591 1168606 1168611) (-757 "MULTFACT.spad" 1164957 1164974 1165564 1165569) (-756 "MTSCAT.spad" 1163051 1163072 1164855 1164952) (-755 "MTHING.spad" 1162710 1162720 1163041 1163046) (-754 "MSYSCMD.spad" 1162144 1162152 1162700 1162705) (-753 "MSET.spad" 1160066 1160076 1161814 1161853) (-752 "MSETAGG.spad" 1159911 1159921 1160034 1160061) (-751 "MRING.spad" 1156888 1156900 1159619 1159686) (-750 "MRF2.spad" 1156458 1156472 1156878 1156883) (-749 "MRATFAC.spad" 1156004 1156021 1156448 1156453) (-748 "MPRFF.spad" 1154044 1154063 1155994 1155999) (-747 "MPOLY.spad" 1151515 1151530 1151874 1152001) (-746 "MPCPF.spad" 1150779 1150798 1151505 1151510) (-745 "MPC3.spad" 1150596 1150636 1150769 1150774) (-744 "MPC2.spad" 1150242 1150275 1150586 1150591) (-743 "MONOTOOL.spad" 1148593 1148610 1150232 1150237) (-742 "MONOID.spad" 1147912 1147920 1148583 1148588) (-741 "MONOID.spad" 1147229 1147239 1147902 1147907) (-740 "MONOGEN.spad" 1145977 1145990 1147089 1147224) (-739 "MONOGEN.spad" 1144747 1144762 1145861 1145866) (-738 "MONADWU.spad" 1142777 1142785 1144737 1144742) (-737 "MONADWU.spad" 1140805 1140815 1142767 1142772) (-736 "MONAD.spad" 1139965 1139973 1140795 1140800) (-735 "MONAD.spad" 1139123 1139133 1139955 1139960) (-734 "MOEBIUS.spad" 1137859 1137873 1139103 1139118) (-733 "MODULE.spad" 1137729 1137739 1137827 1137854) (-732 "MODULE.spad" 1137619 1137631 1137719 1137724) (-731 "MODRING.spad" 1136954 1136993 1137599 1137614) (-730 "MODOP.spad" 1135619 1135631 1136776 1136843) (-729 "MODMONOM.spad" 1135350 1135368 1135609 1135614) (-728 "MODMON.spad" 1132052 1132068 1132771 1132924) (-727 "MODFIELD.spad" 1131414 1131453 1131954 1132047) (-726 "MMLFORM.spad" 1130274 1130282 1131404 1131409) (-725 "MMAP.spad" 1130016 1130050 1130264 1130269) (-724 "MLO.spad" 1128475 1128485 1129972 1130011) (-723 "MLIFT.spad" 1127087 1127104 1128465 1128470) (-722 "MKUCFUNC.spad" 1126622 1126640 1127077 1127082) (-721 "MKRECORD.spad" 1126226 1126239 1126612 1126617) (-720 "MKFUNC.spad" 1125633 1125643 1126216 1126221) (-719 "MKFLCFN.spad" 1124601 1124611 1125623 1125628) (-718 "MKBCFUNC.spad" 1124096 1124114 1124591 1124596) (-717 "MINT.spad" 1123535 1123543 1123998 1124091) (-716 "MHROWRED.spad" 1122046 1122056 1123525 1123530) (-715 "MFLOAT.spad" 1120566 1120574 1121936 1122041) (-714 "MFINFACT.spad" 1119966 1119988 1120556 1120561) (-713 "MESH.spad" 1117748 1117756 1119956 1119961) (-712 "MDDFACT.spad" 1115959 1115969 1117738 1117743) (-711 "MDAGG.spad" 1115250 1115260 1115939 1115954) (-710 "MCMPLX.spad" 1110681 1110689 1111295 1111496) (-709 "MCDEN.spad" 1109891 1109903 1110671 1110676) (-708 "MCALCFN.spad" 1107013 1107039 1109881 1109886) (-707 "MAYBE.spad" 1106297 1106308 1107003 1107008) (-706 "MATSTOR.spad" 1103605 1103615 1106287 1106292) (-705 "MATRIX.spad" 1102192 1102202 1102676 1102703) (-704 "MATLIN.spad" 1099536 1099560 1102076 1102081) (-703 "MATCAT.spad" 1091058 1091080 1099504 1099531) (-702 "MATCAT.spad" 1082452 1082476 1090900 1090905) (-701 "MATCAT2.spad" 1081734 1081782 1082442 1082447) (-700 "MAPPKG3.spad" 1080649 1080663 1081724 1081729) (-699 "MAPPKG2.spad" 1079987 1079999 1080639 1080644) (-698 "MAPPKG1.spad" 1078815 1078825 1079977 1079982) (-697 "MAPPAST.spad" 1078130 1078138 1078805 1078810) (-696 "MAPHACK3.spad" 1077942 1077956 1078120 1078125) (-695 "MAPHACK2.spad" 1077711 1077723 1077932 1077937) (-694 "MAPHACK1.spad" 1077355 1077365 1077701 1077706) (-693 "MAGMA.spad" 1075145 1075162 1077345 1077350) (-692 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(-654 "LINEXP.spad" 1024061 1024071 1025308 1025313) (-653 "LINELT.spad" 1023432 1023444 1023944 1023971) (-652 "LINDEP.spad" 1022241 1022253 1023344 1023349) (-651 "LINBASIS.spad" 1021877 1021892 1022231 1022236) (-650 "LIMITRF.spad" 1019805 1019815 1021867 1021872) (-649 "LIMITPS.spad" 1018708 1018721 1019795 1019800) (-648 "LIE.spad" 1016724 1016736 1017998 1018143) (-647 "LIECAT.spad" 1016200 1016210 1016650 1016719) (-646 "LIECAT.spad" 1015704 1015716 1016156 1016161) (-645 "LIB.spad" 1013455 1013463 1013901 1013916) (-644 "LGROBP.spad" 1010808 1010827 1013445 1013450) (-643 "LF.spad" 1009763 1009779 1010798 1010803) (-642 "LFCAT.spad" 1008822 1008830 1009753 1009758) (-641 "LEXTRIPK.spad" 1004325 1004340 1008812 1008817) (-640 "LEXP.spad" 1002328 1002355 1004305 1004320) (-639 "LETAST.spad" 1002027 1002035 1002318 1002323) (-638 "LEADCDET.spad" 1000425 1000442 1002017 1002022) (-637 "LAZM3PK.spad" 999129 999151 1000415 1000420) (-636 "LAUPOL.spad" 997729 997742 998629 998698) (-635 "LAPLACE.spad" 997312 997328 997719 997724) (-634 "LA.spad" 996752 996766 997234 997273) (-633 "LALG.spad" 996528 996538 996732 996747) (-632 "LALG.spad" 996312 996324 996518 996523) (-631 "KVTFROM.spad" 996047 996057 996302 996307) (-630 "KTVLOGIC.spad" 995559 995567 996037 996042) (-629 "KRCFROM.spad" 995297 995307 995549 995554) (-628 "KOVACIC.spad" 994020 994037 995287 995292) (-627 "KONVERT.spad" 993742 993752 994010 994015) (-626 "KOERCE.spad" 993479 993489 993732 993737) (-625 "KERNEL.spad" 992134 992144 993263 993268) (-624 "KERNEL2.spad" 991837 991849 992124 992129) (-623 "KDAGG.spad" 990946 990968 991817 991832) (-622 "KDAGG.spad" 990063 990087 990936 990941) (-621 "KAFILE.spad" 988917 988933 989152 989179) (-620 "JORDAN.spad" 986746 986758 988207 988352) (-619 "JOINAST.spad" 986440 986448 986736 986741) (-618 "JAVACODE.spad" 986306 986314 986430 986435) (-617 "IXAGG.spad" 984439 984463 986296 986301) (-616 "IXAGG.spad" 982427 982453 984286 984291) (-615 "IVECTOR.spad" 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889109 889987 889992) (-553 "INNMFACT.spad" 888060 888077 889075 889080) (-552 "INMODGCD.spad" 887548 887578 888050 888055) (-551 "INFSP.spad" 885845 885867 887538 887543) (-550 "INFPROD0.spad" 884925 884944 885835 885840) (-549 "INFORM.spad" 882124 882132 884915 884920) (-548 "INFORM1.spad" 881749 881759 882114 882119) (-547 "INFINITY.spad" 881301 881309 881739 881744) (-546 "INETCLTS.spad" 881278 881286 881291 881296) (-545 "INEP.spad" 879816 879838 881268 881273) (-544 "INDE.spad" 879465 879482 879726 879731) (-543 "INCRMAPS.spad" 878886 878896 879455 879460) (-542 "INBFILE.spad" 877958 877966 878876 878881) (-541 "INBFF.spad" 873752 873763 877948 877953) (-540 "INBCON.spad" 872042 872050 873742 873747) (-539 "INBCON.spad" 870330 870340 872032 872037) (-538 "INAST.spad" 869991 869999 870320 870325) (-537 "IMPTAST.spad" 869699 869707 869981 869986) (-536 "IMATRIX.spad" 868527 868553 869039 869066) (-535 "IMATQF.spad" 867621 867665 868483 868488) (-534 "IMATLIN.spad" 866226 866250 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(-472 "GENUPS.spad" 773442 773455 777139 777144) (-471 "GENUFACT.spad" 773019 773029 773432 773437) (-470 "GENPGCD.spad" 772605 772622 773009 773014) (-469 "GENMFACT.spad" 772057 772076 772595 772600) (-468 "GENEEZ.spad" 770008 770021 772047 772052) (-467 "GDMP.spad" 767064 767081 767838 767965) (-466 "GCNAALG.spad" 760987 761014 766858 766925) (-465 "GCDDOM.spad" 760163 760171 760913 760982) (-464 "GCDDOM.spad" 759401 759411 760153 760158) (-463 "GB.spad" 756927 756965 759357 759362) (-462 "GBINTERN.spad" 752947 752985 756917 756922) (-461 "GBF.spad" 748714 748752 752937 752942) (-460 "GBEUCLID.spad" 746596 746634 748704 748709) (-459 "GAUSSFAC.spad" 745909 745917 746586 746591) (-458 "GALUTIL.spad" 744235 744245 745865 745870) (-457 "GALPOLYU.spad" 742689 742702 744225 744230) (-456 "GALFACTU.spad" 740862 740881 742679 742684) (-455 "GALFACT.spad" 731051 731062 740852 740857) (-454 "FVFUN.spad" 728074 728082 731041 731046) (-453 "FVC.spad" 727126 727134 728064 728069) (-452 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694233) (-431 "FR.spad" 686815 686825 692123 692192) (-430 "FRNAALG.spad" 682084 682094 686757 686810) (-429 "FRNAALG.spad" 677365 677377 682040 682045) (-428 "FRNAAF2.spad" 676821 676839 677355 677360) (-427 "FRMOD.spad" 676231 676261 676752 676757) (-426 "FRIDEAL.spad" 675456 675477 676211 676226) (-425 "FRIDEAL2.spad" 675060 675092 675446 675451) (-424 "FRETRCT.spad" 674571 674581 675050 675055) (-423 "FRETRCT.spad" 673948 673960 674429 674434) (-422 "FRAMALG.spad" 672296 672309 673904 673943) (-421 "FRAMALG.spad" 670676 670691 672286 672291) (-420 "FRAC.spad" 667682 667692 668085 668258) (-419 "FRAC2.spad" 667287 667299 667672 667677) (-418 "FR2.spad" 666623 666635 667277 667282) (-417 "FPS.spad" 663438 663446 666513 666618) (-416 "FPS.spad" 660281 660291 663358 663363) (-415 "FPC.spad" 659327 659335 660183 660276) (-414 "FPC.spad" 658459 658469 659317 659322) (-413 "FPATMAB.spad" 658221 658231 658449 658454) (-412 "FPARFRAC.spad" 657071 657088 658211 658216) (-411 "FORTRAN.spad" 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"FEVALAB.spad" 526009 526021 526293 526298) (-348 "FDIV.spad" 525451 525475 525999 526004) (-347 "FDIVCAT.spad" 523515 523539 525441 525446) (-346 "FDIVCAT.spad" 521577 521603 523505 523510) (-345 "FDIV2.spad" 521233 521273 521567 521572) (-344 "FCTRDATA.spad" 520241 520249 521223 521228) (-343 "FCPAK1.spad" 518808 518816 520231 520236) (-342 "FCOMP.spad" 518187 518197 518798 518803) (-341 "FC.spad" 508194 508202 518177 518182) (-340 "FAXF.spad" 501165 501179 508096 508189) (-339 "FAXF.spad" 494188 494204 501121 501126) (-338 "FARRAY.spad" 492185 492195 493218 493245) (-337 "FAMR.spad" 490321 490333 492083 492180) (-336 "FAMR.spad" 488441 488455 490205 490210) (-335 "FAMONOID.spad" 488109 488119 488395 488400) (-334 "FAMONC.spad" 486405 486417 488099 488104) (-333 "FAGROUP.spad" 486029 486039 486301 486328) (-332 "FACUTIL.spad" 484233 484250 486019 486024) (-331 "FACTFUNC.spad" 483427 483437 484223 484228) (-330 "EXPUPXS.spad" 480260 480283 481559 481708) (-329 "EXPRTUBE.spad" 477548 477556 480250 480255) (-328 "EXPRODE.spad" 474708 474724 477538 477543) (-327 "EXPR.spad" 469883 469893 470597 470892) (-326 "EXPR2UPS.spad" 466005 466018 469873 469878) (-325 "EXPR2.spad" 465710 465722 465995 466000) (-324 "EXPEXPAN.spad" 462511 462536 463143 463236) (-323 "EXIT.spad" 462182 462190 462501 462506) (-322 "EXITAST.spad" 461918 461926 462172 462177) (-321 "EVALCYC.spad" 461378 461392 461908 461913) (-320 "EVALAB.spad" 460950 460960 461368 461373) (-319 "EVALAB.spad" 460520 460532 460940 460945) (-318 "EUCDOM.spad" 458094 458102 460446 460515) (-317 "EUCDOM.spad" 455730 455740 458084 458089) (-316 "ESTOOLS.spad" 447576 447584 455720 455725) (-315 "ESTOOLS2.spad" 447179 447193 447566 447571) (-314 "ESTOOLS1.spad" 446864 446875 447169 447174) (-313 "ES.spad" 439679 439687 446854 446859) (-312 "ES.spad" 432400 432410 439577 439582) (-311 "ESCONT.spad" 429193 429201 432390 432395) (-310 "ESCONT1.spad" 428942 428954 429183 429188) (-309 "ES2.spad" 428447 428463 428932 428937) (-308 "ES1.spad" 428017 428033 428437 428442) (-307 "ERROR.spad" 425344 425352 428007 428012) (-306 "EQTBL.spad" 423374 423396 423583 423610) (-305 "EQ.spad" 418179 418189 420966 421078) (-304 "EQ2.spad" 417897 417909 418169 418174) (-303 "EP.spad" 414223 414233 417887 417892) (-302 "ENV.spad" 412901 412909 414213 414218) (-301 "ENTIRER.spad" 412569 412577 412845 412896) (-300 "EMR.spad" 411857 411898 412495 412564) (-299 "ELTAGG.spad" 410111 410130 411847 411852) (-298 "ELTAGG.spad" 408329 408350 410067 410072) (-297 "ELTAB.spad" 407804 407817 408319 408324) (-296 "ELFUTS.spad" 407191 407210 407794 407799) (-295 "ELEMFUN.spad" 406880 406888 407181 407186) (-294 "ELEMFUN.spad" 406567 406577 406870 406875) (-293 "ELAGG.spad" 404538 404548 406547 406562) (-292 "ELAGG.spad" 402446 402458 404457 404462) (-291 "ELABOR.spad" 401792 401800 402436 402441) (-290 "ELABEXPR.spad" 400724 400732 401782 401787) (-289 "EFUPXS.spad" 397500 397530 400680 400685) (-288 "EFULS.spad" 394336 394359 397456 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"DRAW.spad" 347283 347296 354397 354402) (-266 "DRAWHACK.spad" 346591 346601 347273 347278) (-265 "DRAWCX.spad" 344061 344069 346581 346586) (-264 "DRAWCURV.spad" 343608 343623 344051 344056) (-263 "DRAWCFUN.spad" 333140 333148 343598 343603) (-262 "DQAGG.spad" 331318 331328 333108 333135) (-261 "DPOLCAT.spad" 326667 326683 331186 331313) (-260 "DPOLCAT.spad" 322102 322120 326623 326628) (-259 "DPMO.spad" 313862 313878 314000 314213) (-258 "DPMM.spad" 305635 305653 305760 305973) (-257 "DOMTMPLT.spad" 305406 305414 305625 305630) (-256 "DOMCTOR.spad" 305161 305169 305396 305401) (-255 "DOMAIN.spad" 304248 304256 305151 305156) (-254 "DMP.spad" 301508 301523 302078 302205) (-253 "DMEXT.spad" 301375 301385 301476 301503) (-252 "DLP.spad" 300727 300737 301365 301370) (-251 "DLIST.spad" 299153 299163 299757 299784) (-250 "DLAGG.spad" 297570 297580 299143 299148) (-249 "DIVRING.spad" 297112 297120 297514 297565) (-248 "DIVRING.spad" 296698 296708 297102 297107) (-247 "DISPLAY.spad" 294888 294896 296688 296693) (-246 "DIRPROD.spad" 282435 282451 283075 283174) (-245 "DIRPROD2.spad" 281253 281271 282425 282430) (-244 "DIRPCAT.spad" 280446 280462 281149 281248) (-243 "DIRPCAT.spad" 279266 279284 279971 279976) (-242 "DIOSP.spad" 278091 278099 279256 279261) (-241 "DIOPS.spad" 277087 277097 278071 278086) (-240 "DIOPS.spad" 276057 276069 277043 277048) (-239 "DIFRING.spad" 275895 275903 276037 276052) (-238 "DIFFSPC.spad" 275474 275482 275885 275890) (-237 "DIFFSPC.spad" 275051 275061 275464 275469) (-236 "DIFFMOD.spad" 274540 274550 275019 275046) (-235 "DIFFDOM.spad" 273705 273716 274530 274535) (-234 "DIFFDOM.spad" 272868 272881 273695 273700) (-233 "DIFEXT.spad" 272687 272697 272848 272863) (-232 "DIAGG.spad" 272317 272327 272667 272682) (-231 "DIAGG.spad" 271955 271967 272307 272312) (-230 "DHMATRIX.spad" 270150 270160 271295 271322) (-229 "DFSFUN.spad" 263790 263798 270140 270145) (-228 "DFLOAT.spad" 260521 260529 263680 263785) (-227 "DFINTTLS.spad" 258752 258768 260511 260516) (-226 "DERHAM.spad" 256666 256698 258732 258747) (-225 "DEQUEUE.spad" 255873 255883 256156 256183) (-224 "DEGRED.spad" 255490 255504 255863 255868) (-223 "DEFINTRF.spad" 253027 253037 255480 255485) (-222 "DEFINTEF.spad" 251537 251553 253017 253022) (-221 "DEFAST.spad" 250905 250913 251527 251532) (-220 "DECIMAL.spad" 248914 248922 249275 249368) (-219 "DDFACT.spad" 246727 246744 248904 248909) (-218 "DBLRESP.spad" 246327 246351 246717 246722) (-217 "DBASIS.spad" 245953 245968 246317 246322) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 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163248) (-146 "CHARNZ.spad" 162516 162524 162743 162758) (-145 "CHAR.spad" 160390 160398 162506 162511) (-144 "CFCAT.spad" 159718 159726 160380 160385) (-143 "CDEN.spad" 158914 158928 159708 159713) (-142 "CCLASS.spad" 157025 157033 158287 158326) (-141 "CATEGORY.spad" 156067 156075 157015 157020) (-140 "CATCTOR.spad" 155958 155966 156057 156062) (-139 "CATAST.spad" 155576 155584 155948 155953) (-138 "CASEAST.spad" 155290 155298 155566 155571) (-137 "CARTEN.spad" 150657 150681 155280 155285) (-136 "CARTEN2.spad" 150047 150074 150647 150652) (-135 "CARD.spad" 147342 147350 150021 150042) (-134 "CAPSLAST.spad" 147116 147124 147332 147337) (-133 "CACHSET.spad" 146740 146748 147106 147111) (-132 "CABMON.spad" 146295 146303 146730 146735) (-131 "BYTEORD.spad" 145970 145978 146285 146290) (-130 "BYTE.spad" 145397 145405 145960 145965) (-129 "BYTEBUF.spad" 143095 143103 144405 144432) (-128 "BTREE.spad" 142051 142061 142585 142612) (-127 "BTOURN.spad" 140939 140949 141541 141568) (-126 "BTCAT.spad" 140331 140341 140907 140934) (-125 "BTCAT.spad" 139743 139755 140321 140326) (-124 "BTAGG.spad" 139209 139217 139711 139738) (-123 "BTAGG.spad" 138695 138705 139199 139204) (-122 "BSTREE.spad" 137319 137329 138185 138212) (-121 "BRILL.spad" 135516 135527 137309 137314) (-120 "BRAGG.spad" 134456 134466 135506 135511) (-119 "BRAGG.spad" 133360 133372 134412 134417) (-118 "BPADICRT.spad" 131234 131246 131489 131582) (-117 "BPADIC.spad" 130898 130910 131160 131229) (-116 "BOUNDZRO.spad" 130554 130571 130888 130893) (-115 "BOP.spad" 125736 125744 130544 130549) (-114 "BOP1.spad" 123202 123212 125726 125731) (-113 "BOOLE.spad" 122852 122860 123192 123197) (-112 "BOOLEAN.spad" 122290 122298 122842 122847) (-111 "BMODULE.spad" 122002 122014 122258 122285) (-110 "BITS.spad" 121385 121393 121600 121627) (-109 "BINDING.spad" 120798 120806 121375 121380) (-108 "BINARY.spad" 118812 118820 119168 119261) (-107 "BGAGG.spad" 118017 118027 118792 118807) (-106 "BGAGG.spad" 117230 117242 118007 118012) (-105 "BFUNCT.spad" 116794 116802 117210 117225) (-104 "BEZOUT.spad" 115934 115961 116744 116749) (-103 "BBTREE.spad" 112662 112672 115424 115451) (-102 "BASTYPE.spad" 112158 112166 112652 112657) (-101 "BASTYPE.spad" 111652 111662 112148 112153) (-100 "BALFACT.spad" 111111 111124 111642 111647) (-99 "AUTOMOR.spad" 110562 110571 111091 111106) (-98 "ATTREG.spad" 107285 107292 110314 110557) (-97 "ATTRBUT.spad" 103308 103315 107265 107280) (-96 "ATTRAST.spad" 103025 103032 103298 103303) (-95 "ATRIG.spad" 102495 102502 103015 103020) (-94 "ATRIG.spad" 101963 101972 102485 102490) (-93 "ASTCAT.spad" 101867 101874 101953 101958) (-92 "ASTCAT.spad" 101769 101778 101857 101862) (-91 "ASTACK.spad" 100991 101000 101259 101286) (-90 "ASSOCEQ.spad" 99817 99828 100947 100952) (-89 "ASP9.spad" 98898 98911 99807 99812) (-88 "ASP8.spad" 97941 97954 98888 98893) (-87 "ASP80.spad" 97263 97276 97931 97936) (-86 "ASP7.spad" 96423 96436 97253 97258) (-85 "ASP78.spad" 95874 95887 96413 96418) (-84 "ASP77.spad" 95243 95256 95864 95869) (-83 "ASP74.spad" 94335 94348 95233 95238) (-82 "ASP73.spad" 93606 93619 94325 94330) (-81 "ASP6.spad" 92473 92486 93596 93601) (-80 "ASP55.spad" 90982 90995 92463 92468) (-79 "ASP50.spad" 88799 88812 90972 90977) (-78 "ASP4.spad" 88094 88107 88789 88794) (-77 "ASP49.spad" 87093 87106 88084 88089) (-76 "ASP42.spad" 85500 85539 87083 87088) (-75 "ASP41.spad" 84079 84118 85490 85495) (-74 "ASP35.spad" 83067 83080 84069 84074) (-73 "ASP34.spad" 82368 82381 83057 83062) (-72 "ASP33.spad" 81928 81941 82358 82363) (-71 "ASP31.spad" 81068 81081 81918 81923) (-70 "ASP30.spad" 79960 79973 81058 81063) (-69 "ASP29.spad" 79426 79439 79950 79955) (-68 "ASP28.spad" 70699 70712 79416 79421) (-67 "ASP27.spad" 69596 69609 70689 70694) (-66 "ASP24.spad" 68683 68696 69586 69591) (-65 "ASP20.spad" 68147 68160 68673 68678) (-64 "ASP1.spad" 67528 67541 68137 68142) (-63 "ASP19.spad" 62214 62227 67518 67523) (-62 "ASP12.spad" 61628 61641 62204 62209) (-61 "ASP10.spad" 60899 60912 61618 61623) (-60 "ARRAY2.spad" 60142 60151 60389 60416) (-59 "ARRAY1.spad" 58826 58835 59172 59199) (-58 "ARRAY12.spad" 57539 57550 58816 58821) (-57 "ARR2CAT.spad" 53313 53334 57507 57534) (-56 "ARR2CAT.spad" 49107 49130 53303 53308) (-55 "ARITY.spad" 48479 48486 49097 49102) (-54 "APPRULE.spad" 47739 47761 48469 48474) (-53 "APPLYORE.spad" 47358 47371 47729 47734) (-52 "ANY.spad" 46217 46224 47348 47353) (-51 "ANY1.spad" 45288 45297 46207 46212) (-50 "ANTISYM.spad" 43733 43749 45268 45283) (-49 "ANON.spad" 43426 43433 43723 43728) (-48 "AN.spad" 41735 41742 43242 43335) (-47 "AMR.spad" 39920 39931 41633 41730) (-46 "AMR.spad" 37942 37955 39657 39662) (-45 "ALIST.spad" 34842 34863 35192 35219) (-44 "ALGSC.spad" 33977 34003 34714 34767) (-43 "ALGPKG.spad" 29760 29771 33933 33938) (-42 "ALGMFACT.spad" 28953 28967 29750 29755) (-41 "ALGMANIP.spad" 26427 26442 28786 28791) (-40 "ALGFF.spad" 24068 24095 24285 24441) (-39 "ALGFACT.spad" 23195 23205 24058 24063) (-38 "ALGEBRA.spad" 23028 23037 23151 23190) (-37 "ALGEBRA.spad" 22893 22904 23018 23023) (-36 "ALAGG.spad" 22405 22426 22861 22888) (-35 "AHYP.spad" 21786 21793 22395 22400) (-34 "AGG.spad" 20103 20110 21776 21781) (-33 "AGG.spad" 18384 18393 20059 20064) (-32 "AF.spad" 16815 16830 18319 18324) (-31 "ADDAST.spad" 16493 16500 16805 16810) (-30 "ACPLOT.spad" 15084 15091 16483 16488) (-29 "ACFS.spad" 12893 12902 14986 15079) (-28 "ACFS.spad" 10788 10799 12883 12888) (-27 "ACF.spad" 7470 7477 10690 10783) (-26 "ACF.spad" 4238 4247 7460 7465) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2296396 2296401 2296406 2296411) (-2 NIL 2296376 2296381 2296386 2296391) (-1 NIL 2296356 2296361 2296366 2296371) (0 NIL 2296336 2296341 2296346 2296351) (-1326 "ZMOD.spad" 2296145 2296158 2296274 2296331) (-1325 "ZLINDEP.spad" 2295211 2295222 2296135 2296140) (-1324 "ZDSOLVE.spad" 2285156 2285178 2295201 2295206) (-1323 "YSTREAM.spad" 2284651 2284662 2285146 2285151) (-1322 "YDIAGRAM.spad" 2284285 2284294 2284641 2284646) (-1321 "XRPOLY.spad" 2283505 2283525 2284141 2284210) (-1320 "XPR.spad" 2281300 2281313 2283223 2283322) (-1319 "XPOLY.spad" 2280855 2280866 2281156 2281225) (-1318 "XPOLYC.spad" 2280174 2280190 2280781 2280850) (-1317 "XPBWPOLY.spad" 2278611 2278631 2279954 2280023) (-1316 "XF.spad" 2277074 2277089 2278513 2278606) (-1315 "XF.spad" 2275517 2275534 2276958 2276963) (-1314 "XFALG.spad" 2272565 2272581 2275443 2275512) (-1313 "XEXPPKG.spad" 2271816 2271842 2272555 2272560) (-1312 "XDPOLY.spad" 2271430 2271446 2271672 2271741) (-1311 "XALG.spad" 2271090 2271101 2271386 2271425) (-1310 "WUTSET.spad" 2266893 2266910 2270700 2270727) (-1309 "WP.spad" 2266092 2266136 2266751 2266818) (-1308 "WHILEAST.spad" 2265890 2265899 2266082 2266087) (-1307 "WHEREAST.spad" 2265561 2265570 2265880 2265885) (-1306 "WFFINTBS.spad" 2263224 2263246 2265551 2265556) (-1305 "WEIER.spad" 2261446 2261457 2263214 2263219) (-1304 "VSPACE.spad" 2261119 2261130 2261414 2261441) (-1303 "VSPACE.spad" 2260812 2260825 2261109 2261114) (-1302 "VOID.spad" 2260489 2260498 2260802 2260807) (-1301 "VIEW.spad" 2258169 2258178 2260479 2260484) (-1300 "VIEWDEF.spad" 2253370 2253379 2258159 2258164) (-1299 "VIEW3D.spad" 2237331 2237340 2253360 2253365) (-1298 "VIEW2D.spad" 2225222 2225231 2237321 2237326) (-1297 "VECTOR.spad" 2223743 2223754 2223994 2224021) (-1296 "VECTOR2.spad" 2222382 2222395 2223733 2223738) (-1295 "VECTCAT.spad" 2220286 2220297 2222350 2222377) (-1294 "VECTCAT.spad" 2217997 2218010 2220063 2220068) (-1293 "VARIABLE.spad" 2217777 2217792 2217987 2217992) (-1292 "UTYPE.spad" 2217421 2217430 2217767 2217772) (-1291 "UTSODETL.spad" 2216716 2216740 2217377 2217382) (-1290 "UTSODE.spad" 2214932 2214952 2216706 2216711) (-1289 "UTS.spad" 2209879 2209907 2213399 2213496) (-1288 "UTSCAT.spad" 2207358 2207374 2209777 2209874) (-1287 "UTSCAT.spad" 2204481 2204499 2206902 2206907) (-1286 "UTS2.spad" 2204076 2204111 2204471 2204476) (-1285 "URAGG.spad" 2198749 2198760 2204066 2204071) (-1284 "URAGG.spad" 2193386 2193399 2198705 2198710) (-1283 "UPXSSING.spad" 2191031 2191057 2192467 2192600) (-1282 "UPXS.spad" 2188327 2188355 2189163 2189312) (-1281 "UPXSCONS.spad" 2186086 2186106 2186459 2186608) (-1280 "UPXSCCA.spad" 2184657 2184677 2185932 2186081) (-1279 "UPXSCCA.spad" 2183370 2183392 2184647 2184652) (-1278 "UPXSCAT.spad" 2181959 2181975 2183216 2183365) (-1277 "UPXS2.spad" 2181502 2181555 2181949 2181954) (-1276 "UPSQFREE.spad" 2179916 2179930 2181492 2181497) (-1275 "UPSCAT.spad" 2177703 2177727 2179814 2179911) (-1274 "UPSCAT.spad" 2175196 2175222 2177309 2177314) (-1273 "UPOLYC.spad" 2170236 2170247 2175038 2175191) (-1272 "UPOLYC.spad" 2165168 2165181 2169972 2169977) (-1271 "UPOLYC2.spad" 2164639 2164658 2165158 2165163) (-1270 "UP.spad" 2161745 2161760 2162132 2162285) (-1269 "UPMP.spad" 2160645 2160658 2161735 2161740) (-1268 "UPDIVP.spad" 2160210 2160224 2160635 2160640) (-1267 "UPDECOMP.spad" 2158455 2158469 2160200 2160205) (-1266 "UPCDEN.spad" 2157664 2157680 2158445 2158450) (-1265 "UP2.spad" 2157028 2157049 2157654 2157659) (-1264 "UNISEG.spad" 2156381 2156392 2156947 2156952) (-1263 "UNISEG2.spad" 2155878 2155891 2156337 2156342) (-1262 "UNIFACT.spad" 2154981 2154993 2155868 2155873) (-1261 "ULS.spad" 2144765 2144793 2145710 2146139) (-1260 "ULSCONS.spad" 2135899 2135919 2136269 2136418) (-1259 "ULSCCAT.spad" 2133636 2133656 2135745 2135894) (-1258 "ULSCCAT.spad" 2131481 2131503 2133592 2133597) (-1257 "ULSCAT.spad" 2129713 2129729 2131327 2131476) (-1256 "ULS2.spad" 2129227 2129280 2129703 2129708) (-1255 "UINT8.spad" 2129104 2129113 2129217 2129222) (-1254 "UINT64.spad" 2128980 2128989 2129094 2129099) (-1253 "UINT32.spad" 2128856 2128865 2128970 2128975) (-1252 "UINT16.spad" 2128732 2128741 2128846 2128851) (-1251 "UFD.spad" 2127797 2127806 2128658 2128727) (-1250 "UFD.spad" 2126924 2126935 2127787 2127792) (-1249 "UDVO.spad" 2125805 2125814 2126914 2126919) (-1248 "UDPO.spad" 2123298 2123309 2125761 2125766) (-1247 "TYPE.spad" 2123230 2123239 2123288 2123293) (-1246 "TYPEAST.spad" 2123149 2123158 2123220 2123225) (-1245 "TWOFACT.spad" 2121801 2121816 2123139 2123144) (-1244 "TUPLE.spad" 2121287 2121298 2121700 2121705) (-1243 "TUBETOOL.spad" 2118154 2118163 2121277 2121282) (-1242 "TUBE.spad" 2116801 2116818 2118144 2118149) (-1241 "TS.spad" 2115400 2115416 2116366 2116463) (-1240 "TSETCAT.spad" 2102527 2102544 2115368 2115395) (-1239 "TSETCAT.spad" 2089640 2089659 2102483 2102488) (-1238 "TRMANIP.spad" 2084006 2084023 2089346 2089351) (-1237 "TRIMAT.spad" 2082969 2082994 2083996 2084001) (-1236 "TRIGMNIP.spad" 2081496 2081513 2082959 2082964) (-1235 "TRIGCAT.spad" 2081008 2081017 2081486 2081491) (-1234 "TRIGCAT.spad" 2080518 2080529 2080998 2081003) (-1233 "TREE.spad" 2078976 2078987 2080008 2080035) (-1232 "TRANFUN.spad" 2078815 2078824 2078966 2078971) (-1231 "TRANFUN.spad" 2078652 2078663 2078805 2078810) (-1230 "TOPSP.spad" 2078326 2078335 2078642 2078647) (-1229 "TOOLSIGN.spad" 2077989 2078000 2078316 2078321) (-1228 "TEXTFILE.spad" 2076550 2076559 2077979 2077984) (-1227 "TEX.spad" 2073696 2073705 2076540 2076545) (-1226 "TEX1.spad" 2073252 2073263 2073686 2073691) (-1225 "TEMUTL.spad" 2072807 2072816 2073242 2073247) (-1224 "TBCMPPK.spad" 2070900 2070923 2072797 2072802) (-1223 "TBAGG.spad" 2069950 2069973 2070880 2070895) (-1222 "TBAGG.spad" 2069008 2069033 2069940 2069945) (-1221 "TANEXP.spad" 2068416 2068427 2068998 2069003) (-1220 "TALGOP.spad" 2068140 2068151 2068406 2068411) (-1219 "TABLE.spad" 2066109 2066132 2066379 2066406) (-1218 "TABLEAU.spad" 2065590 2065601 2066099 2066104) (-1217 "TABLBUMP.spad" 2062393 2062404 2065580 2065585) (-1216 "SYSTEM.spad" 2061621 2061630 2062383 2062388) (-1215 "SYSSOLP.spad" 2059104 2059115 2061611 2061616) (-1214 "SYSPTR.spad" 2059003 2059012 2059094 2059099) (-1213 "SYSNNI.spad" 2058194 2058205 2058993 2058998) (-1212 "SYSINT.spad" 2057598 2057609 2058184 2058189) (-1211 "SYNTAX.spad" 2053804 2053813 2057588 2057593) (-1210 "SYMTAB.spad" 2051872 2051881 2053794 2053799) (-1209 "SYMS.spad" 2047895 2047904 2051862 2051867) (-1208 "SYMPOLY.spad" 2046901 2046912 2046983 2047110) (-1207 "SYMFUNC.spad" 2046402 2046413 2046891 2046896) (-1206 "SYMBOL.spad" 2043905 2043914 2046392 2046397) (-1205 "SWITCH.spad" 2040676 2040685 2043895 2043900) (-1204 "SUTS.spad" 2037724 2037752 2039143 2039240) (-1203 "SUPXS.spad" 2035007 2035035 2035856 2036005) (-1202 "SUP.spad" 2031727 2031738 2032500 2032653) (-1201 "SUPFRACF.spad" 2030832 2030850 2031717 2031722) (-1200 "SUP2.spad" 2030224 2030237 2030822 2030827) (-1199 "SUMRF.spad" 2029198 2029209 2030214 2030219) (-1198 "SUMFS.spad" 2028835 2028852 2029188 2029193) (-1197 "SULS.spad" 2018606 2018634 2019564 2019993) (-1196 "SUCHTAST.spad" 2018375 2018384 2018596 2018601) (-1195 "SUCH.spad" 2018057 2018072 2018365 2018370) (-1194 "SUBSPACE.spad" 2010172 2010187 2018047 2018052) (-1193 "SUBRESP.spad" 2009342 2009356 2010128 2010133) (-1192 "STTF.spad" 2005441 2005457 2009332 2009337) (-1191 "STTFNC.spad" 2001909 2001925 2005431 2005436) (-1190 "STTAYLOR.spad" 1994544 1994555 2001790 2001795) (-1189 "STRTBL.spad" 1992595 1992612 1992744 1992771) (-1188 "STRING.spad" 1991382 1991391 1991603 1991630) (-1187 "STREAM.spad" 1988183 1988194 1990790 1990805) (-1186 "STREAM3.spad" 1987756 1987771 1988173 1988178) (-1185 "STREAM2.spad" 1986884 1986897 1987746 1987751) (-1184 "STREAM1.spad" 1986590 1986601 1986874 1986879) (-1183 "STINPROD.spad" 1985526 1985542 1986580 1986585) (-1182 "STEP.spad" 1984727 1984736 1985516 1985521) (-1181 "STEPAST.spad" 1983961 1983970 1984717 1984722) (-1180 "STBL.spad" 1982045 1982073 1982212 1982227) (-1179 "STAGG.spad" 1981120 1981131 1982035 1982040) (-1178 "STAGG.spad" 1980193 1980206 1981110 1981115) (-1177 "STACK.spad" 1979433 1979444 1979683 1979710) (-1176 "SREGSET.spad" 1977101 1977118 1979043 1979070) (-1175 "SRDCMPK.spad" 1975662 1975682 1977091 1977096) (-1174 "SRAGG.spad" 1970805 1970814 1975630 1975657) (-1173 "SRAGG.spad" 1965968 1965979 1970795 1970800) (-1172 "SQMATRIX.spad" 1963511 1963529 1964427 1964514) (-1171 "SPLTREE.spad" 1957907 1957920 1962791 1962818) (-1170 "SPLNODE.spad" 1954495 1954508 1957897 1957902) (-1169 "SPFCAT.spad" 1953304 1953313 1954485 1954490) (-1168 "SPECOUT.spad" 1951856 1951865 1953294 1953299) (-1167 "SPADXPT.spad" 1943451 1943460 1951846 1951851) (-1166 "spad-parser.spad" 1942916 1942925 1943441 1943446) (-1165 "SPADAST.spad" 1942617 1942626 1942906 1942911) (-1164 "SPACEC.spad" 1926816 1926827 1942607 1942612) (-1163 "SPACE3.spad" 1926592 1926603 1926806 1926811) (-1162 "SORTPAK.spad" 1926141 1926154 1926548 1926553) (-1161 "SOLVETRA.spad" 1923904 1923915 1926131 1926136) (-1160 "SOLVESER.spad" 1922432 1922443 1923894 1923899) (-1159 "SOLVERAD.spad" 1918458 1918469 1922422 1922427) (-1158 "SOLVEFOR.spad" 1916920 1916938 1918448 1918453) (-1157 "SNTSCAT.spad" 1916520 1916537 1916888 1916915) (-1156 "SMTS.spad" 1914792 1914818 1916085 1916182) (-1155 "SMP.spad" 1912267 1912287 1912657 1912784) (-1154 "SMITH.spad" 1911112 1911137 1912257 1912262) (-1153 "SMATCAT.spad" 1909222 1909252 1911056 1911107) (-1152 "SMATCAT.spad" 1907264 1907296 1909100 1909105) (-1151 "SKAGG.spad" 1906227 1906238 1907232 1907259) (-1150 "SINT.spad" 1905167 1905176 1906093 1906222) (-1149 "SIMPAN.spad" 1904895 1904904 1905157 1905162) (-1148 "SIG.spad" 1904225 1904234 1904885 1904890) (-1147 "SIGNRF.spad" 1903343 1903354 1904215 1904220) (-1146 "SIGNEF.spad" 1902622 1902639 1903333 1903338) (-1145 "SIGAST.spad" 1902007 1902016 1902612 1902617) (-1144 "SHP.spad" 1899935 1899950 1901963 1901968) (-1143 "SHDP.spad" 1887613 1887640 1888122 1888221) (-1142 "SGROUP.spad" 1887221 1887230 1887603 1887608) (-1141 "SGROUP.spad" 1886827 1886838 1887211 1887216) (-1140 "SGCF.spad" 1879966 1879975 1886817 1886822) (-1139 "SFRTCAT.spad" 1878896 1878913 1879934 1879961) (-1138 "SFRGCD.spad" 1877959 1877979 1878886 1878891) (-1137 "SFQCMPK.spad" 1872596 1872616 1877949 1877954) (-1136 "SFORT.spad" 1872035 1872049 1872586 1872591) (-1135 "SEXOF.spad" 1871878 1871918 1872025 1872030) (-1134 "SEX.spad" 1871770 1871779 1871868 1871873) (-1133 "SEXCAT.spad" 1869542 1869582 1871760 1871765) (-1132 "SET.spad" 1867830 1867841 1868927 1868966) (-1131 "SETMN.spad" 1866280 1866297 1867820 1867825) (-1130 "SETCAT.spad" 1865765 1865774 1866270 1866275) (-1129 "SETCAT.spad" 1865248 1865259 1865755 1865760) (-1128 "SETAGG.spad" 1861797 1861808 1865228 1865243) (-1127 "SETAGG.spad" 1858354 1858367 1861787 1861792) (-1126 "SEQAST.spad" 1858057 1858066 1858344 1858349) (-1125 "SEGXCAT.spad" 1857213 1857226 1858047 1858052) (-1124 "SEG.spad" 1857026 1857037 1857132 1857137) (-1123 "SEGCAT.spad" 1855951 1855962 1857016 1857021) (-1122 "SEGBIND.spad" 1855709 1855720 1855898 1855903) (-1121 "SEGBIND2.spad" 1855407 1855420 1855699 1855704) (-1120 "SEGAST.spad" 1855121 1855130 1855397 1855402) (-1119 "SEG2.spad" 1854556 1854569 1855077 1855082) (-1118 "SDVAR.spad" 1853832 1853843 1854546 1854551) (-1117 "SDPOL.spad" 1851165 1851176 1851456 1851583) (-1116 "SCPKG.spad" 1849254 1849265 1851155 1851160) (-1115 "SCOPE.spad" 1848407 1848416 1849244 1849249) (-1114 "SCACHE.spad" 1847103 1847114 1848397 1848402) (-1113 "SASTCAT.spad" 1847012 1847021 1847093 1847098) (-1112 "SAOS.spad" 1846884 1846893 1847002 1847007) (-1111 "SAERFFC.spad" 1846597 1846617 1846874 1846879) (-1110 "SAE.spad" 1844067 1844083 1844678 1844813) (-1109 "SAEFACT.spad" 1843768 1843788 1844057 1844062) (-1108 "RURPK.spad" 1841427 1841443 1843758 1843763) (-1107 "RULESET.spad" 1840880 1840904 1841417 1841422) (-1106 "RULE.spad" 1839120 1839144 1840870 1840875) (-1105 "RULECOLD.spad" 1838972 1838985 1839110 1839115) (-1104 "RTVALUE.spad" 1838707 1838716 1838962 1838967) (-1103 "RSTRCAST.spad" 1838424 1838433 1838697 1838702) (-1102 "RSETGCD.spad" 1834802 1834822 1838414 1838419) (-1101 "RSETCAT.spad" 1824738 1824755 1834770 1834797) (-1100 "RSETCAT.spad" 1814694 1814713 1824728 1824733) (-1099 "RSDCMPK.spad" 1813146 1813166 1814684 1814689) (-1098 "RRCC.spad" 1811530 1811560 1813136 1813141) (-1097 "RRCC.spad" 1809912 1809944 1811520 1811525) (-1096 "RPTAST.spad" 1809614 1809623 1809902 1809907) (-1095 "RPOLCAT.spad" 1788974 1788989 1809482 1809609) (-1094 "RPOLCAT.spad" 1768047 1768064 1788557 1788562) (-1093 "ROUTINE.spad" 1763468 1763477 1766232 1766259) (-1092 "ROMAN.spad" 1762796 1762805 1763334 1763463) (-1091 "ROIRC.spad" 1761876 1761908 1762786 1762791) (-1090 "RNS.spad" 1760779 1760788 1761778 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(-456 "GALFACTU.spad" 740862 740881 742679 742684) (-455 "GALFACT.spad" 731051 731062 740852 740857) (-454 "FVFUN.spad" 728074 728082 731041 731046) (-453 "FVC.spad" 727126 727134 728064 728069) (-452 "FUNDESC.spad" 726804 726812 727116 727121) (-451 "FUNCTION.spad" 726653 726665 726794 726799) (-450 "FT.spad" 724950 724958 726643 726648) (-449 "FTEM.spad" 724115 724123 724940 724945) (-448 "FSUPFACT.spad" 723015 723034 724051 724056) (-447 "FST.spad" 721101 721109 723005 723010) (-446 "FSRED.spad" 720581 720597 721091 721096) (-445 "FSPRMELT.spad" 719463 719479 720538 720543) (-444 "FSPECF.spad" 717554 717570 719453 719458) (-443 "FS.spad" 711822 711832 717329 717549) (-442 "FS.spad" 705868 705880 711377 711382) (-441 "FSINT.spad" 705528 705544 705858 705863) (-440 "FSERIES.spad" 704719 704731 705348 705447) (-439 "FSCINT.spad" 704036 704052 704709 704714) (-438 "FSAGG.spad" 703153 703163 703992 704031) (-437 "FSAGG.spad" 702232 702244 703073 703078) (-436 "FSAGG2.spad" 700975 700991 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"FPC.spad" 659327 659335 660183 660276) (-414 "FPC.spad" 658459 658469 659317 659322) (-413 "FPATMAB.spad" 658221 658231 658449 658454) (-412 "FPARFRAC.spad" 657071 657088 658211 658216) (-411 "FORTRAN.spad" 655577 655620 657061 657066) (-410 "FORT.spad" 654526 654534 655567 655572) (-409 "FORTFN.spad" 651696 651704 654516 654521) (-408 "FORTCAT.spad" 651380 651388 651686 651691) (-407 "FORMULA.spad" 648854 648862 651370 651375) (-406 "FORMULA1.spad" 648333 648343 648844 648849) (-405 "FORDER.spad" 648024 648048 648323 648328) (-404 "FOP.spad" 647225 647233 648014 648019) (-403 "FNLA.spad" 646649 646671 647193 647220) (-402 "FNCAT.spad" 645244 645252 646639 646644) (-401 "FNAME.spad" 645136 645144 645234 645239) (-400 "FMTC.spad" 644934 644942 645062 645131) (-399 "FMONOID.spad" 644599 644609 644890 644895) (-398 "FMONCAT.spad" 641752 641762 644589 644594) (-397 "FM.spad" 641367 641379 641606 641633) (-396 "FMFUN.spad" 638397 638405 641357 641362) (-395 "FMC.spad" 637449 637457 638387 638392) (-394 "FMCAT.spad" 635117 635135 637417 637444) (-393 "FM1.spad" 634474 634486 635051 635078) (-392 "FLOATRP.spad" 632209 632223 634464 634469) (-391 "FLOAT.spad" 625523 625531 632075 632204) (-390 "FLOATCP.spad" 622954 622968 625513 625518) (-389 "FLINEXP.spad" 622676 622686 622944 622949) (-388 "FLINEXP.spad" 622342 622354 622612 622617) (-387 "FLASORT.spad" 621668 621680 622332 622337) (-386 "FLALG.spad" 619314 619333 621594 621663) (-385 "FLAGG.spad" 616356 616366 619294 619309) (-384 "FLAGG.spad" 613299 613311 616239 616244) (-383 "FLAGG2.spad" 612024 612040 613289 613294) (-382 "FINRALG.spad" 610085 610098 611980 612019) (-381 "FINRALG.spad" 608072 608087 609969 609974) (-380 "FINITE.spad" 607224 607232 608062 608067) (-379 "FINAALG.spad" 596345 596355 607166 607219) (-378 "FINAALG.spad" 585478 585490 596301 596306) (-377 "FILE.spad" 585061 585071 585468 585473) (-376 "FILECAT.spad" 583587 583604 585051 585056) (-375 "FIELD.spad" 582993 583001 583489 583582) (-374 "FIELD.spad" 582485 582495 582983 582988) (-373 "FGROUP.spad" 581132 581142 582465 582480) (-372 "FGLMICPK.spad" 579919 579934 581122 581127) (-371 "FFX.spad" 579294 579309 579635 579728) (-370 "FFSLPE.spad" 578797 578818 579284 579289) (-369 "FFPOLY.spad" 570059 570070 578787 578792) (-368 "FFPOLY2.spad" 569119 569136 570049 570054) (-367 "FFP.spad" 568516 568536 568835 568928) (-366 "FF.spad" 567964 567980 568197 568290) (-365 "FFNBX.spad" 566476 566496 567680 567773) (-364 "FFNBP.spad" 564989 565006 566192 566285) (-363 "FFNB.spad" 563454 563475 564670 564763) (-362 "FFINTBAS.spad" 560968 560987 563444 563449) (-361 "FFIELDC.spad" 558545 558553 560870 560963) (-360 "FFIELDC.spad" 556208 556218 558535 558540) (-359 "FFHOM.spad" 554956 554973 556198 556203) (-358 "FFF.spad" 552391 552402 554946 554951) (-357 "FFCGX.spad" 551238 551258 552107 552200) (-356 "FFCGP.spad" 550127 550147 550954 551047) (-355 "FFCG.spad" 548919 548940 549808 549901) (-354 "FFCAT.spad" 542092 542114 548758 548914) (-353 "FFCAT.spad" 535344 535368 542012 542017) (-352 "FFCAT2.spad" 535091 535131 535334 535339) (-351 "FEXPR.spad" 526808 526854 534847 534886) (-350 "FEVALAB.spad" 526516 526526 526798 526803) (-349 "FEVALAB.spad" 526009 526021 526293 526298) (-348 "FDIV.spad" 525451 525475 525999 526004) (-347 "FDIVCAT.spad" 523515 523539 525441 525446) (-346 "FDIVCAT.spad" 521577 521603 523505 523510) (-345 "FDIV2.spad" 521233 521273 521567 521572) (-344 "FCTRDATA.spad" 520241 520249 521223 521228) (-343 "FCPAK1.spad" 518808 518816 520231 520236) (-342 "FCOMP.spad" 518187 518197 518798 518803) (-341 "FC.spad" 508194 508202 518177 518182) (-340 "FAXF.spad" 501165 501179 508096 508189) (-339 "FAXF.spad" 494188 494204 501121 501126) (-338 "FARRAY.spad" 492185 492195 493218 493245) (-337 "FAMR.spad" 490321 490333 492083 492180) (-336 "FAMR.spad" 488441 488455 490205 490210) (-335 "FAMONOID.spad" 488109 488119 488395 488400) (-334 "FAMONC.spad" 486405 486417 488099 488104) (-333 "FAGROUP.spad" 486029 486039 486301 486328) (-332 "FACUTIL.spad" 484233 484250 486019 486024) (-331 "FACTFUNC.spad" 483427 483437 484223 484228) (-330 "EXPUPXS.spad" 480260 480283 481559 481708) (-329 "EXPRTUBE.spad" 477548 477556 480250 480255) (-328 "EXPRODE.spad" 474708 474724 477538 477543) (-327 "EXPR.spad" 469883 469893 470597 470892) (-326 "EXPR2UPS.spad" 466005 466018 469873 469878) (-325 "EXPR2.spad" 465710 465722 465995 466000) (-324 "EXPEXPAN.spad" 462511 462536 463143 463236) (-323 "EXIT.spad" 462182 462190 462501 462506) (-322 "EXITAST.spad" 461918 461926 462172 462177) (-321 "EVALCYC.spad" 461378 461392 461908 461913) (-320 "EVALAB.spad" 460950 460960 461368 461373) (-319 "EVALAB.spad" 460520 460532 460940 460945) (-318 "EUCDOM.spad" 458094 458102 460446 460515) (-317 "EUCDOM.spad" 455730 455740 458084 458089) (-316 "ESTOOLS.spad" 447576 447584 455720 455725) (-315 "ESTOOLS2.spad" 447179 447193 447566 447571) (-314 "ESTOOLS1.spad" 446864 446875 447169 447174) (-313 "ES.spad" 439679 439687 446854 446859) (-312 "ES.spad" 432400 432410 439577 439582) (-311 "ESCONT.spad" 429193 429201 432390 432395) (-310 "ESCONT1.spad" 428942 428954 429183 429188) (-309 "ES2.spad" 428447 428463 428932 428937) (-308 "ES1.spad" 428017 428033 428437 428442) (-307 "ERROR.spad" 425344 425352 428007 428012) (-306 "EQTBL.spad" 423374 423396 423583 423610) (-305 "EQ.spad" 418179 418189 420966 421078) (-304 "EQ2.spad" 417897 417909 418169 418174) (-303 "EP.spad" 414223 414233 417887 417892) (-302 "ENV.spad" 412901 412909 414213 414218) (-301 "ENTIRER.spad" 412569 412577 412845 412896) (-300 "EMR.spad" 411857 411898 412495 412564) (-299 "ELTAGG.spad" 410111 410130 411847 411852) (-298 "ELTAGG.spad" 408329 408350 410067 410072) (-297 "ELTAB.spad" 407804 407817 408319 408324) (-296 "ELFUTS.spad" 407191 407210 407794 407799) (-295 "ELEMFUN.spad" 406880 406888 407181 407186) (-294 "ELEMFUN.spad" 406567 406577 406870 406875) (-293 "ELAGG.spad" 404538 404548 406547 406562) (-292 "ELAGG.spad" 402446 402458 404457 404462) (-291 "ELABOR.spad" 401792 401800 402436 402441) (-290 "ELABEXPR.spad" 400724 400732 401782 401787) (-289 "EFUPXS.spad" 397500 397530 400680 400685) (-288 "EFULS.spad" 394336 394359 397456 397461) (-287 "EFSTRUC.spad" 392351 392367 394326 394331) (-286 "EF.spad" 387127 387143 392341 392346) (-285 "EAB.spad" 385403 385411 387117 387122) (-284 "E04UCFA.spad" 384939 384947 385393 385398) (-283 "E04NAFA.spad" 384516 384524 384929 384934) (-282 "E04MBFA.spad" 384096 384104 384506 384511) (-281 "E04JAFA.spad" 383632 383640 384086 384091) (-280 "E04GCFA.spad" 383168 383176 383622 383627) (-279 "E04FDFA.spad" 382704 382712 383158 383163) (-278 "E04DGFA.spad" 382240 382248 382694 382699) (-277 "E04AGNT.spad" 378090 378098 382230 382235) (-276 "DVARCAT.spad" 374980 374990 378080 378085) (-275 "DVARCAT.spad" 371868 371880 374970 374975) (-274 "DSMP.spad" 369242 369256 369547 369674) (-273 "DSEXT.spad" 368544 368554 369232 369237) (-272 "DSEXT.spad" 367753 367765 368443 368448) (-271 "DROPT.spad" 361712 361720 367743 367748) (-270 "DROPT1.spad" 361377 361387 361702 361707) (-269 "DROPT0.spad" 356234 356242 361367 361372) (-268 "DRAWPT.spad" 354407 354415 356224 356229) (-267 "DRAW.spad" 347283 347296 354397 354402) (-266 "DRAWHACK.spad" 346591 346601 347273 347278) (-265 "DRAWCX.spad" 344061 344069 346581 346586) (-264 "DRAWCURV.spad" 343608 343623 344051 344056) (-263 "DRAWCFUN.spad" 333140 333148 343598 343603) (-262 "DQAGG.spad" 331318 331328 333108 333135) (-261 "DPOLCAT.spad" 326667 326683 331186 331313) (-260 "DPOLCAT.spad" 322102 322120 326623 326628) (-259 "DPMO.spad" 313862 313878 314000 314213) (-258 "DPMM.spad" 305635 305653 305760 305973) (-257 "DOMTMPLT.spad" 305406 305414 305625 305630) (-256 "DOMCTOR.spad" 305161 305169 305396 305401) (-255 "DOMAIN.spad" 304248 304256 305151 305156) (-254 "DMP.spad" 301508 301523 302078 302205) (-253 "DMEXT.spad" 301375 301385 301476 301503) (-252 "DLP.spad" 300727 300737 301365 301370) (-251 "DLIST.spad" 299153 299163 299757 299784) (-250 "DLAGG.spad" 297570 297580 299143 299148) (-249 "DIVRING.spad" 297112 297120 297514 297565) (-248 "DIVRING.spad" 296698 296708 297102 297107) (-247 "DISPLAY.spad" 294888 294896 296688 296693) (-246 "DIRPROD.spad" 282435 282451 283075 283174) (-245 "DIRPROD2.spad" 281253 281271 282425 282430) (-244 "DIRPCAT.spad" 280446 280462 281149 281248) (-243 "DIRPCAT.spad" 279266 279284 279971 279976) (-242 "DIOSP.spad" 278091 278099 279256 279261) (-241 "DIOPS.spad" 277087 277097 278071 278086) (-240 "DIOPS.spad" 276057 276069 277043 277048) (-239 "DIFRING.spad" 275895 275903 276037 276052) (-238 "DIFFSPC.spad" 275474 275482 275885 275890) (-237 "DIFFSPC.spad" 275051 275061 275464 275469) (-236 "DIFFMOD.spad" 274540 274550 275019 275046) (-235 "DIFFDOM.spad" 273705 273716 274530 274535) (-234 "DIFFDOM.spad" 272868 272881 273695 273700) (-233 "DIFEXT.spad" 272687 272697 272848 272863) (-232 "DIAGG.spad" 272317 272327 272667 272682) (-231 "DIAGG.spad" 271955 271967 272307 272312) (-230 "DHMATRIX.spad" 270150 270160 271295 271322) (-229 "DFSFUN.spad" 263790 263798 270140 270145) (-228 "DFLOAT.spad" 260521 260529 263680 263785) (-227 "DFINTTLS.spad" 258752 258768 260511 260516) (-226 "DERHAM.spad" 256666 256698 258732 258747) (-225 "DEQUEUE.spad" 255873 255883 256156 256183) (-224 "DEGRED.spad" 255490 255504 255863 255868) (-223 "DEFINTRF.spad" 253027 253037 255480 255485) (-222 "DEFINTEF.spad" 251537 251553 253017 253022) (-221 "DEFAST.spad" 250905 250913 251527 251532) (-220 "DECIMAL.spad" 248914 248922 249275 249368) (-219 "DDFACT.spad" 246727 246744 248904 248909) (-218 "DBLRESP.spad" 246327 246351 246717 246722) (-217 "DBASIS.spad" 245953 245968 246317 246322) (-216 "DBASE.spad" 244617 244627 245943 245948) (-215 "DATAARY.spad" 244079 244092 244607 244612) (-214 "D03FAFA.spad" 243907 243915 244069 244074) (-213 "D03EEFA.spad" 243727 243735 243897 243902) (-212 "D03AGNT.spad" 242813 242821 243717 243722) (-211 "D02EJFA.spad" 242275 242283 242803 242808) (-210 "D02CJFA.spad" 241753 241761 242265 242270) (-209 "D02BHFA.spad" 241243 241251 241743 241748) (-208 "D02BBFA.spad" 240733 240741 241233 241238) (-207 "D02AGNT.spad" 235547 235555 240723 240728) (-206 "D01WGTS.spad" 233866 233874 235537 235542) (-205 "D01TRNS.spad" 233843 233851 233856 233861) (-204 "D01GBFA.spad" 233365 233373 233833 233838) (-203 "D01FCFA.spad" 232887 232895 233355 233360) (-202 "D01ASFA.spad" 232355 232363 232877 232882) (-201 "D01AQFA.spad" 231801 231809 232345 232350) (-200 "D01APFA.spad" 231225 231233 231791 231796) (-199 "D01ANFA.spad" 230719 230727 231215 231220) (-198 "D01AMFA.spad" 230229 230237 230709 230714) (-197 "D01ALFA.spad" 229769 229777 230219 230224) (-196 "D01AKFA.spad" 229295 229303 229759 229764) (-195 "D01AJFA.spad" 228818 228826 229285 229290) (-194 "D01AGNT.spad" 224885 224893 228808 228813) (-193 "CYCLOTOM.spad" 224391 224399 224875 224880) (-192 "CYCLES.spad" 221183 221191 224381 224386) (-191 "CVMP.spad" 220600 220610 221173 221178) (-190 "CTRIGMNP.spad" 219100 219116 220590 220595) (-189 "CTOR.spad" 218791 218799 219090 219095) (-188 "CTORKIND.spad" 218394 218402 218781 218786) (-187 "CTORCAT.spad" 217643 217651 218384 218389) (-186 "CTORCAT.spad" 216890 216900 217633 217638) (-185 "CTORCALL.spad" 216479 216489 216880 216885) (-184 "CSTTOOLS.spad" 215724 215737 216469 216474) (-183 "CRFP.spad" 209448 209461 215714 215719) (-182 "CRCEAST.spad" 209168 209176 209438 209443) (-181 "CRAPACK.spad" 208219 208229 209158 209163) (-180 "CPMATCH.spad" 207723 207738 208144 208149) (-179 "CPIMA.spad" 207428 207447 207713 207718) (-178 "COORDSYS.spad" 202437 202447 207418 207423) (-177 "CONTOUR.spad" 201848 201856 202427 202432) (-176 "CONTFRAC.spad" 197598 197608 201750 201843) (-175 "CONDUIT.spad" 197356 197364 197588 197593) (-174 "COMRING.spad" 197030 197038 197294 197351) (-173 "COMPPROP.spad" 196548 196556 197020 197025) (-172 "COMPLPAT.spad" 196315 196330 196538 196543) (-171 "COMPLEX.spad" 191692 191702 191936 192197) (-170 "COMPLEX2.spad" 191407 191419 191682 191687) (-169 "COMPILER.spad" 190956 190964 191397 191402) (-168 "COMPFACT.spad" 190558 190572 190946 190951) (-167 "COMPCAT.spad" 188630 188640 190292 190553) (-166 "COMPCAT.spad" 186430 186442 188094 188099) (-165 "COMMUPC.spad" 186178 186196 186420 186425) (-164 "COMMONOP.spad" 185711 185719 186168 186173) (-163 "COMM.spad" 185522 185530 185701 185706) (-162 "COMMAAST.spad" 185285 185293 185512 185517) (-161 "COMBOPC.spad" 184200 184208 185275 185280) (-160 "COMBINAT.spad" 182967 182977 184190 184195) (-159 "COMBF.spad" 180349 180365 182957 182962) (-158 "COLOR.spad" 179186 179194 180339 180344) (-157 "COLONAST.spad" 178852 178860 179176 179181) (-156 "CMPLXRT.spad" 178563 178580 178842 178847) (-155 "CLLCTAST.spad" 178225 178233 178553 178558) (-154 "CLIP.spad" 174333 174341 178215 178220) (-153 "CLIF.spad" 172988 173004 174289 174328) (-152 "CLAGG.spad" 169493 169503 172978 172983) (-151 "CLAGG.spad" 165869 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. -1125) T) ((-529 . -19) 194264) ((-509 . -19) 194248) ((-59 . -617) 194225) ((-1028 . -238) 194162) ((-924 . -102) 194112) ((-872 . -742) T) ((-798 . -1125) T) ((-529 . -617) 194089) ((-509 . -617) 194066) ((-796 . -1125) T) ((-796 . -1090) 194033) ((-474 . -1125) T) ((-467 . -1125) T) ((-599 . -733) 194008) ((-665 . -1125) T) ((-1284 . -47) 193985) ((-1278 . -102) T) ((-1277 . -47) 193955) ((-1256 . -47) 193932) ((-1236 . -174) 193883) ((-1198 . -318) 193862) ((-1192 . -318) 193841) ((-1121 . -629) 193822) ((-1115 . -629) 193803) ((-1105 . -569) 193754) ((-1105 . -1246) 193705) ((-1098 . -629) 193686) ((-1029 . -921) NIL) ((-1091 . -629) 193667) ((-686 . -132) T) ((-640 . -1137) T) ((-1061 . -629) 193648) ((-1044 . -629) 193629) ((-730 . -1081) 193599) ((-728 . -915) 193502) ((-715 . -662) 193452) ((-285 . -1125) T) ((-85 . -454) T) ((-85 . -408) T) ((-727 . -174) T) ((-653 . -1081) 193436) ((-50 . -1125) T) ((-608 . -47) 193413) ((-228 . -664) 193378) ((-594 . -1125) T) ((-531 . 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. -808) T) ((-487 . -1081) 184811) ((-513 . -113) T) ((-355 . -1125) T) ((-324 . -1177) NIL) ((-300 . -132) T) ((-407 . -1125) T) ((-888 . -1083) T) ((-710 . -382) 184778) ((-366 . -662) 184708) ((-226 . -633) 184685) ((-338 . -297) 184637) ((-487 . -111) 184458) ((-1276 . -1074) T) ((-1255 . -1074) T) ((-832 . -389) 184442) ((-840 . -1242) T) ((-171 . -742) T) ((-1307 . -1242) T) ((-670 . -102) T) ((-1276 . -249) 184421) ((-1276 . -239) 184373) ((-1255 . -239) 184278) ((-1255 . -249) 184257) ((-1028 . -415) NIL) ((-686 . -654) 184205) ((-327 . -38) 184115) ((-324 . -38) 184044) ((-69 . -626) 184026) ((-330 . -506) 183992) ((-48 . -662) 183942) ((-1214 . -299) 183921) ((-1250 . -865) T) ((-1138 . -1137) 183899) ((-83 . -1242) T) ((-61 . -626) 183881) ((-882 . -868) T) ((-492 . -299) 183860) ((-1307 . -1063) 183837) ((-1189 . -1125) T) ((-1138 . -23) 183689) ((-832 . -921) 183625) ((-1265 . -742) T) ((-1127 . -1242) T) ((-487 . -629) 183451) ((-363 . -238) T) ((-1112 . -301) 183382) ((-989 . -1125) T) ((-912 . -102) T) ((-798 . -301) 183293) ((-338 . -19) 183277) ((-59 . -299) 183254) ((-796 . -301) 183185) ((-873 . -742) T) ((-118 . -864) NIL) ((-529 . -299) 183162) ((-338 . -617) 183139) ((-509 . -299) 183116) ((-467 . -301) 183047) ((-1060 . -320) 182898) ((-894 . -503) 182879) ((-894 . -626) 182845) ((-697 . -503) 182826) ((-584 . -742) T) ((-692 . -503) 182807) ((-697 . -626) 182757) ((-692 . -626) 182723) ((-678 . -626) 182705) ((-491 . -503) 182686) ((-491 . -626) 182652) ((-251 . -627) 182613) ((-251 . -503) 182590) ((-139 . -503) 182571) ((-138 . -503) 182552) ((-134 . -503) 182533) ((-251 . -626) 182425) ((-215 . -102) T) ((-139 . -626) 182391) ((-138 . -626) 182357) ((-134 . -626) 182323) ((-1172 . -34) T) ((-966 . -1242) T) ((-355 . -733) 182268) ((-686 . -25) T) ((-686 . -21) T) ((-1201 . -629) 182249) ((-342 . -1242) T) ((-487 . -1074) T) ((-648 . -430) 182214) ((-620 . -430) 182179) ((-1145 . -1177) T) ((-1277 . -318) 182158) ((-728 . -1076) 181981) ((-594 . -301) T) ((-531 . -301) T) ((-1256 . -318) 181960) ((-487 . -239) 181912) ((-487 . -249) 181891) ((-452 . -1242) T) ((-728 . -656) 181720) ((-1256 . -1047) NIL) ((-1105 . -132) T) ((-890 . -811) 181699) ((-145 . -102) T) ((-40 . -1125) T) ((-890 . -808) 181678) ((-660 . -1035) 181662) ((-593 . -1083) T) ((-577 . -1083) T) ((-508 . -1083) T) ((-420 . -465) T) ((-371 . -132) T) ((-327 . -413) 181646) ((-324 . -413) 181607) ((-365 . -132) T) ((-357 . -132) T) ((-1206 . -1125) T) ((-1145 . -38) 181594) ((-1119 . -626) 181561) ((-108 . -132) T) ((-977 . -1125) T) ((-944 . -1125) T) ((-787 . -1125) T) ((-688 . -1125) T) ((-717 . -148) T) ((-117 . -148) T) ((-1314 . -21) T) ((-1314 . -25) T) ((-1312 . -21) T) ((-1312 . -25) T) ((-680 . -1081) 181545) ((-544 . -865) T) ((-513 . -865) T) ((-377 . -1242) T) ((-367 . -1081) 181497) ((-364 . -1081) 181449) ((-356 . -1081) 181401) ((-259 . -1242) T) ((-258 . -1242) T) ((-274 . -1081) 181244) ((-254 . -1081) 181087) ((-680 . -111) 181066) ((-833 . -1246) 181045) ((-560 . -860) T) ((-327 . -923) 181011) ((-367 . -111) 180949) ((-364 . -111) 180887) ((-356 . -111) 180825) ((-274 . -111) 180654) ((-254 . -111) 180483) ((-324 . -923) NIL) ((-636 . -424) 180467) ((-44 . -21) T) ((-44 . -25) T) ((-928 . -868) 180418) ((-831 . -654) 180324) ((-833 . -569) 180303) ((-500 . -868) T) ((-259 . -1063) 180130) ((-258 . -1063) 179957) ((-127 . -120) 179941) ((-220 . -868) T) ((-933 . -1081) 179906) ((-728 . -102) T) ((-715 . -1083) T) ((-610 . -629) 179887) ((-598 . -629) 179868) ((-549 . -631) 179771) ((-355 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -626) 179753) ((-933 . -111) 179709) ((-40 . -733) 179654) ((-888 . -1125) T) ((-680 . -629) 179631) ((-661 . -629) 179612) ((-367 . -629) 179549) ((-364 . -629) 179486) ((-356 . -629) 179423) ((-560 . -1125) T) ((-338 . -627) 179384) ((-338 . -626) 179296) ((-274 . -629) 179049) ((-254 . -629) 178834) ((-188 . -1242) T) ((-1255 . -808) 178787) ((-1255 . -811) 178740) ((-259 . -389) 178709) ((-258 . -389) 178678) ((-562 . -868) T) ((-670 . -38) 178648) ((-621 . -34) T) ((-495 . -1137) 178626) ((-488 . -34) T) ((-1138 . -132) 178497) ((-987 . -25) 178308) ((-933 . -629) 178258) ((-892 . -626) 178240) ((-217 . -860) T) ((-987 . -21) 178195) ((-831 . -25) 178028) ((-831 . -21) 177939) ((-1248 . -380) T) ((-636 . -1083) T) ((-1203 . -569) 177918) ((-1197 . -47) 177895) ((-367 . -1074) T) ((-364 . -1074) T) ((-495 . -23) 177747) ((-356 . -1074) T) ((-274 . -1074) T) ((-254 . -1074) T) ((-1150 . -47) 177719) ((-118 . -1083) T) ((-1059 . -664) 177693) ((-981 . -34) T) ((-367 . -239) 177672) ((-367 . -249) T) ((-364 . -239) 177651) ((-364 . -249) T) ((-356 . -239) 177630) ((-356 . -249) T) ((-274 . -337) 177602) ((-254 . -337) 177559) ((-274 . -239) 177538) ((-1182 . -152) 177522) ((-259 . -921) 177454) ((-258 . -921) 177386) ((-1167 . -915) 177307) ((-1107 . -865) T) ((-1259 . -1242) 177285) ((-427 . -1137) T) ((-1236 . -1027) 177251) ((-1079 . -23) T) ((-1049 . -864) T) ((-933 . -1074) T) ((-333 . -664) 177233) ((-717 . -238) T) ((-686 . -235) 177178) ((-1198 . -943) 177157) ((-1192 . -943) 177136) ((-1192 . -836) NIL) ((-1024 . -1076) 177032) ((-990 . -1242) T) ((-933 . -249) T) ((-833 . -375) 177011) ((-217 . -1125) T) ((-397 . -23) T) ((-128 . -1125) 176989) ((-122 . -1125) 176967) ((-933 . -239) T) ((-129 . -34) T) ((-391 . -664) 176932) ((-1024 . -656) 176880) ((-888 . -733) 176867) ((-1321 . -662) 176839) ((-1071 . -152) 176804) ((-1018 . -1242) T) ((-880 . -1242) T) ((-40 . -174) T) ((-710 . -424) 176786) ((-728 . -320) 176773) ((-852 . -664) 176733) ((-843 . -664) 176707) ((-330 . -25) T) ((-330 . -21) T) ((-674 . -297) 176686) ((-593 . -1125) T) ((-577 . -1125) T) ((-508 . -1125) T) ((-1197 . -1242) T) ((-251 . -299) 176663) ((-1150 . -1242) T) ((-872 . -1242) T) ((-324 . -273) 176624) ((-324 . -233) 176585) ((-1247 . -868) T) ((-1197 . -905) NIL) ((-55 . -1125) T) ((-1150 . -905) 176444) ((-130 . -865) T) ((-1197 . -1063) 176324) ((-1150 . -1063) 176207) ((-185 . -626) 176189) ((-872 . -1063) 176085) ((-798 . -297) 176012) ((-833 . -1137) T) ((-1059 . -742) T) ((-1071 . -1001) 175941) ((-615 . -667) 175925) ((-1028 . -915) 175832) ((-1024 . -102) T) ((-833 . -23) T) ((-728 . -1177) 175810) ((-710 . -1083) T) ((-615 . -385) 175794) ((-363 . -465) T) ((-355 . -301) T) ((-1293 . -1125) T) ((-255 . -1125) T) ((-412 . -102) T) ((-300 . -21) T) ((-300 . -25) T) ((-373 . -742) T) ((-726 . -1125) T) ((-715 . -1125) T) ((-373 . -486) T) ((-1236 . -626) 175776) ((-1197 . -389) 175760) ((-1150 . -389) 175744) ((-1049 . -424) 175706) ((-142 . -232) 175688) ((-391 . -810) T) ((-391 . -807) T) ((-888 . -174) T) ((-391 . -742) T) ((-727 . -626) 175670) ((-728 . -38) 175499) ((-1292 . -1290) 175483) ((-363 . -415) T) ((-1292 . -1125) 175433) ((-1215 . -1125) T) ((-593 . -733) 175420) ((-577 . -733) 175407) ((-508 . -733) 175372) ((-1278 . -662) 175262) ((-327 . -642) 175241) ((-852 . -742) T) ((-843 . -742) T) ((-1140 . -1242) T) ((-660 . -1242) T) ((-1105 . -654) 175189) ((-1197 . -921) 175132) ((-1150 . -921) 175116) ((-831 . -235) 175007) ((-678 . -1081) 174991) ((-108 . -654) 174973) ((-495 . -132) 174844) ((-1203 . -1137) T) ((-835 . -1242) T) ((-975 . -47) 174813) ((-636 . -1125) T) ((-678 . -111) 174792) ((-504 . -626) 174758) ((-338 . -299) 174735) ((-399 . -1242) T) ((-335 . -1242) T) ((-494 . -47) 174692) ((-1203 . -23) T) ((-118 . -1125) T) ((-103 . -102) 174642) ((-1304 . -1137) T) ((-561 . -865) T) ((-228 . -1242) T) ((-1079 . -132) T) ((-1049 . -1083) T) ((-1304 . -23) T) ((-1222 . -626) 174624) ((-835 . -1063) 174608) ((-1145 . -844) T) ((-1028 . -740) 174580) ((-1130 . -1125) T) ((-715 . -733) 174545) ((-599 . -626) 174527) ((-399 . -1063) 174511) ((-366 . -1083) T) ((-397 . -132) T) ((-335 . -1063) 174495) ((-1105 . -21) T) ((-1105 . -25) T) ((-1029 . -836) T) ((-228 . -905) 174477) ((-1029 . -943) T) ((-91 . -34) T) ((-1024 . -320) 174442) ((-937 . -943) T) ((-894 . -629) 174423) ((-730 . -664) 174383) ((-500 . -1246) T) ((-697 . -629) 174364) ((-692 . -629) 174345) ((-653 . -664) 174329) ((-220 . -1246) T) ((-420 . -915) 174250) ((-228 . -1063) 174210) ((-40 . -301) T) ((-500 . -569) T) ((-491 . -629) 174191) ((-371 . -25) T) ((-327 . -662) 173846) ((-324 . -662) 173760) ((-371 . -21) T) ((-365 . -25) T) ((-365 . -21) T) ((-220 . -569) T) ((-357 . -25) T) ((-357 . -21) T) ((-330 . -235) 173706) ((-251 . -629) 173683) ((-139 . -629) 173664) ((-138 . -629) 173645) ((-134 . -629) 173626) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1083) T) ((-593 . -174) T) ((-577 . -174) T) ((-508 . -174) T) ((-1087 . -1242) T) ((-975 . -1242) T) ((-729 . -1242) T) ((-655 . -297) 173593) ((-674 . -626) 173575) ((-494 . -1242) T) ((-753 . -752) 173559) ((-348 . -626) 173541) ((-68 . -395) T) ((-68 . -408) T) ((-1127 . -107) 173525) ((-1087 . -905) 173507) ((-975 . -905) 173432) ((-669 . -1137) T) ((-636 . -733) 173419) ((-494 . -905) NIL) ((-1171 . -102) T) ((-1119 . -631) 173403) ((-1087 . -1063) 173385) ((-97 . -626) 173367) ((-490 . -148) T) ((-975 . -1063) 173247) ((-118 . -733) 173192) ((-728 . -923) 173099) ((-669 . -23) T) ((-494 . -1063) 172975) ((-1112 . -627) NIL) ((-1112 . -626) 172957) ((-798 . -627) NIL) ((-798 . -626) 172918) ((-796 . -627) 172552) ((-796 . -626) 172466) ((-1138 . -654) 172372) ((-815 . -868) 172351) ((-474 . -626) 172333) ((-467 . -626) 172315) ((-467 . -627) 172176) ((-1060 . -232) 172122) ((-890 . -932) 172101) ((-127 . -34) T) ((-833 . -132) T) ((-665 . -626) 172083) ((-591 . -102) T) ((-367 . -1311) 172067) ((-364 . -1311) 172051) ((-356 . -1311) 172035) ((-122 . -527) 171968) ((-128 . -527) 171901) ((-524 . -808) T) ((-524 . -811) T) ((-523 . -810) T) ((-103 . -320) 171839) ((-225 . -102) 171789) ((-715 . -174) T) ((-710 . -1125) T) ((-890 . -664) 171705) ((-65 . -396) T) ((-285 . -626) 171687) ((-65 . -408) T) ((-975 . -389) 171671) ((-888 . -301) T) ((-50 . -626) 171653) ((-1024 . -38) 171601) ((-1145 . -662) 171573) ((-594 . -626) 171555) ((-494 . -389) 171539) ((-594 . -627) 171521) ((-531 . -626) 171503) ((-933 . -1311) 171490) ((-889 . -1242) T) ((-717 . -465) T) ((-508 . -527) 171456) ((-1303 . -1242) T) ((-1302 . -1242) T) ((-500 . -375) T) ((-367 . -380) 171435) ((-364 . -380) 171414) ((-356 . -380) 171393) ((-730 . -742) T) ((-220 . -375) T) ((-117 . -465) T) ((-1315 . -1306) 171377) ((-889 . -903) 171354) ((-889 . -905) NIL) ((-987 . -865) 171253) ((-831 . -865) 171204) ((-1249 . -102) T) ((-670 . -672) 171188) ((-1228 . -34) T) ((-173 . -626) 171170) ((-1138 . -25) 171003) ((-1138 . -21) 170914) ((-889 . -1063) 170891) ((-975 . -921) 170872) ((-1265 . -47) 170849) ((-933 . -380) T) ((-606 . -868) T) ((-59 . -667) 170833) ((-529 . -667) 170817) ((-494 . -921) 170794) ((-71 . -454) T) ((-71 . -408) T) ((-509 . -667) 170778) ((-59 . -385) 170762) ((-636 . -174) T) ((-529 . -385) 170746) ((-509 . -385) 170730) ((-559 . -1242) T) ((-843 . -724) 170714) ((-1197 . -318) 170693) ((-1203 . -132) T) ((-1167 . -1076) 170677) ((-118 . -174) T) ((-1167 . -656) 170609) ((-1171 . -320) 170547) ((-171 . -1242) T) ((-1304 . -132) T) ((-1277 . -943) 170526) ((-1256 . -943) 170505) ((-1256 . -836) NIL) ((-884 . -1076) 170475) ((-648 . -760) 170459) ((-620 . -760) 170443) ((-1255 . -932) 170396) ((-1049 . -1125) T) ((-928 . -1137) T) ((-884 . -656) 170366) ((-710 . -733) 170316) ((-919 . -1242) T) ((-889 . -389) 170293) ((-889 . -350) 170270) ((-857 . -1242) T) ((-824 . -1242) T) ((-171 . -903) 170254) ((-171 . -905) 170179) ((-785 . -1242) T) ((-693 . -1242) T) ((-1292 . -527) 170112) ((-1276 . -664) 170009) ((-1105 . -235) 169882) ((-500 . -1137) T) ((-366 . -1125) T) ((-220 . -1137) T) ((-76 . -454) T) ((-76 . -408) T) ((-171 . -1063) 169778) ((-305 . -915) 169735) ((-330 . -865) T) ((-1255 . -664) 169543) ((-890 . -810) 169522) ((-890 . -807) 169501) ((-890 . -742) T) ((-500 . -23) T) ((-371 . -235) 169474) ((-365 . -235) 169447) ((-357 . -235) 169420) ((-176 . -465) T) ((-86 . -454) T) ((-225 . -320) 169358) ((-86 . -408) T) ((-226 . -626) 169340) ((-108 . -235) 169327) ((-220 . -23) T) ((-1316 . -1309) 169306) ((-693 . -1063) 169290) ((-593 . -301) T) ((-577 . -301) T) ((-508 . -301) T) ((-1265 . -1242) T) ((-137 . -483) 169245) ((-873 . -1242) T) ((-670 . -662) 169204) ((-48 . -1125) T) ((-728 . -273) 169188) ((-728 . -233) 169172) ((-889 . -921) NIL) ((-584 . -1242) T) ((-1265 . -905) NIL) ((-908 . -102) T) ((-904 . -102) T) ((-655 . -626) 169154) ((-401 . -1125) T) ((-171 . -389) 169138) ((-171 . -350) 169122) ((-1265 . -1063) 169002) ((-873 . -1063) 168898) ((-1167 . -102) T) ((-1024 . -923) 168821) ((-678 . -808) 168800) ((-669 . -132) T) ((-678 . -811) 168779) ((-118 . -527) 168687) ((-584 . -1063) 168669) ((-305 . -1299) 168639) ((-1192 . -868) NIL) ((-884 . -102) T) ((-986 . -569) 168618) ((-1236 . -1081) 168501) ((-1028 . -1076) 168446) ((-495 . -654) 168352) ((-927 . -1125) T) ((-1049 . -733) 168289) ((-727 . -1081) 168254) ((-1028 . -656) 168199) ((-630 . -102) T) ((-615 . -34) T) ((-1172 . -1242) T) ((-1236 . -111) 168068) ((-487 . -664) 167965) ((-366 . -733) 167910) ((-171 . -921) 167869) ((-715 . -301) T) ((-710 . -174) T) ((-727 . -111) 167825) ((-1321 . -1083) T) ((-1265 . -389) 167809) ((-431 . -1246) 167787) ((-1143 . -626) 167769) ((-324 . -864) NIL) ((-431 . -569) T) ((-228 . -318) T) ((-1255 . -807) 167722) ((-1255 . -810) 167675) ((-1276 . -742) T) ((-1255 . -742) T) ((-48 . -733) 167640) ((-228 . -1047) T) ((-1278 . -424) 167606) ((-1265 . -921) 167549) ((-363 . -1299) 167526) ((-1236 . -629) 167408) ((-734 . -742) T) ((-344 . -626) 167390) ((-533 . -868) 167369) ((-1138 . -235) 167260) ((-112 . -626) 167242) ((-112 . -627) 167224) ((-734 . -486) T) ((-727 . -629) 167174) ((-1315 . -1076) 167158) ((-495 . -25) 166991) ((-128 . -502) 166975) ((-122 . -502) 166959) ((-495 . -21) 166870) ((-1315 . -656) 166840) ((-636 . -301) T) ((-599 . -1081) 166815) ((-450 . -1125) T) ((-1087 . -318) T) ((-118 . -301) T) ((-1129 . -102) T) ((-1028 . -102) T) ((-599 . -111) 166783) ((-1236 . -1074) T) ((-1167 . -320) 166721) ((-1087 . -1047) T) ((-1079 . -25) T) ((-66 . -1242) T) ((-911 . -1242) T) ((-1079 . -21) T) ((-727 . -1074) T) ((-397 . -21) T) ((-397 . -25) T) ((-710 . -527) NIL) ((-1049 . -174) T) ((-727 . -249) T) ((-1087 . -558) T) ((-728 . -662) 166631) ((-519 . -102) T) ((-515 . -102) T) ((-366 . -174) T) ((-355 . -626) 166613) ((-420 . -1076) 166565) ((-407 . -626) 166547) ((-1145 . -864) T) ((-487 . -742) T) ((-911 . -1063) 166515) ((-420 . -656) 166467) ((-108 . -865) T) ((-674 . -1081) 166451) ((-500 . -132) T) ((-1278 . -1083) T) ((-220 . -132) T) ((-1182 . -102) 166401) ((-99 . -1125) T) ((-246 . -868) 166352) ((-251 . -682) 166336) ((-251 . -667) 166320) ((-674 . -111) 166299) ((-599 . -629) 166283) ((-327 . -424) 166267) ((-251 . -385) 166251) ((-1184 . -241) 166198) ((-1024 . -273) 166182) ((-1024 . -233) 166166) ((-74 . -1242) T) ((-48 . -174) T) ((-717 . -400) T) ((-717 . -144) T) ((-1315 . -102) T) ((-1223 . -1242) T) ((-1222 . -629) 166148) ((-1113 . -1242) T) ((-1112 . -1081) 165991) ((-1101 . -1242) T) ((-274 . -932) 165970) ((-254 . -932) 165949) ((-798 . -1081) 165772) ((-796 . -1081) 165615) ((-621 . -1242) T) ((-1189 . -626) 165597) ((-1112 . -111) 165426) ((-1071 . -102) T) ((-488 . -1242) T) ((-474 . -1081) 165397) ((-467 . -1081) 165240) ((-680 . -664) 165224) ((-889 . -318) T) ((-798 . -111) 165033) ((-796 . -111) 164862) ((-367 . -664) 164814) ((-364 . -664) 164766) ((-356 . -664) 164718) ((-274 . -664) 164607) ((-254 . -664) 164496) ((-1183 . -865) T) ((-1113 . -1063) 164480) ((-1101 . -1063) 164457) ((-1029 . -868) T) ((-1025 . -34) T) ((-474 . -111) 164418) ((-467 . -111) 164247) ((-996 . -868) T) ((-989 . -626) 164229) ((-986 . -1137) T) ((-981 . -1242) T) ((-127 . -1035) 164213) ((-866 . -1242) T) ((-889 . -1047) NIL) ((-751 . -1137) T) ((-731 . -1137) T) ((-674 . -629) 164131) ((-1292 . -502) 164115) ((-1209 . -1242) T) ((-1208 . -1242) T) ((-1167 . -38) 164075) ((-986 . -23) T) ((-933 . -664) 164040) ((-883 . -1125) T) ((-859 . -102) T) ((-833 . -21) T) ((-648 . -1076) 164024) ((-620 . -1076) 164008) ((-833 . -25) T) ((-751 . -23) T) ((-731 . -23) T) ((-648 . -656) 163992) ((-110 . -677) T) ((-620 . -656) 163976) ((-594 . -1081) 163941) ((-531 . -1081) 163886) ((-230 . -57) 163844) ((-466 . -23) T) ((-420 . -102) T) ((-1207 . -1242) T) ((-271 . -102) T) ((-110 . -113) T) ((-710 . -301) T) ((-884 . -38) 163814) ((-1112 . -629) 163550) ((-594 . -111) 163506) ((-531 . -111) 163435) ((-431 . -1137) T) ((-327 . -1083) 163325) ((-324 . -1083) T) ((-129 . -1242) T) ((-131 . -1242) T) ((-798 . -629) 163073) ((-796 . -629) 162839) ((-674 . -1074) T) ((-1321 . -1125) T) ((-467 . -629) 162624) ((-171 . -318) 162555) ((-431 . -23) T) ((-40 . -626) 162537) ((-40 . -627) 162521) ((-108 . -1017) 162503) ((-117 . -887) 162487) ((-665 . -629) 162471) ((-48 . -527) 162437) ((-1228 . -1035) 162421) ((-1206 . -626) 162388) ((-1214 . -34) T) ((-977 . -626) 162354) 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-1063) 160609) ((-655 . -1081) 160593) ((-205 . -803) T) ((-204 . -803) T) ((-203 . -803) T) ((-202 . -803) T) ((-201 . -803) T) ((-200 . -803) T) ((-199 . -803) T) ((-198 . -803) T) ((-197 . -803) T) ((-196 . -803) T) ((-560 . -626) 160575) ((-508 . -1027) T) ((-284 . -855) T) ((-283 . -855) T) ((-282 . -855) T) ((-281 . -855) T) ((-48 . -301) T) ((-280 . -855) T) ((-279 . -855) T) ((-278 . -855) T) ((-195 . -803) T) ((-655 . -111) 160554) ((-625 . -865) T) ((-670 . -424) 160538) ((-686 . -238) 160489) ((-226 . -629) 160451) ((-110 . -865) T) ((-669 . -21) T) ((-669 . -25) T) ((-1315 . -38) 160421) ((-118 . -297) 160372) ((-1292 . -19) 160356) ((-1256 . -868) NIL) ((-1292 . -617) 160333) ((-1305 . -1125) T) ((-363 . -1076) 160278) ((-1102 . -1125) T) ((-1012 . -1125) T) ((-986 . -132) T) ((-833 . -235) 160265) ((-753 . -1125) T) ((-363 . -656) 160210) ((-751 . -132) T) ((-731 . -132) T) ((-524 . -809) T) ((-524 . -810) T) ((-466 . -132) T) ((-420 . -1177) 160188) ((-226 . -1074) T) 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159094) ((-1197 . -943) 159073) ((-747 . -1137) T) ((-651 . -102) T) ((-528 . -1242) T) ((-523 . -1242) T) ((-521 . -1242) T) ((-363 . -102) T) ((-1241 . -1108) T) ((-1145 . -860) T) ((-834 . -865) T) ((-747 . -23) T) ((-355 . -1081) 159018) ((-1172 . -107) 159002) ((-1293 . -626) 158984) ((-653 . -1242) T) ((-1199 . -23) T) ((-1199 . -1137) T) ((-1198 . -1137) T) ((-1198 . -23) T) ((-528 . -1063) 158968) ((-1192 . -1137) T) ((-1151 . -1137) T) ((-355 . -111) 158897) ((-1029 . -1246) T) ((-127 . -1242) T) ((-937 . -1246) T) ((-1192 . -23) T) ((-1167 . -273) 158881) ((-710 . -297) NIL) ((-730 . -1242) T) ((-1167 . -233) 158865) ((-1151 . -23) T) ((-1100 . -1125) T) ((-1029 . -569) T) ((-937 . -569) T) ((-256 . -1242) T) ((-189 . -1242) T) ((-163 . -1242) T) ((-158 . -1242) T) ((-255 . -626) 158847) ((-831 . -238) 158744) ((-815 . -132) T) ((-726 . -626) 158726) ((-327 . -733) 158636) ((-324 . -733) 158565) ((-715 . -626) 158547) ((-715 . -627) 158492) ((-420 . -413) 158476) ((-451 . -1125) T) ((-500 . -25) T) ((-500 . -21) T) ((-1145 . -1125) T) ((-220 . -25) T) ((-220 . -21) T) ((-728 . -424) 158460) ((-730 . -1063) 158429) ((-1292 . -626) 158341) ((-1292 . -627) 158302) ((-1278 . -174) T) ((-1215 . -626) 158284) ((-251 . -34) T) ((-355 . -629) 158214) ((-407 . -629) 158196) ((-949 . -999) T) ((-1228 . -1242) T) ((-678 . -807) 158175) ((-678 . -810) 158154) ((-411 . -408) T) ((-536 . -102) 158104) ((-1248 . -1242) T) ((-1060 . -1125) T) ((-420 . -923) 158027) ((-225 . -1020) 158011) ((-854 . -1242) T) ((-517 . -102) T) ((-636 . -626) 157993) ((-45 . -865) NIL) ((-636 . -627) 157970) ((-1060 . -623) 157945) ((-924 . -527) 157878) ((-330 . -238) 157830) ((-355 . -1074) T) ((-118 . -627) NIL) ((-118 . -626) 157812) ((-890 . -1242) T) ((-686 . -430) 157796) ((-686 . -1148) 157741) ((-513 . -152) 157723) ((-355 . -239) T) ((-355 . -249) T) ((-40 . -1081) 157668) ((-890 . -903) 157652) ((-890 . -905) 157577) ((-728 . -1083) T) ((-710 . -1027) NIL) ((-1276 . -47) 157547) ((-1255 . -47) 157524) ((-1166 . -1035) 157495) ((-1145 . -733) 157482) ((-3 . |UnionCategory|) T) ((-1130 . -626) 157464) ((-1105 . -148) 157443) ((-1105 . -146) 157394) ((-1029 . -375) T) ((-989 . -629) 157378) ((-228 . -943) T) ((-40 . -111) 157307) ((-890 . -1063) 157171) ((-1028 . -233) 157148) ((-1028 . -273) 157125) ((-717 . -1076) 157112) ((-937 . -375) T) ((-717 . -656) 157099) ((-330 . -1230) 157065) ((-391 . -318) T) ((-330 . -1227) 157031) ((-327 . -174) 157010) ((-324 . -174) T) ((-621 . -1218) 156986) ((-594 . -1311) 156973) ((-531 . -1311) 156950) ((-117 . -1076) 156937) ((-371 . -148) 156916) ((-371 . -146) 156867) ((-365 . -148) 156846) ((-365 . -146) 156797) ((-357 . -148) 156776) ((-117 . -656) 156763) ((-357 . -146) 156714) ((-330 . -35) 156680) ((-488 . -1218) 156659) ((0 . |EnumerationCategory|) T) ((-330 . -95) 156625) ((-391 . -1047) T) ((-108 . -148) T) ((-108 . -146) NIL) ((-45 . -241) 156575) ((-670 . -1125) T) ((-621 . -107) 156522) ((-498 . -132) T) 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-662) 155439) ((-937 . -1137) T) ((-937 . -23) T) ((-890 . -921) 155398) ((-363 . -38) 155363) ((-888 . -1081) 155350) ((-342 . -868) T) ((-82 . -626) 155332) ((-40 . -1074) T) ((-888 . -111) 155317) ((-734 . -1242) T) ((-717 . -102) T) ((-710 . -626) 155299) ((-615 . -1242) T) ((-609 . -569) 155278) ((-440 . -1137) T) ((-351 . -1076) 155262) ((-215 . -1125) T) ((-176 . -1076) 155194) ((-487 . -47) 155164) ((-40 . -239) 155136) ((-40 . -249) T) ((-135 . -102) T) ((-117 . -102) T) ((-608 . -569) 155115) ((-351 . -656) 155099) ((-710 . -627) 155007) ((-327 . -527) 154973) ((-176 . -656) 154905) ((-324 . -527) 154797) ((-500 . -235) 154784) ((-1276 . -1063) 154768) ((-1255 . -1063) 154554) ((-1024 . -424) 154538) ((-220 . -235) 154525) ((-440 . -23) T) ((-1145 . -174) T) ((-1278 . -301) T) ((-670 . -733) 154495) ((-145 . -1125) T) ((-48 . -1027) T) ((-420 . -273) 154479) ((-420 . -233) 154463) ((-306 . -241) 154413) ((-889 . -943) T) ((-889 . -836) NIL) ((-888 . -629) 154385) ((-259 . -868) 154336) ((-258 . -868) 154287) ((-882 . -865) T) ((-1255 . -350) 154257) ((-1255 . -389) 154227) ((-1105 . -238) 154106) ((-225 . -1146) 154090) ((-305 . -923) 154049) ((-1292 . -299) 154026) ((-371 . -238) 154005) ((-365 . -238) 153984) ((-487 . -1242) T) ((-357 . -238) 153963) ((-108 . -238) T) ((-1236 . -664) 153888) ((-1028 . -662) 153818) ((-986 . -21) T) ((-986 . -25) T) ((-751 . -21) T) ((-751 . -25) T) ((-731 . -21) T) ((-731 . -25) T) ((-727 . -664) 153783) ((-466 . -21) T) ((-466 . -25) T) ((-351 . -102) T) ((-176 . -102) T) ((-1024 . -1083) T) ((-888 . -1074) T) ((-790 . -102) T) ((-1277 . -375) 153762) ((-1276 . -921) 153668) ((-1256 . -375) 153647) ((-1255 . -921) 153498) ((-1201 . -1242) T) ((-1049 . -626) 153480) ((-420 . -844) 153433) ((-1199 . -506) 153399) ((-171 . -943) 153330) ((-1198 . -506) 153296) ((-1192 . -506) 153262) ((-728 . -1125) T) ((-1151 . -506) 153228) ((-593 . -1081) 153215) ((-577 . -1081) 153202) ((-508 . -1081) 153167) ((-327 . -301) 153146) 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-107) 151867) ((-937 . -132) T) ((-928 . -865) 151818) ((-717 . -1177) T) ((-715 . -111) 151774) ((-859 . -662) 151691) ((-609 . -1137) T) ((-608 . -1137) T) ((-728 . -733) 151520) ((-727 . -742) T) ((-815 . -25) T) ((-815 . -21) T) ((-500 . -865) T) ((-610 . -1242) T) ((-609 . -23) T) ((-598 . -1242) T) ((-220 . -865) T) ((-420 . -662) 151457) ((-593 . -1074) T) ((-577 . -1074) T) ((-549 . -1242) T) ((-508 . -1074) T) ((-355 . -1311) 151434) ((-330 . -465) 151413) ((-351 . -320) 151400) ((-608 . -23) T) ((-440 . -132) T) ((-674 . -664) 151374) ((-251 . -1035) 151358) ((-890 . -318) T) ((-1316 . -1306) 151342) ((-787 . -808) T) ((-787 . -811) T) ((-717 . -38) 151329) ((-577 . -239) T) ((-508 . -249) T) ((-508 . -239) T) ((-1305 . -502) 151313) ((-1288 . -1242) T) ((-1175 . -241) 151263) ((-1112 . -932) 151242) ((-117 . -38) 151229) ((-211 . -816) T) ((-210 . -816) T) ((-209 . -816) T) ((-208 . -816) T) ((-890 . -1047) 151207) ((-680 . -1242) T) ((-661 . -1242) T) ((-798 . -932) 151186) 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148559) ((-254 . -921) 148536) ((-118 . -1074) T) ((-1112 . -742) T) ((-832 . -1137) T) ((-835 . -868) T) ((-636 . -239) 148515) ((-634 . -102) T) ((-524 . -1242) T) ((-520 . -1242) T) ((-798 . -742) T) ((-796 . -742) T) ((-1247 . -865) T) ((-426 . -1137) T) ((-118 . -249) T) ((-40 . -380) NIL) ((-118 . -239) NIL) ((-399 . -868) 148494) ((-467 . -742) T) ((-832 . -23) T) ((-747 . -25) T) ((-747 . -21) T) ((-686 . -915) 148415) ((-1102 . -297) 148394) ((-78 . -409) T) ((-78 . -408) T) ((-546 . -783) 148376) ((-228 . -868) T) ((-710 . -1081) 148326) ((-1317 . -102) T) ((-1284 . -132) T) ((-1277 . -132) T) ((-1256 . -132) T) ((-1199 . -25) T) ((-1167 . -424) 148310) ((-648 . -379) 148242) ((-620 . -379) 148174) ((-1182 . -1174) 148158) ((-103 . -1125) 148136) ((-1199 . -21) T) ((-1198 . -21) T) ((-883 . -626) 148118) ((-1024 . -733) 148066) ((-226 . -664) 148033) ((-710 . -111) 147967) ((-50 . -742) T) ((-1198 . -25) T) ((-363 . -361) T) ((-1192 . -21) T) ((-1105 . -465) 147918) ((-1192 . -25) T) ((-728 . -527) 147865) ((-594 . -742) T) ((-531 . -742) T) ((-1151 . -21) T) ((-1151 . -25) T) ((-609 . -132) T) ((-608 . -132) T) ((-305 . -662) 147600) ((-495 . -238) 147497) ((-371 . -465) T) ((-365 . -465) T) ((-357 . -465) T) ((-487 . -318) 147476) ((-1250 . -102) T) ((-324 . -297) 147411) ((-108 . -465) T) ((-79 . -454) T) ((-79 . -408) T) ((-490 . -102) T) ((-707 . -629) 147395) ((-1321 . -626) 147377) ((-1321 . -627) 147359) ((-1105 . -415) 147338) ((-1060 . -502) 147269) ((-655 . -664) 147253) ((-137 . -297) 147230) ((-577 . -811) T) ((-577 . -808) T) ((-1088 . -241) 147176) ((-1087 . -868) T) ((-729 . -868) T) ((-371 . -415) 147127) ((-365 . -415) 147078) ((-357 . -415) 147029) ((-1307 . -1137) T) ((-1316 . -1076) 147013) ((-393 . -1076) 146997) ((-1316 . -656) 146967) ((-834 . -238) T) ((-393 . -656) 146937) ((-710 . -629) 146872) ((-1307 . -23) T) ((-1294 . -102) T) ((-351 . -923) 146853) ((-177 . -626) 146835) ((-1167 . -1083) T) ((-560 . -380) T) ((-686 . -760) 146819) ((-1203 . -146) 146798) ((-1203 . -148) 146777) ((-1171 . -1125) T) ((-1171 . -1096) 146746) ((-69 . -1242) T) ((-1049 . -1081) 146683) ((-363 . -662) 146613) ((-884 . -1083) T) ((-246 . -654) 146519) ((-710 . -1074) T) ((-366 . -1081) 146464) ((-61 . -1242) T) ((-1049 . -111) 146380) ((-924 . -626) 146291) ((-710 . -249) T) ((-710 . -239) NIL) ((-859 . -864) 146270) ((-715 . -811) T) ((-715 . -808) T) ((-1028 . -424) 146247) ((-366 . -111) 146176) ((-391 . -943) T) ((-420 . -864) 146155) ((-728 . -301) 146066) ((-226 . -742) T) ((-1284 . -506) 146032) ((-1277 . -506) 145998) ((-1256 . -506) 145964) ((-591 . -1125) T) ((-327 . -1027) 145943) ((-225 . -1125) 145921) ((-1249 . -860) T) ((-330 . -998) 145883) ((-105 . -102) T) ((-48 . -1081) 145848) ((-889 . -868) NIL) ((-1316 . -102) T) ((-393 . -102) T) ((-1278 . -626) 145830) ((-1158 . -1159) 145814) ((-1029 . -654) 145796) ((-894 . -1242) T) ((-48 . -111) 145752) ((-697 . -1242) T) ((-692 . -1242) T) ((-678 . -1242) T) ((-831 . -915) 145619) ((-491 . -1242) T) ((-251 . -1242) T) ((-544 . -102) T) ((-513 . -102) T) ((-153 . -1299) 145603) ((-139 . -1242) T) ((-138 . -1242) T) ((-134 . -1242) T) ((-1241 . -102) T) ((-1049 . -629) 145540) ((-833 . -238) T) ((-1197 . -1246) 145519) ((-217 . -380) T) ((-366 . -629) 145449) ((-1150 . -1246) 145428) ((-246 . -25) 145261) ((-246 . -21) 145172) ((-128 . -120) 145156) ((-122 . -120) 145140) ((-44 . -760) 145124) ((-1197 . -569) 145035) ((-1150 . -569) 144966) ((-1249 . -1125) T) ((-559 . -868) T) ((-1060 . -297) 144941) ((-1191 . -1108) T) ((-1019 . -1108) T) ((-832 . -132) T) ((-118 . -811) NIL) ((-118 . -808) NIL) ((-367 . -318) T) ((-364 . -318) T) ((-356 . -318) T) ((-1119 . -1242) 144919) ((-259 . -1137) 144897) ((-258 . -1137) 144875) ((-1049 . -1074) T) ((-1028 . -1083) T) ((-48 . -629) 144808) ((-355 . -664) 144753) ((-1305 . -626) 144715) ((-1305 . -627) 144676) ((-634 . -38) 144660) ((-1199 . -235) 144613) ((-1198 . -235) 144559) ((-1102 . -626) 144541) 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T) ((-1107 . -102) T) ((-88 . -1242) T) ((-513 . -320) NIL) ((-1025 . -107) 143439) ((-908 . -1125) T) ((-904 . -1125) T) ((-1292 . -667) 143423) ((-1292 . -385) 143407) ((-338 . -1242) T) ((-606 . -865) T) ((-1167 . -1125) T) ((-1167 . -1078) 143347) ((-103 . -527) 143280) ((-950 . -626) 143262) ((-355 . -742) T) ((-30 . -626) 143244) ((-884 . -1125) T) ((-859 . -1083) 143223) ((-40 . -664) 143130) ((-228 . -1246) T) ((-420 . -1083) T) ((-1183 . -152) 143112) ((-1024 . -301) 143063) ((-892 . -1242) T) ((-630 . -1125) T) ((-228 . -569) T) ((-330 . -1273) 143047) ((-330 . -1270) 143017) ((-717 . -662) 142989) ((-1214 . -1218) 142968) ((-1100 . -626) 142950) ((-1214 . -107) 142900) ((-663 . -152) 142884) ((-645 . -152) 142830) ((-117 . -662) 142802) ((-492 . -1218) 142781) ((-500 . -148) T) ((-500 . -146) NIL) ((-1145 . -627) 142696) ((-451 . -626) 142678) ((-220 . -148) T) ((-220 . -146) NIL) ((-1145 . -626) 142660) ((-130 . -102) T) ((-52 . -102) T) ((-1256 . -654) 142612) ((-492 . -107) 142562) ((-1018 . -23) T) ((-1316 . -38) 142532) ((-1197 . -1137) T) ((-1150 . -1137) T) ((-1087 . -1246) T) ((-246 . -235) 142423) ((-322 . -102) T) ((-872 . -1137) T) ((-975 . -1246) 142402) ((-494 . -1246) 142381) ((-1087 . -569) T) ((-975 . -569) 142312) ((-1197 . -23) T) ((-1176 . -1108) T) ((-1150 . -23) T) ((-872 . -23) T) ((-494 . -569) 142243) ((-1167 . -733) 142175) ((-686 . -1076) 142159) ((-1171 . -527) 142092) ((-686 . -656) 142076) ((-1060 . -627) NIL) ((-1060 . -626) 142058) ((-96 . -1108) T) ((-1321 . -1081) 142045) ((-884 . -733) 142015) ((-1321 . -111) 142000) ((-1236 . -47) 141969) ((-1192 . -865) NIL) ((-259 . -132) T) ((-258 . -132) T) ((-1129 . -1125) T) ((-1028 . -1125) T) ((-62 . -626) 141951) ((-1105 . -915) 141820) ((-1049 . -808) T) ((-1049 . -811) T) ((-1284 . -25) T) ((-1284 . -21) T) ((-1277 . -21) T) ((-1277 . -25) T) ((-888 . -664) 141807) ((-1256 . -21) T) ((-1256 . -25) T) ((-1052 . -152) 141791) ((-1029 . -235) 141778) ((-890 . -836) 141757) 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T) ((-833 . -465) 141168) ((-153 . -1076) 141152) ((-1071 . -1096) 141081) ((-1052 . -1001) 141050) ((-835 . -1137) T) ((-1028 . -733) 140995) ((-153 . -656) 140979) ((-399 . -1137) T) ((-489 . -1001) 140948) ((-476 . -1001) 140917) ((-1208 . -868) T) ((-110 . -152) 140899) ((-73 . -626) 140881) ((-912 . -626) 140863) ((-1207 . -868) T) ((-1105 . -740) 140842) ((-1321 . -1074) T) ((-832 . -654) 140790) ((-305 . -1083) 140732) ((-171 . -1246) 140637) ((-228 . -1137) T) ((-335 . -23) T) ((-1192 . -1017) 140589) ((-1278 . -1081) 140494) ((-859 . -1125) T) ((-129 . -868) T) ((-1151 . -756) 140473) ((-1276 . -943) 140452) ((-1255 . -943) 140431) ((-888 . -742) T) ((-171 . -569) 140342) ((-593 . -664) 140329) ((-577 . -664) 140301) ((-420 . -1125) T) ((-271 . -1125) T) ((-215 . -626) 140283) ((-508 . -664) 140233) ((-228 . -23) T) ((-1255 . -836) 140186) ((-1314 . -102) T) ((-504 . -1242) T) ((-366 . -1311) 140163) ((-1312 . -102) T) ((-1278 . -111) 140055) ((-1138 . -915) 139922) ((-831 . -1076) 139823) ((-831 . -656) 139745) ((-145 . -626) 139727) ((-1018 . -132) T) ((-44 . -102) T) ((-246 . -865) 139678) ((-599 . -1242) T) ((-1265 . -1246) 139657) ((-103 . -502) 139641) ((-1315 . -733) 139611) ((-1112 . -47) 139572) ((-1087 . -1137) T) ((-975 . -1137) T) ((-128 . -34) T) ((-122 . -34) T) ((-1265 . -569) 139483) ((-798 . -47) 139460) ((-796 . -47) 139432) ((-1222 . -1242) T) ((-1197 . -132) T) ((-366 . -380) T) ((-494 . -1137) T) ((-1150 . -132) T) ((-889 . -375) T) ((-467 . -47) 139411) ((-872 . -132) T) ((-333 . -868) 139390) ((-153 . -102) T) ((-1087 . -23) T) ((-975 . -23) T) ((-584 . -569) T) ((-832 . -25) T) ((-832 . -21) T) ((-1167 . -527) 139323) ((-605 . -1108) T) ((-599 . -1063) 139307) ((-1278 . -629) 139181) ((-494 . -23) T) ((-363 . -1083) T) ((-391 . -868) T) ((-1236 . -921) 139162) ((-686 . -320) 139100) ((-1284 . -235) 139053) ((-1138 . -1299) 139023) ((-715 . -664) 138988) ((-1029 . -865) T) ((-1028 . -174) T) ((-986 . -146) 138967) ((-648 . -1125) T) 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137169) ((-665 . -1242) T) ((-798 . -905) NIL) ((-796 . -905) 137028) ((-1307 . -25) T) ((-1307 . -21) T) ((-1239 . -102) 137006) ((-1131 . -408) T) ((-636 . -664) 136993) ((-467 . -905) NIL) ((-691 . -102) 136943) ((-1112 . -1063) 136770) ((-889 . -23) T) ((-798 . -1063) 136629) ((-796 . -1063) 136486) ((-118 . -664) 136431) ((-467 . -1063) 136307) ((-285 . -1242) T) ((-327 . -629) 135871) ((-324 . -629) 135754) ((-50 . -1242) T) ((-403 . -662) 135723) ((-665 . -1063) 135707) ((-640 . -102) T) ((-594 . -1242) T) ((-531 . -1242) T) ((-225 . -502) 135691) ((-1292 . -34) T) ((-634 . -662) 135650) ((-300 . -1076) 135637) ((-137 . -629) 135621) ((-300 . -656) 135608) ((-648 . -733) 135592) ((-620 . -733) 135576) ((-686 . -38) 135536) ((-330 . -102) T) ((-1145 . -1081) 135523) ((-85 . -626) 135505) ((-50 . -1063) 135489) ((-1112 . -389) 135473) ((-798 . -389) 135457) ((-715 . -742) T) ((-715 . -810) T) ((-715 . -807) T) ((-60 . -57) 135419) ((-594 . -1063) 135406) ((-531 . -1063) 135383) 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T) ((-356 . -943) T) ((-995 . -1108) T) ((-975 . -132) T) ((-832 . -235) 134039) ((-118 . -810) NIL) ((-118 . -807) NIL) ((-118 . -742) T) ((-1071 . -527) 133940) ((-710 . -932) NIL) ((-584 . -23) T) ((-494 . -132) T) ((-431 . -238) 133891) ((-691 . -320) 133829) ((-226 . -1242) T) ((-651 . -1125) T) ((-648 . -777) T) ((-620 . -777) T) ((-1256 . -865) NIL) ((-1105 . -1076) 133739) ((-1028 . -301) T) ((-710 . -664) 133689) ((-259 . -25) T) ((-363 . -1125) T) ((-259 . -21) T) ((-258 . -25) T) ((-258 . -21) T) ((-153 . -38) 133673) ((-2 . -102) T) ((-933 . -943) T) ((-1105 . -656) 133541) ((-495 . -1299) 133511) ((-1145 . -1074) T) ((-727 . -318) T) ((-717 . -1083) T) ((-371 . -1076) 133463) ((-365 . -1076) 133415) ((-357 . -1076) 133367) ((-371 . -656) 133319) ((-226 . -1063) 133296) ((-365 . -656) 133248) ((-108 . -1076) 133198) ((-357 . -656) 133150) ((-305 . -733) 133092) ((-655 . -1242) T) ((-500 . -465) T) ((-420 . -527) 133004) ((-108 . -656) 132954) ((-220 . -465) T) ((-1145 . -239) T) ((-306 . -152) 132904) ((-1024 . -627) 132865) ((-1024 . -626) 132847) ((-1014 . -626) 132829) ((-117 . -1083) T) ((-670 . -1081) 132813) ((-228 . -506) T) ((-412 . -626) 132795) ((-412 . -627) 132772) ((-1079 . -1299) 132742) ((-670 . -111) 132721) ((-686 . -923) 132644) ((-1167 . -502) 132628) ((-1316 . -662) 132587) ((-393 . -662) 132556) ((-63 . -454) T) ((-63 . -408) T) ((-1184 . -102) T) ((-889 . -132) T) ((-497 . -102) 132506) ((-1143 . -1242) T) ((-1248 . -868) T) ((-1321 . -380) T) ((-1105 . -102) T) ((-1086 . -102) T) ((-363 . -733) 132451) ((-890 . -868) 132402) ((-747 . -148) 132381) ((-747 . -146) 132360) ((-670 . -629) 132278) ((-1049 . -664) 132215) ((-536 . -1125) 132193) ((-371 . -102) T) ((-365 . -102) T) ((-357 . -102) T) ((-108 . -102) T) ((-517 . -1125) T) ((-366 . -664) 132138) ((-1197 . -654) 132086) ((-1150 . -654) 132034) ((-397 . -522) 132013) ((-849 . -864) 131992) ((-710 . -742) T) ((-391 . -1246) T) ((-344 . -1242) T) ((-1256 . -1017) 131944) 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-102) 130626) ((-645 . -102) T) ((-1171 . -627) 130587) ((-584 . -132) T) ((-634 . -864) 130566) ((-1049 . -807) T) ((-1049 . -810) T) ((-1049 . -742) T) ((-831 . -923) 130435) ((-728 . -1081) 130258) ((-615 . -868) 130237) ((-497 . -320) 130175) ((-466 . -430) 130145) ((-363 . -174) T) ((-300 . -38) 130132) ((-259 . -235) 130023) ((-258 . -235) 129914) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-355 . -1063) 129891) ((-278 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -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) ((-728 . -111) 129700) ((-366 . -742) T) ((-686 . -273) 129684) ((-686 . -233) 129668) ((-594 . -318) T) ((-531 . -318) T) ((-305 . -527) 129617) ((-1189 . -1242) T) ((-108 . -320) NIL) 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-95) 128070) ((-1059 . -23) T) ((-1192 . -35) 128036) ((-584 . -506) T) ((-1151 . -35) 128002) ((-1151 . -95) 127968) ((-1151 . -1230) 127934) ((-1151 . -1227) 127900) ((-373 . -1137) T) ((-371 . -1177) 127879) ((-365 . -1177) 127858) ((-357 . -1177) 127837) ((-1129 . -297) 127793) ((-977 . -1242) T) ((-944 . -1242) T) ((-108 . -1177) T) ((-849 . -1083) 127772) ((-787 . -1242) T) ((-663 . -320) 127710) ((-645 . -320) 127561) ((-688 . -1242) T) ((-728 . -1074) T) ((-1087 . -654) 127543) ((-1105 . -38) 127411) ((-975 . -654) 127359) ((-1029 . -148) T) ((-1029 . -146) NIL) ((-391 . -1137) T) ((-335 . -25) T) ((-333 . -23) T) ((-966 . -865) 127338) ((-728 . -337) 127315) ((-494 . -654) 127263) ((-40 . -1063) 127151) ((-728 . -239) T) ((-717 . -733) 127138) ((-351 . -1125) T) ((-176 . -1125) T) ((-342 . -865) T) ((-431 . -465) 127088) ((-391 . -23) T) ((-371 . -38) 127053) ((-365 . -38) 127018) ((-357 . -38) 126983) ((-80 . -454) T) ((-80 . -408) T) ((-228 . -25) T) ((-228 . -21) T) ((-852 . -1137) T) ((-108 . -38) 126933) ((-843 . -1137) T) ((-790 . -1125) T) ((-117 . -733) 126920) ((-688 . -1063) 126904) ((-625 . -102) T) ((-852 . -23) T) ((-843 . -23) T) ((-1182 . -297) 126856) ((-1138 . -320) 126794) ((-495 . -1076) 126695) ((-1127 . -241) 126679) ((-64 . -409) T) ((-64 . -408) T) ((-1176 . -102) T) ((-110 . -102) T) ((-495 . -656) 126601) ((-40 . -389) 126578) ((-96 . -102) T) ((-669 . -870) 126562) ((-1197 . -235) 126549) ((-1160 . -1108) T) ((-1087 . -21) T) ((-1087 . -25) T) ((-1079 . -1076) 126533) ((-831 . -273) 126502) ((-831 . -233) 126471) ((-975 . -25) T) ((-975 . -21) T) ((-1145 . -380) T) ((-1079 . -656) 126413) ((-634 . -1083) T) ((-1052 . -320) 126351) ((-908 . -626) 126333) ((-686 . -662) 126292) ((-494 . -25) T) ((-494 . -21) T) ((-397 . -1076) 126276) ((-904 . -626) 126258) ((-888 . -1242) T) ((-536 . -527) 126191) ((-259 . -865) 126142) ((-258 . -865) 126093) ((-397 . -656) 126063) ((-889 . -654) 126040) ((-489 . -320) 125978) ((-560 . -1242) T) 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-1242) T) ((-49 . -1125) T) ((-1278 . -664) 123473) ((-1276 . -569) 123424) ((-1255 . -569) 123375) ((-730 . -1137) T) ((-653 . -23) T) ((-577 . -1063) 123357) ((-608 . -148) 123336) ((-608 . -146) 123315) ((-508 . -1063) 123258) ((-1160 . -1162) T) ((-87 . -396) T) ((-87 . -408) T) ((-890 . -375) T) ((-852 . -132) T) ((-843 . -132) T) ((-987 . -662) 123202) ((-730 . -23) T) ((-519 . -626) 123152) ((-515 . -626) 123134) ((-831 . -662) 122913) ((-1316 . -1083) T) ((-391 . -1085) T) ((-1051 . -1125) 122891) ((-55 . -1063) 122873) ((-924 . -34) T) ((-495 . -320) 122811) ((-605 . -102) T) ((-1182 . -627) 122772) ((-1182 . -626) 122704) ((-1203 . -1076) 122587) ((-45 . -102) T) ((-833 . -102) T) ((-1203 . -656) 122484) ((-1293 . -1242) T) ((-1265 . -25) T) ((-1265 . -21) T) ((-1087 . -235) 122471) ((-873 . -25) T) ((-524 . -868) T) ((-255 . -1242) T) ((-44 . -379) 122455) ((-873 . -21) T) ((-747 . -465) 122406) ((-1315 . -626) 122388) ((-726 . -1242) T) ((-715 . -1242) T) ((-1304 . -1076) 122358) ((-1079 . -320) 122296) ((-687 . -1108) T) ((-619 . -1108) T) ((-403 . -1125) T) ((-584 . -25) T) ((-584 . -21) T) ((-182 . -1108) T) ((-162 . -1108) T) ((-157 . -1108) T) ((-155 . -1108) T) ((-1304 . -656) 122266) ((-634 . -1125) T) ((-715 . -905) 122248) ((-1292 . -1242) T) ((-230 . -320) 122186) ((-145 . -380) T) ((-1215 . -1242) T) ((-1071 . -627) 122128) ((-1071 . -626) 122071) ((-324 . -932) NIL) ((-1250 . -860) T) ((-1138 . -923) 121940) ((-715 . -1063) 121885) ((-727 . -943) T) ((-487 . -1246) 121864) ((-1198 . -465) 121843) ((-1192 . -465) 121822) ((-341 . -102) T) ((-890 . -1137) T) ((-330 . -662) 121704) ((-327 . -664) 121433) ((-324 . -664) 121362) ((-487 . -569) 121313) ((-351 . -527) 121279) ((-563 . -152) 121229) ((-40 . -318) T) ((-859 . -626) 121211) ((-717 . -301) T) ((-890 . -23) T) ((-391 . -506) T) ((-1105 . -273) 121181) ((-1105 . -233) 121151) ((-525 . -102) T) ((-420 . -627) 120958) ((-420 . -626) 120940) ((-271 . -626) 120922) ((-117 . -301) T) ((-1278 . -742) T) ((-636 . -1242) T) ((-1317 . -1125) T) ((-1276 . -375) 120901) ((-1255 . -375) 120880) ((-1305 . -34) T) ((-1250 . -1125) T) ((-118 . -1242) T) ((-108 . -273) 120862) ((-108 . -233) 120844) ((-1203 . -102) T) ((-490 . -1125) T) ((-536 . -502) 120828) ((-753 . -34) T) ((-669 . -1076) 120812) ((-669 . -656) 120782) ((-889 . -235) NIL) ((-142 . -34) T) ((-118 . -903) 120759) ((-118 . -905) NIL) ((-636 . -1063) 120642) ((-1304 . -102) T) ((-1284 . -238) 120601) ((-660 . -865) 120580) ((-1277 . -238) 120532) ((-1256 . -238) 120355) ((-306 . -102) T) ((-728 . -380) 120334) ((-118 . -1063) 120311) ((-403 . -733) 120295) ((-608 . -238) 120254) ((-634 . -733) 120238) ((-1130 . -1242) T) ((-45 . -320) 120042) ((-832 . -146) 120021) ((-832 . -148) 120000) ((-300 . -662) 119972) ((-1315 . -394) 119951) ((-835 . -865) T) ((-1294 . -1125) T) ((-1184 . -232) 119898) ((-399 . -865) 119877) ((-1284 . -35) 119843) ((-1284 . -1230) 119809) ((-1284 . -1227) 119775) ((-1277 . -1227) 119741) 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118698) ((-1316 . -1125) T) ((-393 . -1125) T) ((-1265 . -235) 118685) ((-1241 . -1125) T) ((-82 . -1242) T) ((-1138 . -273) 118654) ((-1087 . -865) T) ((-118 . -921) NIL) ((-798 . -943) 118633) ((-729 . -865) T) ((-544 . -1125) T) ((-513 . -1125) T) ((-367 . -1246) T) ((-364 . -1246) T) ((-356 . -1246) T) ((-274 . -1246) 118612) ((-254 . -1246) 118591) ((-546 . -878) T) ((-1138 . -233) 118560) ((-1183 . -844) T) ((-1167 . -1081) 118544) ((-403 . -777) T) ((-710 . -1242) T) ((-707 . -1063) 118528) ((-367 . -569) T) ((-364 . -569) T) ((-356 . -569) T) ((-274 . -569) 118459) ((-254 . -569) 118390) ((-538 . -1108) T) ((-1167 . -111) 118369) ((-466 . -760) 118339) ((-884 . -1081) 118309) ((-833 . -38) 118251) ((-710 . -903) 118233) ((-710 . -905) 118215) ((-306 . -320) 118019) ((-1182 . -299) 117996) ((-933 . -1246) T) ((-1105 . -662) 117891) ((-1029 . -465) T) ((-686 . -424) 117875) ((-884 . -111) 117840) ((-937 . -465) T) ((-710 . -1063) 117785) ((-933 . -569) T) ((-546 . -626) 117767) 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. -1083) T) ((-747 . -972) 116302) ((-1167 . -239) 116281) ((-366 . -1242) T) ((-1107 . -1125) T) ((-1059 . -25) T) ((-1059 . -21) T) ((-1028 . -1081) 116226) ((-338 . -868) 116205) ((-928 . -102) T) ((-884 . -1074) T) ((-710 . -921) NIL) ((-367 . -340) 116189) ((-367 . -375) T) ((-364 . -340) 116173) ((-364 . -375) T) ((-356 . -340) 116157) ((-356 . -375) T) ((-500 . -102) T) ((-1304 . -38) 116127) ((-559 . -865) T) ((-536 . -703) 116077) ((-220 . -102) T) ((-1049 . -1063) 115957) ((-1028 . -111) 115886) ((-651 . -626) 115868) ((-1199 . -998) 115837) ((-1198 . -998) 115799) ((-533 . -152) 115783) ((-1105 . -382) 115762) ((-363 . -626) 115744) ((-333 . -21) T) ((-366 . -1063) 115721) ((-333 . -25) T) ((-1192 . -998) 115690) ((-48 . -1242) T) ((-76 . -626) 115672) ((-1151 . -998) 115639) ((-715 . -318) T) ((-130 . -860) T) ((-933 . -375) T) ((-391 . -25) T) ((-391 . -21) T) ((-933 . -340) 115626) ((-86 . -626) 115608) ((-715 . -1047) T) ((-693 . -865) T) ((-401 . -1242) T) ((-1276 . -132) T) ((-1255 . -132) T) ((-924 . -1035) 115592) ((-852 . -21) T) ((-48 . -1063) 115535) ((-852 . -25) T) ((-843 . -25) T) ((-843 . -21) T) ((-1138 . -662) 115314) ((-1314 . -1083) T) ((-562 . -102) T) ((-1312 . -1083) T) ((-670 . -742) T) ((-1129 . -631) 115217) ((-1028 . -629) 115147) ((-1315 . -1081) 115131) ((-927 . -1242) T) ((-831 . -424) 115100) ((-103 . -120) 115084) ((-130 . -1125) T) ((-52 . -1125) T) ((-949 . -626) 115066) ((-889 . -1017) 115043) ((-839 . -102) T) ((-1315 . -111) 115022) ((-747 . -915) 114997) ((-669 . -38) 114967) ((-584 . -865) T) ((-367 . -1137) T) ((-364 . -1137) T) ((-356 . -1137) T) ((-274 . -1137) T) ((-254 . -1137) T) ((-1175 . -320) 114771) ((-1113 . -235) 114758) ((-636 . -318) 114737) ((-680 . -23) T) ((-537 . -1108) T) ((-322 . -1125) T) ((-495 . -273) 114706) ((-495 . -233) 114675) ((-153 . -1083) T) ((-367 . -23) T) ((-364 . -23) T) ((-356 . -23) T) ((-118 . -318) T) ((-274 . -23) T) ((-254 . -23) T) ((-1028 . -1074) T) ((-728 . -932) 114654) ((-1199 . -915) 114542) ((-1198 . -915) 114423) ((-1192 . -915) 114159) ((-1182 . -629) 114136) ((-1028 . -239) 114108) ((-1028 . -249) T) ((-1151 . -915) 114090) ((-118 . -1047) NIL) ((-933 . -1137) T) ((-1277 . -465) 114069) ((-1256 . -465) 114048) ((-536 . -626) 113980) ((-728 . -664) 113869) ((-420 . -1081) 113821) ((-517 . -626) 113803) ((-933 . -23) T) ((-500 . -320) NIL) ((-1315 . -629) 113759) ((-487 . -132) T) ((-220 . -320) NIL) ((-420 . -111) 113697) ((-831 . -1083) 113675) ((-753 . -1123) 113659) ((-1276 . -506) 113625) ((-1255 . -506) 113591) ((-450 . -1242) T) ((-561 . -860) T) ((-142 . -1123) 113573) ((-490 . -301) T) ((-1315 . -1074) T) ((-259 . -238) 113470) ((-258 . -238) 113367) ((-1247 . -102) T) ((-1088 . -102) T) ((-859 . -629) 113235) ((-513 . -527) NIL) ((-495 . -244) 113214) ((-420 . -629) 113112) ((-986 . -1076) 112995) ((-751 . -1076) 112965) ((-986 . -656) 112862) ((-1197 . -146) 112841) ((-751 . -656) 112811) ((-466 . -1076) 112781) ((-1197 . -148) 112760) ((-1150 . -148) 112739) ((-1150 . -146) 112718) ((-648 . -1081) 112702) ((-620 . -1081) 112686) ((-466 . -656) 112656) ((-1199 . -1283) 112640) ((-1199 . -1270) 112617) ((-1198 . -1275) 112578) ((-686 . -1125) T) ((-686 . -1078) 112518) ((-1198 . -1270) 112488) ((-561 . -1125) T) ((-500 . -1177) T) ((-1198 . -1273) 112472) ((-1192 . -1254) 112433) ((-834 . -276) 112417) ((-220 . -1177) T) ((-355 . -943) T) ((-99 . -1242) T) ((-648 . -111) 112396) ((-620 . -111) 112375) ((-1192 . -1270) 112352) ((-859 . -1074) 112331) ((-1192 . -1252) 112315) ((-528 . -25) T) ((-508 . -313) T) ((-524 . -23) T) ((-523 . -25) T) ((-521 . -25) T) ((-520 . -23) T) ((-431 . -1076) 112289) ((-420 . -1074) T) ((-330 . -1083) T) ((-710 . -318) T) ((-431 . -656) 112263) ((-108 . -864) T) ((-728 . -742) T) ((-420 . -249) T) ((-420 . -239) 112242) ((-391 . -235) 112229) ((-500 . -38) 112179) ((-220 . -38) 112129) ((-487 . -506) 112095) ((-653 . -21) T) ((-653 . -25) T) ((-1249 . -380) T) ((-1183 . -1169) T) ((-1126 . -102) T) ((-843 . -235) 112068) ((-717 . -626) 112050) ((-717 . -627) 111965) ((-730 . -21) T) ((-730 . -25) T) ((-1160 . -102) T) ((-495 . -662) 111744) ((-246 . -915) 111611) ((-135 . -626) 111593) ((-117 . -626) 111575) ((-158 . -25) T) ((-1314 . -1125) T) ((-890 . -654) 111523) ((-1312 . -1125) T) ((-883 . -1242) T) ((-986 . -102) T) ((-751 . -102) T) ((-731 . -102) T) ((-466 . -102) T) ((-832 . -465) 111474) ((-44 . -1125) T) ((-1113 . -865) T) ((-1088 . -320) 111325) ((-680 . -132) T) ((-1079 . -662) 111294) ((-686 . -733) 111278) ((-300 . -1083) T) ((-367 . -132) T) ((-364 . -132) T) ((-356 . -132) T) ((-274 . -132) T) ((-254 . -132) T) ((-397 . -662) 111247) ((-1321 . -1242) T) ((-431 . -102) T) ((-153 . -1125) T) ((-45 . -232) 111197) ((-1029 . -915) NIL) ((-815 . -1076) 111181) ((-981 . -865) 111160) ((-1024 . -664) 111062) ((-815 . -656) 111046) ((-246 . -1299) 111016) ((-1049 . -318) T) ((-305 . -1081) 110937) ((-933 . -132) T) ((-40 . -943) T) ((-500 . -413) 110919) ((-366 . -318) T) ((-220 . -413) 110901) ((-1105 . -424) 110885) ((-305 . -111) 110801) ((-1208 . -865) T) ((-1207 . -865) T) ((-890 . -25) T) ((-890 . -21) T) ((-1278 . -47) 110745) ((-351 . -626) 110727) ((-1197 . -238) T) ((-228 . -148) T) ((-176 . -626) 110709) ((-790 . -626) 110691) ((-129 . -865) T) ((-621 . -241) 110638) ((-488 . -241) 110588) ((-1314 . -733) 110558) ((-48 . -318) T) ((-1312 . -733) 110528) ((-65 . -629) 110457) ((-987 . -1125) T) ((-831 . -1125) 110209) ((-323 . -102) T) ((-924 . -1242) T) ((-48 . -1047) T) ((-1255 . -654) 110117) ((-705 . -102) 110067) ((-44 . -733) 110051) ((-563 . -102) T) ((-305 . -629) 109982) ((-67 . -395) T) ((-500 . -923) NIL) ((-67 . -408) T) ((-285 . -868) T) ((-220 . -923) NIL) ((-678 . -23) T) ((-833 . -662) 109918) ((-686 . -777) T) ((-1239 . -1125) 109896) ((-363 . -1081) 109841) ((-691 . -1125) 109819) ((-1087 . -148) T) ((-975 . -148) 109798) ((-975 . -146) 109777) ((-815 . -102) T) ((-153 . -733) 109761) ((-494 . -148) 109740) ((-494 . -146) 109719) ((-363 . -111) 109648) ((-1105 . -1083) T) ((-333 . -865) 109627) ((-1284 . -998) 109596) ((-1278 . -1242) T) ((-640 . -1125) T) ((-1277 . -998) 109558) ((-524 . -132) T) ((-520 . -132) T) ((-306 . -232) 109508) ((-371 . -1083) T) ((-365 . -1083) T) ((-357 . -1083) T) ((-305 . -1074) 109450) ((-1256 . -998) 109419) ((-391 . -865) T) ((-108 . -1083) T) ((-1024 . -742) T) ((-888 . -943) T) ((-859 . -811) 109398) ((-859 . -808) 109377) ((-431 . -320) 109316) ((-481 . -102) T) ((-608 . -998) 109285) ((-330 . -1125) T) ((-420 . -811) 109264) ((-420 . -808) 109243) ((-513 . -502) 109225) ((-1278 . -1063) 109191) ((-1276 . -21) T) ((-1276 . -25) T) ((-1255 . -21) T) ((-1255 . -25) T) ((-651 . -629) 109168) ((-831 . -733) 109110) ((-363 . -629) 109040) ((-715 . -417) T) ((-1305 . -1242) T) ((-1138 . -424) 109009) ((-1102 . -1242) T) ((-619 . -102) T) ((-1028 . -380) NIL) ((-1012 . -1242) T) ((-687 . -102) T) ((-182 . -102) T) ((-162 . -102) T) ((-157 . -102) T) 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. -569) T) ((-608 . -915) 106249) ((-327 . -903) 106233) ((-327 . -905) 106158) ((-324 . -903) 106119) ((-140 . -1242) T) ((-137 . -1242) T) ((-115 . -1242) T) ((-324 . -905) NIL) ((-815 . -320) 106084) ((-330 . -733) 105925) ((-399 . -398) 105909) ((-335 . -334) 105886) ((-498 . -102) T) ((-487 . -25) T) ((-487 . -21) T) ((-431 . -38) 105860) ((-327 . -1063) 105523) ((-228 . -1227) T) ((-228 . -1230) T) ((-3 . -626) 105505) ((-324 . -1063) 105435) ((-890 . -235) 105380) ((-2 . -1125) T) ((-2 . |RecordCategory|) T) ((-1138 . -1083) 105358) ((-849 . -626) 105340) ((-1087 . -238) T) ((-593 . -943) T) ((-577 . -836) T) ((-577 . -943) T) ((-508 . -943) T) ((-137 . -1063) 105324) ((-228 . -95) T) ((-171 . -148) 105303) ((-75 . -454) T) ((0 . -626) 105285) ((-75 . -408) T) ((-171 . -146) 105236) ((-228 . -35) T) ((-49 . -626) 105218) ((-490 . -1083) T) ((-500 . -273) 105200) ((-500 . -233) 105182) ((-497 . -993) 105166) ((-220 . -273) 105148) ((-220 . -233) 105130) ((-81 . -454) T) ((-81 . -408) T) ((-1171 . -34) T) ((-747 . -102) T) ((-669 . -662) 105089) ((-1051 . -626) 105056) ((-513 . -297) 105006) ((-327 . -389) 104975) ((-324 . -389) 104936) ((-324 . -350) 104897) ((-1110 . -626) 104879) ((-832 . -972) 104826) ((-678 . -132) T) ((-1265 . -146) 104805) ((-1265 . -148) 104784) ((-1199 . -102) T) ((-1198 . -102) T) ((-1192 . -102) T) ((-1184 . -1125) T) ((-1151 . -102) T) ((-1100 . -1242) T) ((-225 . -34) T) ((-300 . -733) 104771) ((-1284 . -1283) 104755) ((-1184 . -623) 104731) ((-606 . -320) NIL) ((-1284 . -1270) 104708) ((-1175 . -232) 104658) ((-497 . -1125) 104636) ((-451 . -1242) T) ((-403 . -626) 104618) ((-523 . -865) T) ((-1145 . -1242) T) ((-1277 . -1275) 104579) ((-1277 . -1270) 104549) ((-1277 . -1273) 104533) ((-1256 . -1254) 104494) ((-1256 . -1270) 104471) ((-1256 . -1252) 104455) ((-1199 . -295) 104421) ((-634 . -626) 104403) ((-1198 . -295) 104369) ((-715 . -943) T) ((-1192 . -295) 104335) ((-1151 . -295) 104301) ((-1145 . -905) 104283) ((-1105 . -1125) T) ((-1086 . -1125) T) ((-48 . -313) T) ((-327 . -921) 104249) ((-324 . -921) NIL) ((-1086 . -1093) 104228) ((-815 . -38) 104212) ((-274 . -654) 104160) ((-112 . -868) T) ((-254 . -654) 104108) ((-717 . -1081) 104095) ((-608 . -1270) 104072) ((-1145 . -1063) 104054) ((-330 . -174) 103985) ((-371 . -1125) T) ((-365 . -1125) T) ((-357 . -1125) T) ((-513 . -19) 103967) ((-1127 . -152) 103951) ((-889 . -238) NIL) ((-108 . -1125) T) ((-117 . -1081) 103938) ((-727 . -375) T) ((-513 . -617) 103913) ((-717 . -111) 103898) ((-1317 . -626) 103865) ((-1317 . -503) 103847) ((-1276 . -235) 103793) ((-1255 . -235) 103646) ((-449 . -102) T) ((-894 . -1287) T) ((-257 . -102) T) ((-45 . -1174) 103596) ((-117 . -111) 103581) ((-1294 . -626) 103563) ((-1265 . -238) T) ((-1250 . -626) 103545) ((-1248 . -865) T) ((-648 . -736) T) ((-620 . -736) T) ((-1236 . -1137) T) ((-1236 . -23) T) ((-1197 . -465) 103476) ((-1192 . -320) 103361) ((-1191 . -1125) T) ((-831 . -527) 103294) ((-1060 . -1242) T) 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-408) T) ((-135 . -629) 101773) ((-117 . -629) 101745) ((-1029 . -656) 101695) ((-966 . -1005) 101679) ((-937 . -656) 101631) ((-937 . -1076) 101583) ((-933 . -21) T) ((-933 . -25) T) ((-890 . -865) 101534) ((-884 . -664) 101494) ((-727 . -1137) T) ((-727 . -23) T) ((-717 . -1074) T) ((-717 . -239) T) ((-300 . -174) T) ((-670 . -1242) T) ((-322 . -93) T) ((-663 . -1125) 101472) ((-645 . -623) 101447) ((-645 . -1125) T) ((-594 . -1246) T) ((-594 . -569) T) ((-531 . -1246) T) ((-531 . -569) T) ((-500 . -662) 101397) ((-487 . -235) 101343) ((-440 . -1076) 101327) ((-440 . -656) 101311) ((-371 . -733) 101263) ((-365 . -733) 101215) ((-351 . -1081) 101199) ((-357 . -733) 101151) ((-351 . -111) 101130) ((-176 . -1081) 101062) ((-176 . -111) 100973) ((-108 . -733) 100923) ((-220 . -662) 100873) ((-284 . -1125) T) ((-283 . -1125) T) ((-282 . -1125) T) ((-281 . -1125) T) ((-280 . -1125) T) ((-279 . -1125) T) ((-278 . -1125) T) ((-214 . -1125) T) ((-213 . -1125) T) ((-171 . -1230) 100851) ((-171 . -1227) 100829) ((-211 . -1125) T) ((-210 . -1125) T) ((-117 . -1074) T) ((-209 . -1125) T) ((-208 . -1125) T) ((-205 . -1125) T) ((-204 . -1125) T) ((-203 . -1125) T) ((-202 . -1125) T) ((-201 . -1125) T) ((-200 . -1125) T) ((-199 . -1125) T) ((-198 . -1125) T) ((-197 . -1125) T) ((-196 . -1125) T) ((-195 . -1125) T) ((-246 . -102) 100561) ((-171 . -35) 100539) ((-171 . -95) 100517) ((-670 . -1063) 100413) ((-495 . -1083) 100391) ((-1138 . -1125) 100143) ((-1167 . -34) T) ((-686 . -502) 100127) ((-73 . -1242) T) ((-105 . -626) 100109) ((-912 . -1242) T) ((-1316 . -626) 100091) ((-393 . -626) 100073) ((-351 . -629) 100025) ((-176 . -629) 99942) ((-1241 . -503) 99923) ((-747 . -38) 99772) ((-584 . -1230) T) ((-584 . -1227) T) ((-544 . -626) 99754) ((-533 . -320) 99692) ((-513 . -626) 99674) ((-513 . -627) 99656) ((-1241 . -626) 99622) ((-1192 . -1177) NIL) ((-215 . -1242) T) ((-1052 . -1096) 99591) ((-1052 . -1125) T) ((-1029 . -102) T) ((-996 . -102) T) ((-937 . -102) T) ((-912 . -1063) 99568) ((-1167 . -742) T) ((-1028 . -664) 99475) ((-489 . -1125) T) ((-476 . -1125) T) ((-599 . -23) T) ((-584 . -35) T) ((-584 . -95) T) ((-440 . -102) T) ((-1088 . -232) 99421) ((-1199 . -38) 99318) ((-1198 . -38) 99159) ((-944 . -868) T) ((-884 . -742) T) ((-787 . -868) T) ((-710 . -943) T) ((-688 . -868) T) ((-524 . -25) T) ((-520 . -21) T) ((-520 . -25) T) ((-1192 . -38) 98955) ((-351 . -1074) T) ((-145 . -1242) T) ((-1105 . -174) T) ((-176 . -1074) T) ((-1151 . -38) 98852) ((-728 . -47) 98829) ((-371 . -174) T) ((-365 . -174) T) ((-532 . -57) 98803) ((-510 . -57) 98753) ((-363 . -1311) 98730) ((-228 . -465) T) ((-330 . -301) 98681) ((-357 . -174) T) ((-176 . -249) T) ((-1255 . -865) 98580) ((-108 . -174) T) ((-890 . -1017) 98564) ((-674 . -1137) T) ((-594 . -375) T) ((-594 . -340) 98551) ((-531 . -340) 98528) ((-531 . -375) T) ((-327 . -318) 98507) ((-324 . -318) T) ((-615 . -865) 98486) ((-1138 . -733) 98428) ((-533 . -293) 98412) ((-674 . -23) T) ((-431 . -233) 98396) 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96435) ((-560 . -868) T) ((-1107 . -627) 96416) ((-420 . -932) 96395) ((-1236 . -132) T) ((-50 . -1137) T) ((-1192 . -413) 96347) ((-1049 . -943) T) ((-1028 . -742) T) ((-859 . -664) 96320) ((-728 . -905) NIL) ((-609 . -1076) 96280) ((-594 . -1137) T) ((-531 . -1137) T) ((-608 . -1076) 96163) ((-1182 . -34) T) ((-1029 . -320) NIL) ((-831 . -502) 96147) ((-609 . -656) 96120) ((-366 . -943) T) ((-608 . -656) 96017) ((-933 . -235) 96004) ((-420 . -664) 95920) ((-50 . -23) T) ((-727 . -132) T) ((-728 . -1063) 95800) ((-594 . -23) T) ((-108 . -527) NIL) ((-531 . -23) T) ((-171 . -422) 95771) ((-1165 . -1125) T) ((-1307 . -1306) 95755) ((-747 . -923) 95732) ((-717 . -811) T) ((-717 . -808) T) ((-1145 . -318) T) ((-391 . -148) T) ((-291 . -626) 95714) ((-290 . -626) 95696) ((-1255 . -1017) 95666) ((-48 . -943) T) ((-691 . -502) 95650) ((-259 . -1299) 95620) ((-258 . -1299) 95590) ((-1113 . -238) T) ((-1201 . -865) T) ((-1145 . -1047) T) ((-1071 . -34) T) ((-852 . -148) 95569) ((-852 . -146) 95548) ((-753 . -107) 95532) ((-625 . -133) T) ((-1203 . -1083) T) ((-495 . -1125) 95284) ((-1199 . -923) 95197) ((-1198 . -923) 95103) ((-1192 . -923) 94864) ((-889 . -465) T) ((-85 . -1242) T) ((-142 . -107) 94846) ((-1151 . -923) 94830) ((-728 . -389) 94814) ((-849 . -629) 94682) ((-1315 . -742) T) ((-1304 . -1083) T) ((-1284 . -102) T) ((-1277 . -102) T) ((-1145 . -558) T) ((-592 . -102) T) ((-130 . -503) 94664) ((-1197 . -972) 94633) ((-403 . -1081) 94617) ((-1150 . -972) 94584) ((-44 . -297) 94561) ((-130 . -626) 94528) ((-52 . -626) 94510) ((-217 . -868) T) ((-669 . -424) 94494) ((-1256 . -102) T) ((-1183 . -527) NIL) ((-678 . -25) T) ((-634 . -1081) 94478) ((-678 . -21) T) ((-986 . -662) 94388) ((-751 . -662) 94333) ((-731 . -662) 94305) ((-403 . -111) 94284) ((-225 . -262) 94268) ((-1079 . -1078) 94208) ((-1079 . -1125) T) ((-1029 . -1177) T) ((-834 . -1125) T) ((-466 . -662) 94123) ((-648 . -664) 94107) ((-634 . -111) 94086) ((-620 . -664) 94070) ((-355 . -1246) T) ((-609 . -102) T) ((-322 . -503) 94051) ((-599 . -132) T) ((-608 . -102) T) ((-427 . -1125) T) ((-397 . -1125) T) ((-322 . -626) 94017) ((-230 . -1125) 93995) ((-663 . -527) 93928) ((-645 . -527) 93772) ((-849 . -1074) 93751) ((-660 . -152) 93735) ((-355 . -569) T) ((-728 . -921) 93678) ((-563 . -232) 93628) ((-1284 . -295) 93594) ((-1277 . -295) 93560) ((-1105 . -301) 93511) ((-577 . -868) T) ((-500 . -864) T) ((-226 . -1137) T) ((-1256 . -295) 93477) ((-1236 . -506) 93443) ((-1029 . -38) 93393) ((-220 . -864) T) ((-431 . -662) 93352) ((-937 . -38) 93304) ((-859 . -810) 93283) ((-859 . -807) 93262) ((-859 . -742) 93241) ((-371 . -301) T) ((-365 . -301) T) ((-357 . -301) T) ((-171 . -465) 93172) ((-440 . -38) 93156) ((-226 . -23) T) ((-108 . -301) T) ((-420 . -810) 93135) ((-420 . -807) 93114) ((-420 . -742) T) ((-513 . -299) 93089) ((-490 . -1081) 93054) ((-674 . -132) T) ((-634 . -629) 93023) ((-1138 . -527) 92956) ((-348 . -132) T) ((-171 . -415) 92935) ((-495 . -733) 92877) ((-831 . -297) 92854) ((-490 . -111) 92810) ((-669 . -1083) T) ((-655 . -23) T) ((-1197 . -915) 92713) ((-1150 . -915) 92695) ((-832 . -1076) 92538) ((-1303 . -1108) T) ((-1265 . -465) 92469) ((-832 . -656) 92318) ((-1302 . -1108) T) ((-1112 . -132) T) ((-1079 . -733) 92260) ((-1052 . -527) 92193) ((-798 . -132) T) ((-796 . -132) T) ((-715 . -868) T) ((-584 . -465) T) ((-634 . -1074) T) ((-605 . -1125) T) ((-546 . -175) T) ((-474 . -132) T) ((-467 . -132) T) ((-391 . -238) T) ((-1024 . -1242) T) ((-45 . -1125) T) ((-397 . -733) 92163) ((-833 . -1125) T) ((-489 . -527) 92096) ((-476 . -527) 92029) ((-1317 . -629) 92011) ((-466 . -379) 91981) ((-45 . -623) 91960) ((-412 . -1242) T) ((-327 . -313) T) ((-1292 . -868) 91939) ((-843 . -238) 91918) ((-490 . -629) 91868) ((-1256 . -320) 91753) ((-686 . -626) 91715) ((-59 . -865) 91694) ((-1029 . -413) 91676) ((-561 . -626) 91658) ((-815 . -662) 91617) ((-831 . -617) 91594) ((-529 . -865) 91573) ((-509 . -865) 91552) ((-1024 . -1063) 91448) ((-40 . -1246) T) 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-742) T) ((-879 . -626) 87147) ((-1198 . -662) 87029) ((-1192 . -662) 86866) ((-1151 . -662) 86776) ((-1256 . -413) 86728) ((-1138 . -502) 86712) ((-60 . -320) 86650) ((-342 . -102) T) ((-1236 . -21) T) ((-1236 . -25) T) ((-40 . -1137) T) ((-727 . -21) T) ((-640 . -626) 86632) ((-528 . -334) 86611) ((-727 . -25) T) ((-452 . -102) T) ((-108 . -297) NIL) ((-944 . -1137) T) ((-40 . -23) T) ((-787 . -1137) T) ((-577 . -1246) T) ((-508 . -1246) T) ((-1029 . -273) 86593) ((-330 . -626) 86575) ((-1029 . -233) 86557) ((-171 . -167) 86541) ((-593 . -569) T) ((-577 . -569) T) ((-508 . -569) T) ((-787 . -23) T) ((-1276 . -148) 86520) ((-1276 . -146) 86499) ((-1184 . -617) 86475) ((-1255 . -146) 86400) ((-1052 . -502) 86384) ((-1249 . -1242) T) ((-1255 . -148) 86309) ((-1307 . -1313) 86288) ((-889 . -915) NIL) ((-489 . -502) 86272) ((-476 . -502) 86256) ((-536 . -34) T) ((-669 . -733) 86226) ((-1284 . -923) 86139) ((-1277 . -923) 86045) ((-1256 . -923) 85806) ((-112 . -992) T) ((-1203 . -174) 85757) ((-678 . -865) 85736) ((-377 . -102) T) ((-608 . -923) 85649) ((-246 . -244) 85628) ((-259 . -102) T) ((-258 . -102) T) ((-1265 . -972) 85597) ((-251 . -865) 85576) ((-1049 . -868) T) ((-832 . -38) 85425) ((-45 . -527) 85217) ((-1183 . -297) 85167) ((-216 . -1125) T) ((-1175 . -1125) T) ((-890 . -238) 85118) ((-1175 . -623) 85097) ((-599 . -25) T) ((-599 . -21) T) ((-1127 . -320) 85035) ((-986 . -424) 85019) ((-715 . -1246) T) ((-645 . -297) 84972) ((-1112 . -654) 84920) ((-928 . -1125) T) ((-798 . -654) 84868) ((-796 . -654) 84816) ((-355 . -132) T) ((-300 . -626) 84798) ((-888 . -1137) T) ((-715 . -569) T) ((-130 . -629) 84780) ((-467 . -654) 84728) ((-171 . -915) 84649) ((-928 . -926) 84633) ((-391 . -465) T) ((-500 . -1125) T) ((-966 . -320) 84571) ((-717 . -664) 84543) ((-562 . -860) T) ((-220 . -1125) T) ((-327 . -943) 84522) ((-324 . -943) T) ((-324 . -836) NIL) ((-403 . -736) T) ((-888 . -23) T) ((-117 . -664) 84509) ((-487 . -146) 84488) ((-431 . -424) 84472) ((-487 . -148) 84451) ((-110 . -502) 84433) ((-322 . -629) 84414) ((-2 . -626) 84396) ((-188 . -102) T) ((-1183 . -19) 84378) ((-1183 . -617) 84353) ((-674 . -21) T) ((-674 . -25) T) ((-606 . -1169) T) ((-1138 . -297) 84330) ((-348 . -25) T) ((-348 . -21) T) ((-908 . -1242) T) ((-904 . -1242) T) ((-1314 . -1081) 84314) ((-246 . -662) 84093) ((-508 . -375) T) ((-1312 . -1081) 84077) ((-1307 . -38) 84047) ((-1276 . -1227) 84013) ((-1276 . -1230) 83979) ((-1265 . -915) 83882) ((-1197 . -1076) 83705) ((-1167 . -1242) T) ((-1150 . -1076) 83548) ((-872 . -1076) 83532) ((-645 . -617) 83507) ((-1276 . -95) 83473) ((-1276 . -238) 83425) ((-1259 . -102) 83403) ((-1197 . -656) 83232) ((-1150 . -656) 83081) ((-872 . -656) 83051) ((-1256 . -233) 83003) ((-1112 . -25) T) ((-562 . -1125) T) ((-1112 . -21) T) ((-986 . -1083) T) ((-544 . -808) T) ((-544 . -811) T) ((-118 . -1246) T) ((-884 . -1242) T) ((-636 . -569) T) ((-798 . -25) T) ((-798 . -21) T) ((-796 . -21) T) ((-796 . -25) T) ((-751 . -1083) T) ((-731 . -1083) T) ((-686 . -1081) 82987) ((-530 . -1108) T) ((-474 . -25) T) ((-118 . -569) T) ((-474 . -21) T) ((-467 . -25) T) ((-467 . -21) T) ((-1256 . -273) 82939) ((-1176 . -93) T) ((-1167 . -1063) 82835) ((-833 . -301) 82814) ((-1255 . -1227) 82780) ((-839 . -1125) T) ((-989 . -992) T) ((-686 . -111) 82759) ((-630 . -1242) T) ((-306 . -527) 82551) ((-1255 . -1230) 82517) ((-1255 . -238) 82376) ((-1250 . -380) T) ((-259 . -320) 82314) ((-258 . -320) 82252) ((-1247 . -860) T) ((-1184 . -627) NIL) ((-1184 . -626) 82234) ((-1167 . -389) 82218) ((-1145 . -836) T) ((-1145 . -943) T) ((-96 . -93) T) ((-1138 . -617) 82195) ((-1105 . -627) 82179) ((-1105 . -626) 82161) ((-1029 . -662) 82111) ((-937 . -662) 82048) ((-831 . -299) 82025) ((-497 . -626) 81957) ((-621 . -152) 81904) ((-500 . -733) 81854) ((-431 . -1083) T) ((-495 . -502) 81838) ((-440 . -662) 81797) ((-338 . -865) 81776) ((-351 . -664) 81750) ((-50 . -21) T) ((-50 . -25) T) ((-220 . -733) 81700) ((-171 . -740) 81671) ((-176 . -664) 81603) ((-594 . -21) T) ((-594 . -25) T) ((-531 . -25) T) ((-531 . -21) T) ((-488 . -152) 81553) ((-1086 . -626) 81535) ((-1018 . -102) T) ((-880 . -102) T) ((-832 . -923) 81435) ((-815 . -424) 81398) ((-40 . -132) T) ((-715 . -375) T) ((-717 . -742) T) ((-717 . -810) T) ((-717 . -807) T) ((-214 . -916) T) ((-593 . -1137) T) ((-577 . -1137) T) ((-508 . -1137) T) ((-371 . -626) 81380) ((-365 . -626) 81362) ((-357 . -626) 81344) ((-66 . -409) T) ((-66 . -408) T) ((-108 . -627) 81274) ((-108 . -626) 81216) ((-213 . -916) T) ((-981 . -152) 81200) ((-787 . -132) T) ((-686 . -629) 81118) ((-135 . -742) T) ((-117 . -742) T) ((-1276 . -35) 81084) ((-1079 . -502) 81068) ((-593 . -23) T) ((-577 . -23) T) ((-508 . -23) T) ((-1255 . -95) 81034) ((-1255 . -35) 81000) ((-1197 . -102) T) ((-1150 . -102) T) ((-872 . -102) T) ((-230 . -502) 80984) ((-1314 . -111) 80963) ((-1312 . -111) 80942) ((-44 . -1081) 80926) ((-1315 . -1242) T) ((-1314 . -629) 80872) ((-1314 . -1074) T) ((-1312 . -629) 80801) 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T) ((-515 . -1242) T) ((-933 . -146) T) ((-933 . -148) 79900) ((-888 . -132) T) ((-831 . -1081) 79821) ((-715 . -23) T) ((-710 . -569) T) ((-228 . -1076) 79786) ((-663 . -626) 79718) ((-663 . -627) 79679) ((-645 . -627) NIL) ((-645 . -626) 79661) ((-500 . -174) T) ((-228 . -656) 79626) ((-220 . -174) T) ((-226 . -21) T) ((-226 . -25) T) ((-487 . -1230) 79592) ((-487 . -1227) 79558) ((-284 . -626) 79540) ((-283 . -626) 79522) ((-282 . -626) 79504) ((-281 . -626) 79486) ((-280 . -626) 79468) ((-513 . -667) 79450) ((-279 . -626) 79432) ((-351 . -742) T) ((-278 . -626) 79414) ((-110 . -19) 79396) ((-176 . -742) T) ((-513 . -385) 79378) ((-214 . -626) 79360) ((-533 . -1174) 79344) ((-513 . -124) T) ((-110 . -617) 79319) ((-213 . -626) 79301) ((-487 . -35) 79267) ((-487 . -95) 79233) ((-211 . -626) 79215) ((-210 . -626) 79197) ((-209 . -626) 79179) ((-208 . -626) 79161) ((-205 . -626) 79143) ((-204 . -626) 79125) ((-203 . -626) 79107) ((-202 . -626) 79089) ((-201 . -626) 79071) ((-200 . -626) 79053) ((-199 . -626) 79035) ((-549 . -1128) 78987) ((-198 . -626) 78969) ((-197 . -626) 78951) ((-45 . -502) 78888) ((-196 . -626) 78870) ((-195 . -626) 78852) ((-153 . -629) 78821) ((-1140 . -102) T) ((-831 . -111) 78737) ((-660 . -102) 78667) ((-655 . -21) T) ((-655 . -25) T) ((-495 . -297) 78644) ((-1315 . -1063) 78628) ((-1138 . -626) 78321) ((-1126 . -1125) T) ((-1071 . -1242) T) ((-1197 . -320) 78308) ((-1087 . -1076) 78295) ((-1160 . -1125) T) ((-975 . -1076) 78138) ((-1150 . -320) 78125) ((-1121 . -1108) T) ((-636 . -1137) T) ((-1087 . -656) 78112) ((-1115 . -1108) T) ((-975 . -656) 77961) ((-1112 . -235) 77906) ((-494 . -1076) 77749) ((-1098 . -1108) T) ((-1091 . -1108) T) ((-1061 . -1108) T) ((-1044 . -1108) T) ((-118 . -1137) T) ((-494 . -656) 77598) ((-798 . -235) 77585) ((-835 . -102) T) ((-639 . -1108) T) ((-636 . -23) T) ((-1175 . -527) 77377) ((-496 . -1108) T) ((-986 . -1125) T) ((-399 . -102) T) ((-335 . -102) T) ((-221 . -1108) T) ((-859 . -1242) T) ((-153 . -1074) T) ((-747 . -424) 77361) ((-118 . -23) T) ((-1028 . -921) 77313) ((-751 . -1125) T) ((-731 . -1125) T) ((-1284 . -662) 77223) ((-1277 . -662) 77105) ((-466 . -1125) T) ((-420 . -1242) T) ((-327 . -443) 77089) ((-605 . -93) T) ((-1052 . -627) 77050) ((-271 . -1242) T) ((-1049 . -1246) T) ((-228 . -102) T) ((-1052 . -626) 77012) ((-832 . -273) 76996) ((-832 . -233) 76980) ((-831 . -629) 76778) ((-1256 . -662) 76615) ((-1049 . -569) T) ((-849 . -664) 76588) ((-366 . -1246) T) ((-489 . -626) 76550) ((-489 . -627) 76511) ((-476 . -627) 76472) ((-476 . -626) 76434) ((-609 . -662) 76393) ((-420 . -903) 76377) ((-330 . -1081) 76212) ((-420 . -905) 76137) ((-608 . -662) 76047) ((-859 . -1063) 75943) ((-500 . -527) NIL) ((-495 . -617) 75920) ((-594 . -235) 75907) ((-366 . -569) T) ((-531 . -235) 75894) ((-220 . -527) NIL) ((-890 . -465) T) ((-431 . -1125) T) ((-420 . -1063) 75758) ((-330 . -111) 75579) ((-710 . -375) T) ((-228 . -295) T) ((-1239 . -629) 75556) ((-48 . -1246) T) ((-1197 . 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. -465) T) ((-928 . -297) 65638) ((-831 . -380) 65617) ((-523 . -522) 65596) ((-521 . -522) 65575) ((-890 . -915) 65496) ((-500 . -297) NIL) ((-495 . -299) 65473) ((-431 . -301) T) ((-366 . -132) T) ((-220 . -297) NIL) ((-710 . -506) NIL) ((-99 . -1137) T) ((-40 . -235) 65404) ((-171 . -38) 65232) ((-975 . -923) 65213) ((-1276 . -998) 65175) ((-1255 . -998) 65144) ((-1172 . -320) 65082) ((-494 . -923) 65059) ((-1138 . -1074) 65037) ((-933 . -415) T) ((-653 . -522) 65009) ((-1278 . -569) T) ((-1175 . -617) 64988) ((-112 . -865) T) ((-1088 . -502) 64919) ((-593 . -21) T) ((-593 . -25) T) ((-577 . -21) T) ((-577 . -25) T) ((-508 . -25) T) ((-508 . -21) T) ((-1265 . -1177) 64897) ((-1138 . -239) 64849) ((-48 . -132) T) ((-1223 . -102) T) ((-246 . -1125) 64601) ((-889 . -413) 64578) ((-1113 . -102) T) ((-1101 . -102) T) ((-912 . -868) T) ((-621 . -102) T) ((-488 . -102) T) ((-1265 . -38) 64407) ((-873 . -38) 64377) ((-1059 . -1076) 64351) ((-747 . -174) 64262) ((-669 . -626) 64244) ((-661 . 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. -1081) 35785) ((-1028 . -1246) T) ((-1119 . -102) 35763) ((-831 . -389) 35732) ((-592 . -626) 35714) ((-559 . -1125) T) ((-1028 . -569) T) ((-1199 . -111) 35583) ((-1198 . -111) 35404) ((-1192 . -111) 35173) ((-1151 . -111) 35042) ((-1130 . -1128) 35006) ((-391 . -864) T) ((-1284 . -626) 34988) ((-1277 . -626) 34970) ((-890 . -662) 34907) ((-1256 . -626) 34889) ((-1256 . -627) NIL) ((-246 . -299) 34866) ((-40 . -465) T) ((-228 . -174) T) ((-171 . -1125) T) ((-747 . -629) 34651) ((-710 . -148) T) ((-710 . -146) NIL) ((-609 . -626) 34633) ((-608 . -626) 34615) ((-1145 . -235) 34602) ((-919 . -1125) T) ((-857 . -1125) T) ((-824 . -1125) T) ((-274 . -923) 34512) ((-254 . -923) 34489) ((-785 . -1125) T) ((-693 . -1125) T) ((-674 . -870) 34473) ((-636 . -238) 34424) ((-831 . -921) 34356) ((-876 . -868) T) ((-1247 . -380) T) ((-40 . -415) NIL) ((-118 . -238) NIL) ((-1199 . -629) 34238) ((-1145 . -677) T) ((-889 . -733) 34183) ((-259 . -502) 34167) ((-258 . -502) 34151) ((-1198 . -629) 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. -320) 20349) ((-496 . -1125) T) ((-1150 . -627) 20097) ((-1059 . -174) T) ((-966 . -299) 20074) ((-221 . -1125) T) ((-872 . -626) 20056) ((-621 . -527) 19839) ((-81 . -629) 19780) ((-834 . -1063) 19764) ((-488 . -527) 19556) ((-849 . -868) 19535) ((-986 . -742) T) ((-751 . -742) T) ((-731 . -742) T) ((-363 . -1137) T) ((-1204 . -626) 19517) ((-226 . -102) T) ((-495 . -389) 19486) ((-528 . -1125) T) ((-523 . -1125) T) ((-521 . -1125) T) ((-815 . -664) 19460) ((-1049 . -465) T) ((-981 . -527) 19393) ((-363 . -23) T) ((-648 . -132) T) ((-620 . -132) T) ((-366 . -465) T) ((-246 . -380) 19372) ((-391 . -174) T) ((-1276 . -1083) T) ((-1255 . -1083) T) ((-228 . -1027) T) ((-832 . -629) 19109) ((-715 . -400) T) ((-431 . -742) T) ((-717 . -1246) T) ((-1167 . -654) 19057) ((-653 . -1125) T) ((-655 . -102) T) ((-593 . -887) 19041) ((-1307 . -1081) 19025) ((-1184 . -1218) 19001) ((-717 . -569) T) ((-127 . -1125) 18979) ((-730 . -1125) T) ((-674 . -38) 18949) ((-495 . -921) 18881) ((-256 . -1125) 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. -238) T) ((-40 . -102) T) ((-933 . -1083) T) ((-710 . -915) NIL) ((-1206 . -102) T) ((-129 . -502) 13258) ((-1199 . -742) T) ((-1198 . -742) T) ((-1192 . -742) T) ((-1192 . -807) NIL) ((-1192 . -810) NIL) ((-977 . -102) T) ((-944 . -102) T) ((-888 . -1076) 13245) ((-1151 . -742) T) ((-787 . -102) T) ((-688 . -102) T) ((-888 . -656) 13232) ((-559 . -626) 13214) ((-487 . -1125) T) ((-351 . -1137) T) ((-176 . -1137) T) ((-330 . -943) 13193) ((-1276 . -733) 13034) ((-890 . -174) T) ((-1255 . -733) 12848) ((-859 . -21) 12800) ((-859 . -25) 12752) ((-251 . -1174) 12736) ((-127 . -527) 12669) ((-420 . -25) T) ((-420 . -21) T) ((-351 . -23) T) ((-171 . -627) 12435) ((-171 . -626) 12417) ((-176 . -23) T) ((-660 . -299) 12394) ((-533 . -34) T) ((-919 . -626) 12376) ((-89 . -1242) T) ((-857 . -626) 12358) ((-824 . -626) 12340) ((-785 . -626) 12322) ((-693 . -626) 12304) ((-246 . -664) 12137) ((-630 . -113) T) ((-1201 . -1125) T) ((-1197 . -1081) 11960) ((-216 . -1242) T) ((-1175 . -1242) T) 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((-531 . -1130) T) ((-500 . -841) T) ((-500 . -948) T) ((-371 . -1251) T) ((-365 . -1251) T) ((-357 . -1251) T) ((-330 . -1142) T) ((-327 . -1081) 193545) ((-324 . -1081) 193474) ((-108 . -1251) T) ((-644 . -634) 193455) ((-371 . -569) T) ((-220 . -948) T) ((-220 . -841) T) ((-327 . -661) 193365) ((-324 . -661) 193294) ((-365 . -569) T) ((-357 . -569) T) ((-658 . -111) 193273) ((-496 . -634) 193254) ((-108 . -569) T) ((-1197 . -1052) NIL) ((-679 . -738) 193224) ((-495 . -873) 193175) ((-221 . -634) 193156) ((-330 . -23) T) ((-67 . -1247) T) ((-1030 . -631) 193088) ((-1326 . -1182) T) ((-715 . -273) 193070) ((-715 . -233) 193052) ((-1321 . -21) T) ((-735 . -111) 193017) ((-1321 . -25) T) ((-665 . -34) T) ((-251 . -502) 193001) ((-1319 . -132) T) ((-1317 . -132) T) ((-1310 . -102) T) ((-1293 . -631) 192967) ((-1132 . -1128) 192951) ((-173 . -1130) T) ((-1289 . -1247) T) ((-1282 . -1247) T) ((-1282 . -1068) 192886) ((-1261 . -1247) T) ((-1261 . -910) NIL) ((-980 . -937) 192865) ((-1261 . -908) 192817) ((-1261 . -1068) 192783) ((-1241 . -527) 192750) ((-528 . -634) 192734) ((-1219 . -632) NIL) ((-1219 . -631) 192716) ((-1172 . -1153) 192661) ((-494 . -937) 192640) ((-1117 . -738) 192489) ((-1092 . -669) 192461) ((-980 . -669) 192350) ((-839 . -873) T) ((-803 . -738) 192179) ((-610 . -503) 192160) ((-598 . -503) 192141) ((-610 . -631) 192107) ((-598 . -631) 192073) ((-549 . -631) 192055) ((-592 . -1247) T) ((-549 . -632) 192036) ((-801 . -738) 191885) ((-1107 . -102) T) ((-641 . -667) 191857) ((-393 . -25) T) ((-393 . -21) T) ((-494 . -669) 191746) ((-474 . -738) 191717) ((-467 . -738) 191566) ((-1017 . -102) T) ((-1076 . -1240) 191495) ((-929 . -320) 191433) ((-758 . -102) T) ((-658 . -634) 191410) ((-118 . -667) 191340) ((-899 . -93) T) ((-735 . -634) 191294) ((-702 . -93) T) ((-544 . -25) T) ((-697 . -93) T) ((-685 . -631) 191276) ((-666 . -503) 191257) ((-666 . -631) 191210) ((-142 . -102) T) ((-44 . -132) T) ((-609 . -1247) T) ((-608 . -1247) T) ((-355 . -1088) T) ((-300 . -1142) T) ((-491 . -93) T) ((-420 . -238) 191161) ((-367 . -631) 191143) ((-364 . -631) 191125) ((-356 . -631) 191107) ((-274 . -632) 190855) ((-274 . -631) 190837) ((-254 . -631) 190819) ((-254 . -632) 190680) ((-139 . -93) T) ((-138 . -93) T) ((-134 . -93) T) ((-1171 . -631) 190662) ((-1150 . -661) 190649) ((-1150 . -1081) 190636) ((-840 . -747) T) ((-840 . -880) T) ((-615 . -299) 190613) ((-594 . -738) 190578) ((-492 . -632) NIL) ((-492 . -631) 190560) ((-531 . -738) 190505) ((-327 . -102) T) ((-324 . -102) T) ((-300 . -23) T) ((-153 . -132) T) ((-938 . -631) 190487) ((-938 . -632) 190469) ((-399 . -747) T) ((-895 . -1086) 190421) ((-895 . -111) 190359) ((-735 . -1079) T) ((-733 . -1273) 190343) ((-715 . -361) NIL) ((-115 . -102) T) ((-140 . -102) T) ((-137 . -102) T) ((-532 . -631) 190275) ((-391 . -816) T) ((-169 . -1247) T) ((-226 . -1130) T) ((-391 . -813) T) ((-59 . -632) 190236) ((-228 . -815) T) ((-228 . -812) T) ((-59 . -631) 190148) ((-228 . -747) T) ((-529 . -632) 190109) ((-529 . -631) 190021) ((-510 . -631) 189953) ((-509 . -632) 189914) ((-509 . -631) 189826) ((-1110 . -375) 189777) ((-40 . -424) 189754) ((-77 . -1247) T) ((-894 . -937) NIL) ((-371 . -340) 189738) ((-371 . -375) T) ((-365 . -340) 189722) ((-365 . -375) T) ((-357 . -340) 189706) ((-357 . -375) T) ((-327 . -295) 189685) ((-108 . -375) T) ((-70 . -1247) T) ((-660 . -1130) T) ((-1261 . -350) 189637) ((-894 . -669) 189582) ((-1261 . -389) 189534) ((-992 . -132) 189389) ((-836 . -132) 189260) ((-45 . -873) NIL) ((-986 . -672) 189244) ((-1117 . -174) 189155) ((-986 . -385) 189139) ((-1092 . -815) T) ((-1092 . -812) T) ((-895 . -634) 189037) ((-803 . -174) 188928) ((-801 . -174) 188839) ((-837 . -47) 188801) ((-1092 . -747) T) ((-338 . -502) 188785) ((-980 . -747) T) ((-1310 . -320) 188723) ((-1289 . -926) 188636) ((-467 . -174) 188547) ((-251 . -297) 188499) ((-1282 . -926) 188405) ((-1281 . -1086) 188240) ((-1261 . -926) 188073) ((-494 . -747) T) ((-1260 . -1086) 187881) ((-1241 . -301) 187860) ((-1216 . -1247) T) ((-1213 . -380) T) ((-1212 . -380) T) ((-1176 . -152) 187844) ((-1150 . -102) T) ((-1148 . -1130) T) ((-1110 . -23) T) ((-1110 . -1142) T) ((-1105 . -102) T) ((-1087 . -631) 187811) ((-1033 . -422) 187783) ((-955 . -983) T) ((-758 . -320) 187721) ((-75 . -1247) T) ((-685 . -394) 187693) ((-171 . -937) 187646) ((-30 . -983) T) ((-112 . -865) T) ((-1 . -631) 187628) ((-1029 . -920) 187549) ((-129 . -672) 187531) ((-50 . -638) 187515) ((-715 . -667) 187450) ((-608 . -926) 187363) ((-451 . -102) T) ((-129 . -385) 187345) ((-142 . -320) NIL) ((-895 . -1079) T) ((-854 . -870) 187324) ((-81 . -1247) T) ((-732 . -301) T) ((-40 . -1088) T) ((-594 . -174) T) ((-531 . -174) T) ((-524 . -631) 187306) ((-171 . -669) 187180) ((-520 . -631) 187162) ((-363 . -148) 187144) ((-363 . -146) T) ((-371 . -1142) T) ((-365 . -1142) T) ((-357 . -1142) T) ((-1034 . -318) T) ((-942 . -318) T) ((-895 . -249) T) ((-108 . -1142) T) ((-895 . -239) 187123) ((-1281 . -111) 186944) ((-1260 . -111) 186733) ((-251 . -1285) 186717) ((-577 . -869) T) ((-371 . -23) T) ((-366 . -361) T) ((-327 . -320) 186704) ((-324 . -320) 186645) ((-365 . -23) T) ((-330 . -132) T) ((-357 . -23) T) ((-1034 . -1052) T) ((-31 . -634) 186626) ((-108 . -23) T) ((-675 . -1081) 186610) ((-251 . -617) 186587) ((-660 . -738) 186571) ((-344 . -1130) T) ((-675 . -661) 186541) ((-1283 . -38) 186433) ((-1270 . -937) 186412) ((-112 . -1130) T) ((-837 . -1247) T) ((-426 . -1247) T) ((-1065 . -102) T) ((-1270 . -669) 186301) ((-894 . -815) NIL) ((-878 . -669) 186275) ((-894 . -812) NIL) ((-837 . -910) NIL) ((-894 . -747) T) ((-1117 . -527) 186148) ((-803 . -527) 186095) ((-801 . -527) 186047) ((-584 . -669) 186034) ((-837 . -1068) 185862) ((-467 . -527) 185805) ((-401 . -402) T) ((-1281 . -634) 185618) ((-1260 . -634) 185366) ((-60 . -1247) T) ((-639 . -870) 185345) ((-513 . -682) T) ((-1176 . -1006) 185314) ((-1054 . -667) 185251) ((-1033 . -465) T) ((-720 . -869) T) ((-523 . -813) T) ((-487 . -1086) 185086) ((-513 . -113) T) ((-355 . -1130) T) ((-324 . -1182) NIL) ((-300 . -132) T) ((-407 . -1130) T) ((-893 . -1088) T) ((-715 . -382) 185053) ((-366 . -667) 184983) ((-226 . -638) 184960) ((-338 . -297) 184912) ((-487 . -111) 184733) ((-1281 . -1079) T) ((-1260 . -1079) T) ((-837 . -389) 184717) ((-845 . -1247) T) ((-171 . -747) T) ((-1312 . -1247) T) ((-675 . -102) T) ((-1281 . -249) 184696) ((-1281 . -239) 184648) ((-1260 . -239) 184553) ((-1260 . -249) 184532) ((-1033 . -415) NIL) ((-691 . -659) 184480) ((-327 . -38) 184390) ((-324 . -38) 184319) ((-69 . -631) 184301) ((-330 . -506) 184267) ((-48 . -667) 184217) ((-1219 . -299) 184196) ((-1255 . -870) T) ((-1143 . -1142) 184174) ((-83 . -1247) T) ((-61 . -631) 184156) ((-887 . -873) T) ((-492 . -299) 184135) ((-1312 . -1068) 184112) ((-1194 . -1130) T) ((-1143 . -23) 183964) ((-837 . -926) 183900) ((-1270 . -747) T) ((-1132 . -1247) T) ((-487 . -634) 183726) ((-363 . -238) T) ((-1117 . -301) 183657) ((-994 . -1130) T) ((-917 . -102) T) ((-803 . -301) 183568) ((-338 . -19) 183552) ((-59 . -299) 183529) ((-801 . -301) 183460) ((-878 . -747) T) ((-118 . -869) NIL) ((-529 . -299) 183437) ((-338 . -617) 183414) ((-509 . -299) 183391) ((-467 . -301) 183322) ((-1065 . -320) 183173) ((-899 . -503) 183154) ((-899 . -631) 183120) ((-702 . -503) 183101) ((-584 . -747) T) ((-697 . -503) 183082) ((-702 . -631) 183032) ((-697 . -631) 182998) ((-683 . -631) 182980) ((-491 . -503) 182961) ((-491 . -631) 182927) ((-251 . -632) 182888) ((-251 . -503) 182865) ((-139 . -503) 182846) ((-138 . -503) 182827) ((-134 . -503) 182808) ((-251 . -631) 182700) ((-215 . -102) T) ((-139 . -631) 182666) ((-138 . -631) 182632) ((-134 . -631) 182598) ((-1177 . -34) T) ((-971 . -1247) T) ((-355 . -738) 182543) ((-691 . -25) T) ((-691 . -21) T) ((-1206 . -634) 182524) ((-342 . -1247) T) ((-487 . -1079) T) ((-653 . -430) 182489) ((-619 . -430) 182454) ((-1150 . -1182) T) ((-1282 . -318) 182433) ((-733 . -1081) 182256) ((-594 . -301) T) ((-531 . -301) T) ((-1261 . -318) 182235) ((-487 . -239) 182187) ((-487 . -249) 182166) ((-452 . -1247) T) ((-733 . -661) 181995) ((-1261 . -1052) NIL) ((-1110 . -132) T) ((-895 . -816) 181974) ((-145 . -102) T) ((-40 . -1130) T) ((-895 . -813) 181953) ((-665 . -1040) 181937) ((-593 . -1088) T) ((-577 . -1088) T) ((-508 . -1088) T) ((-420 . -465) T) ((-371 . -132) T) ((-327 . -413) 181921) ((-324 . -413) 181882) ((-365 . -132) T) ((-357 . -132) T) ((-1211 . -1130) T) ((-1150 . -38) 181869) ((-1124 . -631) 181836) ((-108 . -132) T) ((-982 . -1130) T) ((-949 . -1130) T) ((-792 . -1130) T) ((-693 . -1130) T) ((-722 . -148) T) ((-622 . -102) T) ((-117 . -148) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-1317 . -21) T) ((-1317 . -25) T) ((-685 . -1086) 181820) ((-544 . -870) T) ((-513 . -870) T) ((-377 . -1247) T) ((-367 . -1086) 181772) ((-364 . -1086) 181724) ((-356 . -1086) 181676) ((-259 . -1247) T) ((-258 . -1247) T) ((-274 . -1086) 181519) ((-254 . -1086) 181362) ((-685 . -111) 181341) ((-838 . -1251) 181320) ((-560 . -865) T) ((-327 . -928) 181286) ((-367 . -111) 181224) ((-364 . -111) 181162) ((-356 . -111) 181100) ((-274 . -111) 180929) ((-254 . -111) 180758) ((-324 . -928) NIL) ((-641 . -424) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-933 . -873) 180693) ((-130 . -682) T) ((-836 . -659) 180599) ((-838 . -569) 180578) ((-500 . -873) T) ((-259 . -1068) 180405) ((-258 . -1068) 180232) ((-127 . -120) 180216) ((-220 . -873) T) ((-938 . -1086) 180181) ((-733 . -102) T) ((-720 . -1088) T) ((-610 . -634) 180162) ((-598 . -634) 180143) ((-549 . -636) 180046) ((-355 . -174) T) ((-153 . -21) T) ((-153 . -25) T) ((-88 . -631) 180028) ((-938 . -111) 179984) ((-40 . -738) 179929) ((-893 . -1130) T) ((-685 . -634) 179906) ((-666 . -634) 179887) ((-367 . -634) 179824) ((-364 . -634) 179761) ((-356 . -634) 179698) ((-560 . -1130) T) ((-338 . -632) 179659) ((-338 . -631) 179571) ((-274 . -634) 179324) ((-254 . -634) 179109) ((-188 . -1247) T) ((-1260 . -813) 179062) ((-1260 . -816) 179015) ((-259 . -389) 178984) ((-258 . -389) 178953) ((-562 . -873) T) ((-675 . -38) 178923) ((-626 . -34) T) ((-495 . -1142) 178901) ((-488 . -34) T) ((-1143 . -132) 178772) ((-992 . -25) 178583) ((-938 . -634) 178533) ((-897 . -631) 178515) ((-217 . -865) T) ((-992 . -21) 178470) ((-836 . -25) 178303) ((-836 . -21) 178214) ((-1253 . -380) T) ((-641 . -1088) T) ((-1208 . -569) 178193) ((-1202 . -47) 178170) ((-367 . -1079) T) ((-364 . -1079) T) ((-495 . -23) 178022) ((-356 . -1079) T) ((-274 . -1079) T) ((-254 . -1079) T) ((-1155 . -47) 177994) ((-118 . -1088) T) ((-1064 . -669) 177968) ((-986 . -34) T) ((-367 . -239) 177947) ((-367 . -249) T) ((-364 . -239) 177926) ((-364 . -249) T) ((-356 . -239) 177905) ((-356 . -249) T) ((-274 . -337) 177877) ((-254 . -337) 177834) ((-274 . -239) 177813) ((-1187 . -152) 177797) ((-259 . -926) 177729) ((-258 . -926) 177661) ((-1172 . -920) 177582) ((-1112 . -870) T) ((-1264 . -1247) 177560) ((-427 . -1142) T) ((-1241 . -1032) 177526) ((-1084 . -23) T) ((-1054 . -869) T) ((-938 . -1079) T) ((-333 . -669) 177508) ((-722 . -238) T) ((-691 . -235) 177453) ((-1203 . -948) 177432) ((-1197 . -948) 177411) ((-1197 . -841) NIL) ((-1029 . -1081) 177307) ((-995 . -1247) T) ((-938 . -249) T) ((-838 . -375) 177286) ((-217 . -1130) T) ((-397 . -23) T) ((-128 . -1130) 177264) ((-122 . -1130) 177242) ((-938 . -239) T) ((-129 . -34) T) ((-391 . -669) 177207) ((-1029 . -661) 177155) ((-893 . -738) 177142) ((-1326 . -667) 177114) ((-1076 . -152) 177079) ((-1023 . -1247) T) ((-885 . -1247) T) ((-40 . -174) T) ((-715 . -424) 177061) ((-733 . -320) 177048) ((-857 . -669) 177008) ((-848 . -669) 176982) ((-330 . -25) T) ((-330 . -21) T) ((-679 . -297) 176961) ((-593 . -1130) T) ((-577 . -1130) T) ((-508 . -1130) T) ((-1202 . -1247) T) ((-251 . -299) 176938) ((-1155 . -1247) T) ((-877 . -1247) T) ((-324 . -273) 176899) ((-324 . -233) 176860) ((-1252 . -873) T) ((-1202 . -910) NIL) ((-55 . -1130) T) ((-1155 . -910) 176719) ((-130 . -870) T) ((-1202 . -1068) 176599) ((-1155 . -1068) 176482) ((-185 . -631) 176464) ((-877 . -1068) 176360) ((-803 . -297) 176287) ((-838 . -1142) T) ((-1064 . -747) T) ((-1076 . -1006) 176216) ((-615 . -672) 176200) ((-1033 . -920) 176107) ((-1029 . -102) T) ((-838 . -23) T) ((-733 . -1182) 176085) ((-715 . -1088) T) ((-615 . -385) 176069) ((-363 . -465) T) ((-355 . -301) T) ((-1298 . -1130) T) ((-255 . -1130) T) ((-412 . -102) T) ((-300 . -21) T) ((-300 . -25) T) ((-373 . -747) T) ((-731 . -1130) T) ((-720 . -1130) T) ((-373 . -486) T) ((-1241 . -631) 176051) ((-1202 . -389) 176035) ((-1155 . -389) 176019) ((-1054 . -424) 175981) ((-142 . -232) 175963) ((-391 . -815) T) ((-391 . -812) T) ((-893 . -174) T) ((-391 . -747) T) ((-732 . -631) 175945) ((-733 . -38) 175774) ((-1297 . -1295) 175758) ((-363 . -415) T) ((-1297 . -1130) 175708) ((-1220 . -1130) T) ((-593 . -738) 175695) ((-577 . -738) 175682) ((-508 . -738) 175647) ((-1283 . -667) 175537) ((-327 . -647) 175516) ((-857 . -747) T) ((-848 . -747) T) ((-1145 . -1247) T) ((-665 . -1247) T) ((-1110 . -659) 175464) ((-1202 . -926) 175407) ((-1155 . -926) 175391) ((-836 . -235) 175282) ((-683 . -1086) 175266) ((-108 . -659) 175248) ((-495 . -132) 175119) ((-1208 . -1142) T) ((-840 . -1247) T) ((-980 . -47) 175088) ((-641 . -1130) T) ((-683 . -111) 175067) ((-504 . -631) 175033) ((-338 . -299) 175010) ((-399 . -1247) T) ((-335 . -1247) T) ((-494 . -47) 174967) ((-1208 . -23) T) ((-118 . -1130) T) ((-103 . -102) 174917) ((-1309 . -1142) T) ((-561 . -870) T) ((-228 . -1247) T) ((-1084 . -132) T) ((-1054 . -1088) T) ((-1309 . -23) T) ((-1227 . -631) 174899) ((-840 . -1068) 174883) ((-1150 . -849) T) ((-1033 . -745) 174855) ((-1135 . -1130) T) ((-720 . -738) 174820) ((-599 . -631) 174802) ((-399 . -1068) 174786) ((-366 . -1088) T) ((-397 . -132) T) ((-335 . -1068) 174770) ((-1110 . -21) T) ((-1110 . -25) T) ((-1034 . -841) T) ((-228 . -910) 174752) ((-1034 . -948) T) ((-91 . -34) T) ((-1029 . -320) 174717) ((-942 . -948) T) ((-899 . -634) 174698) ((-735 . -669) 174658) ((-500 . -1251) T) ((-702 . -634) 174639) ((-697 . -634) 174620) ((-658 . -669) 174604) ((-220 . -1251) T) ((-420 . -920) 174525) ((-228 . -1068) 174485) ((-40 . -301) T) ((-500 . -569) T) ((-491 . -634) 174466) ((-371 . -25) T) ((-327 . -667) 174121) ((-324 . -667) 174035) ((-371 . -21) T) ((-365 . -25) T) ((-365 . -21) T) ((-220 . -569) T) ((-357 . -25) T) ((-357 . -21) T) ((-330 . -235) 173981) ((-251 . -634) 173958) ((-139 . -634) 173939) ((-138 . -634) 173920) ((-134 . -634) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-593 . -174) T) ((-577 . -174) T) ((-508 . -174) T) ((-1092 . -1247) T) ((-980 . -1247) T) ((-734 . -1247) T) ((-660 . -297) 173868) ((-679 . -631) 173850) ((-494 . -1247) T) ((-758 . -757) 173834) ((-348 . -631) 173816) ((-68 . -395) T) ((-68 . -408) T) ((-1132 . -107) 173800) ((-1092 . -910) 173782) ((-980 . -910) 173707) ((-674 . -1142) T) ((-641 . -738) 173694) ((-494 . -910) NIL) ((-1176 . -102) T) ((-1124 . -636) 173678) ((-1092 . -1068) 173660) ((-97 . -631) 173642) ((-490 . -148) T) ((-980 . -1068) 173522) ((-118 . -738) 173467) ((-733 . -928) 173374) ((-674 . -23) T) ((-494 . -1068) 173250) ((-1117 . -632) NIL) ((-1117 . -631) 173232) ((-803 . -632) NIL) ((-803 . -631) 173193) ((-801 . -632) 172827) ((-801 . -631) 172741) ((-1143 . -659) 172647) ((-820 . -873) 172626) ((-474 . -631) 172608) ((-467 . -631) 172590) ((-467 . -632) 172451) ((-1065 . -232) 172397) ((-895 . -937) 172376) ((-127 . -34) T) ((-838 . -132) T) ((-670 . -631) 172358) ((-591 . -102) T) ((-367 . -1316) 172342) ((-364 . -1316) 172326) ((-356 . -1316) 172310) ((-122 . -527) 172243) ((-128 . -527) 172176) ((-524 . -813) T) ((-524 . -816) T) ((-523 . -815) T) ((-103 . -320) 172114) ((-225 . -102) 172064) ((-720 . -174) T) ((-715 . -1130) T) ((-895 . -669) 171980) ((-65 . -396) T) ((-285 . -631) 171962) ((-65 . -408) T) ((-980 . -389) 171946) ((-893 . -301) T) ((-50 . -631) 171928) ((-1150 . -667) 171900) ((-1029 . -38) 171848) ((-625 . -1130) T) ((-620 . -1130) T) ((-594 . -631) 171830) ((-494 . -389) 171814) ((-594 . -632) 171796) ((-531 . -631) 171778) ((-938 . -1316) 171765) ((-894 . -1247) T) ((-722 . -465) T) ((-508 . -527) 171731) ((-1308 . -1247) T) ((-1307 . -1247) T) ((-500 . -375) T) ((-367 . -380) 171710) ((-364 . -380) 171689) ((-356 . -380) 171668) ((-735 . -747) T) ((-220 . -375) T) ((-117 . -465) T) ((-1320 . -1311) 171652) ((-894 . -908) 171629) ((-894 . -910) NIL) ((-992 . -870) 171528) ((-836 . -870) 171479) ((-1254 . -102) T) ((-675 . -677) 171463) ((-1233 . -34) T) ((-173 . -631) 171445) ((-1143 . -25) 171278) ((-1143 . -21) 171189) ((-894 . -1068) 171166) ((-980 . -926) 171147) ((-1270 . -47) 171124) ((-938 . -380) T) ((-606 . -873) T) ((-59 . -672) 171108) ((-529 . -672) 171092) ((-494 . -926) 171069) ((-71 . -454) T) ((-71 . -408) T) ((-509 . -672) 171053) ((-59 . -385) 171037) ((-641 . -174) T) ((-529 . -385) 171021) ((-509 . -385) 171005) ((-559 . -1247) T) ((-848 . -729) 170989) ((-1202 . -318) 170968) ((-1208 . -132) T) ((-1172 . -1081) 170952) ((-118 . -174) T) ((-1172 . -661) 170884) ((-1176 . -320) 170822) ((-171 . -1247) T) ((-1309 . -132) T) ((-1282 . -948) 170801) ((-1261 . -948) 170780) ((-1261 . -841) NIL) ((-889 . -1081) 170750) ((-653 . -765) 170734) ((-619 . -765) 170718) ((-1260 . -937) 170671) ((-1054 . -1130) T) ((-933 . -1142) T) ((-889 . -661) 170641) ((-715 . -738) 170591) ((-924 . -1247) T) ((-894 . -389) 170568) ((-894 . -350) 170545) ((-862 . -1247) T) ((-829 . -1247) T) ((-171 . -908) 170529) ((-171 . -910) 170454) ((-790 . -1247) T) ((-698 . -1247) T) ((-1297 . -527) 170387) ((-1281 . -669) 170284) ((-1110 . -235) 170157) ((-500 . -1142) T) ((-366 . -1130) T) ((-220 . -1142) T) ((-76 . -454) T) ((-76 . -408) T) ((-171 . -1068) 170053) ((-305 . -920) 170010) ((-330 . -870) T) ((-1260 . -669) 169818) ((-895 . -815) 169797) ((-895 . -812) 169776) ((-895 . -747) T) ((-500 . -23) T) ((-371 . -235) 169749) ((-365 . -235) 169722) ((-357 . -235) 169695) ((-176 . -465) T) ((-86 . -454) T) ((-225 . -320) 169633) ((-86 . -408) T) ((-226 . -631) 169615) ((-108 . -235) 169602) ((-220 . -23) T) ((-1321 . -1314) 169581) ((-698 . -1068) 169565) ((-593 . -301) T) ((-577 . -301) T) ((-508 . -301) T) ((-1270 . -1247) T) ((-137 . -483) 169520) ((-878 . -1247) T) ((-675 . -667) 169479) ((-48 . -1130) T) ((-733 . -273) 169463) ((-733 . -233) 169447) ((-894 . -926) NIL) ((-584 . -1247) T) ((-1270 . -910) NIL) ((-913 . -102) T) ((-909 . -102) T) ((-660 . -631) 169429) ((-401 . -1130) T) ((-171 . -389) 169413) ((-171 . -350) 169397) ((-1270 . -1068) 169277) ((-878 . -1068) 169173) ((-1172 . -102) T) ((-1029 . -928) 169096) ((-683 . -813) 169075) ((-674 . -132) T) ((-683 . -816) 169054) ((-118 . -527) 168962) ((-584 . -1068) 168944) ((-305 . -1304) 168914) ((-1197 . -873) NIL) ((-889 . -102) T) ((-991 . -569) 168893) ((-1241 . -1086) 168776) ((-1033 . -1081) 168721) ((-495 . -659) 168627) ((-932 . -1130) T) ((-1054 . -738) 168564) 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T) ((-722 . -400) T) ((-722 . -144) T) ((-1320 . -102) T) ((-1228 . -1247) T) ((-1227 . -634) 166423) ((-1118 . -1247) T) ((-1117 . -1086) 166266) ((-1106 . -1247) T) ((-274 . -937) 166245) ((-254 . -937) 166224) ((-803 . -1086) 166047) ((-801 . -1086) 165890) ((-626 . -1247) T) ((-1194 . -631) 165872) ((-1117 . -111) 165701) ((-1076 . -102) T) ((-488 . -1247) T) ((-474 . -1086) 165672) ((-467 . -1086) 165515) ((-685 . -669) 165499) ((-894 . -318) T) ((-803 . -111) 165308) ((-801 . -111) 165137) ((-367 . -669) 165089) ((-364 . -669) 165041) ((-356 . -669) 164993) ((-274 . -669) 164882) ((-254 . -669) 164771) ((-1188 . -870) T) ((-1118 . -1068) 164755) ((-1106 . -1068) 164732) ((-1034 . -873) T) ((-1030 . -34) T) ((-474 . -111) 164693) ((-467 . -111) 164522) ((-1001 . -873) T) ((-994 . -631) 164504) ((-991 . -1142) T) ((-986 . -1247) T) ((-127 . -1040) 164488) ((-871 . -1247) T) ((-894 . -1052) NIL) ((-756 . -1142) T) ((-736 . -1142) T) ((-679 . -634) 164406) ((-1297 . -502) 164390) ((-1214 . -1247) T) ((-1213 . -1247) T) ((-1172 . -38) 164350) ((-991 . -23) T) ((-938 . -669) 164315) ((-888 . -1130) T) ((-864 . -102) T) ((-838 . -21) T) ((-653 . -1081) 164299) ((-619 . -1081) 164283) ((-838 . -25) T) ((-756 . -23) T) ((-736 . -23) T) ((-653 . -661) 164267) ((-110 . -682) T) ((-619 . -661) 164251) ((-594 . -1086) 164216) ((-531 . -1086) 164161) ((-230 . -57) 164119) ((-466 . -23) T) ((-420 . -102) T) ((-1212 . -1247) T) ((-271 . -102) T) ((-110 . -113) T) ((-715 . -301) T) ((-889 . -38) 164089) ((-1117 . -634) 163825) ((-594 . -111) 163781) ((-531 . -111) 163710) ((-431 . -1142) T) ((-327 . -1088) 163600) ((-324 . -1088) T) ((-129 . -1247) T) ((-131 . -1247) T) ((-803 . -634) 163348) ((-801 . -634) 163114) ((-679 . -1079) T) ((-1326 . -1130) T) ((-467 . -634) 162899) ((-171 . -318) 162830) ((-431 . -23) T) ((-40 . -631) 162812) ((-40 . -632) 162796) ((-108 . -1022) 162778) ((-117 . -892) 162762) ((-670 . -634) 162746) ((-48 . -527) 162712) ((-1233 . -1040) 162696) 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. -747) T) ((-356 . -747) T) ((-274 . -747) T) ((-254 . -747) T) ((-391 . -1247) T) ((-1309 . -21) T) ((-1076 . -320) 161767) ((-1309 . -25) T) ((-929 . -1130) 161745) ((-839 . -235) 161732) ((-50 . -1079) T) ((-1204 . -569) 161711) ((-1203 . -1251) 161690) ((-1203 . -569) 161641) ((-1197 . -1251) 161620) ((-1197 . -569) 161571) ((-1054 . -301) T) ((-594 . -1079) T) ((-531 . -1079) T) ((-1033 . -38) 161516) ((-373 . -1068) 161500) ((-333 . -1068) 161484) ((-1029 . -667) 161407) ((-391 . -910) 161389) ((-857 . -1247) T) ((-848 . -1247) T) ((-846 . -1247) T) ((-820 . -1142) T) ((-938 . -747) T) ((-594 . -249) T) ((-594 . -239) T) ((-531 . -239) T) ((-531 . -249) T) ((-1156 . -569) 161368) ((-366 . -301) T) ((-668 . -716) 161352) ((-391 . -1068) 161312) ((-305 . -1081) 161233) ((-351 . -920) 161212) ((-1150 . -1088) T) ((-103 . -126) 161196) ((-305 . -661) 161138) ((-820 . -23) T) ((-1319 . -1314) 161114) ((-1317 . -1314) 161093) ((-1297 . -297) 161045) ((-1283 . -1130) T) ((-420 . -320) 161010) ((-1172 . -928) 160933) ((-893 . -631) 160915) ((-857 . -1068) 160884) ((-660 . -1086) 160868) ((-205 . -808) T) ((-204 . -808) T) ((-203 . -808) T) ((-202 . -808) T) ((-201 . -808) T) ((-200 . -808) T) ((-199 . -808) T) ((-198 . -808) T) ((-197 . -808) T) ((-196 . -808) T) ((-560 . -631) 160850) ((-508 . -1032) T) ((-284 . -860) T) ((-283 . -860) T) ((-282 . -860) T) ((-281 . -860) T) ((-48 . -301) T) ((-280 . -860) T) ((-279 . -860) T) ((-278 . -860) T) ((-195 . -808) T) ((-660 . -111) 160829) ((-630 . -870) T) ((-675 . -424) 160813) ((-691 . -238) 160764) ((-226 . -634) 160726) ((-110 . -870) T) ((-674 . -21) T) ((-674 . -25) T) ((-1320 . -38) 160696) ((-118 . -297) 160647) ((-1297 . -19) 160631) ((-1261 . -873) NIL) ((-1297 . -617) 160608) ((-1310 . -1130) T) ((-363 . -1081) 160553) ((-1107 . -1130) T) ((-1017 . -1130) T) ((-991 . -132) T) ((-838 . -235) 160540) ((-758 . -1130) T) ((-363 . -661) 160485) ((-756 . -132) T) ((-736 . -132) T) ((-524 . -814) T) ((-524 . -815) T) 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159403) ((-228 . -417) T) ((-683 . -669) 159387) ((-55 . -631) 159369) ((-1202 . -948) 159348) ((-752 . -1142) T) ((-656 . -102) T) ((-528 . -1247) T) ((-523 . -1247) T) ((-521 . -1247) T) ((-363 . -102) T) ((-1246 . -1113) T) ((-1150 . -865) T) ((-839 . -870) T) ((-752 . -23) T) ((-355 . -1086) 159293) ((-1177 . -107) 159277) ((-1298 . -631) 159259) ((-1204 . -23) T) ((-1204 . -1142) T) ((-1203 . -1142) T) ((-658 . -1247) T) ((-1203 . -23) T) ((-1197 . -1142) T) ((-1197 . -23) T) ((-1172 . -273) 159243) ((-528 . -1068) 159227) ((-1172 . -233) 159211) ((-1156 . -1142) T) ((-355 . -111) 159140) ((-1034 . -1251) T) ((-127 . -1247) T) ((-942 . -1251) T) ((-1156 . -23) T) ((-1105 . -1130) T) ((-715 . -297) NIL) ((-735 . -1247) T) ((-1034 . -569) T) ((-942 . -569) T) ((-836 . -238) 159037) ((-624 . -682) T) ((-623 . -682) T) ((-256 . -1247) T) ((-189 . -1247) T) ((-163 . -1247) T) ((-158 . -1247) T) ((-255 . -631) 159019) ((-621 . -682) T) ((-820 . -132) T) ((-731 . -631) 159001) ((-327 . -738) 158911) ((-324 . -738) 158840) ((-720 . -631) 158822) ((-720 . -632) 158767) ((-420 . -413) 158751) ((-451 . -1130) T) ((-500 . -25) T) ((-500 . -21) T) ((-1150 . -1130) T) ((-220 . -25) T) ((-220 . -21) T) ((-733 . -424) 158735) ((-735 . -1068) 158704) ((-1297 . -631) 158616) ((-1297 . -632) 158577) ((-1283 . -174) T) ((-1220 . -631) 158559) ((-251 . -34) T) ((-355 . -634) 158489) ((-407 . -634) 158471) ((-954 . -1004) T) ((-1233 . -1247) T) ((-683 . -812) 158450) ((-683 . -815) 158429) ((-411 . -408) T) ((-536 . -102) 158379) ((-1253 . -1247) T) ((-1065 . -1130) T) ((-420 . -928) 158302) ((-225 . -1025) 158286) ((-859 . -1247) T) ((-517 . -102) T) ((-641 . -631) 158268) ((-45 . -870) NIL) ((-641 . -632) 158245) ((-1065 . -628) 158220) ((-929 . -527) 158153) ((-330 . -238) 158105) ((-355 . -1079) T) ((-118 . -632) NIL) ((-118 . -631) 158087) ((-895 . -1247) T) ((-691 . -430) 158071) ((-691 . -1153) 158016) ((-513 . -152) 157998) ((-355 . -239) T) ((-355 . -249) T) ((-40 . -1086) 157943) ((-895 . -908) 157927) ((-895 . -910) 157852) ((-733 . -1088) T) ((-715 . -1032) NIL) ((-1281 . -47) 157822) ((-1260 . -47) 157799) ((-1171 . -1040) 157770) ((-1150 . -738) 157757) ((-3 . |UnionCategory|) T) ((-1135 . -631) 157739) ((-1110 . -148) 157718) ((-1110 . -146) 157669) ((-1034 . -375) T) ((-994 . -634) 157653) ((-228 . -948) T) ((-40 . -111) 157582) ((-895 . -1068) 157446) ((-1033 . -233) 157423) ((-1033 . -273) 157400) ((-722 . -1081) 157387) ((-942 . -375) T) ((-722 . -661) 157374) ((-330 . -1235) 157340) ((-391 . -318) T) ((-330 . -1232) 157306) ((-327 . -174) 157285) ((-324 . -174) T) ((-626 . -1223) 157261) ((-594 . -1316) 157248) ((-531 . -1316) 157225) ((-117 . -1081) 157212) ((-371 . -148) 157191) ((-371 . -146) 157142) ((-365 . -148) 157121) ((-365 . -146) 157072) ((-357 . -148) 157051) ((-117 . -661) 157038) ((-357 . -146) 156989) ((-330 . -35) 156955) ((-488 . -1223) 156934) ((0 . |EnumerationCategory|) T) ((-330 . -95) 156900) ((-391 . -1052) T) ((-108 . 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T) ((-62 . -631) 142043) ((-1110 . -920) 141912) ((-1054 . -813) T) ((-1054 . -816) T) ((-1289 . -25) T) ((-1289 . -21) T) ((-1282 . -21) T) ((-1282 . -25) T) ((-893 . -669) 141899) ((-1261 . -21) T) ((-1261 . -25) T) ((-1057 . -152) 141883) ((-1034 . -235) 141870) ((-895 . -841) 141849) ((-895 . -948) T) ((-733 . -297) 141776) ((-609 . -21) T) ((-351 . -667) 141735) ((-108 . -920) NIL) ((-609 . -25) T) ((-608 . -21) T) ((-176 . -667) 141652) ((-40 . -747) T) ((-225 . -527) 141585) ((-608 . -25) T) ((-489 . -152) 141569) ((-476 . -152) 141553) ((-185 . -1247) T) ((-949 . -815) T) ((-949 . -747) T) ((-792 . -814) T) ((-792 . -815) T) ((-519 . -1130) T) ((-515 . -1130) T) ((-792 . -747) T) ((-228 . -375) T) ((-1319 . -1081) 141537) ((-1317 . -1081) 141521) ((-1319 . -661) 141491) ((-1187 . -1130) 141469) ((-894 . -1251) T) ((-1317 . -661) 141439) ((-1118 . -873) T) ((-675 . -631) 141421) ((-894 . -569) T) ((-715 . -380) NIL) ((-44 . -1081) 141405) ((-1326 . -634) 141387) ((-1320 . -1130) T) ((-691 . -102) T) ((-371 . -1304) 141371) ((-365 . -1304) 141355) ((-44 . -661) 141339) ((-357 . -1304) 141323) ((-561 . -102) T) ((-1241 . -1247) T) ((-533 . -870) 141302) ((-732 . -1247) T) ((-986 . -873) 141281) ((-871 . -873) T) ((-500 . -238) T) ((-220 . -238) T) ((-1076 . -1130) T) ((-838 . -465) 141260) ((-153 . -1081) 141244) ((-1076 . -1101) 141173) ((-1057 . -1006) 141142) ((-840 . -1142) T) ((-1033 . -738) 141087) ((-153 . -661) 141071) ((-399 . -1142) T) ((-489 . -1006) 141040) ((-476 . -1006) 141009) ((-1213 . -873) T) ((-110 . -152) 140991) ((-73 . -631) 140973) ((-917 . -631) 140955) ((-1212 . -873) T) ((-1110 . -745) 140934) ((-1326 . -1079) T) ((-837 . -659) 140882) ((-305 . -1088) 140824) ((-171 . -1251) 140729) ((-228 . -1142) T) ((-335 . -23) T) ((-1197 . -1022) 140681) ((-1283 . -1086) 140586) ((-864 . -1130) T) ((-129 . -873) T) ((-1156 . -761) 140565) ((-1281 . -948) 140544) ((-1260 . -948) 140523) ((-893 . -747) T) ((-171 . -569) 140434) ((-593 . -669) 140421) ((-577 . -669) 140393) ((-420 . -1130) T) ((-271 . -1130) T) ((-215 . -631) 140375) ((-508 . -669) 140325) ((-228 . -23) T) ((-1260 . -841) 140278) ((-1319 . -102) T) ((-504 . -1247) T) ((-366 . -1316) 140255) ((-1317 . -102) T) ((-1283 . -111) 140147) ((-1143 . -920) 140014) ((-836 . -1081) 139915) ((-836 . -661) 139837) ((-145 . -631) 139819) ((-1023 . -132) T) ((-44 . -102) T) ((-246 . -870) 139770) ((-599 . -1247) T) ((-1270 . -1251) 139749) ((-103 . -502) 139733) ((-1320 . -738) 139703) ((-1117 . -47) 139664) ((-1092 . -1142) T) ((-980 . -1142) T) ((-128 . -34) T) ((-122 . -34) T) ((-1270 . -569) 139575) ((-803 . -47) 139552) ((-801 . -47) 139524) ((-1227 . -1247) T) ((-1202 . -132) T) ((-366 . -380) T) ((-494 . -1142) T) ((-1155 . -132) T) ((-894 . -375) T) ((-467 . -47) 139503) ((-877 . -132) T) ((-333 . -873) 139482) ((-153 . -102) T) ((-1092 . -23) T) ((-980 . -23) T) ((-584 . -569) T) ((-837 . -25) T) ((-837 . -21) T) ((-1172 . -527) 139415) ((-622 . -631) 139382) 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137338) ((-593 . -747) T) ((-577 . -815) T) ((-171 . -375) 137289) ((-577 . -812) T) ((-577 . -747) T) ((-508 . -747) T) ((-803 . -1247) T) ((-801 . -1247) T) ((-1176 . -502) 137273) ((-474 . -1247) T) ((-467 . -1247) T) ((-1319 . -1318) 137249) ((-1117 . -910) NIL) ((-894 . -1142) T) ((-118 . -937) NIL) ((-1317 . -1318) 137228) ((-670 . -1247) T) ((-803 . -910) NIL) ((-801 . -910) 137087) ((-1312 . -25) T) ((-1312 . -21) T) ((-1244 . -102) 137065) ((-1136 . -408) T) ((-641 . -669) 137052) ((-467 . -910) NIL) ((-696 . -102) 137002) ((-1117 . -1068) 136829) ((-894 . -23) T) ((-803 . -1068) 136688) ((-801 . -1068) 136545) ((-118 . -669) 136490) ((-467 . -1068) 136366) ((-285 . -1247) T) ((-327 . -634) 135930) ((-324 . -634) 135813) ((-50 . -1247) T) ((-403 . -667) 135782) ((-670 . -1068) 135766) ((-645 . -102) T) ((-594 . -1247) T) ((-531 . -1247) T) ((-225 . -502) 135750) ((-1297 . -34) T) ((-639 . -667) 135709) ((-300 . -1081) 135696) ((-137 . -634) 135680) ((-300 . -661) 135667) 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-926) 134264) ((-1319 . -38) 134234) ((-1317 . -38) 134204) ((-1270 . -1142) T) ((-878 . -1142) T) ((-467 . -926) 134181) ((-881 . -1130) T) ((-1270 . -23) T) ((-1150 . -634) 134153) ((-1092 . -132) T) ((-878 . -23) T) ((-584 . -1142) T) ((-641 . -747) T) ((-523 . -873) T) ((-367 . -948) T) ((-364 . -948) T) ((-300 . -102) T) ((-356 . -948) T) ((-1000 . -1113) T) ((-980 . -132) T) ((-837 . -235) 134098) ((-118 . -815) NIL) ((-118 . -812) NIL) ((-118 . -747) T) ((-1076 . -527) 133999) ((-715 . -937) NIL) ((-584 . -23) T) ((-494 . -132) T) ((-431 . -238) 133950) ((-696 . -320) 133888) ((-226 . -1247) T) ((-656 . -1130) T) ((-653 . -782) T) ((-619 . -782) T) ((-1261 . -870) NIL) ((-1110 . -1081) 133798) ((-1033 . -301) T) ((-715 . -669) 133748) ((-259 . -25) T) ((-363 . -1130) T) ((-259 . -21) T) ((-258 . -25) T) ((-258 . -21) T) ((-153 . -38) 133732) ((-2 . -102) T) ((-938 . -948) T) ((-1110 . -661) 133600) ((-495 . -1304) 133570) ((-1150 . -1079) T) ((-732 . -318) T) ((-722 . -1088) T) 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132274) ((-536 . -1130) 132252) ((-371 . -102) T) ((-365 . -102) T) ((-357 . -102) T) ((-108 . -102) T) ((-517 . -1130) T) ((-366 . -669) 132197) ((-1202 . -659) 132145) ((-1155 . -659) 132093) ((-397 . -522) 132072) ((-854 . -869) 132051) ((-715 . -747) T) ((-391 . -1251) T) ((-344 . -1247) T) ((-1261 . -1022) 132003) ((-351 . -1088) T) ((-112 . -1247) T) ((-176 . -1088) T) ((-103 . -631) 131935) ((-1204 . -146) 131914) ((-1204 . -148) 131893) ((-391 . -569) T) ((-1203 . -148) 131872) ((-1203 . -146) 131851) ((-1197 . -146) 131758) ((-420 . -301) T) ((-1197 . -148) 131665) ((-1156 . -148) 131644) ((-1156 . -146) 131623) ((-330 . -38) 131464) ((-171 . -132) T) ((-324 . -816) NIL) ((-324 . -813) NIL) ((-675 . -1079) T) ((-48 . -669) 131414) ((-1143 . -1081) 131315) ((-917 . -634) 131292) ((-1143 . -661) 131214) ((-1196 . -102) T) ((-1024 . -102) T) ((-1023 . -21) T) ((-128 . -1040) 131198) ((-122 . -1040) 131182) ((-1023 . -25) T) ((-929 . -120) 131166) ((-1188 . -102) T) ((-1270 . -132) T) ((-1260 . -873) 131065) ((-1202 . -25) T) ((-1202 . -21) T) ((-1189 . -320) 130860) ((-355 . -1247) T) ((-1155 . -25) T) ((-878 . -132) T) ((-407 . -1247) T) ((-1155 . -21) T) ((-877 . -25) T) ((-877 . -21) T) ((-803 . -318) 130839) ((-1187 . -502) 130823) ((-1180 . -152) 130773) ((-1176 . -631) 130735) ((-668 . -102) 130685) ((-650 . -102) T) ((-1176 . -632) 130646) ((-584 . -132) T) ((-639 . -869) 130625) ((-1054 . -812) T) ((-1054 . -815) T) ((-1054 . -747) T) ((-836 . -928) 130494) ((-733 . -1086) 130317) ((-615 . -873) 130296) ((-497 . -320) 130234) ((-466 . -430) 130204) ((-363 . -174) T) ((-300 . -38) 130191) ((-259 . -235) 130082) ((-258 . -235) 129973) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-279 . -102) T) ((-355 . -1068) 129950) ((-278 . -102) T) ((-214 . -102) T) ((-213 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-205 . -102) T) ((-204 . -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) ((-733 . -111) 129759) ((-366 . -747) T) ((-691 . -273) 129743) ((-691 . -233) 129727) ((-594 . -318) T) ((-531 . -318) T) ((-305 . -527) 129676) ((-1194 . -1247) T) ((-108 . -320) NIL) ((-72 . -408) T) ((-1143 . -102) 129408) ((-854 . -424) 129392) ((-1150 . -816) T) ((-1150 . -813) T) ((-722 . -1130) T) ((-591 . -631) 129374) ((-391 . -375) T) ((-171 . -506) 129352) ((-225 . -631) 129284) ((-135 . -1130) T) ((-117 . -1130) T) ((-994 . -1247) T) ((-48 . -747) T) ((-1076 . -502) 129249) ((-142 . -438) 129231) ((-142 . -380) T) ((-1057 . -102) T) ((-525 . -522) 129210) ((-733 . -634) 128966) ((-1254 . -631) 128948) ((-1211 . -1247) T) ((-1211 . -1068) 128884) ((-1204 . -238) 128843) ((-489 . -102) T) ((-476 . -102) T) ((-1203 . -238) 128795) ((-1197 . -238) 128618) ((-1064 . -1142) T) ((-330 . -928) 128524) ((-1206 . -873) T) ((-1204 . -35) 128490) 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127374) ((-494 . -659) 127322) ((-40 . -1068) 127210) ((-733 . -239) T) ((-722 . -738) 127197) ((-351 . -1130) T) ((-176 . -1130) T) ((-342 . -870) T) ((-431 . -465) 127147) ((-391 . -23) T) ((-371 . -38) 127112) ((-365 . -38) 127077) ((-357 . -38) 127042) ((-80 . -454) T) ((-80 . -408) T) ((-228 . -25) T) ((-228 . -21) T) ((-857 . -1142) T) ((-108 . -38) 126992) ((-848 . -1142) T) ((-795 . -1130) T) ((-117 . -738) 126979) ((-693 . -1068) 126963) ((-630 . -102) T) ((-857 . -23) T) ((-848 . -23) T) ((-1187 . -297) 126915) ((-1143 . -320) 126853) ((-495 . -1081) 126754) ((-1132 . -241) 126738) ((-64 . -409) T) ((-64 . -408) T) ((-1181 . -102) T) ((-110 . -102) T) ((-495 . -661) 126660) ((-40 . -389) 126637) ((-96 . -102) T) ((-674 . -875) 126621) ((-1202 . -235) 126608) ((-1165 . -1113) T) ((-1092 . -21) T) ((-1092 . -25) T) ((-1084 . -1081) 126592) ((-836 . -273) 126561) ((-836 . -233) 126530) ((-980 . -25) T) ((-980 . -21) T) ((-1150 . -380) T) ((-1084 . -661) 126472) ((-639 . -1088) T) ((-1057 . -320) 126410) ((-913 . -631) 126392) ((-691 . -667) 126351) ((-494 . -25) T) ((-494 . -21) T) ((-397 . -1081) 126335) ((-909 . -631) 126317) ((-893 . -1247) T) ((-536 . -527) 126250) ((-259 . -870) 126201) ((-258 . -870) 126152) ((-397 . -661) 126122) ((-894 . -659) 126099) ((-489 . -320) 126037) ((-560 . -1247) T) ((-476 . -320) 125975) ((-363 . -301) T) ((-1187 . -1285) 125959) ((-1172 . -631) 125921) ((-1172 . -632) 125882) ((-1170 . -102) T) ((-1029 . -1086) 125778) ((-40 . -926) 125730) ((-1187 . -617) 125707) ((-1326 . -669) 125694) ((-1093 . -152) 125640) ((-500 . -920) NIL) ((-889 . -503) 125617) ((-1029 . -111) 125499) ((-895 . -1251) T) ((-220 . -920) NIL) ((-351 . -738) 125483) ((-889 . -631) 125445) ((-176 . -738) 125377) ((-895 . -569) T) ((-420 . -297) 125335) ((-246 . -238) 125232) ((-108 . -413) 125214) ((-84 . -396) T) ((-84 . -408) T) ((-722 . -174) T) ((-635 . -631) 125196) ((-99 . -747) T) ((-495 . -102) 124928) ((-99 . -486) T) ((-117 . -174) T) 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123949) ((-1289 . -148) 123928) ((-1282 . -148) 123907) ((-854 . -1130) T) ((-1282 . -146) 123886) ((-1281 . -1251) 123865) ((-1261 . -146) 123772) ((-1261 . -148) 123679) ((-1260 . -1251) 123658) ((-391 . -132) T) ((-228 . -235) 123645) ((-176 . -174) T) ((-577 . -910) 123627) ((0 . -1130) T) ((-171 . -21) T) ((-171 . -25) T) ((-55 . -1247) T) ((-49 . -1130) T) ((-1283 . -669) 123532) ((-1281 . -569) 123483) ((-1260 . -569) 123434) ((-735 . -1142) T) ((-658 . -23) T) ((-577 . -1068) 123416) ((-608 . -148) 123395) ((-608 . -146) 123374) ((-508 . -1068) 123317) ((-1165 . -1167) T) ((-87 . -396) T) ((-87 . -408) T) ((-895 . -375) T) ((-857 . -132) T) ((-848 . -132) T) ((-992 . -667) 123261) ((-735 . -23) T) ((-519 . -631) 123211) ((-515 . -631) 123193) ((-836 . -667) 122972) ((-1321 . -1088) T) ((-391 . -1090) T) ((-1056 . -1130) 122950) ((-55 . -1068) 122932) ((-929 . -34) T) ((-495 . -320) 122870) ((-605 . -102) T) ((-1187 . -632) 122831) ((-1187 . -631) 122763) ((-1208 . -1081) 122646) ((-45 . -102) T) ((-838 . -102) T) ((-1208 . -661) 122543) ((-1298 . -1247) T) ((-1270 . -25) T) ((-1270 . -21) T) ((-1092 . -235) 122530) ((-878 . -25) T) ((-524 . -873) T) ((-255 . -1247) T) ((-44 . -379) 122514) ((-878 . -21) T) ((-752 . -465) 122465) ((-1320 . -631) 122447) ((-731 . -1247) T) ((-720 . -1247) T) ((-1309 . -1081) 122417) ((-1084 . -320) 122355) ((-692 . -1113) T) ((-618 . -1113) T) ((-403 . -1130) T) ((-584 . -25) T) ((-584 . -21) T) ((-182 . -1113) T) ((-162 . -1113) T) ((-157 . -1113) T) ((-155 . -1113) T) ((-1309 . -661) 122325) ((-639 . -1130) T) ((-720 . -910) 122307) ((-1297 . -1247) T) ((-230 . -320) 122245) ((-145 . -380) T) ((-1220 . -1247) T) ((-1076 . -632) 122187) ((-1076 . -631) 122130) ((-324 . -937) NIL) ((-1255 . -865) T) ((-1143 . -928) 121999) ((-720 . -1068) 121944) ((-732 . -948) T) ((-487 . -1251) 121923) ((-1203 . -465) 121902) ((-1197 . -465) 121881) ((-341 . -102) T) ((-895 . -1142) T) ((-330 . -667) 121763) ((-327 . -669) 121492) 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. -320) 102249) ((-722 . -634) 102221) ((-495 . -424) 102190) ((-641 . -948) 102169) ((-467 . -1251) 102148) ((-696 . -527) 102081) ((-685 . -25) T) ((-411 . -631) 102063) ((-685 . -21) T) ((-467 . -569) 101994) ((-431 . -928) 101917) ((-367 . -25) T) ((-367 . -21) T) ((-364 . -25) T) ((-118 . -948) T) ((-118 . -841) NIL) ((-364 . -21) T) ((-356 . -25) T) ((-356 . -21) T) ((-274 . -25) T) ((-274 . -21) T) ((-254 . -25) T) ((-254 . -21) T) ((-171 . -238) 101848) ((-83 . -396) T) ((-83 . -408) T) ((-135 . -634) 101830) ((-117 . -634) 101802) ((-1034 . -661) 101752) ((-971 . -1010) 101736) ((-942 . -661) 101688) ((-942 . -1081) 101640) ((-938 . -21) T) ((-938 . -25) T) ((-895 . -870) 101591) ((-889 . -669) 101551) ((-732 . -1142) T) ((-732 . -23) T) ((-722 . -1079) T) ((-722 . -239) T) ((-300 . -174) T) ((-675 . -1247) T) ((-322 . -93) T) ((-668 . -1130) 101529) ((-650 . -628) 101504) ((-650 . -1130) T) ((-594 . -1251) T) ((-594 . -569) T) ((-531 . -1251) T) ((-531 . -569) T) ((-500 . 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98886) ((-371 . -174) T) ((-365 . -174) T) ((-532 . -57) 98860) ((-510 . -57) 98810) ((-363 . -1316) 98787) ((-228 . -465) T) ((-330 . -301) 98738) ((-357 . -174) T) ((-176 . -249) T) ((-1260 . -870) 98637) ((-108 . -174) T) ((-895 . -1022) 98621) ((-679 . -1142) T) ((-594 . -375) T) ((-594 . -340) 98608) ((-531 . -340) 98585) ((-531 . -375) T) ((-327 . -318) 98564) ((-324 . -318) T) ((-615 . -870) 98543) ((-1143 . -738) 98485) ((-622 . -1247) T) ((-533 . -293) 98469) ((-679 . -23) T) ((-431 . -233) 98453) ((-431 . -273) 98437) ((-324 . -1052) NIL) ((-348 . -23) T) ((-103 . -1040) 98421) ((-656 . -380) T) ((-45 . -36) 98400) ((-630 . -1130) T) ((-363 . -380) T) ((-537 . -102) T) ((-508 . -27) T) ((-246 . -320) 98338) ((-1117 . -1142) T) ((-1320 . -669) 98312) ((-803 . -1142) T) ((-801 . -1142) T) ((-1208 . -424) 98296) ((-467 . -1142) T) ((-1092 . -465) T) ((-1181 . -1130) T) ((-980 . -465) 98247) ((-1145 . -1113) T) ((-110 . -1130) T) ((-1117 . -23) T) ((-1189 . -527) 98030) ((-838 . -1088) T) ((-803 . -23) T) ((-801 . -23) T) ((-494 . -465) 97981) ((-474 . -23) T) ((-393 . -394) 97960) ((-367 . -235) 97933) ((-364 . -235) 97906) ((-356 . -235) 97879) ((-467 . -23) T) ((-274 . -235) 97824) ((-259 . -920) 97691) ((-258 . -920) 97558) ((-96 . -1130) T) ((-733 . -1247) T) ((-691 . -297) 97535) ((-497 . -527) 97468) ((-1289 . -1081) 97351) ((-1289 . -661) 97248) ((-1282 . -661) 97089) ((-1282 . -1081) 96924) ((-1261 . -661) 96720) ((-1261 . -1081) 96510) ((-300 . -301) T) ((-1112 . -631) 96492) ((-560 . -873) T) ((-1112 . -632) 96473) ((-420 . -937) 96452) ((-1241 . -132) T) ((-50 . -1142) T) ((-1197 . -413) 96404) ((-1054 . -948) T) ((-1033 . -747) T) ((-864 . -669) 96377) ((-733 . -910) NIL) ((-609 . -1081) 96337) ((-594 . -1142) T) ((-531 . -1142) T) ((-608 . -1081) 96220) ((-1187 . -34) T) ((-1034 . -320) NIL) ((-836 . -502) 96204) ((-609 . -661) 96177) ((-366 . -948) T) ((-608 . -661) 96074) ((-938 . -235) 96061) ((-420 . -669) 95977) ((-50 . -23) T) ((-732 . -132) T) ((-733 . -1068) 95857) ((-594 . -23) T) ((-108 . -527) NIL) ((-531 . -23) T) ((-171 . -422) 95828) ((-1170 . -1130) T) ((-1312 . -1311) 95812) ((-752 . -928) 95789) ((-722 . -816) T) ((-722 . -813) T) ((-1150 . -318) T) ((-391 . -148) T) ((-291 . -631) 95771) ((-290 . -631) 95753) ((-1260 . -1022) 95723) ((-48 . -948) T) ((-696 . -502) 95707) ((-259 . -1304) 95677) ((-258 . -1304) 95647) ((-1118 . -238) T) ((-1206 . -870) T) ((-1150 . -1052) T) ((-1076 . -34) T) ((-857 . -148) 95626) ((-857 . -146) 95605) ((-758 . -107) 95589) ((-630 . -133) T) ((-1208 . -1088) T) ((-495 . -1130) 95341) ((-1204 . -928) 95254) ((-1203 . -928) 95160) ((-1197 . -928) 94921) ((-894 . -465) T) ((-85 . -1247) T) ((-142 . -107) 94903) ((-1156 . -928) 94887) ((-733 . -389) 94871) ((-854 . -634) 94739) ((-1320 . -747) T) ((-1309 . -1088) T) ((-1289 . -102) T) ((-1282 . -102) T) ((-1150 . -558) T) ((-592 . -102) T) ((-130 . -503) 94721) ((-1202 . -977) 94690) ((-403 . -1086) 94674) ((-1155 . -977) 94641) ((-44 . -297) 94618) ((-130 . -631) 94585) ((-52 . -631) 94567) ((-217 . -873) T) ((-674 . -424) 94551) ((-1261 . -102) T) ((-1188 . -527) NIL) ((-683 . -25) T) ((-639 . -1086) 94535) ((-683 . -21) T) ((-991 . -667) 94445) ((-756 . -667) 94390) ((-736 . -667) 94362) ((-403 . -111) 94341) ((-225 . -262) 94325) ((-1084 . -1083) 94265) ((-1084 . -1130) T) ((-1034 . -1182) T) ((-839 . -1130) T) ((-466 . -667) 94180) ((-653 . -669) 94164) ((-639 . -111) 94143) ((-619 . -669) 94127) ((-609 . -102) T) ((-355 . -1251) T) ((-322 . -503) 94108) ((-599 . -132) T) ((-608 . -102) T) ((-427 . -1130) T) ((-397 . -1130) T) ((-322 . -631) 94074) ((-230 . -1130) 94052) ((-668 . -527) 93985) ((-650 . -527) 93829) ((-854 . -1079) 93808) ((-665 . -152) 93792) ((-355 . -569) T) ((-733 . -926) 93735) ((-563 . -232) 93685) ((-1289 . -295) 93651) ((-1282 . -295) 93617) ((-1110 . -301) 93568) ((-577 . -873) T) ((-500 . -869) T) ((-226 . -1142) T) ((-1261 . -295) 93534) ((-1241 . -506) 93500) ((-1034 . -38) 93450) ((-220 . -869) T) ((-431 . -667) 93409) ((-942 . -38) 93361) ((-864 . -815) 93340) ((-864 . -812) 93319) ((-864 . -747) 93298) ((-371 . -301) T) ((-365 . -301) T) ((-357 . -301) T) ((-171 . -465) 93229) ((-440 . -38) 93213) ((-226 . -23) T) ((-108 . -301) T) ((-420 . -815) 93192) ((-420 . -812) 93171) ((-420 . -747) T) ((-513 . -299) 93146) ((-490 . -1086) 93111) ((-679 . -132) T) ((-639 . -634) 93080) ((-1143 . -527) 93013) ((-348 . -132) T) ((-171 . -415) 92992) ((-495 . -738) 92934) ((-836 . -297) 92911) ((-490 . -111) 92867) ((-674 . -1088) T) ((-660 . -23) T) ((-1202 . -920) 92770) ((-1155 . -920) 92752) ((-837 . -1081) 92595) ((-1308 . -1113) T) ((-1270 . -465) 92526) ((-837 . -661) 92375) ((-1307 . -1113) T) ((-1117 . -132) T) ((-1084 . -738) 92317) ((-1057 . -527) 92250) ((-803 . -132) T) ((-801 . -132) T) ((-720 . -873) T) ((-584 . -465) T) ((-639 . -1079) T) ((-605 . -1130) T) ((-546 . -175) T) ((-474 . -132) T) ((-467 . -132) T) ((-391 . -238) T) ((-1029 . -1247) T) ((-45 . -1130) T) ((-397 . -738) 92220) ((-838 . -1130) T) ((-489 . -527) 92153) ((-476 . -527) 92086) ((-1322 . -634) 92067) ((-466 . -379) 92037) ((-45 . -628) 92016) ((-412 . -1247) T) ((-327 . -313) T) ((-1297 . -873) 91995) ((-848 . -238) 91974) ((-490 . -634) 91924) ((-1261 . -320) 91809) ((-691 . -631) 91771) ((-59 . -870) 91750) ((-1034 . -413) 91732) ((-561 . -631) 91714) ((-820 . -667) 91673) ((-836 . -617) 91650) ((-529 . -870) 91629) ((-509 . -870) 91608) ((-1029 . -1068) 91504) ((-40 . -1251) T) ((-246 . -928) 91373) ((-50 . -132) T) ((-594 . -132) T) ((-531 . -132) T) ((-305 . -669) 91233) ((-355 . -340) 91210) ((-355 . -375) T) ((-333 . -334) 91187) ((-330 . -297) 91145) ((-40 . -569) T) ((-391 . -1232) T) ((-391 . -1235) T) ((-1065 . -1223) 91120) ((-1219 . -241) 91070) ((-1197 . -233) 91022) ((-1197 . -273) 90974) ((-341 . -1130) T) ((-391 . -95) T) ((-391 . -35) T) ((-1065 . -107) 90920) ((-490 . -1079) T) ((-1321 . -1086) 90904) ((-492 . -241) 90854) ((-1189 . 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. -38) 89884) ((-1282 . -38) 89725) ((-1261 . -38) 89521) ((-500 . -1088) T) ((-393 . -634) 89505) ((-220 . -1088) T) ((-355 . -23) T) ((-153 . -631) 89487) ((-854 . -816) 89466) ((-854 . -813) 89445) ((-1246 . -634) 89426) ((-609 . -38) 89399) ((-608 . -38) 89296) ((-893 . -569) T) ((-226 . -132) T) ((-330 . -1032) 89262) ((-79 . -631) 89244) ((-733 . -318) 89223) ((-305 . -747) 89125) ((-845 . -102) T) ((-887 . -865) T) ((-305 . -486) 89104) ((-1312 . -102) T) ((-40 . -375) T) ((-895 . -148) 89083) ((-498 . -667) 89065) ((-895 . -146) 89044) ((-1188 . -502) 89026) ((-1321 . -1079) T) ((-495 . -527) 88959) ((-660 . -132) T) ((-1176 . -1247) T) ((-992 . -631) 88941) ((-668 . -502) 88925) ((-650 . -502) 88856) ((-836 . -631) 88549) ((-48 . -27) T) ((-1208 . -738) 88446) ((-980 . -920) 88425) ((-674 . -1130) T) ((-884 . -883) T) ((-449 . -376) 88399) ((-752 . -667) 88309) ((-494 . -920) 88284) ((-1132 . -102) T) ((-1000 . -1130) T) ((-887 . -1130) T) ((-837 . -320) 88271) ((-546 . -540) T) ((-546 . -589) T) ((-1317 . -394) 88243) ((-715 . -873) T) ((-1084 . -527) 88176) ((-1189 . -297) 88152) ((-246 . -273) 88121) ((-246 . -233) 88090) ((-259 . -1081) 87991) ((-258 . -1081) 87892) ((-1309 . -738) 87862) ((-1196 . -93) T) ((-1024 . -93) T) ((-838 . -174) 87841) ((-259 . -661) 87763) ((-258 . -661) 87685) ((-1244 . -503) 87662) ((-591 . -1247) T) ((-230 . -527) 87595) ((-639 . -816) 87574) ((-639 . -813) 87553) ((-1244 . -631) 87465) ((-225 . -1247) T) ((-696 . -631) 87397) ((-1204 . -667) 87307) ((-1187 . -1040) 87291) ((-971 . -102) 87221) ((-363 . -747) T) ((-884 . -631) 87203) ((-1203 . -667) 87085) ((-1197 . -667) 86922) ((-1156 . -667) 86832) ((-1261 . -413) 86784) ((-1143 . -502) 86768) ((-60 . -320) 86706) ((-342 . -102) T) ((-1241 . -21) T) ((-1241 . -25) T) ((-40 . -1142) T) ((-732 . -21) T) ((-645 . -631) 86688) ((-528 . -334) 86667) ((-732 . -25) T) ((-452 . -102) T) ((-108 . -297) NIL) ((-949 . -1142) T) ((-40 . -23) T) ((-792 . -1142) T) ((-577 . -1251) T) 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. -1235) 84035) ((-1270 . -920) 83938) ((-1202 . -1081) 83761) ((-1172 . -1247) T) ((-1155 . -1081) 83604) ((-877 . -1081) 83588) ((-650 . -617) 83563) ((-1281 . -95) 83529) ((-1281 . -238) 83481) ((-1264 . -102) 83459) ((-1202 . -661) 83288) ((-1155 . -661) 83137) ((-877 . -661) 83107) ((-1261 . -233) 83059) ((-1117 . -25) T) ((-562 . -1130) T) ((-1117 . -21) T) ((-991 . -1088) T) ((-544 . -813) T) ((-544 . -816) T) ((-118 . -1251) T) ((-889 . -1247) T) ((-641 . -569) T) ((-803 . -25) T) ((-803 . -21) T) ((-801 . -21) T) ((-801 . -25) T) ((-756 . -1088) T) ((-736 . -1088) T) ((-691 . -1086) 83043) ((-530 . -1113) T) ((-474 . -25) T) ((-118 . -569) T) ((-474 . -21) T) ((-467 . -25) T) ((-467 . -21) T) ((-1261 . -273) 82995) ((-1181 . -93) T) ((-1172 . -1068) 82891) ((-838 . -301) 82870) ((-1260 . -1232) 82836) ((-844 . -1130) T) ((-994 . -997) T) ((-691 . -111) 82815) ((-635 . -1247) T) ((-306 . -527) 82607) ((-1260 . -1235) 82573) ((-1260 . -238) 82432) ((-1255 . -380) T) ((-259 . 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. -239) 22068) ((-1261 . -249) 22047) ((-1241 . -38) 21944) ((-609 . -1079) T) ((-608 . -1079) T) ((-1034 . -816) T) ((-1034 . -813) T) ((-1001 . -816) T) ((-1001 . -813) T) ((-895 . -1088) T) ((-109 . -631) 21926) ((-715 . -465) T) ((-391 . -738) 21891) ((-431 . -669) 21865) ((-893 . -892) 21849) ((-732 . -38) 21814) ((-608 . -239) 21773) ((-40 . -745) 21745) ((-363 . -340) 21722) ((-363 . -375) T) ((-1110 . -318) 21673) ((-305 . -1142) 21554) ((-1136 . -1247) T) ((-1029 . -235) 21499) ((-173 . -102) T) ((-1264 . -631) 21466) ((-864 . -132) 21418) ((-857 . -738) 21388) ((-665 . -1285) 21372) ((-848 . -738) 21342) ((-665 . -617) 21319) ((-495 . -1247) T) ((-371 . -318) T) ((-365 . -318) T) ((-357 . -318) T) ((-412 . -235) 21306) ((-420 . -132) T) ((-533 . -687) 21290) ((-108 . -318) T) ((-305 . -23) 21173) ((-533 . -672) 21157) ((-715 . -415) NIL) ((-533 . -385) 21141) ((-660 . -1081) 21125) ((-660 . -661) 21109) ((-302 . -631) 21091) ((-91 . -1130) 21069) ((-108 . -1052) T) ((-577 . 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 86e1faab..80e66244 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3487991531) -(4473 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3488491114) +(4502 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -221,13 +221,15 @@ |InnerTaylorSeries| |InternalTypeForm| |InfiniteTupleFunctions2| |InfiniteTupleFunctions3| |InnerTrigonometricManipulations| |InfiniteTuple| |IndexedVector| |IndexedAggregate&| |IndexedAggregate| - |JavaBytecode| |JoinAst| |AssociatedJordanAlgebra| |KeyedAccessFile| - |KeyedDictionary&| |KeyedDictionary| |KernelFunctions2| |Kernel| - |CoercibleTo| |ConvertibleTo| |Kovacic| |CoercibleFrom| - |KleeneTrivalentLogic| |ConvertibleFrom| |LeftAlgebra&| |LeftAlgebra| - |LocalAlgebra| |LaplaceTransform| |LaurentPolynomial| - |LazardSetSolvingPackage| |LeadingCoefDetermination| |LetAst| - |LieExponentials| |LexTriangularPackage| |LiouvillianFunctionCategory| + |JoinAst| |AssociatedJordanAlgebra| |JVMBytecode| |JVMClassFileAccess| + |JVMConstantTag| |JVMFieldAccess| |JVMMethodAccess| |JVMOpcode| + |KeyedAccessFile| |KeyedDictionary&| |KeyedDictionary| + |KernelFunctions2| |Kernel| |CoercibleTo| |ConvertibleTo| |Kovacic| + |CoercibleFrom| |KleeneTrivalentLogic| |ConvertibleFrom| + |LeftAlgebra&| |LeftAlgebra| |LocalAlgebra| |LaplaceTransform| + |LaurentPolynomial| |LazardSetSolvingPackage| + |LeadingCoefDetermination| |LetAst| |LieExponentials| + |LexTriangularPackage| |LiouvillianFunctionCategory| |LiouvillianFunction| |LinGroebnerPackage| |Library| |LieAlgebra&| |LieAlgebra| |AssociatedLieAlgebra| |PowerSeriesLimitPackage| |RationalFunctionLimitPackage| |LinearBasis| |LinearDependence| @@ -488,663 +490,675 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |errorKind| |bat1| |conjugate| |dom| |iipow| |gensym| - UTS2UP |exprToGenUPS| |merge| |tree| |minimumExponent| |mainValue| - |recoverAfterFail| |startTableInvSet!| |bitLength| |inf| - |totalDifferential| |multiple?| |rootsOf| |upperCase| - |halfExtendedResultant1| |seed| |mapMatrixIfCan| |normDeriv2| |queue| - |rangePascalTriangle| |OMreadFile| |ref| |typeList| |string| - |cyclicParents| |c02agf| |cos2sec| |primintfldpoly| |lllip| |d03faf| - |restorePrecision| |integral?| |coerceS| |mainVariables| |superscript| - |boundOfCauchy| |scale| |times!| |powers| |fixedDivisor| - |viewWriteAvailable| |extendedEuclidean| |floor| |zeroMatrix| |arity| - |s21baf| |asinhIfCan| |exptMod| |adaptive3D?| |removeRedundantFactors| - |title| |firstUncouplingMatrix| |nthFlag| |symbolTableOf| |setUnion| - |simplifyLog| |modularGcdPrimitive| |companionBlocks| |scalarMatrix| - |fmecg| |increment| |OMputError| |constantIfCan| |acschIfCan| - |hypergeometric0F1| |midpoints| |s14aaf| |rewriteIdealWithRemainder| - |isMult| |algebraic?| |lexTriangular| |monomRDEsys| |nullSpace| - |iterationVar| |deepExpand| |genericLeftMinimalPolynomial| |predicate| - |basisOfCentroid| |setMinPoints| |seriesSolve| |fortranInteger| - |OMputAtp| |e| |cylindrical| |iisqrt3| |vark| |pile| |patternVariable| - |OMlistSymbols| |triangular?| |OMwrite| |stFunc2| |numberOfHues| - |e02def| |d01bbf| |Frobenius| |unitNormalize| |over| |stirling1| - |tube| |rootPower| |binaryFunction| |Lazard| |hexDigit| |sumOfSquares| - |tRange| |build| |product| |hash| |sPol| |monicModulo| |adaptive?| - |child?| |yellow| |double| |indiceSubResultant| |makeCos| - |leadingIdeal| |inverseIntegralMatrix| |lieAdmissible?| |count| - |halfExtendedResultant2| |nextItem| |matrixConcat3D| |argumentList!| - |max| |initiallyReduce| |removeZeroes| |constant?| - |createMultiplicationMatrix| |safetyMargin| ** |leftRank| |Nul| - |expandLog| |currentScope| |output| |connectTo| |satisfy?| |arbitrary| - |iteratedInitials| |redPo| |triangularSystems| |contours| - 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|rootKerSimp| |f02axf| |divideExponents| |checkRur| |mainVariable| - |virtualDegree| |shufflein| |noncommutativeJordanAlgebra?| - |fortranReal| |create3Space| |separateFactors| - |semiSubResultantGcdEuclidean1| |roughUnitIdeal?| - |oneDimensionalArray| |localAbs| |cosh2sech| |mpsode| - |complexIntegrate| |sincos| |printStatement| |integerBound| - |generalizedContinuumHypothesisAssumed| |intersect| |basisOfCenter| - |primes| |rootProduct| |hessian| |iicoth| |iprint| |fprindINFO| - |nthRootIfCan| |leastPower| |prepareDecompose| |solveInField| - |setMaxPoints| |innerint| |rotatex| |conjug| |subResultantGcd| - |lookupFunction| |pushdterm| |bubbleSort!| |qqq| |realZeros| - |radicalSolve| |palgRDE0| |xCoord| |f07fdf| |partition| |putGraph| - |ratPoly| |minus!| |pushdown| |hMonic| |imagJ| |derivative| - |palgextint| |symmetricTensors| |clearTable!| |obj| |shrinkable| - |setAdaptive| |isAbsolutelyIrreducible?| |infiniteProduct| |realRoots| - |removeSinSq| |argument| |OMsupportsCD?| |countRealRoots| |aQuadratic| - |cache| |atom?| |nil| |padicallyExpand| |dequeue!| - |selectFiniteRoutines| |taylorRep| |multinomial| |withPredicates| - |applyRules| |writeUInt8!| |increasePrecision| |outputForm| |kmax| - |d02bbf| |nextLatticePermutation| |dioSolve| |monomialIntegrate| - |unitCanonical| |pseudoRemainder| |mapUp!| |completeHensel| - |coerceImages| |isQuotient| |stopTableInvSet!| |integrate| - |lSpaceBasis| |frobenius| |generic?| |zag| |cyclotomic| |second| - |updatD| |c05adf| |OMgetFloat| |preprocess| |doublyTransitive?| - |operation| |approximate| |mappingAst| |extendedSubResultantGcd| - |quadratic| |parametersOf| |tanIfCan| |third| |finiteBound| - |factorSquareFreeByRecursion| |coordinate| |logIfCan| - |sizeMultiplication| |void| |complex| |setprevious!| |ratDsolve| |sh| - |eigenvalues| |initializeGroupForWordProblem| |polynomialZeros| - |mainContent| |principalAncestors| |extension| |getStream| - |resetAttributeButtons| |euclideanSize| |alphabetic| |rk4f| - |groebnerIdeal| |primaryDecomp| |checkForZero| |squareTop| - |strongGenerators| |doubleFloatFormat| |leftAlternative?| - |systemCommand| |redmat| |s17dhf| |numericalOptimization| |height| - |Lazard2| |setTex!| |irreducibleFactors| |mesh?| |iilog| |ratDenom| - |rightOne| |printCode| |rotatez| |getVariableOrder| |maximumExponent| - |rewriteIdealWithHeadRemainder| |currentSubProgram| |rightFactorIfCan| - |trigs2explogs| |failed| |coefficients| |selectSumOfSquaresRoutines| - |csch2sinh| |clipParametric| |d01amf| |whileLoop| |rightTrace| - |pointPlot| |s17ajf| |randomLC| |useSingleFactorBound| |normal| RF2UTS - |exQuo| |table| |basisOfNucleus| |balancedBinaryTree| - |inverseIntegralMatrixAtInfinity| |taylorQuoByVar| |shape| |rotate!| - |leadingSupport| |f02agf| |separate| |semiDegreeSubResultantEuclidean| - |new| |rotatey| |diophantineSystem| |createZechTable| |lyndonIfCan| - |style| |tan2trig| |d01fcf| |crushedSet| |shallowCopy| - |initiallyReduced?| |stoseLastSubResultant| |pointColorDefault| - |constantToUnaryFunction| |rightDivide| |integralBasisAtInfinity| - |minIndex| |e02agf| |complexEigenvectors| |monomials| |cycleTail| - |commutative?| |firstDenom| |solveLinear| |graphState| |plus!| - |stoseInvertible?| |minRowIndex| |cyclicEqual?| |mapDown!| - |changeMeasure| |plenaryPower| |direction| |e02bef| |flexibleArray| - |ef2edf| |jacobian| |stopMusserTrials| |limitedIntegrate| |comment| - |basisOfMiddleNucleus| |reduceBasisAtInfinity| |leftLcm| |buildSyntax| - |quadraticForm| |shade| |center| |areEquivalent?| |prologue| - |fractionFreeGauss!| |gderiv| |cAcos| |maxPoints3D| |bitCoef| - |totalfract| |leftTraceMatrix| |monicDivide| |hex| |zeroDimPrime?| - |cycleLength| |viewThetaDefault| |computeInt| |dmp2rfi| |nthRoot| - |rootPoly| |palgRDE| |mapSolve| |car| |besselJ| |nonSingularModel| - |tanAn| |ip4Address| |monicRightFactorIfCan| |ldf2lst| |next| - |curveColorPalette| |OMunhandledSymbol| |child| |paren| |positive?| - |validExponential| |flagFactor| |laplacian| |partitions| |matrix| - |printInfo| |fortranLinkerArgs| |singular?| |setAttributeButtonStep| - |lazy?| |convergents| |df2mf| |decreasePrecision| |printStats!| - |iiGamma| |abs| |e01bff| |ParCond| |nary?| |maxrank| |key| - |lowerPolynomial| |zeroDimPrimary?| |yCoordinates| |firstNumer| - |charpol| |makeCrit| |mapCoef| |c05pbf| |imagE| |removeCosSq| - |environment| |scalarTypeOf| |getZechTable| |decompose| - |squareFreeLexTriangular| |iitan| |factorSFBRlcUnit| |weierstrass| - |indicialEquations| |removeIrreducibleRedundantFactors| |filename| - |insert!| |ode| |antiCommutative?| |UpTriBddDenomInv| |cycleRagits| - |selectNonFiniteRoutines| |nextsubResultant2| |solveRetract| - |autoReduced?| |getConstant| |createLowComplexityNormalBasis| |e01sbf| - |selectAndPolynomials| |iiexp| |patternMatch| |dictionary| |pack!| - |complexEigenvalues| |clearTheSymbolTable| |parse| |symbolIfCan| - |LyndonBasis| |evaluate| |surface| |explogs2trigs| |writeLine!| - |scaleRoots| |karatsuba| |mapExponents| |cosIfCan| |approximants| - |writeBytes!| |distdfact| |reverseLex| |readUInt32!| |someBasis| - |algebraicCoefficients?| |quote| |headRemainder| |infieldIntegrate| - |units| |super| |repSq| |acoshIfCan| |zeroDim?| |f07aef| |measure| - |parseString| |nullary?| |constantLeft| |complexSolve| |triangulate| - |cAtan| |mainPrimitivePart| |harmonic| |removeRedundantFactorsInPols| - |varselect| |primitive?| |size?| |elliptic| |createIrreduciblePoly| - |aQuartic| |mkAnswer| |shuffle| |f02aaf| |endSubProgram| |clipBoolean| - |Si| |OMmakeConn| |OMencodingXML| |minPol| |sechIfCan| |makeVariable| - |setMinPoints3D| |leftNorm| |leftDivide| |integralAtInfinity?| - |factorByRecursion| |cCot| |removeSuperfluousCases| |paraboloidal| - |subresultantVector| |groebner?| |palgint| |associative?| - |normalizeIfCan| |linearDependence| |factorAndSplit| |lagrange| |code| - |lazyPseudoQuotient| |traceMatrix| |beauzamyBound| |sorted?| - |factorset| |critM| |OMconnInDevice| |palglimint0| |graeffe| |tanNa| - |bounds| |points| |discriminant| |options| |HermiteIntegrate| - |OMopenString| |nil| |infinite| |arbitraryExponent| |approximate| - |complex| |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |viewpoint| |groebner| |coshIfCan| |pdct| + |linearElement| |collectUpper| |littleEndian| |linearPolynomials| + |lazyPseudoQuotient| |SFunction| |moreAlgebraic?| |putGraph| |center| + |insertRoot!| |exprHasAlgebraicWeight| |options| |mainMonomials| + |quasiRegular?| |high| |complexNormalize| |divisorCascade| + |character?| |dom| |cyclicParents| |infieldIntegrate| |rational?| + |diff| |exactQuotient!| |coth2trigh| |quasiComponent| |option?| + |dimensionsOf| |wholePart| |Ci| |OMgetBVar| |uniform01| |create| + |subspace| |getGraph| |shiftLeft| |brillhartTrials| |finiteBasis| + |enumerate| |imagi| |constantOperator| |monicModulo| + |invertibleElseSplit?| |string| |inverseIntegralMatrixAtInfinity| + |regime| |sort| |sin2csc| |viewPhiDefault| |f01brf| |unitVector| + |triangSolve| |rowEchelonLocal| |internalSubPolSet?| |palgRDE0| + |infix| |intcompBasis| |semiResultantEuclidean1| |complexNumericIfCan| + |leftZero| |inconsistent?| |internalZeroSetSplit| |showTheIFTable| + |normalized?| |semiIndiceSubResultantEuclidean| |vectorise| + |reducedForm| |monicLeftDivide| |OMgetEndAtp| |c06fpf| |d02raf| |tab| + |title| |ellipticCylindrical| |s19acf| |OMsupportsSymbol?| + |splitDenominator| |top!| |permutationGroup| |inHallBasis?| + |processTemplate| |constantKernel| |factorSquareFreeByRecursion| + |createNormalPrimitivePoly| |aspFilename| |algDsolve| |cRationalPower| + |partitions| |genericRightTraceForm| |random| |maxIndex| |isTimes| + |lifting| |filterUntil| |mvar| |getProperties| |s17ajf| |OMgetBind| + |rules| |removeCoshSq| |mapUnivariate| |modifyPoint| |rightUnits| + |laguerre| |showIntensityFunctions| |select| |e| |partialDenominators| + |BasicMethod| |startTableGcd!| |units| |ParCondList| + |lastSubResultantEuclidean| |belong?| |symmetricSquare| + |sortConstraints| |GospersMethod| |univariate?| |s18adf| |zeroDim?| + |column| |prem| |symbol?| |cup| |contours| |c06ekf| |rightNorm| + |subscript| |fortranLiteralLine| |linearAssociatedExp| + |jordanAdmissible?| |exp1| |palgextint0| |simplify| ** |hash| |rquo| + |logical?| |bezoutDiscriminant| |any?| |nary?| |dualSignature| + |tableau| |expandPower| |useNagFunctions| |bits| |count| |e02akf| + |eisensteinIrreducible?| |decimal| |seed| |iiGamma| |weakBiRank| + |support| |HermiteIntegrate| |zeroMatrix| |balancedFactorisation| + |totalGroebner| |B1solve| |read!| |makeResult| |compiledFunction| + |code| |whileLoop| |solve1| |listConjugateBases| |expintfldpoly| + |alternating| |subNode?| |readInt16!| |unknown| |over| |trivialIdeal?| + |UnVectorise| |reset| |padecf| |prevPrime| |f07fdf| |weierstrass| + |reflect| |f04mbf| |cubic| |updatD| |OMputAtp| |quasiRegular| + |nthExpon| |solveLinearlyOverQ| |e04ucf| |yCoord| |genericLeftTrace| + |algint| |setleft!| |numberOfComputedEntries| |imagK| |operators| + |write| |rewriteSetWithReduction| |taylorIfCan| |OMclose| + |mainCharacterization| |plotPolar| |OMgetEndError| |lexTriangular| + |notelem| |getSyntaxFormsFromFile| |newTypeLists| |save| + |removeConstantTerm| |f02bjf| |leadingExponent| |resultantReduit| + |sizeMultiplication| |powerAssociative?| |drawCurves| |addMatch| + |antisymmetricTensors| |moebius| |isOpen?| |LazardQuotient2| + |readByte!| |univariatePolynomialsGcds| |numberOfFactors| |baseRDE| + |f04maf| |dequeue| |leadingSupport| |lazyIrreducibleFactors| + |shiftRoots| |froot| |rightTrim| |intersect| |diagonalProduct| + |algSplitSimple| |e02dcf| |e01sef| |tubePoints| |lowerPolynomial| + |wordInGenerators| |f04faf| |rotate| |leftTrim| |sparsityIF| + |setCondition!| |abelianGroup| |fixedPoints| |minrank| + |lookupFunction| |bitTruth| |bivariateSLPEBR| + |stiffnessAndStabilityOfODEIF| |fortranCarriageReturn| + |exteriorDifferential| |interval| |genericRightNorm| |f04asf| + |fglmIfCan| |doubleRank| |permutationRepresentation| |pquo| + |countRealRootsMultiple| |maxdeg| |c06fuf| |degree| |f02wef| + |semiSubResultantGcdEuclidean1| |errorKind| |double?| |initials| + |roughUnitIdeal?| |iicsch| |strongGenerators| |basisOfCenter| + |leastPower| |getlo| |clipWithRanges| |OMconnInDevice| |makeop| + |composites| |mapCoef| |complexLimit| |monicDivide| |asec| |rename!| + |critBonD| |minPoints| |s18aff| |setPrologue!| |critT| + |jvmUTF8ConstantTag| |simplifyPower| |omError| |acsc| |mathieu11| + |argscript| |OMgetType| |linSolve| |asimpson| |OMgetEndBind| + |packageCall| |iiexp| |myDegree| |numFunEvals| |d01asf| |sinh| + |internalSubQuasiComponent?| |f02abf| |rank| |chainSubResultants| + |externalList| |f2df| |pdf2ef| |generateIrredPoly| + |selectSumOfSquaresRoutines| |cosh| |orbits| |pushucoef| |OMgetEndApp| + |eigenvectors| |open?| |jvmStringConstantTag| |pole?| + |pointColorPalette| |fortranInteger| |calcRanges| |cycleTail| |tanh| + |laguerreL| |step| |s21baf| |gbasis| |palgint0| |polynomialZeros| + |prindINFO| |pseudoRemainder| |OMopenString| |endSubProgram| |coth| + |isAnd| |headAst| |denominator| |setEmpty!| |conditionP| + |generalizedEigenvector| |mapBivariate| |cExp| |nothing| |redpps| + |sech| |mainVariables| |cAtan| |voidMode| |ParCond| |imaginary| + |finiteBound| |socf2socdf| |newReduc| |shellSort| |csch| + |jacobiIdentity?| |divideIfCan!| |multiEuclidean| |hasHi| + |cycleSplit!| |weights| |makeFR| |root?| |OMputError| |concat| |asinh| + |e02dff| |stiffnessAndStabilityFactor| |karatsubaOnce| |sn| |build| + |setLabelValue| |jvmNameAndTypeConstantTag| |callForm?| |d03eef| + |doubleDisc| |powmod| |acosh| |fortranLogical| |fortranComplex| + |lists| |inputOutputBinaryFile| |internalInfRittWu?| + |jvmMethodrefConstantTag| |OMputString| |f01rcf| |rk4f| |atrapezoidal| + |parametersOf| |atanh| |anticoord| |explicitlyEmpty?| + |generalPosition| |OMencodingUnknown| |upperCase!| |integerBound| + |tryFunctionalDecomposition| |curve?| |repeating?| |acoth| + |cyclicGroup| |gensym| |leftUnit| |removeSuperfluousQuasiComponents| + |jvmLongConstantTag| |OMputEndBVar| |droot| |cAcoth| |minimumExponent| + |topFortranOutputStack| |asech| |halfExtendedSubResultantGcd1| + |iitanh| |check| |in?| |purelyAlgebraic?| |jvmInterfaceConstantTag| + |s17dcf| |environment| |printingInfo?| |unitNormal| |aCubic| + |genericLeftTraceForm| |bothWays| |rightLcm| |imagj| + |OMunhandledSymbol| |irreducibleRepresentation| |maxRowIndex| + |inverse| |initiallyReduced?| |multiple| |nthFactor| |pseudoDivide| + |basisOfRightNucleus| |functionIsFracPolynomial?| |cyclicEntries| + |edf2ef| |jvmIntegerConstantTag| |size?| |makeUnit| + |prepareSubResAlgo| |setAttributeButtonStep| |applyQuote| |acotIfCan| + |compBound| |constantToUnaryFunction| |iiabs| |cycleRagits| + |jvmFloatConstantTag| |atom?| |parents| |tryFunctionalDecomposition?| + |sequence| |var2StepsDefault| |antiCommutator| |OMgetFloat| + |zeroSetSplit| |isPlus| |delta| |setLegalFortranSourceExtensions| + |perfectNthRoot| |OMputEndAttr| |iFTable| |subNodeOf?| |f02aef| + |whatInfinity| |asinhIfCan| |normal01| |iicoth| |ran| |perfectSqrt| + |e02bbf| |jvmFieldrefConstantTag| |s13aaf| |minus!| |dimensions| + |bitLength| |randomR| |ruleset| |fmecg| |isNot| |d02cjf| |separant| + |cCos| |qroot| |rubiksGroup| |roman| |parameters| |s18dcf| + |tubeRadiusDefault| |exprHasLogarithmicWeights| |saturate| + |palglimint0| |fortranDouble| |permutations| |critMTonD1| |s19adf| + |mainCoefficients| |quote| |nthr| |push!| |simplifyExp| + |binarySearchTree| |f01ref| |evenInfiniteProduct| |trueEqual| |cond| + |parent| |precision| |rootSimp| |jvmDoubleConstantTag| |rombergo| + |iiatan| |connect| |linearMatrix| |iicot| |acschIfCan| |suchThat| + |kind| |bumptab1| |llprop| |sqfrFactor| |integer?| |computePowers| + |extension| GF2FG |dioSolve| |s15aef| |nthRootIfCan| |op| |integrate| + |readInt32!| |useSingleFactorBound| |shuffle| |findCycle| + |extendedint| |getGoodPrime| |getMultiplicationMatrix| |OMencodingXML| + |errorInfo| |pleskenSplit| |lambda| |currentCategoryFrame| |just| + |second| |jvmClassConstantTag| |setAdaptive| |showTheRoutinesTable| + |retractable?| |LagrangeInterpolation| |airyAi| |safeFloor| |light| + |isOr| |third| |remove!| |basisOfRightNucloid| |clip| + |antiCommutative?| |splitSquarefree| |sech2cosh| |void| |isMult| + |rationalIfCan| |reduceBasisAtInfinity| |writeUInt8!| |cartesian| + |e02def| |setchildren!| |nextsubResultant2| |noKaratsuba| |c05pbf| + |groebnerIdeal| |OMputInteger| |resultantEuclideannaif| |firstDenom| + SEGMENT |euclideanNormalForm| |cAcsch| |indicialEquations| + |lieAlgebra?| |certainlySubVariety?| |readable?| |iicos| |mapExpon| + |cycles| |reverseLex| |coerceListOfPairs| |rightFactorCandidate| + |var2Steps| |singular?| |directSum| |union| |setPoly| + |exportedOperators| |extendedEuclidean| |swap!| |logIfCan| |unary?| + |moduloP| |lazyEvaluate| |rootOf| |recolor| |ratDsolve| |outputFixed| + |lllp| |OMopenFile| |subHeight| |rootNormalize| |clearCache| + |hitherPlane| |basisOfCommutingElements| |leftFactor| + |generalInfiniteProduct| |nextPrime| |readUInt8!| |invertibleSet| + |cap| |setelt| |cAcsc| |selectsecond| |modularFactor| |integral| + |ddFact| |internalAugment| |algebraicOf| |mindegTerm| |lexico| + |degreePartition| |setlast!| |setColumn!| |pr2dmp| |cyclotomic| + |cscIfCan| |fillPascalTriangle| |overbar| |nativeModuleExtension| + |expenseOfEvaluation| |copy| |palgLODE0| |f2st| |makeMulti| + |constantRight| |rightMult| |firstUncouplingMatrix| |subCase?| + |vspace| |any| |s13adf| |partition| |mapmult| |primaryDecomp| + |ScanFloatIgnoreSpaces| |functorData| |realElementary| + |realEigenvectors| |edf2fi| |curry| |genericLeftNorm| |resetBadValues| + |fibonacci| |rspace| |addPoint2| |setMaxPoints| |lazyVariations| + |nextItem| |OMgetError| |primPartElseUnitCanonical| |imagE| + |solveLinearPolynomialEquation| |cSec| |horizConcat| + |fortranCompilerName| |opeval| |declare| |reorder| |sturmSequence| + |ratDenom| |style| |solveLinearPolynomialEquationByFractions| + |stoseInvertible?reg| |rightAlternative?| |normalDenom| |tanh2trigh| + |cotIfCan| |setleaves!| |point?| |getVariableOrder| + |nextsousResultant2| |match?| |scaleRoots| |curryRight| + |setProperties| |associator| |numberOfComposites| |HenselLift| + |autoCoerce| |reciprocalPolynomial| |df2fi| |lintgcd| |readIfCan!| + |close| |has?| |prefixRagits| |nodeOf?| |rightUnit| |polyPart| + |intChoose| |lift| |removeRedundantFactorsInPols| |part?| |write!| + |leadingIndex| |nullary?| |changeNameToObjf| |figureUnits| + |infieldint| |kmax| F |prime| |scopes| |reduce| + |tableForDiscreteLogarithm| |discriminantEuclidean| |pushup| |display| + |charpol| |algebraic?| |completeHermite| |f02agf| |hconcat| + |normalForm| |argumentList!| |terms| |lazyPseudoDivide| + |monicCompleteDecompose| |supDimElseRittWu?| |baseRDEsys| |sinIfCan| + |updatF| |symbolTableOf| |addMatchRestricted| |alphanumeric| + |writeInt8!| |factorPolynomial| |groebnerFactorize| |endOfFile?| + |fTable| |extractIfCan| |physicalLength| |wrregime| + |sumOfKthPowerDivisors| |li| |variable?| |rightZero| |prinshINFO| + |radicalEigenvectors| |appendPoint| + |rewriteSetByReducingWithParticularGenerators| |groebner?| + |divergence| |reverse| |standardBasisOfCyclicSubmodule| |monomials| + |nextPartition| |basis| |depth| |distribute| |sts2stst| |binding| + |refine| |increasePrecision| |s18acf| |arguments| |separateDegrees| + |leftMinimalPolynomial| |e02bef| |insertMatch| |arg1| |parts| + |pointColor| |infinityNorm| |fprindINFO| |input| |lexGroebner| + |upperCase?| |updateStatus!| |sub| |factors| |OMsetEncoding| + |selectPDERoutines| EQ |arg2| |systemSizeIF| + |conditionsForIdempotents| |cAsec| |library| |trapezoidal| |f02akf| + |collectQuasiMonic| |seriesToOutputForm| |s21bbf| |setEpilogue!| + |FormatRoman| |inc| |f02aff| UTS2UP |reduceLODE| |iterationVar| + |direction| |idealSimplify| |setFieldInfo| |elRow2!| |members| + |tanSum| |conditions| |digit?| |typeForm| |clearTheSymbolTable| + |aQuadratic| |tubePointsDefault| |inputBinaryFile| + |oddInfiniteProduct| |composite| |weight| |generators| |rootRadius| + |match| |basisOfLeftNucloid| |leftLcm| |computeInt| |imagk| + |sumOfDivisors| |squareFreeLexTriangular| |cAsinh| |writable?| + |xCoord| |limit| |yellow| |duplicates?| |isAtom| |fortranReal| |set| + |host| |tanintegrate| |leftMult| |Lazard| |powers| |jordanAlgebra?| + |jvmSuper| |byte| |copy!| |binaryFunction| |setelt!| |multisect| + |vedf2vef| |toseInvertibleSet| |bindings| |s13acf| |factorials| + |pmintegrate| |bombieriNorm| |leftCharacteristicPolynomial| + |insertBottom!| |quotient| |e02bcf| |solve| |areEquivalent?| + |selectOptimizationRoutines| |elaborateFile| |writeBytes!| + |degreeSubResultantEuclidean| |palgLODE| |gethi| |primitiveElement| + |deepCopy| |abs| |viewThetaDefault| |extractIndex| |getCurve| + |hasSolution?| |d01amf| |triangular?| |exponential1| |putColorInfo| + |ScanArabic| |copies| |integerIfCan| |bezoutMatrix| |iisec| |irDef| + |call| |findBinding| |cn| |indices| |jvmInterface| + |removeRoughlyRedundantFactorsInContents| |condition| |acoshIfCan| + |besselK| |OMputBVar| |factorByRecursion| |clearTheFTable| + |complexEigenvectors| |pow| |rectangularMatrix| |sinh2csch| + |showTheSymbolTable| |dAndcExp| |psolve| |disjunction| |dmpToHdmp| + |lazyPquo| |uniform| |f04qaf| |presub| |pade| |child?| |interpret| + |radicalSimplify| |algebraicCoefficients?| |complexSolve| + |unitCanonical| |representationType| |category| |musserTrials| + |tValues| |roughSubIdeal?| |mathieu22| |pop!| |int| + |createLowComplexityNormalBasis| |postfix| |critpOrder| + |numberOfCycles| |associatorDependence| |bezoutResultant| + |leftRankPolynomial| |domain| |sechIfCan| |expextendedint| + |mainContent| |eq| |coerceP| |setfirst!| |summation| + |incrementKthElement| |setTopPredicate| |package| |true| + |roughEqualIdeals?| |acosIfCan| |univcase| |removeSuperfluousCases| + |e01daf| |iter| |s01eaf| |OMlistSymbols| |patternVariable| + |OMputEndAtp| |show| |principalAncestors| |interReduce| + |deleteRoutine!| |mapMatrixIfCan| |slash| |sample| |setFormula!| + |chebyshevT| |computeCycleEntry| |tan2trig| |odd?| |cross| + |quotientByP| |car| |makeCrit| |solid?| |cLog| |insert| |trace| + |rightFactorIfCan| |mpsode| |iteratedInitials| |bottom!| |e01baf| + |selectPolynomials| |basisOfLeftNucleus| |laplacian| |surface| + |exponent| |printStats!| |lllip| |randomLC| |completeHensel| + |algebraicSort| |interactiveEnv| |iiasec| |readUInt32!| |enterInCache| + |copyInto!| |checkPrecision| |OMputEndApp| |inrootof| |nonLinearPart| + |generator| |bivariate?| |nil?| |minimalPolynomial| |pseudoQuotient| + |ffactor| |taylorRep| |orbit| |mergeDifference| |outputArgs| |tRange| + |unexpand| |exp| |associatedEquations| |leader| + |useSingleFactorBound?| |search| |changeName| |root| |bumptab| + |revert| |mkcomm| |nextIrreduciblePoly| |mainValue| |formula| + |complexExpand| |generic?| |zeroOf| |drawStyle| |fortranTypeOf| + |basisOfRightAnnihilator| |matrix| |singularAtInfinity?| |d01bbf| + |mightHaveRoots| |debug| |rewriteIdealWithRemainder| + |removeSquaresIfCan| |permutation| |makeFloatFunction| |central?| + |c06fqf| |represents| |pToHdmp| |localIntegralBasis| |curveColor| D + |deref| |createZechTable| |head| |lazyGintegrate| |s17akf| + |findConstructor| |listexp| |toroidal| |compile| |mapGen| + |OMconnectTCP| |primeFactor| |c05nbf| |thenBranch| |lhs| + |OMgetInteger| |monicDecomposeIfCan| |content| |nrows| |distance| + |structuralConstants| |graphState| |colorDef| |atoms| |twoFactor| + |testDim| |rhs| |numer| |lambert| |OMlistCDs| |ncols| |quadraticNorm| + |squareTop| |forLoop| |twist| |patternMatch| |cPower| + |genericLeftMinimalPolynomial| |OMgetEndObject| |denom| + |clipParametric| |ceiling| |toseSquareFreePart| |e04gcf| + |createGenericMatrix| |equality| |stoseInternalLastSubResultant| + |width| |OMUnknownSymbol?| |acothIfCan| |innerint| |e04mbf| |lprop| + |init| |transpose| |log10| |matrixDimensions| |integers| + |generalizedContinuumHypothesisAssumed?| |addmod| |pi| |cdr| |lfunc| + |rk4| |upperBound| |torsionIfCan| |constant?| |nsqfree| |bitand| + |ideal| |cAsin| |infinity| |definingInequation| |adaptive?| + |makeRecord| |minPoly| |clikeUniv| |cCsch| |makeYoungTableau| |bitior| + |numFunEvals3D| |radicalEigenvalues| |resultantEuclidean| + |stoseInvertible?| |applyRules| |generate| |showFortranOutputStack| + |initiallyReduce| |subtractIfCan| |e01bef| |linear| + |symmetricDifference| |iisqrt3| |derivative| |var1Steps| |directory| + |commutator| |isImplies| |invmultisect| |listBranches| |seriesSolve| + |arrayStack| |accuracyIF| |lowerBound| |algebraicVariables| + |sizeLess?| |totolex| |linGenPos| |polynomial| |stoseInvertibleSet| + |highCommonTerms| |rightDiscriminant| |leftRemainder| |sinhIfCan| + |partialQuotients| |hclf| |checkRur| |isQuotient| |thetaCoord| + |currentEnv| |plenaryPower| |lquo| |makeVariable| |unitNormalize| + |mapUnivariateIfCan| |predicates| |optional| |trigs2explogs| |se2rfi| + |remainder| |iiatanh| |skewSFunction| |s17aff| |OMmakeConn| |points| + |ksec| |univariatePolynomials| |plus!| |primitivePart!| |quadratic?| + |randnum| |setnext!| |elem?| |degreeSubResultant| |f02aaf| + |ListOfTerms| |sdf2lst| |createIrreduciblePoly| |unit?| + |normalizedAssociate| |permanent| |irreducibleFactors| |epilogue| + |solid| |initial| |innerEigenvectors| |divisors| |isExpt| + |setProperty| |mapSolve| |find| |binary| |goto| |height| |cycleEntry| + |removeCosSq| |monicRightFactorIfCan| |lSpaceBasis| |pushdown| + |useEisensteinCriterion| |pmComplexintegrate| |fill!| |concat!| + |euclideanGroebner| |setScreenResolution| |deepExpand| + |compactFraction| |rangePascalTriangle| |extend| |cCot| |c06ecf| + |edf2efi| |bytes| Y |fixedPoint| |enterPointData| |binomThmExpt| + |primextintfrac| |sign| |leastAffineMultiple| |curryLeft| + |OMcloseConn| |topPredicate| |fixPredicate| |s18def| |debug3D| + |primintegrate| |padicFraction| |halfExtendedResultant2| |iiperm| + |lifting1| |complementaryBasis| |readLine!| |dec| |explimitedint| + |cosh2sech| |fortranLiteral| |prepareDecompose| |bipolar| + |stripCommentsAndBlanks| |ramified?| |rk4a| |approxSqrt| |f02awf| + |denominators| |startTable!| |localAbs| |minordet| |ldf2lst| + |reverse!| |d01gaf| |symFunc| |squareFreePart| |enqueue!| |weighted| + |next| FG2F |midpoints| |cyclePartition| |stopTableGcd!| |linearForm| + |numericIfCan| |interpretString| |printInfo| |label| |cyclic?| + |putProperties| |bat1| |rationalPoints| |sort!| |computeBasis| + |printInfo!| |returnType!| |linearDependence| |complexRoots| + |viewport2D| |basisOfMiddleNucleus| |someBasis| |adaptive| |kovacic| + |newSubProgram| |scale| |measure2Result| |before?| |harmonic| + |OMreceive| |isPower| |stronglyReduced?| |distdfact| |negative?| + |external?| UP2UTS |makeprod| |s17dhf| |OMgetObject| |middle| |output| + |perfectNthPower?| |integralLastSubResultant| |redPol| |subMatrix| + |raisePolynomial| |numberOfMonomials| |linearlyDependent?| |numeric| + |setLength!| |readUInt16!| |mainDefiningPolynomial| |clearDenominator| + |resize| |separateFactors| |square?| |s18aef| |zCoord| |radical| + |e02agf| |cCosh| |hMonic| |e01bgf| |reducedContinuedFraction| |nodes| + |f07fef| |monic?| |stosePrepareSubResAlgo| |status| + |intermediateResultsIF| |lookup| |empty?| |tail| |perspective| + |exists?| |maximumExponent| |basisOfLeftAnnihilator| |jokerMode| + |OMputSymbol| |constructor| |monomial?| |removeDuplicates!| + |palglimint| |setRow!| |innerSolve1| |sqfree| |generalSqFr| |times!| + |setrest!| |OMReadError?| |orthonormalBasis| |erf| |charthRoot| + |option| |subset?| |explicitEntries?| |meshPar1Var| |polCase| |mirror| + |showSummary| |An| |selectMultiDimensionalRoutines| |bfKeys| |d01aqf| + |OMUnknownCD?| |outputSpacing| |hypergeometric0F1| |separate| |d01ajf| + |bsolve| |irreducible?| |entry| |nthFlag| |wronskianMatrix| |say| + |hyperelliptic| |lieAdmissible?| |rst| |e01sbf| |rdHack1| |untab| + |cycleLength| |properties| |rotatex| |showAttributes| |cAcosh| + |f04mcf| |expint| |dilog| |setMaxPoints3D| |OMgetEndAttr| |tanhIfCan| + |nlde| |validExponential| |elaboration| |translate| |f01maf| + |quasiAlgebraicSet| |paren| |viewWriteDefault| |flexibleArray| |sin| + |name| |result| |zeroDimensional?| |rightExactQuotient| |duplicates| + |rightRemainder| |null| |subSet| |shrinkable| |getStream| |addPoint| + |leftScalarTimes!| BY |exptMod| |cos| |body| |meshPar2Var| |linear?| + |stopTableInvSet!| |internalDecompose| |s20adf| |not| |wholeRadix| + |internalLastSubResultant| |ignore?| |lagrange| |s20acf| |tan| + |inspect| |integralBasis| |getCode| |inGroundField?| |and| |cycle| + |factorGroebnerBasis| |rightDivide| |norm| |subResultantChain| + |primitivePart| |cot| |integral?| |leftNorm| |extractSplittingLeaf| + |product| |or| |viewDefaults| |consnewpol| |bernoulli| |nthCoef| + |lepol| |d01akf| |sec| |jacobi| |e02zaf| |dual| |qqq| |xor| |split!| + |mkIntegral| |supRittWu?| |coord| |quasiMonicPolynomials| |even?| + |csc| |Aleph| |close!| |tubeRadius| |SturmHabichtCoefficients| + |sumSquares| |case| |super| |qfactor| |besselY| |doubleFloatFormat| + |bat| |empty| |asin| |problemPoints| |finite?| |e02ajf| + |reducedDiscriminant| |Zero| |componentUpperBound| |top| + |headRemainder| |digamma| |e02gaf| |mainForm| |stFunc1| |acos| + |outputFloating| |LyndonWordsList1| |mappingAst| |e02daf| |infRittWu?| + |One| NOT |continue| |removeRedundantFactors| |bumprow| + |cyclotomicDecomposition| |OMputFloat| |numericalIntegration| |atan| + |rangeIsFinite| |trailingCoefficient| |f04atf| |eyeDistance| + |setStatus| OR |assert| |addBadValue| |diagonals| |doubleResultant| + |generic| |headReduced?| |acot| |doublyTransitive?| |port| + |setprevious!| |pattern| |stoseSquareFreePart| |outputForm| + |limitedIntegrate| AND |d01alf| |bounds| |physicalLength!| + |generalLambert| |nthExponent| |e02baf| |routines| |getOperator| + |ScanRoman| |aLinear| |stop| |generalizedInverse| |alternatingGroup| + |mkPrim| |evenlambert| |modularGcdPrimitive| |t| |SturmHabicht| + |traceMatrix| |mathieu24| |normDeriv2| |assign| |listOfLists| + |userOrdered?| |box| |pascalTriangle| |jacobian| + |selectIntegrationRoutines| |s21bcf| |coleman| |isConnected?| |hasoln| + |leftExactQuotient| |elt| |macroExpand| |genus| |rur| + |numberOfChildren| |linearDependenceOverZ| |qualifier| |bfEntry| + |rischNormalize| |e01sff| |message| |UP2ifCan| |gradient| |element?| + |max| |anfactor| |characteristicPolynomial| |nor| |f07adf| |basicSet| + |double| |setValue!| |simpsono| |autoReduced?| |symmetricRemainder| + |OMParseError?| |normalise| |leastMonomial| |leadingBasisTerm| + |iExquo| |ocf2ocdf| |selectOrPolynomials| |rootProduct| |flexible?| + |constantIfCan| |collect| |getConstant| |RemainderList| + |genericRightMinimalPolynomial| |legendre| |setsubMatrix!| + |selectfirst| |blankSeparate| |removeRedundantFactorsInContents| + |internalIntegrate| |goodnessOfFit| |leftRegularRepresentation| + |d02kef| |factorial| |chineseRemainder| |leftAlternative?| |asecIfCan| + |bipolarCylindrical| |squareFreePolynomial| |semiResultantEuclidean2| + |expandTrigProducts| |overlabel| |inverseColeman| |denomRicDE| + |minIndex| |substring?| |listRepresentation| |signature| + |continuedFraction| |rename| |sinhcosh| * |normalDeriv| + |createNormalElement| |bandedHessian| |cons| |csc2sin| |rotatez| + |e02adf| |binomial| |numberOfImproperPartitions| |unravel| |LiePoly| + |predicate| |reseed| |pushNewContour| |chvar| |mainKernel| + |integralMatrix| |suffix?| |substitute| |expressIdealMember| |d02bbf| + |OMgetString| |size| |lazyIntegrate| |capacity| |dflist| |rightTrace| + |commaSeparate| |e02ahf| |Beta| |OMputBind| |midpoint| |declare!| + |elColumn2!| |UpTriBddDenomInv| = |factorset| |purelyTranscendental?| + |f04arf| |lex| |nextPrimitiveNormalPoly| |categories| |prefix?| + |besselI| |viewSizeDefault| |transcendent?| |df2st| |matrixGcd| + |const| |rk4qc| |probablyZeroDim?| |fortranLinkerArgs| |Is| + |lastSubResultantElseSplit| |cAcos| |discreteLog| + |removeIrreducibleRedundantFactors| |perfectSquare?| + |replaceKthElement| < |distFact| |interpolate| |algebraicDecompose| + |digits| |solveInField| |solveid| |plusInfinity| |critMonD1| |gderiv| + |setDifference| |rroot| > |cAtanh| |f01rdf| |returnTypeOf| + |fixedDivisor| |source| |selectNonFiniteRoutines| |minusInfinity| + |zoom| |specialTrigs| |changeThreshhold| |secIfCan| + |nextLatticePermutation| <= |backOldPos| |rationalPower| |leftGcd| + |schema| |f01mcf| |transcendenceDegree| |OMsend| |lineColorDefault| + |collectUnder| |startStats!| >= |mantissa| + |rewriteIdealWithHeadRemainder| |stoseInvertible?sqfreg| |presuper| + |semiDegreeSubResultantEuclidean| |polar| |getButtonValue| |toScale| + |triangulate| |explogs2trigs| |principalIdeal| |quickSort| + |rightScalarTimes!| |qinterval| |usingTable?| |infix?| + |genericRightDiscriminant| |segment| |ode1| |selectFiniteRoutines| + |lazyResidueClass| |char| |blue| |changeMeasure| |hostByteOrder| + |cyclicEqual?| |irCtor| |mask| |subResultantsChain| |node| + |indiceSubResultantEuclidean| |lowerCase| |tanIfCan| |LiePolyIfCan| + |datalist| + |rootKerSimp| |block| |target| |oddintegers| + |showClipRegion| |type| |ptFunc| |real?| |nextSublist| |extractClosed| + |ptree| |vconcat| |stopTable!| - |tube| |var1StepsDefault| |flatten| + |invertible?| |closedCurve| |failed?| |LyndonWordsList| |setImagSteps| + |clipBoolean| |expand| / |lyndon| |resetVariableOrder| |extractTop!| + |clearTheIFTable| |zeroDimPrime?| |removeZero| |insertTop!| |pureLex| + |extendedResultant| |filterWhile| |leftFactorIfCan| |nextNormalPoly| + |region| |approxNthRoot| |monomRDEsys| |OMserve| |primlimintfrac| + |OMputApp| |replace| |point| |startPolynomial| |ldf2vmf| |prinb| + |leftReducedSystem| |toseLastSubResultant| |difference| |s17acf| + |recip| |tablePow| |pushdterm| |universe| |sylvesterSequence| |float| + |property| |unrankImproperPartitions0| |npcoef| |e04ycf| |expPot| + |rischDE| |rootSplit| |associatedSystem| |graphImage| + |semiSubResultantGcdEuclidean2| |front| |characteristicSerie| + |operation| |viewZoomDefault| |reducedSystem| |leaf?| + |mainSquareFreePart| |series| |yCoordinates| |maxint| |btwFact| + |lazyPseudoRemainder| |string?| |leaves| |SturmHabichtSequence| + |arbitrary| |numberOfDivisors| |linearAssociatedOrder| |coerceS| + |lazy?| |firstNumer| |exponents| |extract!| |squareFree| |iisinh| + |hermiteH| |iicosh| |fintegrate| |antiAssociative?| |extractProperty| + |totalLex| |rightRegularRepresentation| |positiveRemainder| |implies| + |children| |iiasinh| |freeOf?| |OMgetVariable| |plus| |corrPoly| + |table| |leftExtendedGcd| |parse| |clearTable!| |setRealSteps| + |idealiserMatrix| |categoryFrame| |completeEval| |outerProduct| + |minColIndex| |stoseIntegralLastSubResultant| |hermite| |latex| |new| + |min| |f02bbf| |removeSinhSq| |gcdcofact| |positiveSolve| + |expenseOfEvaluationIF| |bernoulliB| |divideIfCan| |ridHack1| |f02xef| + |readLineIfCan!| |pile| |initializeGroupForWordProblem| + |cyclotomicFactorization| |categoryMode| |rightRecip| |c02agf| |value| + |integralAtInfinity?| |times| |setOfMinN| |removeZeroes| |mathieu12| + |round| GE |d02gaf| |cosSinInfo| |iiacot| |setPredicates| + |beauzamyBound| |dn| |printCode| |wholeRagits| + |genericLeftDiscriminant| |mdeg| GT |unit| |sPol| |primitive?| + |decomposeFunc| |axes| |printHeader| |sorted?| |rowEchelon| + |setMinPoints| |list?| LE |edf2df| |hspace| |c02aff| |s19abf| + |isobaric?| |showTheFTable| |sequences| |f07aef| |rule| |moebiusMu| + |OMputEndBind| |expr| LT |makeSketch| |cTan| |frobenius| |crushedSet| + |f01qef| |e04dgf| |subTriSet?| |extractPoint| |monom| |hessian| + |s14abf| |ranges| |limitPlus| |coerceImages| |removeSinSq| + |safetyMargin| |subscriptedVariables| |e01bhf| |float?| + |halfExtendedResultant1| |OMgetSymbol| |nextSubsetGray| |parseString| + |countable?| |eof?| |radix| |setScreenResolution3D| |critB| + |completeSmith| |unparse| |OMputVariable| |biRank| |resultantnaif| + |OMputEndError| |characteristic| |factorSquareFree| |common| |laplace| + |inR?| |ricDsolve| |left| |stirling1| |janko2| |iiacsc| |variable| + |iidprod| |commutativeEquality| |unvectorise| |sec2cos| |f02adf| + |decrease| |bright| |elaborate| |changeBase| |modulus| |right| + |dfRange| |index| |red| |iterators| |one?| |f01bsf| |byteBuffer| + |irreducibleFactor| |conjunction| |simpleBounds?| |medialSet| |mesh| + |outlineRender| |algintegrate| |comp| |nthRoot| |setVariableOrder| + |linearPart| |maxColIndex| |divide| |eval| |elliptic?| |c06frf| + |OMputAttr| |getMatch| |solveLinearPolynomialEquationByRecursion| + |totalfract| |exactQuotient| |tubePlot| |partialFraction| + |buildSyntax| |clearFortranOutputStack| |cyclicCopy| |cfirst| |pair| + |removeRoughlyRedundantFactorsInPol| |superscript| |rootsOf| + |attributeData| |phiCoord| |isAbsolutelyIrreducible?| + |unitsColorDefault| |lazyPremWithDefault| |evaluateInverse| |color| + |ratpart| |e04naf| |binaryTree| |delay| |iroot| |power| + |defineProperty| |error| |optAttributes| |BumInSepFFE| |palgRDE| + |fractionFreeGauss!| |id| |mathieu23| |exprToGenUPS| |factorList| + |henselFact| |bivariatePolynomials| |currentSubProgram| + |extensionDegree| |iisin| |firstSubsetGray| |c06gbf| |lazyPrem| + |determinant| |lo| |iibinom| |LyndonCoordinates| |upDateBranches| + |rightExtendedGcd| |OMencodingBinary| |normalizeIfCan| |eulerPhi| + |scalarTypeOf| |shufflein| |range| |PollardSmallFactor| |complement| + |diag| |factorSFBRlcUnit| |less?| |symmetricTensors| |mapDown!| + |domainTemplate| |iprint| |c06ebf| |cyclicSubmodule| |symbolTable| + |every?| |palgint| |conjug| |optimize| |largest| |convergents| |sum| + |partialNumerators| |innerSolve| |makeSeries| |tanQ| + |createNormalPoly| |d03faf| |infinite?| |trace2PowMod| + |subResultantGcdEuclidean| |d02gbf| |sumOfSquares| |nilFactor| + |symbol| |outputAsScript| |linearAssociatedLog| |exprToXXP| + |pushFortranOutputStack| |dictionary| |expandLog| |ODESolve| + |subResultantGcd| |cycleElt| |createPrimitiveElement| |OMbindTCP| + |expression| |tanNa| |cTanh| |nullity| |popFortranOutputStack| |lp| + |function| |rightRank| |internal?| |singularitiesOf| |supersub| + |leftOne| |localUnquote| |writeLine!| |indicialEquation| |integer| + |vark| |rightGcd| |outputAsFortran| |newLine| |FormatArabic| + |eigenvalues| |youngGroup| |f02axf| |iiacos| |screenResolution3D| + |triangularSystems| |ref| |compound?| |nonSingularModel| + |companionBlocks| |df2ef| |symbolIfCan| |listYoungTableaus| |radPoly| + |factor1| |f02fjf| |unknownEndian| |oddlambert| |s17def| |aQuartic| + |low| |member?| |conical| |normalizedDivide| |f04jgf| |setTex!| + |normal?| |f04adf| |exprex| |unmakeSUP| |schwerpunkt| |identity| + |reduction| |rem| |rootOfIrreduciblePoly| |powern| |coHeight| + |leftRecip| |optional?| |knownInfBasis| |numberOfOperations| + |makeGraphImage| |subresultantVector| |quo| |closeComponent| |f04axf| + |f01qcf| |fixedPointExquo| |createMultiplicationMatrix| |maxrow| + |open| |balancedBinaryTree| |semiLastSubResultantEuclidean| |nand| + |att2Result| |s14baf| |univariatePolynomial| |denomLODE| |fractRadix| + |getMultiplicationTable| |LyndonBasis| |inRadical?| |printTypes| + |s17agf| |redmat| |div| |plot| |leftTrace| |prod| |prime?| + |localReal?| |subPolSet?| |drawComplex| |pToDmp| |OMread| + |shallowCopy| |exquo| |quoByVar| |addPointLast| |multiEuclideanTree| + |controlPanel| |credPol| |toseInvertible?| |iomode| |c06eaf| + |polyRicDE| |hdmpToP| |elliptic| ~= |delete| |infLex?| + |removeDuplicates| |rootBound| |log2| |zag| |operations| + |printStatement| |numberOfVariables| |subQuasiComponent?| |stack| + |csch2sinh| |nonQsign| |#| |fullPartialFraction| |identification| + |numberOfComponents| |integralBasisAtInfinity| |setOrder| |lcm| + |constDsolve| |numerator| |createMultiplicationTable| |truncate| ~ + |OMputObject| |tower| |wordInStrongGenerators| |geometric| + |LowTriBddDenomInv| |rationalPoint?| |linears| |SturmHabichtMultiple| + |outputAsTex| |reindex| |arity| |prologue| |adaptive3D?| |quartic| + |divideExponents| |mappingMode| |rarrow| |vector| |append| + |setPosition| |commonDenominator| |oblateSpheroidal| + |branchPointAtInfinity?| |reify| |s19aaf| |e02ddf| |deepestInitial| + |safeCeiling| |changeVar| |differentiate| |gcd| + |functionIsContinuousAtEndPoints| |padicallyExpand| |cSin| + |bubbleSort!| |/\\| |scanOneDimSubspaces| |leadingTerm| + |diagonalMatrix| |dim| |countRealRoots| |pointPlot| |atanhIfCan| + |false| |argument| |pointColorDefault| |maxPoints3D| |squareMatrix| + |\\/| |explicitlyFinite?| |queue| |normFactors| |crest| |optpair| + |cos2sec| |rewriteIdealWithQuasiMonicGenerators| |realZeros| |cAsech| + |c06gsf| |tan2cot| |increase| |tensorProduct| |swapRows!| + |complexNumeric| |iidsum| RF2UTS |associative?| |getOrder| |OMgetAtp| + |euler| |iiacoth| |principal?| |mat| |setIntersection| |repSq| + |argumentListOf| |s17dlf| |leadingCoefficientRicDE| |e04jaf| |csubst| + |mainVariable?| |kernels| |complexForm| |relerror| LODO2FUN + |reducedQPowers| |d02ejf| |fullDisplay| |exponential| |eq?| + |absolutelyIrreducible?| |cosIfCan| |basisOfNucleus| + |generalizedContinuumHypothesisAssumed| |operator| |badValues| + |superHeight| |coerce| |integralRepresents| |power!| |rightPower| + |setref| |level| |elements| |graeffe| |addiag| + |factorsOfCyclicGroupSize| |exprToUPS| |multiplyExponents| |f01qdf| + |construct| |roughBase?| |splitNodeOf!| |getBadValues| |equiv| + |numberOfFractionalTerms| |diophantineSystem| |axesColorDefault| + |select!| |cCsc| |univariate| |commutative?| |taylorQuoByVar| |swap| + |legendreP| |comparison| |monomialIntPoly| |getMeasure| + |primintfldpoly| |varselect| |createRandomElement| |dihedral| + |leftPower| |getZechTable| |transcendentalDecompose| + |rightMinimalPolynomial| |OMgetAttr| |leftDiscriminant| + |fortranDoubleComplex| |exQuo| |rationalFunction| |roughBasicSet| + |noLinearFactor?| |choosemon| |useEisensteinCriterion?| |rightOne| + |coefChoose| |factor| |outputBinaryFile| |pdf2df| |coordinates| + |rCoord| |leftTraceMatrix| |kroneckerDelta| |numericalOptimization| + |hexDigit| |increment| |rightRankPolynomial| |sqrt| |merge| + |readInt8!| |selectAndPolynomials| |polyred| |lfextendedint| + |leadingIdeal| |extendedSubResultantGcd| |ef2edf| + |oneDimensionalArray| |eigenvector| |loadNativeModule| |real| + |retract| |solveRetract| |combineFeatureCompatibility| |s17ahf| + |elseBranch| |trim| |mr| |bit?| |iilog| |overlap| |OMconnOutDevice| + |imag| |nextNormalPrimitivePoly| |shiftRight| |df2mf| + |polarCoordinates| |mapdiv| |stronglyReduce| |shape| |Gamma| + |multiset| |cot2trig| |directProduct| |s17adf| |hue| |setStatus!| + |splitLinear| |hex| |overset?| |iipow| |vertConcat| |poisson| + |functionIsOscillatory| |gcdPrimitive| |heap| |KrullNumber| |reopen!| + |rightTraceMatrix| |radicalEigenvector| |intPatternMatch| |brace| + |makeTerm| |log| |lfextlimint| |complexIntegrate| |iCompose| + |parabolicCylindrical| |dmpToP| |component| |s15adf| |destruct| + |Vectorise| |repeating| |merge!| |alphabetic| |monomialIntegrate| + |initTable!| |ip4Address| |sin?| |stoseInvertibleSetsqfreg| |ravel| + |contains?| |mix| |discriminant| |inf| |matrixConcat3D| |tanAn| |expt| + |deleteProperty!| |nullary| |reshape| |trapezoidalo| |dequeue!| + |quasiMonic?| |viewPosDefault| |compdegd| |spherical| |drawToScale| + |heapSort| |more?| |fractRagits| |lflimitedint| |selectODEIVPRoutines| + |modTree| |goodPoint| |resultant| |setClipValue| |colorFunction| + |radicalSolve| |monomial| |returns| |conjugates| |univariateSolve| + |homogeneous?| |digit| |insertionSort!| |alphabetic?| + |semiDiscriminantEuclidean| |headReduce| |multivariate| |fracPart| + |iifact| |imagI| |bag| |complex?| |bitCoef| |curve| |upperCase| + |variables| |d01fcf| |entry?| |reduced?| |child| |uncouplingMatrices| + |leviCivitaSymbol| |symmetricProduct| |identityMatrix| |showRegion| + |update| |makeViewport3D| |wreath| |viewDeltaXDefault| |graphCurves| + |clipSurface| |rootPower| |quadraticForm| |irForm| |expintegrate| + |outputGeneral| |dimensionOfIrreducibleRepresentation| + |restorePrecision| |Hausdorff| |palgextint| + |noncommutativeJordanAlgebra?| |imports| |ratPoly| |singRicDE| + |prolateSpheroidal| |regularRepresentation| |minPol| |besselJ| + |d02bhf| |mapUp!| |cot2tan| |qPot| |leftQuotient| |acscIfCan| + |testModulus| |magnitude| |bringDown| |logGamma| |s14aaf| + |integralCoordinates| |sizePascalTriangle| |sincos| |taylor| + |parabolic| |s17aef| |floor| |evaluate| |d03edf| |parametric?| + |gcdPolynomial| |mainVariable| |reduceByQuasiMonic| |position| + |laurent| |palginfieldint| |mkAnswer| |infiniteProduct| |lfinfieldint| + |jvmSynchronized| |constantOpIfCan| |multiplyCoefficients| + |lfintegrate| |messagePrint| |removeRoughlyRedundantFactorsInPols| + |puiseux| |sh| |satisfy?| |maxPoints| |cothIfCan| + |generalizedEigenvectors| |linearlyDependentOverZ?| |Si| |typeList| + |cyclic| |writeByte!| |rootDirectory| |index?| |polygon?| + |binaryTournament| |jvmStrict| |pack!| |node?| |invertIfCan| + |PDESolve| |factorFraction| |inv| |groebSolve| |factorAndSplit| |move| + |curveColorPalette| |jvmStatic| |primeFrobenius| |ground?| + |pushuconst| |birth| |cCoth| |leftDivide| |back| + |brillhartIrreducible?| |elementary| |nextColeman| |setErrorBound| + |zeroVector| |ground| |listOfMonoms| |keys| |submod| |tab1| |remove| + |purelyAlgebraicLeadingMonomial?| |zerosOf| |realRoots| |extendIfCan| + |exprHasWeightCosWXorSinWX| |flagFactor| |gcdprim| |OMputEndObject| + |OMgetApp| |leadingMonomial| |zeroSetSplitIntoTriangularSystems| + |frst| |showAll?| |putProperty| |jvmPublic| |inverseLaplace| + |rightQuotient| |rowEch| |components| |htrigs| |leadingCoefficient| + |last| |createLowComplexityTable| |elRow1!| |OMreadStr| |order| + |jvmProtected| |singleFactorBound| |isEquiv| |badNum| |rational| + |laurentIfCan| |primitiveMonomials| |assoc| |stoseInvertibleSetreg| + |derivationCoordinates| |d01gbf| |normalizeAtInfinity| |idealiser| + |d01anf| |lastSubResultant| |chiSquare| |dot| |reductum| |e01bff| + |connectTo| |minRowIndex| |Ei| |viewDeltaYDefault| |quotedOperators| + |karatsuba| |cSech| |hasPredicate?| |factorSquareFreePolynomial| + |entries| |viewport3D| |iisqrt2| |patternMatchTimes| + |drawComplexVectorField| |branchPoint?| |key?| |whitePoint| + |possiblyNewVariety?| |delete!| |primPartElseUnitCanonical!| |po| + |iitan| |prinpolINFO| |getDatabase| |readBytes!| |meshFun2Var| + |pointSizeDefault| |charClass| |relativeApprox| |virtualDegree| + |jvmPrivate| |euclideanSize| |ScanFloatIgnoreSpacesIfCan| |pointData| + |zero| |eulerE| |symmetricGroup| |youngDiagram| |computeCycleLength| + |airyBi| |mainExpression| |polyRDE| |setButtonValue| |OMencodingSGML| + |stopMusserTrials| |branchIfCan| |bigEndian| |invmod| |mulmod| + |encodingDirectory| |LazardQuotient| |diagonal?| |mainPrimitivePart| + |And| |semicolonSeparate| |showAllElements| |cschIfCan| |rootPoly| + |maxrank| |getPickedPoints| |jvmNative| |getOperands| |primes| |zero?| + |Or| |basisOfCentroid| |signatureAst| |tree| |radicalOfLeftTraceForm| + |squareFreeFactors| |makeSUP| |relationsIdeal| |jvmFinal| + |exponentialOrder| |associates?| |Not| |simplifyLog| |c05adf| + |intensity| |stirling2| |numerators| |rischDEsys| |laurentRep| |test| + |listLoops| |position!| |OMwrite| |bandedJacobian| |withPredicates| + |closed| |symmetric?| |null?| |morphism| |module| |primlimitedint| + |lighting| |alternative?| |startTableInvSet!| |doubleComplex?| |irVar| + |dihedralGroup| |hostPlatform| |xn| |jvmAbstract| |showScalarValues| + |resultantReduitEuclidean| |stFunc2| |divisor| |minimize| + |screenResolution| |sayLength| |rotatey| |modifyPointData| + |identitySquareMatrix| |e01saf| |complete| |length| + |particularSolution| |leftUnits| |polygon| |incrementBy| |coefficient| + |polygamma| |Frobenius| |torsion?| |genericRightTrace| |totalDegree| + |scripts| |halfExtendedSubResultantGcd2| |escape| |gramschmidt| |pol| + |numberOfPrimitivePoly| |shade| |sylvesterMatrix| |nil| |makeEq| + |multMonom| |characteristicSet| |showArrayValues| |realSolve| + |realEigenvalues| |prefix| |factorOfDegree| |dark| + |createPrimitiveNormalPoly| |isList| |augment| |compose| + |resetAttributeButtons| |coordinate| |inverseIntegralMatrix| + |nullSpace| |mainMonomial| |redPo| |solveLinear| |paraboloidal| + |iisech| |sup| |viewWriteAvailable| |transform| |unaryFunction| + |constant| |monicRightDivide| |unprotectedRemoveRedundantFactors| + |approximate| |shanksDiscLogAlgorithm| |deepestTail| + |completeEchelonBasis| |deriv| |equation| |minset| |quoted?| |coerceL| + |ReduceOrder| |complex| |create3Space| |s17dgf| |constantLeft| + |indicialEquationAtInfinity| |leftRank| |mesh?| |coth2tanh| |logpart| + |lowerCase!| |normalElement| |possiblyInfinite?| |normalize| + |traverse| |indiceSubResultant| |makeViewport2D| |is?| + |rightCharacteristicPolynomial| |OMgetEndBVar| |tracePowMod| + |outputMeasure| |multiple?| |conjugate| |modularGcd| |trunc| + |alphanumeric?| |makingStats?| |fortran| |internalIntegrate0| + |outputList| |symmetricPower| |scan| |setright!| |rotate!| |critM| + |c06gqf| |trigs| |failed| |definingPolynomial| |scripted?| + |numberOfIrreduciblePoly| |asinIfCan| |decompose| |complexElementary| + |totalDifferential| |lyndonIfCan| |OMsupportsCD?| |ipow| + |nextPrimitivePoly| |octon| |romberg| |e04fdf| |pair?| |powerSum| + |createThreeSpace| |semiResultantEuclideannaif| |eigenMatrix| + |generalTwoFactor| |approximants| |iiacosh| |minGbasis| |push| + |factorsOfDegree| |boundOfCauchy| |getIdentifier| |aromberg| + |rowEchLocal| |iflist2Result| |diagonal| |varList| |cAcot| |getRef| + |integralMatrixAtInfinity| |mergeFactors| |setClosed| |quatern| + |cSinh| |getExplanations| |recur| |pastel| |squareFreePrim| |makeSin| + |smith| |changeWeightLevel| |c06gcf| |rdregime| |cylindrical| + |expIfCan| |subst| |obj| |definingEquations| |scalarMatrix| + |variationOfParameters| |setUnion| |semiResultantReduitEuclidean| + |iiasech| |groebgen| |currentScope| |complexZeros| |cache| + |graphStates| |decreasePrecision| |iiasin| |ode2| |mapExponents| + |fortranCharacter| |allRootsOf| |e02bdf| |nthFractionalTerm| + |palgintegrate| |retractIfCan| |zeroDimPrimary?| |slex| + |ramifiedAtInfinity?| |positive?| |minimumDegree| |setMinPoints3D| + |radicalRoots| |coefficients| |coercePreimagesImages| |quadratic| + |objects| |stFuncN| |integralDerivationMatrix| F2FG |hcrf| |space| + |dominantTerm| |qelt| |atanIfCan| |resetNew| |base| + |unrankImproperPartitions1| |script| |numberOfNormalPoly| |contract| + |hdmpToDmp| |iicsc| |hasTopPredicate?| |qsetelt| |pomopo!| |dimension| + |closed?| |d01apf| |monomRDE| |hexDigit?| |chiSquare1| |closedCurve?| + |iiacsch| |xRange| |insert!| |key| |noValueMode| |fractionPart| + |recoverAfterFail| |loopPoints| |checkForZero| |apply| |yRange| + |wordsForStrongGenerators| |extractBottom!| |neglist| |shift| |ode| + |tex| |createPrimitivePoly| |fi2df| |filename| |print| |contractSolve| + |linkToFortran| |zRange| |first| |bracket| |kernel| |green| |meatAxe| + |RittWuCompare| |pointLists| |getProperty| |resolve| |systemCommand| + |f02ajf| |cardinality| |map!| |rest| |simpson| |rationalApproximation| + |asechIfCan| |stoseLastSubResultant| |list| |e02aef| |map| + |shallowExpand| |graphs| |qsetelt!| |draw| |s21bdf| |measure| + |dmp2rfi| |primextendedint| |jvmVolatile| |extendedIntegrate| + |minPoints3D| |numberOfHues| |makeCos| |chebyshevU| |ord| |preprocess| + |differentialVariables| |jvmTransient| |moduleSum| |normal| + |constantCoefficientRicDE| |clipPointsDefault| |adjoint| + |zeroSquareMatrix| |setAdaptive3D| |tanh2coth| |antisymmetric?| + |gcdcofactprim| |limitedint| |complexEigenvalues| |row| |incr| + |setvalue!| |multinomial| |split| |Nul| |repeatUntilLoop| |typeLists| + |normInvertible?| |hi| |lowerCase?| |swapColumns!| |makeObject| + |mindeg| |karatsubaDivide| |convert| |lyndon?| |OMreadFile| |sncndn| + |sturmVariationsOf| |acsch| |previous| |genericPosition| |Lazard2| + |subresultantSequence| |coef| |splitConstant| |isOp| |imagJ| |number?| + |signAround| |comment| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-420 (-577))) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-38 |#1|) . T) ((-38 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-35) |has| |#1| (-1227)) ((-95) |has| |#1| (-1227)) ((-102) . T) ((-111 #0# #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-132) . T) ((-146) -2811 (|has| |#1| (-361)) (|has| |#1| (-146))) ((-148) |has| |#1| (-148)) ((-629 #0#) -2811 (|has| |#1| (-1063 (-420 (-577)))) (|has| |#1| (-361)) (|has| |#1| (-375))) ((-629 (-577)) . T) ((-629 |#1|) . T) ((-629 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-626 (-880)) . T) ((-174) . T) ((-627 (-171 (-228))) |has| |#1| (-1047)) ((-627 (-171 (-391))) |has| |#1| (-1047)) ((-627 (-549)) |has| |#1| (-627 (-549))) ((-627 (-911 (-391))) |has| |#1| (-627 (-911 (-391)))) ((-627 (-911 (-577))) |has| |#1| (-627 (-911 (-577)))) ((-627 #1=(-1197 |#1|)) . T) ((-235 $) -2811 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-233 |#1|) . T) ((-239) -2811 (|has| |#1| (-361)) (|has| |#1| (-239))) ((-238) -2811 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-273 |#1|) . T) ((-249) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-295) |has| |#1| (-1227)) ((-297 |#1| $) |has| |#1| (-297 |#1| |#1|)) ((-301) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-318) -2811 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-320 |#1|) |has| |#1| (-320 |#1|)) ((-375) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-415) |has| |#1| (-361)) ((-380) -2811 (|has| |#1| (-380)) (|has| |#1| (-361))) ((-361) |has| |#1| (-361)) ((-382 |#1| #1#) . T) ((-422 |#1| #1#) . T) ((-350 |#1|) . T) ((-389 |#1|) . T) ((-413 |#1|) . T) ((-424 |#1|) . T) ((-465) -2811 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-506) |has| |#1| (-1227)) ((-527 (-1201) |#1|) |has| |#1| (-527 (-1201) |#1|)) ((-527 |#1| |#1|) |has| |#1| (-320 |#1|)) ((-569) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-662 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-664 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-664 #2=(-577)) |has| |#1| (-654 (-577))) ((-664 |#1|) . T) ((-664 $) . T) ((-656 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-656 |#1|) . T) ((-656 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-654 #2#) |has| |#1| (-654 (-577))) ((-654 |#1|) . T) ((-733 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-733 |#1|) . T) ((-733 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-740 |#1| #1#) . T) ((-742) . T) ((-915 $ #3=(-1201)) -2811 (|has| |#1| (-923 (-1201))) (|has| |#1| (-921 (-1201)))) ((-921 (-1201)) |has| |#1| (-921 (-1201))) ((-923 #3#) -2811 (|has| |#1| (-923 (-1201))) (|has| |#1| (-921 (-1201)))) ((-905 (-391)) |has| |#1| (-905 (-391))) ((-905 (-577)) |has| |#1| (-905 (-577))) ((-903 |#1|) . T) ((-932) -12 (|has| |#1| (-318)) (|has| |#1| (-932))) ((-943) -2811 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-1027) -12 (|has| |#1| (-1027)) (|has| |#1| (-1227))) ((-1063 (-420 (-577))) |has| |#1| (-1063 (-420 (-577)))) ((-1063 (-577)) |has| |#1| (-1063 (-577))) ((-1063 |#1|) . T) ((-1076 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1076 |#1|) . T) ((-1076 $) . T) ((-1081 #0#) -2811 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1081 |#1|) . T) ((-1081 $) . T) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) |has| |#1| (-361)) ((-1227) |has| |#1| (-1227)) ((-1230) |has| |#1| (-1227)) ((-1242) . 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T) ((-235 $) -2867 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-233 |#1|) . T) ((-239) -2867 (|has| |#1| (-361)) (|has| |#1| (-239))) ((-238) -2867 (|has| |#1| (-361)) (|has| |#1| (-238)) (|has| |#1| (-239))) ((-273 |#1|) . T) ((-249) -2867 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-295) |has| |#1| (-1232)) ((-297 |#1| $) |has| |#1| (-297 |#1| |#1|)) ((-301) -2867 (|has| |#1| (-569)) (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-318) -2867 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-320 |#1|) |has| |#1| (-320 |#1|)) ((-375) -2867 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-415) |has| |#1| (-361)) ((-380) -2867 (|has| |#1| (-380)) (|has| |#1| (-361))) ((-361) |has| |#1| (-361)) ((-382 |#1| #1#) . T) ((-422 |#1| #1#) . T) ((-350 |#1|) . T) ((-389 |#1|) . T) ((-413 |#1|) . T) ((-424 |#1|) . 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T) ((-920 $ #3=(-1206)) -2867 (|has| |#1| (-928 (-1206))) (|has| |#1| (-926 (-1206)))) ((-926 (-1206)) |has| |#1| (-926 (-1206))) ((-928 #3#) -2867 (|has| |#1| (-928 (-1206))) (|has| |#1| (-926 (-1206)))) ((-910 (-391)) |has| |#1| (-910 (-391))) ((-910 (-577)) |has| |#1| (-910 (-577))) ((-908 |#1|) . T) ((-937) -12 (|has| |#1| (-318)) (|has| |#1| (-937))) ((-948) -2867 (|has| |#1| (-361)) (|has| |#1| (-375)) (|has| |#1| (-318))) ((-1032) -12 (|has| |#1| (-1032)) (|has| |#1| (-1232))) ((-1068 (-420 (-577))) |has| |#1| (-1068 (-420 (-577)))) ((-1068 (-577)) |has| |#1| (-1068 (-577))) ((-1068 |#1|) . T) ((-1081 #0#) -2867 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1081 |#1|) . T) ((-1081 $) . T) ((-1086 #0#) -2867 (|has| |#1| (-361)) (|has| |#1| (-375))) ((-1086 |#1|) . T) ((-1086 $) . T) ((-1079) . T) ((-1088) . T) ((-1142) . T) ((-1130) . T) ((-1182) |has| |#1| (-361)) ((-1232) |has| |#1| (-1232)) ((-1235) |has| |#1| (-1232)) ((-1247) . 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T) ((-102) -2811 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2811 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-132) -2811 (|has| |#2| (-1074)) (|has| |#2| (-809)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-629 #0=(-420 (-577))) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-629 (-577)) -2811 (|has| |#2| (-1074)) (-12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125)))) ((-629 |#2|) |has| |#2| (-1125)) ((-626 (-880)) -2811 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-626 (-880))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-626 (-1292 |#2|)) . T) ((-235 $) -2811 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-233 |#2|) |has| |#2| (-1074)) ((-239) -12 (|has| |#2| (-239)) (|has| |#2| (-1074))) ((-238) -2811 (-12 (|has| |#2| (-238)) (|has| |#2| (-1074))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1074)))) ((-273 |#2|) |has| |#2| (-1074)) ((-297 #1=(-577) |#2|) . T) ((-299 #1# |#2|) . T) ((-320 |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-380) |has| |#2| (-380)) ((-389 |#2|) |has| |#2| (-1074)) ((-424 |#2|) |has| |#2| (-1125)) ((-502 |#2|) . T) ((-617 #1# |#2|) . T) ((-527 |#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1125))) ((-662 (-577)) -2811 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-662 |#2|) -2811 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-662 $) |has| |#2| (-1074)) ((-664 #2=(-577)) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-664 |#2|) -2811 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-664 $) |has| |#2| (-1074)) ((-656 |#2|) -2811 (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-654 #2#) -12 (|has| |#2| (-654 (-577))) (|has| |#2| (-1074))) ((-654 |#2|) |has| |#2| (-1074)) ((-733 |#2|) -2811 (|has| |#2| (-375)) (|has| |#2| (-174))) ((-742) |has| |#2| (-1074)) ((-808) |has| |#2| (-809)) ((-809) |has| |#2| (-809)) ((-810) |has| |#2| (-809)) ((-811) |has| |#2| (-809)) ((-865) -2811 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-868) -2811 (|has| |#2| (-865)) (|has| |#2| (-809))) ((-915 $ #3=(-1201)) -2811 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-921 (-1201)) -12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074))) ((-923 #3#) -2811 (-12 (|has| |#2| (-923 (-1201))) (|has| |#2| (-1074))) (-12 (|has| |#2| (-921 (-1201))) (|has| |#2| (-1074)))) ((-1063 #0#) -12 (|has| |#2| (-1063 (-420 (-577)))) (|has| |#2| (-1125))) ((-1063 (-577)) -12 (|has| |#2| (-1063 (-577))) (|has| |#2| (-1125))) ((-1063 |#2|) |has| |#2| (-1125)) ((-1076 |#2|) -2811 (|has| |#2| (-1074)) (|has| |#2| (-742)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1081 |#2|) -2811 (|has| |#2| (-1074)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1074) |has| |#2| (-1074)) ((-1083) |has| |#2| (-1074)) ((-1137) |has| |#2| (-1074)) ((-1125) -2811 (|has| |#2| (-1125)) (|has| |#2| (-1074)) (|has| |#2| (-865)) (|has| |#2| (-809)) (|has| |#2| (-742)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1242) . T) ((-1299 |#2|) |has| |#2| (-375))) -((-1979 (((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 21 T ELT)) (-2498 ((|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 23 T ELT)) (-2124 (((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)) 18 T ELT))) -(((-245 |#1| |#2| |#3|) (-10 -7 (-15 -1979 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -2498 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -2124 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) (-787) (-1242) (-1242)) (T -245)) -((-2124 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *7 (-1242)) (-5 *2 (-246 *5 *7)) (-5 *1 (-245 *5 *6 *7)))) (-2498 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-787)) (-4 *6 (-1242)) (-4 *2 (-1242)) (-5 *1 (-245 *5 *6 *2)))) (-1979 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-246 *6 *7)) (-14 *6 (-787)) (-4 *7 (-1242)) (-4 *5 (-1242)) (-5 *2 (-246 *6 *5)) (-5 *1 (-245 *6 *7 *5))))) 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(|has| $ (-6 -4499)) ELT))) +(((-244 |#1| |#2|) (-141) (-792) (-1247)) (T -244)) +((-3805 (*1 *1 *2) (-12 (-5 *2 (-1297 *4)) (-4 *4 (-1247)) (-4 *1 (-244 *3 *4)))) (-1385 (*1 *1 *2) (-12 (-5 *2 (-949)) (-4 *1 (-244 *3 *4)) (-4 *4 (-1079)) (-4 *4 (-1247)))) (-4047 (*1 *2 *1 *1) (-12 (-4 *1 (-244 *3 *2)) (-4 *2 (-1247)) (-4 *2 (-1079))))) +(-13 (-617 (-577) |t#2|) (-631 (-1297 |t#2|)) (-10 -8 (-6 -4499) (-15 -3805 ($ (-1297 |t#2|))) (IF (|has| |t#2| (-1130)) (-6 (-424 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1079)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-233 |t#2|)) (-6 (-389 |t#2|)) (-15 -1385 ($ (-949))) (-15 -4047 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-132)) (-6 (-132)) |%noBranch|) (IF (|has| |t#2| (-23)) (-6 (-23)) |%noBranch|) (IF (|has| |t#2| (-21)) (-6 (-21)) |%noBranch|) (IF (|has| |t#2| (-747)) (-6 (-661 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-380)) (-6 (-380)) |%noBranch|) (IF (|has| |t#2| (-174)) (-6 (-738 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-6 -4496)) (-6 -4496) |%noBranch|) (IF (|has| |t#2| (-870)) (-6 (-870)) |%noBranch|) (IF (|has| |t#2| (-814)) (-6 (-814)) |%noBranch|) (IF (|has| |t#2| (-375)) (-6 (-1304 |t#2|)) |%noBranch|))) +(((-21) -2867 (|has| |#2| (-1079)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-23) -2867 (|has| |#2| (-1079)) (|has| |#2| (-814)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-25) -2867 (|has| |#2| (-1079)) (|has| |#2| (-814)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-34) . T) ((-102) -2867 (|has| |#2| (-1130)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|has| |#2| (-814)) (|has| |#2| (-747)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2867 (|has| |#2| (-1079)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-132) -2867 (|has| |#2| (-1079)) (|has| |#2| (-814)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-21))) ((-634 #0=(-420 (-577))) -12 (|has| |#2| (-1068 (-420 (-577)))) (|has| |#2| (-1130))) ((-634 (-577)) -2867 (|has| |#2| (-1079)) (-12 (|has| |#2| (-1068 (-577))) (|has| |#2| (-1130)))) ((-634 |#2|) |has| |#2| (-1130)) ((-631 (-885)) -2867 (|has| |#2| (-1130)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|has| |#2| (-814)) (|has| |#2| (-747)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-631 (-885))) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-631 (-1297 |#2|)) . T) ((-235 $) -2867 (-12 (|has| |#2| (-238)) (|has| |#2| (-1079))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1079)))) ((-233 |#2|) |has| |#2| (-1079)) ((-239) -12 (|has| |#2| (-239)) (|has| |#2| (-1079))) ((-238) -2867 (-12 (|has| |#2| (-238)) (|has| |#2| (-1079))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1079)))) ((-273 |#2|) |has| |#2| (-1079)) ((-297 #1=(-577) |#2|) . T) ((-299 #1# |#2|) . T) ((-320 |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1130))) ((-380) |has| |#2| (-380)) ((-389 |#2|) |has| |#2| (-1079)) ((-424 |#2|) |has| |#2| (-1130)) ((-502 |#2|) . T) ((-617 #1# |#2|) . T) ((-527 |#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1130))) ((-667 (-577)) -2867 (|has| |#2| (-1079)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-21))) ((-667 |#2|) -2867 (|has| |#2| (-1079)) (|has| |#2| (-747)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-667 $) |has| |#2| (-1079)) ((-669 #2=(-577)) -12 (|has| |#2| (-659 (-577))) (|has| |#2| (-1079))) ((-669 |#2|) -2867 (|has| |#2| (-1079)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-669 $) |has| |#2| (-1079)) ((-661 |#2|) -2867 (|has| |#2| (-747)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-659 #2#) -12 (|has| |#2| (-659 (-577))) (|has| |#2| (-1079))) ((-659 |#2|) |has| |#2| (-1079)) ((-738 |#2|) -2867 (|has| |#2| (-375)) (|has| |#2| (-174))) ((-747) |has| |#2| (-1079)) ((-813) |has| |#2| (-814)) ((-814) |has| |#2| (-814)) ((-815) |has| |#2| (-814)) ((-816) |has| |#2| (-814)) ((-870) -2867 (|has| |#2| (-870)) (|has| |#2| (-814))) ((-873) -2867 (|has| |#2| (-870)) (|has| |#2| (-814))) ((-920 $ #3=(-1206)) -2867 (-12 (|has| |#2| (-928 (-1206))) (|has| |#2| (-1079))) (-12 (|has| |#2| (-926 (-1206))) (|has| |#2| (-1079)))) ((-926 (-1206)) -12 (|has| |#2| (-926 (-1206))) (|has| |#2| (-1079))) ((-928 #3#) -2867 (-12 (|has| |#2| (-928 (-1206))) (|has| |#2| (-1079))) (-12 (|has| |#2| (-926 (-1206))) (|has| |#2| (-1079)))) ((-1068 #0#) -12 (|has| |#2| (-1068 (-420 (-577)))) (|has| |#2| (-1130))) ((-1068 (-577)) -12 (|has| |#2| (-1068 (-577))) (|has| |#2| (-1130))) ((-1068 |#2|) |has| |#2| (-1130)) ((-1081 |#2|) -2867 (|has| |#2| (-1079)) (|has| |#2| (-747)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1086 |#2|) -2867 (|has| |#2| (-1079)) (|has| |#2| (-375)) (|has| |#2| (-174))) ((-1079) |has| |#2| (-1079)) ((-1088) |has| |#2| (-1079)) ((-1142) |has| |#2| (-1079)) ((-1130) -2867 (|has| |#2| (-1130)) (|has| |#2| (-1079)) (|has| |#2| (-870)) (|has| |#2| (-814)) (|has| |#2| (-747)) (|has| |#2| (-380)) (|has| |#2| (-375)) (|has| |#2| (-174)) (|has| |#2| (-132)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1247) . T) ((-1304 |#2|) |has| |#2| (-375))) +((-4256 (((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 21 T ELT)) (-2060 ((|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|) 23 T ELT)) (-4417 (((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)) 18 T ELT))) +(((-245 |#1| |#2| |#3|) (-10 -7 (-15 -4256 ((-246 |#1| |#3|) (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -2060 (|#3| (-1 |#3| |#2| |#3|) (-246 |#1| |#2|) |#3|)) (-15 -4417 ((-246 |#1| |#3|) (-1 |#3| |#2|) (-246 |#1| |#2|)))) (-792) (-1247) (-1247)) (T -245)) +((-4417 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-246 *5 *6)) (-14 *5 (-792)) (-4 *6 (-1247)) (-4 *7 (-1247)) (-5 *2 (-246 *5 *7)) (-5 *1 (-245 *5 *6 *7)))) (-2060 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-246 *5 *6)) (-14 *5 (-792)) (-4 *6 (-1247)) (-4 *2 (-1247)) (-5 *1 (-245 *5 *6 *2)))) (-4256 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-246 *6 *7)) (-14 *6 (-792)) (-4 *7 (-1247)) (-4 *5 (-1247)) (-5 *2 (-246 *6 *5)) (-5 *1 (-245 *6 *7 *5))))) 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T) ((-465) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-569) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-662 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-662 #1#) . T) ((-662 (-577)) . T) ((-662 $) . T) ((-664 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-664 #1#) . T) ((-664 #2=(-577)) |has| (-420 |#2|) (-654 (-577))) ((-664 $) . T) ((-656 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-656 #1#) . T) ((-656 $) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-654 #1#) . T) ((-654 #2#) |has| (-420 |#2|) (-654 (-577))) ((-733 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-733 #1#) . T) ((-733 $) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-740 #1# |#3|) . T) ((-742) . T) ((-915 $ #3=(-1201)) -2811 (-12 (|has| (-420 |#2|) (-375)) (|has| (-420 |#2|) (-923 (-1201)))) (-12 (|has| (-420 |#2|) (-375)) (|has| (-420 |#2|) (-921 (-1201))))) ((-921 (-1201)) -12 (|has| (-420 |#2|) (-375)) (|has| (-420 |#2|) (-921 (-1201)))) ((-923 #3#) -2811 (-12 (|has| (-420 |#2|) (-375)) (|has| (-420 |#2|) (-923 (-1201)))) (-12 (|has| (-420 |#2|) (-375)) (|has| (-420 |#2|) (-921 (-1201))))) ((-943) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-1063 (-420 (-577))) |has| (-420 |#2|) (-1063 (-420 (-577)))) ((-1063 #1#) . T) ((-1063 (-577)) |has| (-420 |#2|) (-1063 (-577))) ((-1076 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-1076 #1#) . T) ((-1076 $) . T) ((-1081 #0#) -2811 (|has| (-420 |#2|) (-361)) (|has| (-420 |#2|) (-375))) ((-1081 #1#) . T) ((-1081 $) . T) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) |has| (-420 |#2|) (-361)) ((-1242) . 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T) ((-313) . T) ((-375) |has| |#1| (-569)) ((-389 |#1|) |has| |#1| (-1079)) ((-413 |#1|) . T) ((-424 |#1|) . T) ((-465) |has| |#1| (-569)) ((-486) |has| |#1| (-486)) ((-527 (-630 $) $) . T) ((-527 $ $) . 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|lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -4375 ($ (-2 (|:| -4376 (-2 (|:| |var| (-1206)) (|:| |fn| (-327 (-228))) (|:| -3433 (-1124 (-864 (-228)))) (|:| |abserr| (-228)) (|:| |relerr| (-228)))) (|:| -2727 (-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| (-1187 (-228))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -3433 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| 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T) ((-23) . T) ((-25) . T) ((-34) . T) ((-38 |#2|) |has| |#2| (-6 (-4501 "*"))) ((-102) . T) ((-111 |#2| |#2|) . T) ((-132) . T) ((-634 #0=(-420 (-577))) |has| |#2| (-1068 (-420 (-577)))) ((-634 (-577)) . T) ((-634 |#2|) . T) ((-631 (-885)) . T) ((-235 $) -2867 (|has| |#2| (-238)) (|has| |#2| (-239))) ((-233 |#2|) . T) ((-239) |has| |#2| (-239)) ((-238) -2867 (|has| |#2| (-238)) (|has| |#2| (-239))) ((-273 |#2|) . T) ((-320 |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1130))) ((-389 |#2|) . T) ((-424 |#2|) . T) ((-502 |#2|) . T) ((-527 |#2| |#2|) -12 (|has| |#2| (-320 |#2|)) (|has| |#2| (-1130))) ((-667 (-577)) . T) ((-667 |#2|) . T) ((-667 $) . T) ((-669 #1=(-577)) |has| |#2| (-659 (-577))) ((-669 |#2|) . T) ((-669 $) . T) ((-661 |#2|) -2867 (|has| |#2| (-174)) (|has| |#2| (-6 (-4501 "*")))) ((-659 #1#) |has| |#2| (-659 (-577))) ((-659 |#2|) . T) ((-738 |#2|) -2867 (|has| |#2| (-174)) (|has| |#2| (-6 (-4501 "*")))) ((-747) . 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T) ((-297 |#2| $) -12 (|has| |#1| (-375)) (|has| |#2| (-297 |#2| |#2|))) ((-297 $ $) |has| (-577) (-1137)) ((-301) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-320 |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-375) |has| |#1| (-375)) ((-350 |#2|) |has| |#1| (-375)) ((-389 |#2|) |has| |#1| (-375)) ((-413 |#2|) |has| |#1| (-375)) ((-465) |has| |#1| (-375)) ((-506) |has| |#1| (-38 (-420 (-577)))) ((-527 (-1201) |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-527 (-1201) |#2|))) ((-527 |#2| |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-569) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-662 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 |#2|) |has| |#1| (-375)) ((-662 $) . T) ((-664 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-664 #3=(-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-664 |#1|) . T) ((-664 |#2|) |has| |#1| (-375)) ((-664 $) . T) ((-656 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-656 |#1|) |has| |#1| (-174)) ((-656 |#2|) |has| |#1| (-375)) ((-656 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-654 #3#) -12 (|has| |#1| (-375)) (|has| |#2| (-654 (-577)))) ((-654 |#2|) |has| |#1| (-375)) ((-733 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-733 |#1|) |has| |#1| (-174)) ((-733 |#2|) |has| |#1| (-375)) ((-733 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-742) . 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T) ((-943) |has| |#1| (-375)) ((-1017 |#2|) |has| |#1| (-375)) ((-1027) |has| |#1| (-38 (-420 (-577)))) ((-1047) -12 (|has| |#1| (-375)) (|has| |#2| (-1047))) ((-1063 (-420 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-577)))) ((-1063 #2#) -12 (|has| |#1| (-375)) (|has| |#2| (-1063 (-1201)))) ((-1063 |#2|) . T) ((-1076 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1076 |#1|) . T) ((-1076 |#2|) |has| |#1| (-375)) ((-1076 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1081 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-375)) ((-1081 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1177) -12 (|has| |#1| (-375)) (|has| |#2| (-1177))) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . 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T) ((-569) -2811 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-662 #1#) |has| |#1| (-38 (-420 (-577)))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-664 #1#) |has| |#1| (-38 (-420 (-577)))) ((-664 #3=(-577)) |has| |#1| (-654 (-577))) ((-664 |#1|) . T) ((-664 $) . T) ((-656 #1#) |has| |#1| (-38 (-420 (-577)))) ((-656 |#1|) |has| |#1| (-174)) ((-656 $) -2811 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-654 #3#) |has| |#1| (-654 (-577))) ((-654 |#1|) . T) ((-733 #1#) |has| |#1| (-38 (-420 (-577)))) ((-733 |#1|) |has| |#1| (-174)) ((-733 $) -2811 (|has| |#1| (-932)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-742) . T) ((-915 $ #2#) . T) ((-915 $ #4=(-1201)) -2811 (|has| |#1| (-923 (-1201))) (|has| |#1| (-921 (-1201)))) ((-921 #2#) . T) ((-921 (-1201)) |has| |#1| (-921 (-1201))) ((-923 #2#) . 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T) ((-23) . T) ((-47 |#1| #0=(-420 (-577))) . T) ((-25) . T) ((-38 #1=(-420 (-577))) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-35) |has| |#1| (-38 (-420 (-577)))) ((-95) |has| |#1| (-38 (-420 (-577)))) ((-102) . T) ((-111 #1# #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-629 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-629 (-577)) . T) ((-629 |#1|) |has| |#1| (-174)) ((-629 |#2|) . T) ((-629 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-626 (-880)) . T) ((-174) -2811 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-235 $) |has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) ((-238) |has| |#1| (-15 * (|#1| (-420 (-577)) |#1|))) ((-249) |has| |#1| (-375)) ((-295) |has| |#1| (-38 (-420 (-577)))) ((-297 #0# |#1|) . T) ((-297 $ $) |has| (-420 (-577)) (-1137)) ((-301) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-375) |has| |#1| (-375)) ((-465) |has| |#1| (-375)) ((-506) |has| |#1| (-38 (-420 (-577)))) ((-569) -2811 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-662 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-662 (-577)) . T) ((-662 |#1|) . T) ((-662 $) . T) ((-664 #1#) -2811 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-664 |#1|) . T) ((-664 $) . 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T) ((-1076 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1081 #1#) |has| |#1| (-38 (-420 (-577)))) ((-1081 |#1|) . T) ((-1081 $) -2811 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1074) . T) ((-1083) . T) ((-1137) . T) ((-1125) . T) ((-1227) |has| |#1| (-38 (-420 (-577)))) ((-1230) |has| |#1| (-38 (-420 (-577)))) ((-1242) . T) ((-1270 |#1| #0#) . 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(-1185 2973650 2975715 2977509 "STTAYLOR" 2980774 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1184 2966404 2973514 2973597 "STRTBL" 2973602 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1183 2960801 2966113 2966212 "STRING" 2966327 T STRING (NIL) -8 NIL NIL NIL) (-1182 2952911 2958420 2959031 "STREAM" 2960225 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1181 2952415 2952498 2952642 "STREAM3" 2952828 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1180 2951379 2951580 2951815 "STREAM2" 2952228 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1179 2951061 2951119 2951212 "STREAM1" 2951321 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1178 2950053 2950258 2950489 "STINPROD" 2950877 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1177 2949549 2949801 2949831 "STEP" 2949911 T STEP (NIL) -9 NIL 2949989 NIL) (-1176 2948664 2949038 2949186 "STEPAST" 2949423 T STEPAST (NIL) -8 NIL NIL NIL) (-1175 2941720 2948563 2948640 "STBL" 2948645 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1174 2936278 2940883 2940926 "STAGG" 2941079 NIL STAGG (NIL T) -9 NIL 2941168 NIL) (-1173 2933830 2934582 2935454 "STAGG-" 2935459 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1172 2931802 2933600 2933692 "STACK" 2933773 NIL STACK (NIL T) -8 NIL NIL NIL) (-1171 2923809 2929943 2930399 "SREGSET" 2931432 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1170 2916156 2917603 2919116 "SRDCMPK" 2922415 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1169 2908465 2913515 2913545 "SRAGG" 2914848 T SRAGG (NIL) -9 NIL 2915456 NIL) (-1168 2907416 2907737 2908116 "SRAGG-" 2908121 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1167 2901000 2906363 2906784 "SQMATRIX" 2907042 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1166 2894412 2897718 2898445 "SPLTREE" 2900345 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1165 2890237 2891068 2891714 "SPLNODE" 2893838 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1164 2889212 2889517 2889547 "SPFCAT" 2889991 T SPFCAT (NIL) -9 NIL NIL NIL) (-1163 2887907 2888159 2888423 "SPECOUT" 2888970 T SPECOUT (NIL) -7 NIL NIL NIL) (-1162 2878559 2880875 2880905 "SPADXPT" 2885581 T SPADXPT (NIL) -9 NIL 2887745 NIL) (-1161 2878314 2878360 2878429 "SPADPRSR" 2878512 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1160 2875919 2878269 2878300 "SPADAST" 2878305 T SPADAST (NIL) -8 NIL NIL NIL) (-1159 2867520 2869623 2869666 "SPACEC" 2874039 NIL SPACEC (NIL T) -9 NIL 2875855 NIL) (-1158 2865320 2867452 2867501 "SPACE3" 2867506 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1157 2864052 2864243 2864534 "SORTPAK" 2865125 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1156 2862114 2862447 2862859 "SOLVETRA" 2863716 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1155 2861152 2861386 2861647 "SOLVESER" 2861887 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1154 2856384 2857344 2858339 "SOLVERAD" 2860204 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1153 2852109 2852808 2853537 "SOLVEFOR" 2855751 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1152 2845720 2851457 2851554 "SNTSCAT" 2851559 NIL SNTSCAT (NIL T T T T) -9 NIL 2851629 NIL) (-1151 2839264 2844043 2844434 "SMTS" 2845410 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1150 2832979 2839152 2839229 "SMP" 2839234 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1149 2831108 2831439 2831837 "SMITH" 2832676 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1148 2822640 2827687 2827790 "SMATCAT" 2829141 NIL SMATCAT (NIL NIL T T T) -9 NIL 2829691 NIL) (-1147 2819412 2820403 2821581 "SMATCAT-" 2821586 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1146 2816881 2818620 2818663 "SKAGG" 2818924 NIL SKAGG (NIL T) -9 NIL 2819059 NIL) (-1145 2812375 2816354 2816538 "SINT" 2816690 T SINT (NIL) -8 NIL NIL 2816852) (-1144 2812141 2812185 2812251 "SIMPAN" 2812331 T SIMPAN (NIL) -7 NIL NIL NIL) (-1143 2811366 2811676 2811816 "SIG" 2812023 T SIG (NIL) -8 NIL NIL NIL) (-1142 2810186 2810425 2810700 "SIGNRF" 2811125 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1141 2809001 2809170 2809454 "SIGNEF" 2810015 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1140 2808241 2808584 2808708 "SIGAST" 2808899 T SIGAST (NIL) -8 NIL NIL NIL) (-1139 2805893 2806385 2806891 "SHP" 2807782 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1138 2799266 2805794 2805870 "SHDP" 2805875 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1137 2798777 2799017 2799047 "SGROUP" 2799140 T SGROUP (NIL) -9 NIL 2799202 NIL) (-1136 2798629 2798661 2798734 "SGROUP-" 2798739 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1135 2795348 2796118 2796841 "SGCF" 2797928 T SGCF (NIL) -7 NIL NIL NIL) (-1134 2789057 2794794 2794891 "SFRTCAT" 2794896 NIL SFRTCAT (NIL T T T T) -9 NIL 2794935 NIL) (-1133 2782376 2783496 2784632 "SFRGCD" 2788040 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1132 2775394 2776575 2777761 "SFQCMPK" 2781309 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2774996 2775103 2775214 "SFORT" 2775335 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1130 2773922 2774836 2774957 "SEXOF" 2774962 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1129 2772837 2773803 2773871 "SEX" 2773876 T SEX (NIL) -8 NIL NIL NIL) (-1128 2768426 2769333 2769428 "SEXCAT" 2772050 NIL SEXCAT (NIL T T T T T) -9 NIL 2772610 NIL) (-1127 2765235 2768360 2768408 "SET" 2768413 NIL SET (NIL T) -8 NIL NIL NIL) (-1126 2763357 2763948 2764253 "SETMN" 2764976 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1125 2762887 2763075 2763105 "SETCAT" 2763222 T SETCAT (NIL) -9 NIL 2763307 NIL) (-1124 2762655 2762719 2762818 "SETCAT-" 2762823 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1123 2758758 2761116 2761159 "SETAGG" 2762029 NIL SETAGG (NIL T) -9 NIL 2762369 NIL) (-1122 2758180 2758332 2758569 "SETAGG-" 2758574 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1121 2757563 2757876 2757977 "SEQAST" 2758101 T SEQAST (NIL) -8 NIL NIL NIL) (-1120 2756690 2757056 2757117 "SEGXCAT" 2757403 NIL SEGXCAT (NIL T T) -9 NIL 2757523 NIL) (-1119 2755606 2756356 2756538 "SEG" 2756543 NIL SEG (NIL T) -8 NIL NIL NIL) (-1118 2754531 2754799 2754842 "SEGCAT" 2755364 NIL SEGCAT (NIL T) -9 NIL 2755585 NIL) (-1117 2753421 2753894 2754102 "SEGBIND" 2754358 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1116 2753036 2753101 2753214 "SEGBIND2" 2753356 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1115 2752555 2752837 2752914 "SEGAST" 2752981 T SEGAST (NIL) -8 NIL NIL NIL) (-1114 2751764 2751900 2752104 "SEG2" 2752399 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1113 2750997 2751699 2751746 "SDVAR" 2751751 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1112 2742348 2750767 2750897 "SDPOL" 2750902 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1111 2740917 2741207 2741526 "SCPKG" 2742063 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1110 2740039 2740253 2740445 "SCOPE" 2740747 T SCOPE (NIL) -8 NIL NIL NIL) (-1109 2739235 2739393 2739572 "SCACHE" 2739894 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1108 2738819 2739053 2739083 "SASTCAT" 2739088 T SASTCAT (NIL) -9 NIL 2739101 NIL) (-1107 2738222 2738654 2738730 "SAOS" 2738765 T SAOS (NIL) -8 NIL NIL NIL) (-1106 2737781 2737822 2737995 "SAERFFC" 2738181 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1105 2730808 2737678 2737758 "SAE" 2737763 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1104 2730395 2730436 2730595 "SAEFACT" 2730767 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1103 2728698 2729030 2729431 "RURPK" 2730061 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1102 2727275 2727641 2727946 "RULESET" 2728532 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1101 2724390 2725028 2725486 "RULE" 2726956 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1100 2723960 2724184 2724267 "RULECOLD" 2724342 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1099 2723744 2723778 2723849 "RTVALUE" 2723911 T RTVALUE (NIL) -8 NIL NIL NIL) (-1098 2723155 2723461 2723555 "RSTRCAST" 2723672 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1097 2717925 2718798 2719718 "RSETGCD" 2722354 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1096 2706496 2712233 2712330 "RSETCAT" 2716449 NIL RSETCAT (NIL T T T T) -9 NIL 2717546 NIL) (-1095 2704315 2704962 2705786 "RSETCAT-" 2705791 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1094 2696623 2698077 2699597 "RSDCMPK" 2702914 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2694492 2695055 2695129 "RRCC" 2696215 NIL RRCC (NIL T T) -9 NIL 2696559 NIL) (-1092 2693813 2694017 2694296 "RRCC-" 2694301 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1091 2693196 2693509 2693610 "RPTAST" 2693734 T RPTAST (NIL) -8 NIL NIL NIL) (-1090 2665582 2676308 2676375 "RPOLCAT" 2687041 NIL RPOLCAT (NIL T T T) -9 NIL 2690201 NIL) (-1089 2656552 2659420 2662542 "RPOLCAT-" 2662547 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1088 2647005 2654763 2655245 "ROUTINE" 2656092 T ROUTINE (NIL) -8 NIL NIL NIL) (-1087 2643054 2646631 2646771 "ROMAN" 2646887 T ROMAN (NIL) -8 NIL NIL NIL) (-1086 2641166 2641914 2642174 "ROIRC" 2642859 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1085 2636884 2639655 2639685 "RNS" 2639989 T RNS (NIL) -9 NIL 2640263 NIL) (-1084 2635291 2635776 2636310 "RNS-" 2636385 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1083 2634584 2635088 2635118 "RNG" 2635123 T RNG (NIL) -9 NIL 2635144 NIL) (-1082 2633545 2633949 2634151 "RNGBIND" 2634435 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1081 2632840 2633318 2633361 "RMODULE" 2633366 NIL RMODULE (NIL T) -9 NIL 2633393 NIL) (-1080 2631664 2631770 2632106 "RMCAT2" 2632741 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1079 2628166 2631010 2631307 "RMATRIX" 2631426 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1078 2620665 2623253 2623368 "RMATCAT" 2626727 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2627709 NIL) (-1077 2620004 2620187 2620494 "RMATCAT-" 2620499 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1076 2619577 2619791 2619834 "RLINSET" 2619896 NIL RLINSET (NIL T) -9 NIL 2619940 NIL) (-1075 2619138 2619219 2619347 "RINTERP" 2619496 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1074 2618062 2618736 2618766 "RING" 2618822 T RING (NIL) -9 NIL 2618914 NIL) (-1073 2617842 2617898 2617995 "RING-" 2618000 NIL RING- (NIL T) -8 NIL NIL NIL) (-1072 2616653 2616920 2617178 "RIDIST" 2617606 T RIDIST (NIL) -7 NIL NIL NIL) (-1071 2607278 2616121 2616327 "RGCHAIN" 2616501 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1070 2606536 2607020 2607061 "RGBCSPC" 2607119 NIL RGBCSPC (NIL T) -9 NIL 2607171 NIL) (-1069 2605602 2606061 2606102 "RGBCMDL" 2606334 NIL RGBCMDL (NIL T) -9 NIL 2606448 NIL) (-1068 2602542 2603210 2603880 "RF" 2604966 NIL RF (NIL T) -7 NIL NIL NIL) (-1067 2602182 2602251 2602354 "RFFACTOR" 2602473 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1066 2601901 2601942 2602039 "RFFACT" 2602141 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1065 2599952 2600382 2600764 "RFDIST" 2601541 T RFDIST (NIL) -7 NIL NIL NIL) (-1064 2599399 2599497 2599660 "RETSOL" 2599854 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1063 2599017 2599115 2599158 "RETRACT" 2599291 NIL RETRACT (NIL T) -9 NIL 2599378 NIL) (-1062 2598860 2598891 2598978 "RETRACT-" 2598983 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1061 2598408 2598682 2598752 "RETAST" 2598812 T RETAST (NIL) -8 NIL NIL NIL) (-1060 2590758 2598061 2598188 "RESULT" 2598303 T RESULT (NIL) -8 NIL NIL NIL) (-1059 2589193 2590027 2590226 "RESRING" 2590661 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1058 2588817 2588878 2588976 "RESLATC" 2589130 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1057 2588516 2588557 2588664 "REPSQ" 2588776 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1056 2585896 2586518 2587120 "REP" 2587936 T REP (NIL) -7 NIL NIL NIL) (-1055 2585587 2585628 2585739 "REPDB" 2585855 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1054 2579419 2580876 2582099 "REP2" 2584399 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1053 2575722 2576477 2577285 "REP1" 2578646 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1052 2567730 2573863 2574319 "REGSET" 2575352 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1051 2566439 2566878 2567128 "REF" 2567515 NIL REF (NIL T) -8 NIL NIL NIL) (-1050 2565804 2565919 2566086 "REDORDER" 2566323 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1049 2561168 2565017 2565244 "RECLOS" 2565632 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1048 2560202 2560401 2560616 "REALSOLV" 2560975 T REALSOLV (NIL) -7 NIL NIL NIL) (-1047 2560036 2560089 2560119 "REAL" 2560124 T REAL (NIL) -9 NIL 2560159 NIL) (-1046 2556483 2557321 2558205 "REAL0Q" 2559201 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1045 2552036 2553072 2554133 "REAL0" 2555464 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1044 2551447 2551753 2551847 "RDUCEAST" 2551964 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1043 2550846 2550924 2551131 "RDIV" 2551369 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1042 2549896 2550088 2550301 "RDIST" 2550668 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1041 2548481 2548780 2549152 "RDETRS" 2549604 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1040 2546275 2546747 2547285 "RDETR" 2548023 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1039 2544894 2545178 2545575 "RDEEFS" 2545991 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1038 2543397 2543709 2544134 "RDEEF" 2544582 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1037 2536874 2540351 2540381 "RCFIELD" 2541676 T RCFIELD (NIL) -9 NIL 2542407 NIL) (-1036 2534830 2535442 2536138 "RCFIELD-" 2536213 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1035 2530882 2532903 2532946 "RCAGG" 2534030 NIL RCAGG (NIL T) -9 NIL 2534495 NIL) (-1034 2530492 2530604 2530767 "RCAGG-" 2530772 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1033 2529809 2529939 2530104 "RATRET" 2530376 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1032 2529350 2529429 2529550 "RATFACT" 2529737 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1031 2528628 2528778 2528930 "RANDSRC" 2529220 T RANDSRC (NIL) -7 NIL NIL NIL) (-1030 2528356 2528406 2528479 "RADUTIL" 2528577 T RADUTIL (NIL) -7 NIL NIL NIL) (-1029 2520480 2527187 2527498 "RADIX" 2528079 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1028 2510074 2520322 2520452 "RADFF" 2520457 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1027 2509703 2509796 2509826 "RADCAT" 2509986 T RADCAT (NIL) -9 NIL NIL NIL) (-1026 2509473 2509533 2509633 "RADCAT-" 2509638 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1025 2507384 2509243 2509335 "QUEUE" 2509416 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1024 2503223 2507317 2507365 "QUAT" 2507370 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1023 2502848 2502897 2503028 "QUATCT2" 2503174 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2495224 2499271 2499313 "QUATCAT" 2500104 NIL QUATCAT (NIL T) -9 NIL 2500870 NIL) (-1021 2491105 2492400 2493790 "QUATCAT-" 2493886 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2488361 2490153 2490196 "QUAGG" 2490577 NIL QUAGG (NIL T) -9 NIL 2490752 NIL) (-1019 2487909 2488183 2488253 "QQUTAST" 2488313 T QQUTAST (NIL) -8 NIL NIL NIL) (-1018 2486820 2487422 2487587 "QFORM" 2487790 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1017 2476496 2482667 2482709 "QFCAT" 2483377 NIL QFCAT (NIL T) -9 NIL 2484378 NIL) (-1016 2471811 2473264 2474858 "QFCAT-" 2474954 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1015 2471436 2471485 2471616 "QFCAT2" 2471762 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1014 2470867 2471001 2471133 "QEQUAT" 2471326 T QEQUAT (NIL) -8 NIL NIL NIL) (-1013 2463885 2465066 2466252 "QCMPACK" 2469800 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1012 2461335 2461871 2462301 "QALGSET" 2463540 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1011 2460564 2460746 2460982 "QALGSET2" 2461153 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1010 2459231 2459473 2459792 "PWFFINTB" 2460337 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1009 2457376 2457574 2457930 "PUSHVAR" 2459045 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1008 2453103 2454319 2454362 "PTRANFN" 2456273 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1007 2451440 2451785 2452109 "PTPACK" 2452814 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1006 2451063 2451126 2451237 "PTFUNC2" 2451377 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1005 2444988 2449852 2449895 "PTCAT" 2450195 NIL PTCAT (NIL T) -9 NIL 2450348 NIL) (-1004 2444637 2444678 2444804 "PSQFR" 2444947 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1003 2443209 2443525 2443861 "PSEUDLIN" 2444335 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1002 2429729 2432304 2434630 "PSETPK" 2440969 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1001 2422437 2425465 2425563 "PSETCAT" 2428604 NIL PSETCAT (NIL T T T T) -9 NIL 2429418 NIL) (-1000 2420162 2420904 2421728 "PSETCAT-" 2421733 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-999 2419481 2419676 2419704 "PSCURVE" 2419972 T PSCURVE (NIL) -9 NIL 2420139 NIL) (-998 2415207 2416981 2417046 "PSCAT" 2417890 NIL PSCAT (NIL T T T) -9 NIL 2418130 NIL) (-997 2414204 2414486 2414886 "PSCAT-" 2414891 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-996 2412413 2413273 2413536 "PRTITION" 2413961 T PRTITION (NIL) -8 NIL NIL NIL) (-995 2411828 2412134 2412226 "PRTDAST" 2412341 T PRTDAST (NIL) -8 NIL NIL NIL) (-994 2400710 2403132 2405320 "PRS" 2409690 NIL PRS (NIL T T) -7 NIL NIL NIL) (-993 2398330 2400032 2400072 "PRQAGG" 2400255 NIL PRQAGG (NIL T) -9 NIL 2400357 NIL) (-992 2397600 2397971 2397999 "PROPLOG" 2398138 T PROPLOG (NIL) -9 NIL 2398253 NIL) (-991 2397198 2397261 2397384 "PROPFUN2" 2397523 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-990 2396495 2396634 2396806 "PROPFUN1" 2397059 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-989 2394556 2395242 2395539 "PROPFRML" 2396231 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-988 2394001 2394132 2394260 "PROPERTY" 2394448 T PROPERTY (NIL) -8 NIL NIL NIL) (-987 2387889 2392167 2392987 "PRODUCT" 2393227 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-986 2384847 2387347 2387581 "PR" 2387700 NIL PR (NIL T T) -8 NIL NIL NIL) (-985 2384637 2384675 2384734 "PRINT" 2384808 T PRINT (NIL) -7 NIL NIL NIL) (-984 2383953 2384094 2384246 "PRIMES" 2384517 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-983 2382000 2382419 2382885 "PRIMELT" 2383532 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-982 2381717 2381778 2381806 "PRIMCAT" 2381930 T PRIMCAT (NIL) -9 NIL NIL NIL) (-981 2377439 2381655 2381700 "PRIMARR" 2381705 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-980 2376428 2376624 2376852 "PRIMARR2" 2377257 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-979 2376065 2376127 2376238 "PREASSOC" 2376366 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-978 2375516 2375673 2375701 "PPCURVE" 2375906 T PPCURVE (NIL) -9 NIL 2376042 NIL) (-977 2375063 2375311 2375394 "PORTNUM" 2375453 T PORTNUM (NIL) -8 NIL NIL NIL) (-976 2372400 2372821 2373413 "POLYROOT" 2374644 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-975 2365608 2372004 2372164 "POLY" 2372273 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2364985 2365049 2365283 "POLYLIFT" 2365544 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-973 2361206 2361709 2362338 "POLYCATQ" 2364530 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-972 2346854 2352953 2353018 "POLYCAT" 2356532 NIL POLYCAT (NIL T T T) -9 NIL 2358410 NIL) (-971 2339973 2342165 2344549 "POLYCAT-" 2344554 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-970 2339554 2339628 2339748 "POLY2UP" 2339899 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-969 2339180 2339243 2339352 "POLY2" 2339491 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-968 2337841 2338104 2338380 "POLUTIL" 2338954 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-967 2336160 2336473 2336804 "POLTOPOL" 2337563 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-966 2331156 2336094 2336141 "POINT" 2336146 NIL POINT (NIL T) -8 NIL NIL NIL) (-965 2329289 2329700 2330075 "PNTHEORY" 2330801 T PNTHEORY (NIL) -7 NIL NIL NIL) (-964 2327735 2328044 2328443 "PMTOOLS" 2328987 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-963 2327322 2327406 2327523 "PMSYM" 2327651 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-962 2326824 2326899 2327074 "PMQFCAT" 2327247 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-961 2326167 2326289 2326445 "PMPRED" 2326701 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-960 2325548 2325646 2325808 "PMPREDFS" 2326068 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-959 2324202 2324420 2324798 "PMPLCAT" 2325310 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-958 2323728 2323813 2323965 "PMLSAGG" 2324117 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-957 2323195 2323277 2323459 "PMKERNEL" 2323646 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-956 2322806 2322887 2323000 "PMINS" 2323114 NIL PMINS (NIL T) -7 NIL NIL NIL) (-955 2322242 2322317 2322526 "PMFS" 2322731 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-954 2321458 2321588 2321793 "PMDOWN" 2322119 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-953 2320601 2320783 2320964 "PMASS" 2321297 T PMASS (NIL) -7 NIL NIL NIL) (-952 2319850 2319984 2320147 "PMASSFS" 2320488 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-951 2319499 2319573 2319667 "PLOTTOOL" 2319776 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-950 2313920 2315310 2316458 "PLOT" 2318371 T PLOT (NIL) -8 NIL NIL NIL) (-949 2309574 2310768 2311689 "PLOT3D" 2313019 T PLOT3D (NIL) -8 NIL NIL NIL) (-948 2308462 2308663 2308898 "PLOT1" 2309378 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-947 2283637 2288528 2293379 "PLEQN" 2303728 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-946 2282943 2283077 2283257 "PINTERP" 2283502 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-945 2282630 2282683 2282786 "PINTERPA" 2282890 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-944 2281726 2282394 2282481 "PI" 2282521 T PI (NIL) -8 NIL NIL 2282588) (-943 2279811 2280984 2281012 "PID" 2281194 T PID (NIL) -9 NIL 2281328 NIL) (-942 2279556 2279599 2279674 "PICOERCE" 2279768 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-941 2278864 2279015 2279191 "PGROEB" 2279412 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-940 2274307 2275265 2276170 "PGE" 2277979 T PGE (NIL) -7 NIL NIL NIL) (-939 2272388 2272677 2273043 "PGCD" 2274024 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-938 2271714 2271829 2271990 "PFRPAC" 2272272 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-937 2267964 2270262 2270615 "PFR" 2271393 NIL PFR (NIL T) -8 NIL NIL NIL) (-936 2266317 2266597 2266922 "PFOTOOLS" 2267711 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-935 2264832 2265089 2265440 "PFOQ" 2266074 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-934 2263315 2263545 2263901 "PFO" 2264616 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-933 2259240 2263204 2263273 "PF" 2263278 NIL PF (NIL NIL) -8 NIL NIL NIL) (-932 2256318 2257831 2257859 "PFECAT" 2258444 T PFECAT (NIL) -9 NIL 2258828 NIL) (-931 2255745 2255917 2256131 "PFECAT-" 2256136 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-930 2254318 2254600 2254901 "PFBRU" 2255494 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-929 2252148 2252536 2252968 "PFBR" 2253969 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-928 2247954 2249660 2250307 "PERM" 2251534 NIL PERM (NIL T) -8 NIL NIL NIL) (-927 2243008 2244161 2245031 "PERMGRP" 2247117 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-926 2240920 2242032 2242073 "PERMCAT" 2242473 NIL PERMCAT (NIL T) -9 NIL 2242771 NIL) (-925 2240567 2240614 2240738 "PERMAN" 2240873 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-924 2237808 2240232 2240354 "PENDTREE" 2240478 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-923 2236689 2236952 2236993 "PDSPC" 2237526 NIL PDSPC (NIL T) -9 NIL 2237771 NIL) (-922 2235744 2236010 2236372 "PDSPC-" 2236377 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-921 2234458 2235394 2235435 "PDRING" 2235440 NIL PDRING (NIL T) -9 NIL 2235468 NIL) (-920 2233201 2233963 2234017 "PDMOD" 2234022 NIL PDMOD (NIL T T) -9 NIL 2234126 NIL) (-919 2230368 2231194 2231862 "PDEPROB" 2232553 T PDEPROB (NIL) -8 NIL NIL NIL) (-918 2227877 2228417 2228972 "PDEPACK" 2229833 T PDEPACK (NIL) -7 NIL NIL NIL) (-917 2226765 2226979 2227230 "PDECOMP" 2227676 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-916 2224282 2225173 2225201 "PDECAT" 2225988 T PDECAT (NIL) -9 NIL 2226701 NIL) (-915 2223899 2223966 2224020 "PDDOM" 2224185 NIL PDDOM (NIL T T) -9 NIL 2224265 NIL) (-914 2223712 2223748 2223855 "PDDOM-" 2223860 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-913 2223457 2223496 2223586 "PCOMP" 2223673 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-912 2221497 2222258 2222555 "PBWLB" 2223186 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-911 2213676 2215570 2216908 "PATTERN" 2220180 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-910 2213302 2213365 2213474 "PATTERN2" 2213613 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-909 2211011 2211447 2211904 "PATTERN1" 2212891 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-908 2208277 2208960 2209441 "PATRES" 2210576 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-907 2207835 2207908 2208040 "PATRES2" 2208204 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-906 2205688 2206123 2206530 "PATMATCH" 2207502 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-905 2205142 2205393 2205434 "PATMAB" 2205541 NIL PATMAB (NIL T) -9 NIL 2205624 NIL) (-904 2203588 2203996 2204254 "PATLRES" 2204947 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-903 2203126 2203257 2203298 "PATAB" 2203303 NIL PATAB (NIL T) -9 NIL 2203475 NIL) (-902 2201266 2201703 2202126 "PARTPERM" 2202723 T PARTPERM (NIL) -7 NIL NIL NIL) (-901 2200875 2200950 2201052 "PARSURF" 2201197 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-900 2200501 2200564 2200673 "PARSU2" 2200812 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-899 2200259 2200305 2200372 "PARSER" 2200454 T PARSER (NIL) -7 NIL NIL NIL) (-898 2199868 2199943 2200045 "PARSCURV" 2200190 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-897 2199494 2199557 2199666 "PARSC2" 2199805 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-896 2199121 2199191 2199288 "PARPCURV" 2199430 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-895 2198747 2198810 2198919 "PARPC2" 2199058 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-894 2197736 2198120 2198302 "PARAMAST" 2198585 T PARAMAST (NIL) -8 NIL NIL NIL) (-893 2197244 2197342 2197461 "PAN2EXPR" 2197637 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-892 2195937 2196365 2196593 "PALETTE" 2197036 T PALETTE (NIL) -8 NIL NIL NIL) (-891 2194282 2194942 2195302 "PAIR" 2195623 NIL PAIR (NIL T T) 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(NIL) -8 NIL NIL NIL) (-878 2155007 2155202 2155230 "OUTBCON" 2155548 T OUTBCON (NIL) -9 NIL 2155714 NIL) (-877 2154590 2154720 2154877 "OUTBCON-" 2154882 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-876 2153886 2154319 2154408 "OSI" 2154521 T OSI (NIL) -8 NIL NIL NIL) (-875 2153305 2153727 2153755 "OSGROUP" 2153760 T OSGROUP (NIL) -9 NIL 2153782 NIL) (-874 2152016 2152277 2152562 "ORTHPOL" 2153052 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-873 2149267 2151851 2151972 "OREUP" 2151977 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-872 2146370 2148958 2149085 "ORESUP" 2149209 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-871 2143870 2144398 2144959 "OREPCTO" 2145859 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-870 2137248 2139743 2139784 "OREPCAT" 2142132 NIL OREPCAT (NIL T) -9 NIL 2143236 NIL) (-869 2134221 2135177 2136235 "OREPCAT-" 2136240 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-868 2133414 2133691 2133719 "ORDTYPE" 2134028 T ORDTYPE (NIL) -9 NIL 2134191 NIL) (-867 2132715 2132931 2133186 "ORDTYPE-" 2133191 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-866 2132071 2132454 2132612 "ORDSTRCT" 2132617 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-865 2131569 2131939 2131967 "ORDSET" 2131972 T ORDSET (NIL) -9 NIL 2131994 NIL) (-864 2129927 2130898 2130926 "ORDRING" 2131128 T ORDRING (NIL) -9 NIL 2131253 NIL) (-863 2129548 2129666 2129810 "ORDRING-" 2129815 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-862 2128799 2129364 2129392 "ORDMON" 2129397 T ORDMON (NIL) -9 NIL 2129418 NIL) (-861 2127943 2128108 2128303 "ORDFUNS" 2128648 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-860 2127158 2127673 2127701 "ORDFIN" 2127766 T ORDFIN (NIL) -9 NIL 2127840 NIL) (-859 2123505 2125744 2126153 "ORDCOMP" 2126782 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-858 2122759 2122898 2123084 "ORDCOMP2" 2123365 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-857 2119280 2120250 2121064 "OPTPROB" 2121965 T OPTPROB (NIL) -8 NIL NIL NIL) (-856 2116022 2116721 2117425 "OPTPACK" 2118596 T OPTPACK (NIL) -7 NIL NIL NIL) (-855 2113635 2114461 2114489 "OPTCAT" 2115308 T OPTCAT (NIL) -9 NIL 2115958 NIL) (-854 2112953 2113312 2113417 "OPSIG" 2113550 T OPSIG (NIL) -8 NIL NIL NIL) (-853 2112715 2112760 2112826 "OPQUERY" 2112907 T OPQUERY (NIL) -7 NIL NIL NIL) (-852 2109624 2111026 2111530 "OP" 2112244 NIL OP (NIL T) -8 NIL NIL NIL) (-851 2108930 2109210 2109251 "OPERCAT" 2109463 NIL OPERCAT (NIL T) -9 NIL 2109560 NIL) (-850 2108673 2108741 2108858 "OPERCAT-" 2108863 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-849 2105286 2107470 2107839 "ONECOMP" 2108337 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-848 2104579 2104706 2104880 "ONECOMP2" 2105158 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-847 2103980 2104104 2104234 "OMSERVER" 2104469 T OMSERVER (NIL) -7 NIL NIL NIL) (-846 2100494 2103420 2103460 "OMSAGG" 2103521 NIL OMSAGG (NIL T) -9 NIL 2103585 NIL) (-845 2099069 2099380 2099662 "OMPKG" 2100232 T OMPKG (NIL) -7 NIL NIL NIL) (-844 2098475 2098602 2098630 "OM" 2098929 T OM (NIL) -9 NIL NIL NIL) (-843 2096822 2098024 2098193 "OMLO" 2098356 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-842 2095758 2095929 2096149 "OMEXPR" 2096648 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-841 2094995 2095304 2095440 "OMERR" 2095642 T OMERR (NIL) -8 NIL NIL NIL) (-840 2094080 2094416 2094576 "OMERRK" 2094855 T OMERRK (NIL) -8 NIL NIL NIL) (-839 2093471 2093757 2093865 "OMENC" 2093992 T OMENC (NIL) -8 NIL NIL NIL) (-838 2087108 2088551 2089722 "OMDEV" 2092320 T OMDEV (NIL) -8 NIL NIL NIL) (-837 2086141 2086348 2086542 "OMCONN" 2086934 T OMCONN (NIL) -8 NIL NIL NIL) (-836 2084419 2085611 2085639 "OINTDOM" 2085644 T OINTDOM (NIL) -9 NIL 2085665 NIL) (-835 2081493 2083107 2083444 "OFMONOID" 2084114 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-834 2080727 2081430 2081475 "ODVAR" 2081480 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-833 2077864 2080472 2080627 "ODR" 2080632 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-832 2069269 2077640 2077766 "ODPOL" 2077771 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-831 2062612 2069141 2069246 "ODP" 2069251 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-830 2061354 2061593 2061868 "ODETOOLS" 2062386 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-829 2058297 2058979 2059695 "ODESYS" 2060687 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-828 2053127 2054087 2055112 "ODERTRIC" 2057372 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-827 2052547 2052635 2052829 "ODERED" 2053039 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-826 2049399 2049983 2050660 "ODERAT" 2051970 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-825 2046316 2046823 2047420 "ODEPRRIC" 2048928 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-824 2044211 2044855 2045341 "ODEPROB" 2045850 T ODEPROB (NIL) -8 NIL NIL NIL) (-823 2040677 2041216 2041863 "ODEPRIM" 2043690 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-822 2039920 2040028 2040288 "ODEPAL" 2040569 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-821 2036022 2036873 2037737 "ODEPACK" 2039076 T ODEPACK (NIL) -7 NIL NIL NIL) (-820 2035065 2035190 2035412 "ODEINT" 2035911 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-819 2029130 2030591 2032038 "ODEIFTBL" 2033638 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-818 2024480 2025314 2026266 "ODEEF" 2028289 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-817 2023823 2023918 2024141 "ODECONST" 2024385 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-816 2021886 2022595 2022623 "ODECAT" 2023228 T ODECAT (NIL) -9 NIL 2023759 NIL) (-815 2018379 2021591 2021713 "OCT" 2021796 NIL OCT (NIL T) -8 NIL NIL NIL) (-814 2018011 2018060 2018187 "OCTCT2" 2018330 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-813 2012280 2015054 2015094 "OC" 2016191 NIL OC (NIL T) -9 NIL 2017049 NIL) (-812 2009315 2010255 2011245 "OC-" 2011339 NIL OC- (NIL T T) -8 NIL NIL NIL) (-811 2008538 2009108 2009136 "OCAMON" 2009141 T OCAMON (NIL) -9 NIL 2009162 NIL) (-810 2007958 2008383 2008411 "OASGP" 2008416 T OASGP (NIL) -9 NIL 2008436 NIL) (-809 2007084 2007681 2007709 "OAMONS" 2007749 T OAMONS (NIL) -9 NIL 2007792 NIL) (-808 2006375 2006904 2006932 "OAMON" 2006937 T OAMON (NIL) -9 NIL 2006957 NIL) (-807 2005486 2006124 2006152 "OAGROUP" 2006157 T OAGROUP (NIL) -9 NIL 2006177 NIL) (-806 2005170 2005226 2005314 "NUMTUBE" 2005430 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-805 1998689 2000261 2001797 "NUMQUAD" 2003654 T NUMQUAD (NIL) -7 NIL NIL NIL) (-804 1994409 1995433 1996458 "NUMODE" 1997684 T NUMODE (NIL) -7 NIL NIL NIL) (-803 1991690 1992630 1992658 "NUMINT" 1993581 T NUMINT (NIL) -9 NIL 1994345 NIL) (-802 1990602 1990835 1991053 "NUMFMT" 1991492 T NUMFMT (NIL) -7 NIL NIL NIL) (-801 1976785 1979906 1982438 "NUMERIC" 1988109 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-800 1970496 1976233 1976328 "NTSCAT" 1976333 NIL NTSCAT (NIL T T T T) -9 NIL 1976372 NIL) (-799 1969676 1969855 1970048 "NTPOLFN" 1970335 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-798 1956437 1966501 1967313 "NSUP" 1968897 NIL NSUP (NIL T) -8 NIL NIL NIL) (-797 1956063 1956126 1956235 "NSUP2" 1956374 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-796 1944899 1955837 1955970 "NSMP" 1955975 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-795 1943307 1943632 1943989 "NREP" 1944587 NIL NREP (NIL T) -7 NIL NIL NIL) (-794 1941886 1942150 1942508 "NPCOEF" 1943050 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-793 1940934 1941067 1941283 "NORMRETR" 1941767 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-792 1938945 1939265 1939674 "NORMPK" 1940642 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-791 1938624 1938658 1938782 "NORMMA" 1938911 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-790 1938388 1938581 1938610 "NONE" 1938615 T NONE (NIL) -8 NIL NIL NIL) (-789 1938171 1938206 1938275 "NONE1" 1938352 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-788 1937662 1937730 1937909 "NODE1" 1938103 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-787 1935763 1936794 1937049 "NNI" 1937396 T NNI (NIL) -8 NIL NIL 1937631) (-786 1934159 1934496 1934860 "NLINSOL" 1935431 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-785 1930340 1931395 1932294 "NIPROB" 1933280 T NIPROB (NIL) -8 NIL NIL NIL) (-784 1929079 1929331 1929633 "NFINTBAS" 1930102 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-783 1928163 1928729 1928770 "NETCLT" 1928942 NIL NETCLT (NIL T) -9 NIL 1929024 NIL) (-782 1926835 1927102 1927383 "NCODIV" 1927931 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-781 1926591 1926634 1926709 "NCNTFRAC" 1926792 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-780 1924747 1925135 1925555 "NCEP" 1926216 NIL NCEP (NIL T) -7 NIL NIL NIL) (-779 1923410 1924357 1924385 "NASRING" 1924495 T NASRING (NIL) -9 NIL 1924575 NIL) (-778 1923193 1923249 1923343 "NASRING-" 1923348 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-777 1922160 1922811 1922839 "NARNG" 1922956 T NARNG (NIL) -9 NIL 1923047 NIL) (-776 1921834 1921919 1922053 "NARNG-" 1922058 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-775 1920671 1920920 1921155 "NAGSP" 1921619 T NAGSP (NIL) -7 NIL NIL NIL) (-774 1911715 1913627 1915300 "NAGS" 1919018 T NAGS (NIL) -7 NIL NIL NIL) (-773 1910239 1910571 1910902 "NAGF07" 1911404 T NAGF07 (NIL) -7 NIL NIL NIL) (-772 1904711 1906068 1907375 "NAGF04" 1908952 T NAGF04 (NIL) -7 NIL NIL NIL) (-771 1897583 1899293 1900926 "NAGF02" 1903098 T NAGF02 (NIL) -7 NIL NIL NIL) (-770 1892747 1893907 1895024 "NAGF01" 1896486 T NAGF01 (NIL) -7 NIL NIL NIL) (-769 1886327 1887941 1889526 "NAGE04" 1891182 T NAGE04 (NIL) -7 NIL NIL NIL) (-768 1877388 1879617 1881747 "NAGE02" 1884217 T NAGE02 (NIL) -7 NIL NIL NIL) (-767 1873281 1874288 1875252 "NAGE01" 1876444 T NAGE01 (NIL) -7 NIL NIL NIL) (-766 1871058 1871610 1872168 "NAGD03" 1872743 T NAGD03 (NIL) -7 NIL NIL NIL) (-765 1862754 1864736 1866690 "NAGD02" 1869124 T NAGD02 (NIL) -7 NIL NIL NIL) (-764 1856493 1857990 1859430 "NAGD01" 1861334 T NAGD01 (NIL) -7 NIL NIL NIL) (-763 1852630 1853524 1854361 "NAGC06" 1855676 T NAGC06 (NIL) -7 NIL NIL NIL) (-762 1851077 1851427 1851783 "NAGC05" 1852294 T NAGC05 (NIL) -7 NIL NIL NIL) (-761 1850441 1850572 1850716 "NAGC02" 1850953 T NAGC02 (NIL) -7 NIL NIL NIL) (-760 1849242 1849969 1850009 "NAALG" 1850088 NIL NAALG (NIL T) -9 NIL 1850149 NIL) (-759 1849071 1849106 1849196 "NAALG-" 1849201 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-758 1842943 1844129 1845316 "MULTSQFR" 1847967 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-757 1842250 1842337 1842521 "MULTFACT" 1842855 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-756 1834397 1838835 1838888 "MTSCAT" 1839958 NIL MTSCAT (NIL T T) -9 NIL 1840473 NIL) (-755 1834103 1834163 1834255 "MTHING" 1834337 NIL MTHING (NIL T) -7 NIL NIL NIL) (-754 1833889 1833928 1833988 "MSYSCMD" 1834063 T MSYSCMD (NIL) -7 NIL NIL NIL) (-753 1829603 1832644 1832964 "MSET" 1833602 NIL MSET (NIL T) -8 NIL NIL NIL) (-752 1826348 1829164 1829205 "MSETAGG" 1829210 NIL MSETAGG (NIL T) -9 NIL 1829244 NIL) (-751 1821940 1823727 1824472 "MRING" 1825648 NIL MRING (NIL T T) -8 NIL NIL NIL) (-750 1821500 1821573 1821704 "MRF2" 1821867 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-749 1821112 1821153 1821297 "MRATFAC" 1821459 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-748 1818682 1819019 1819450 "MPRFF" 1820817 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-747 1812009 1818536 1818633 "MPOLY" 1818638 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-746 1811493 1811534 1811742 "MPCPF" 1811968 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-745 1811001 1811050 1811234 "MPC3" 1811444 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-744 1810184 1810277 1810498 "MPC2" 1810916 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-743 1808461 1808822 1809212 "MONOTOOL" 1809844 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-742 1807606 1807989 1808017 "MONOID" 1808236 T MONOID (NIL) -9 NIL 1808383 NIL) (-741 1807122 1807271 1807452 "MONOID-" 1807457 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-740 1796076 1802942 1803001 "MONOGEN" 1803675 NIL MONOGEN (NIL T T) -9 NIL 1804131 NIL) (-739 1793126 1794029 1795029 "MONOGEN-" 1795148 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-738 1791843 1792391 1792419 "MONADWU" 1792811 T MONADWU (NIL) -9 NIL 1793049 NIL) (-737 1791173 1791374 1791622 "MONADWU-" 1791627 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-736 1790458 1790762 1790790 "MONAD" 1790997 T MONAD (NIL) -9 NIL 1791109 NIL) (-735 1790125 1790221 1790353 "MONAD-" 1790358 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-734 1788264 1789038 1789317 "MOEBIUS" 1789878 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-733 1787432 1787932 1787972 "MODULE" 1787977 NIL MODULE (NIL T) -9 NIL 1788016 NIL) (-732 1786970 1787096 1787286 "MODULE-" 1787291 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-731 1784500 1785334 1785661 "MODRING" 1786794 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-730 1781222 1782605 1783126 "MODOP" 1784029 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-729 1779708 1780289 1780566 "MODMONOM" 1781085 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-728 1768448 1777999 1778413 "MODMON" 1779345 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-727 1765274 1767292 1767568 "MODFIELD" 1768323 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-726 1764185 1764555 1764745 "MMLFORM" 1765104 T MMLFORM (NIL) -8 NIL NIL NIL) (-725 1763705 1763754 1763933 "MMAP" 1764136 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-724 1761598 1762537 1762578 "MLO" 1763001 NIL MLO (NIL T) -9 NIL 1763243 NIL) (-723 1758946 1759480 1760082 "MLIFT" 1761079 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-722 1758325 1758421 1758575 "MKUCFUNC" 1758857 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-721 1757918 1757994 1758117 "MKRECORD" 1758248 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-720 1756941 1757127 1757355 "MKFUNC" 1757729 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-719 1756317 1756433 1756589 "MKFLCFN" 1756824 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-718 1755582 1755696 1755881 "MKBCFUNC" 1756210 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-717 1751565 1755136 1755272 "MINT" 1755466 T MINT (NIL) -8 NIL NIL NIL) (-716 1750347 1750620 1750897 "MHROWRED" 1751320 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-715 1745091 1748882 1749287 "MFLOAT" 1749962 T MFLOAT (NIL) -8 NIL NIL NIL) (-714 1744436 1744524 1744695 "MFINFACT" 1745003 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-713 1740715 1741599 1742483 "MESH" 1743572 T MESH (NIL) -7 NIL NIL NIL) (-712 1739069 1739417 1739770 "MDDFACT" 1740402 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-711 1735605 1738200 1738241 "MDAGG" 1738496 NIL MDAGG (NIL T) -9 NIL 1738639 NIL) (-710 1723307 1734898 1735105 "MCMPLX" 1735418 T MCMPLX (NIL) -8 NIL NIL NIL) (-709 1722426 1722590 1722791 "MCDEN" 1723156 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-708 1720274 1720586 1720966 "MCALCFN" 1722156 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-707 1719151 1719439 1719672 "MAYBE" 1720080 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-706 1716709 1717286 1717848 "MATSTOR" 1718622 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-705 1712131 1716081 1716329 "MATRIX" 1716494 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-704 1707831 1708604 1709340 "MATLIN" 1711488 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-703 1697177 1700888 1700965 "MATCAT" 1705997 NIL MATCAT (NIL T T T) -9 NIL 1707469 NIL) (-702 1693130 1694440 1695853 "MATCAT-" 1695858 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-701 1691706 1691877 1692210 "MATCAT2" 1692965 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-700 1689782 1690142 1690526 "MAPPKG3" 1691381 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-699 1688739 1688936 1689158 "MAPPKG2" 1689606 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-698 1687196 1687522 1687849 "MAPPKG1" 1688445 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-697 1686197 1686602 1686779 "MAPPAST" 1687039 T MAPPAST (NIL) -8 NIL NIL NIL) (-696 1685802 1685866 1685989 "MAPHACK3" 1686133 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-695 1685382 1685455 1685569 "MAPHACK2" 1685734 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-694 1684808 1684923 1685065 "MAPHACK1" 1685273 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-693 1682731 1683508 1683812 "MAGMA" 1684536 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-692 1682150 1682455 1682546 "MACROAST" 1682660 T MACROAST (NIL) -8 NIL NIL NIL) (-691 1678393 1680389 1680850 "M3D" 1681722 NIL M3D (NIL T) -8 NIL NIL NIL) (-690 1671873 1676704 1676745 "LZSTAGG" 1677527 NIL LZSTAGG (NIL T) -9 NIL 1677822 NIL) (-689 1667555 1669004 1670461 "LZSTAGG-" 1670466 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-688 1664468 1665446 1665933 "LWORD" 1667100 NIL LWORD (NIL T) -8 NIL NIL NIL) (-687 1663990 1664272 1664347 "LSTAST" 1664413 T LSTAST (NIL) -8 NIL NIL NIL) (-686 1655918 1663761 1663895 "LSQM" 1663900 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-685 1655136 1655281 1655509 "LSPP" 1655773 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-684 1652918 1653249 1653705 "LSMP" 1654825 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-683 1649655 1650371 1651101 "LSMP1" 1652220 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-682 1642791 1648745 1648786 "LSAGG" 1648848 NIL LSAGG (NIL T) -9 NIL 1648926 NIL) (-681 1639300 1640410 1641623 "LSAGG-" 1641628 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-680 1636595 1638444 1638693 "LPOLY" 1639095 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-679 1636171 1636262 1636385 "LPEFRAC" 1636504 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-678 1634348 1635265 1635518 "LO" 1636003 NIL LO (NIL T T T) -8 NIL NIL NIL) (-677 1633924 1634098 1634126 "LOGIC" 1634237 T LOGIC (NIL) -9 NIL 1634318 NIL) (-676 1633780 1633809 1633880 "LOGIC-" 1633885 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-675 1632955 1633113 1633306 "LODOOPS" 1633636 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-674 1630050 1632871 1632937 "LODO" 1632942 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-673 1628574 1628823 1629176 "LODOF" 1629797 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-672 1624450 1627209 1627250 "LODOCAT" 1627688 NIL LODOCAT (NIL T) -9 NIL 1627899 NIL) (-671 1624165 1624241 1624368 "LODOCAT-" 1624373 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-670 1621151 1624006 1624124 "LODO2" 1624129 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-669 1618258 1621088 1621133 "LODO1" 1621138 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-668 1617127 1617304 1617609 "LODEEF" 1618081 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-667 1612099 1615293 1615334 "LNAGG" 1616196 NIL LNAGG (NIL T) -9 NIL 1616631 NIL) (-666 1611192 1611460 1611802 "LNAGG-" 1611807 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-665 1607172 1608117 1608756 "LMOPS" 1610607 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-664 1606471 1606949 1606990 "LMODULE" 1606995 NIL LMODULE (NIL T) -9 NIL 1607021 NIL) (-663 1603426 1606116 1606239 "LMDICT" 1606381 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-662 1603002 1603216 1603257 "LLINSET" 1603318 NIL LLINSET (NIL T) -9 NIL 1603362 NIL) (-661 1602647 1602910 1602970 "LITERAL" 1602975 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-660 1595101 1601581 1601885 "LIST" 1602376 NIL LIST (NIL T) -8 NIL NIL NIL) (-659 1594620 1594700 1594839 "LIST3" 1595021 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-658 1593609 1593805 1594033 "LIST2" 1594438 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-657 1591707 1592055 1592454 "LIST2MAP" 1593256 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-656 1591290 1591526 1591567 "LINSET" 1591572 NIL LINSET (NIL T) -9 NIL 1591606 NIL) (-655 1590104 1590798 1590965 "LINFORM" 1591175 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-654 1588403 1589131 1589172 "LINEXP" 1589662 NIL LINEXP (NIL T) -9 NIL 1589935 NIL) (-653 1586979 1587883 1588064 "LINELT" 1588274 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-652 1585536 1585816 1586127 "LINDEP" 1586731 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-651 1584672 1585268 1585378 "LINBASIS" 1585466 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-650 1581409 1582158 1582935 "LIMITRF" 1583927 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-649 1579694 1580008 1580417 "LIMITPS" 1581104 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-648 1573714 1579205 1579433 "LIE" 1579515 NIL LIE (NIL T T) -8 NIL NIL NIL) (-647 1572542 1573117 1573157 "LIECAT" 1573297 NIL LIECAT (NIL T) -9 NIL 1573448 NIL) (-646 1572377 1572410 1572498 "LIECAT-" 1572503 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-645 1564564 1571917 1572073 "LIB" 1572241 T LIB (NIL) -8 NIL NIL NIL) (-644 1560133 1561082 1562017 "LGROBP" 1563681 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-643 1558071 1558405 1558755 "LF" 1559854 NIL LF (NIL T T) -7 NIL NIL NIL) (-642 1556695 1557603 1557631 "LFCAT" 1557838 T LFCAT (NIL) -9 NIL 1557977 NIL) (-641 1553555 1554227 1554915 "LEXTRIPK" 1556059 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-640 1550143 1551125 1551628 "LEXP" 1553135 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-639 1549559 1549864 1549956 "LETAST" 1550071 T LETAST (NIL) -8 NIL NIL NIL) (-638 1547945 1548270 1548671 "LEADCDET" 1549241 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-637 1547123 1547209 1547438 "LAZM3PK" 1547866 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-636 1541634 1545200 1545738 "LAUPOL" 1546635 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-635 1541207 1541257 1541418 "LAPLACE" 1541584 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-634 1538944 1540308 1540559 "LA" 1541040 NIL LA (NIL T T T) -8 NIL NIL NIL) (-633 1537792 1538508 1538549 "LALG" 1538611 NIL LALG (NIL T) -9 NIL 1538670 NIL) (-632 1537488 1537565 1537701 "LALG-" 1537706 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-631 1537317 1537347 1537388 "KVTFROM" 1537450 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-630 1536156 1536684 1536869 "KTVLOGIC" 1537152 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-629 1535985 1536015 1536056 "KRCFROM" 1536118 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-628 1534877 1535076 1535375 "KOVACIC" 1535785 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-627 1534706 1534736 1534777 "KONVERT" 1534839 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-626 1534535 1534565 1534606 "KOERCE" 1534668 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-625 1532222 1533128 1533505 "KERNEL" 1534191 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-624 1531706 1531799 1531931 "KERNEL2" 1532136 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-623 1525177 1530183 1530237 "KDAGG" 1530614 NIL KDAGG (NIL T T) -9 NIL 1530820 NIL) (-622 1524688 1524830 1525035 "KDAGG-" 1525040 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-621 1517388 1524349 1524504 "KAFILE" 1524566 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-620 1511408 1516899 1517127 "JORDAN" 1517209 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1510721 1511057 1511178 "JOINAST" 1511307 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1510549 1510626 1510681 "JAVACODE" 1510686 T JAVACODE (NIL) -8 NIL NIL NIL) (-617 1506584 1508726 1508780 "IXAGG" 1509709 NIL IXAGG (NIL T T) -9 NIL 1510168 NIL) (-616 1505437 1505809 1506228 "IXAGG-" 1506233 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-615 1500526 1505359 1505418 "IVECTOR" 1505423 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-614 1499250 1499529 1499795 "ITUPLE" 1500293 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-613 1497722 1497929 1498224 "ITRIGMNP" 1499072 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-612 1496449 1496671 1496954 "ITFUN3" 1497498 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-611 1496075 1496138 1496247 "ITFUN2" 1496386 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-610 1495180 1495555 1495729 "ITFORM" 1495921 T ITFORM (NIL) -8 NIL NIL NIL) (-609 1492949 1494200 1494478 "ITAYLOR" 1494935 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-608 1481346 1487086 1488249 "ISUPS" 1491819 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-607 1480438 1480590 1480826 "ISUMP" 1481193 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-606 1475288 1480383 1480424 "ISTRING" 1480429 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-605 1474704 1475009 1475101 "ISAST" 1475216 T ISAST (NIL) -8 NIL NIL NIL) (-604 1473901 1473995 1474211 "IRURPK" 1474618 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-603 1472813 1473038 1473278 "IRSN" 1473681 T IRSN (NIL) -7 NIL NIL NIL) (-602 1470858 1471239 1471668 "IRRF2F" 1472451 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-601 1470599 1470643 1470719 "IRREDFFX" 1470814 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-600 1469172 1469473 1469772 "IROOT" 1470332 NIL IROOT (NIL T) -7 NIL NIL NIL) (-599 1465612 1466856 1467548 "IR" 1468512 NIL IR (NIL T) -8 NIL NIL NIL) (-598 1464751 1465105 1465256 "IRFORM" 1465481 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1462340 1462859 1463425 "IR2" 1464229 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-596 1461422 1461553 1461767 "IR2F" 1462223 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-595 1461207 1461247 1461307 "IPRNTPK" 1461382 T IPRNTPK (NIL) -7 NIL NIL NIL) (-594 1457160 1461096 1461165 "IPF" 1461170 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-593 1455181 1457085 1457142 "IPADIC" 1457147 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-592 1454439 1454741 1454871 "IP4ADDR" 1455071 T IP4ADDR (NIL) -8 NIL NIL NIL) (-591 1453777 1454068 1454200 "IOMODE" 1454327 T IOMODE (NIL) -8 NIL NIL NIL) (-590 1452748 1453374 1453501 "IOBFILE" 1453670 T IOBFILE (NIL) -8 NIL NIL NIL) (-589 1452158 1452652 1452680 "IOBCON" 1452685 T IOBCON (NIL) -9 NIL 1452706 NIL) (-588 1451663 1451727 1451910 "INVLAPLA" 1452094 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-587 1441233 1443665 1446051 "INTTR" 1449327 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-586 1437526 1438310 1439175 "INTTOOLS" 1440418 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-585 1437106 1437203 1437320 "INTSLPE" 1437429 T INTSLPE (NIL) -7 NIL NIL NIL) (-584 1434573 1437029 1437088 "INTRVL" 1437093 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-583 1432151 1432687 1433262 "INTRF" 1434058 NIL INTRF (NIL T) -7 NIL NIL NIL) (-582 1431544 1431659 1431801 "INTRET" 1432049 NIL INTRET (NIL T) -7 NIL NIL NIL) (-581 1429517 1429930 1430400 "INTRAT" 1431152 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-580 1426762 1427363 1427982 "INTPM" 1429002 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-579 1423479 1424106 1424844 "INTPAF" 1426148 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-578 1418580 1419620 1420671 "INTPACK" 1422448 T INTPACK (NIL) -7 NIL NIL NIL) (-577 1414768 1418377 1418486 "INT" 1418491 T INT (NIL) -8 NIL NIL NIL) (-576 1414014 1414172 1414380 "INTHERTR" 1414610 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1413447 1413533 1413721 "INTHERAL" 1413928 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1411215 1411736 1412193 "INTHEORY" 1413010 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1402547 1404242 1406014 "INTG0" 1409567 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1383072 1387910 1392720 "INTFTBL" 1397757 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1382297 1382459 1382632 "INTFACT" 1382931 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1379694 1380170 1380727 "INTEF" 1381851 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1377891 1378786 1378814 "INTDOM" 1379115 T INTDOM (NIL) -9 NIL 1379322 NIL) (-568 1377230 1377434 1377676 "INTDOM-" 1377681 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1373104 1375519 1375573 "INTCAT" 1376372 NIL INTCAT (NIL T) -9 NIL 1376693 NIL) (-566 1372558 1372679 1372807 "INTBIT" 1372996 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1371239 1371411 1371718 "INTALG" 1372403 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1370716 1370812 1370969 "INTAF" 1371143 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1363683 1370526 1370666 "INTABL" 1370671 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1362920 1363482 1363547 "INT8" 1363581 T INT8 (NIL) -8 NIL NIL 1363626) (-561 1362156 1362718 1362783 "INT64" 1362817 T INT64 (NIL) -8 NIL NIL 1362862) (-560 1361392 1361954 1362019 "INT32" 1362053 T INT32 (NIL) -8 NIL NIL 1362098) (-559 1360628 1361190 1361255 "INT16" 1361289 T INT16 (NIL) -8 NIL NIL 1361334) (-558 1354729 1358176 1358204 "INS" 1359138 T INS (NIL) -9 NIL 1359803 NIL) (-557 1351783 1352740 1353714 "INS-" 1353787 NIL INS- (NIL T) -8 NIL NIL NIL) (-556 1350540 1350785 1351083 "INPSIGN" 1351536 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-555 1349634 1349775 1349972 "INPRODPF" 1350420 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-554 1348504 1348645 1348882 "INPRODFF" 1349514 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-553 1347492 1347656 1347916 "INNMFACT" 1348340 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-552 1346671 1346786 1346974 "INMODGCD" 1347391 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-551 1345155 1345424 1345748 "INFSP" 1346416 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-550 1344315 1344456 1344639 "INFPROD0" 1345035 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-549 1340882 1342380 1342895 "INFORM" 1343808 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340480 1340552 1340650 "INFORM1" 1340817 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1339985 1340092 1340206 "INFINITY" 1340386 T INFINITY (NIL) -7 NIL NIL NIL) (-546 1339059 1339705 1339806 "INETCLTS" 1339904 T INETCLTS (NIL) -8 NIL NIL NIL) (-545 1337657 1337925 1338246 "INEP" 1338807 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-544 1336718 1337554 1337619 "INDE" 1337624 NIL INDE (NIL T) -8 NIL NIL NIL) (-543 1336270 1336350 1336467 "INCRMAPS" 1336645 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-542 1334992 1335539 1335745 "INBFILE" 1336084 T INBFILE (NIL) -8 NIL NIL NIL) (-541 1330171 1331228 1332172 "INBFF" 1334080 NIL INBFF (NIL T) -7 NIL NIL NIL) (-540 1329025 1329348 1329376 "INBCON" 1329889 T INBCON (NIL) -9 NIL 1330155 NIL) (-539 1328235 1328500 1328776 "INBCON-" 1328781 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-538 1327654 1327959 1328050 "INAST" 1328164 T INAST (NIL) -8 NIL NIL NIL) (-537 1327021 1327333 1327439 "IMPTAST" 1327568 T IMPTAST (NIL) -8 NIL NIL NIL) (-536 1322942 1326865 1326969 "IMATRIX" 1326974 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-535 1321634 1321773 1322089 "IMATQF" 1322798 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-534 1319814 1320081 1320418 "IMATLIN" 1321390 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-533 1313729 1319738 1319796 "ILIST" 1319801 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-532 1311395 1313589 1313702 "IIARRAY2" 1313707 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-531 1306195 1311306 1311370 "IFF" 1311375 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-530 1305476 1305812 1305928 "IFAST" 1306099 T IFAST (NIL) -8 NIL NIL NIL) (-529 1299988 1304768 1304956 "IFARRAY" 1305333 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-528 1299026 1299892 1299965 "IFAMON" 1299970 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-527 1298598 1298675 1298729 "IEVALAB" 1298936 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-526 1298261 1298341 1298501 "IEVALAB-" 1298506 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-525 1297642 1298176 1298238 "IDPO" 1298243 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-524 1296706 1297531 1297606 "IDPOAMS" 1297611 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1295839 1296595 1296670 "IDPOAM" 1296675 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1294319 1294846 1294898 "IDPC" 1295410 NIL IDPC (NIL T T) -9 NIL 1295691 NIL) (-521 1293651 1294211 1294284 "IDPAM" 1294289 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-520 1292866 1293543 1293616 "IDPAG" 1293621 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-519 1292410 1292672 1292762 "IDENT" 1292796 T IDENT (NIL) -8 NIL NIL NIL) (-518 1288629 1289513 1290408 "IDECOMP" 1291567 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-517 1281264 1282552 1283599 "IDEAL" 1287665 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-516 1280406 1280536 1280736 "ICDEN" 1281148 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-515 1279381 1279886 1280033 "ICARD" 1280279 T ICARD (NIL) -8 NIL NIL NIL) (-514 1277411 1277754 1278159 "IBPTOOLS" 1279058 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-513 1272526 1277031 1277144 "IBITS" 1277330 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-512 1269201 1269825 1270520 "IBATOOL" 1271943 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-511 1266962 1267442 1267975 "IBACHIN" 1268736 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-510 1264552 1266808 1266911 "IARRAY2" 1266916 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-509 1260265 1264478 1264535 "IARRAY1" 1264540 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-508 1253275 1258677 1259158 "IAN" 1259804 T IAN (NIL) -8 NIL NIL NIL) (-507 1252780 1252843 1253016 "IALGFACT" 1253212 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-506 1252272 1252421 1252449 "HYPCAT" 1252656 T HYPCAT (NIL) -9 NIL NIL NIL) (-505 1251774 1251927 1252113 "HYPCAT-" 1252118 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-504 1251321 1251569 1251652 "HOSTNAME" 1251711 T HOSTNAME (NIL) -8 NIL NIL NIL) (-503 1251154 1251203 1251244 "HOMOTOP" 1251249 NIL HOMOTOP (NIL T) -9 NIL 1251282 NIL) (-502 1247587 1249086 1249127 "HOAGG" 1250108 NIL HOAGG (NIL T) -9 NIL 1250837 NIL) (-501 1246103 1246580 1247106 "HOAGG-" 1247111 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-500 1239139 1245696 1245846 "HEXADEC" 1245973 T HEXADEC (NIL) -8 NIL NIL NIL) (-499 1237851 1238109 1238372 "HEUGCD" 1238916 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-498 1236783 1237688 1237818 "HELLFDIV" 1237823 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-497 1234793 1236560 1236648 "HEAP" 1236727 NIL HEAP (NIL T) -8 NIL NIL NIL) (-496 1233990 1234345 1234479 "HEADAST" 1234679 T HEADAST (NIL) -8 NIL NIL NIL) (-495 1227377 1233905 1233967 "HDP" 1233972 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-494 1220389 1227012 1227164 "HDMP" 1227278 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-493 1219695 1219853 1220017 "HB" 1220245 T HB (NIL) -7 NIL NIL NIL) (-492 1212705 1219541 1219645 "HASHTBL" 1219650 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-491 1212121 1212426 1212518 "HASAST" 1212633 T HASAST (NIL) -8 NIL NIL NIL) (-490 1209527 1211743 1211925 "HACKPI" 1211959 T HACKPI (NIL) -8 NIL NIL NIL) (-489 1204699 1209380 1209493 "GTSET" 1209498 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-488 1197738 1204577 1204675 "GSTBL" 1204680 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-487 1189487 1196903 1197159 "GSERIES" 1197538 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-486 1188518 1189031 1189059 "GROUP" 1189262 T GROUP (NIL) -9 NIL 1189396 NIL) (-485 1187842 1188043 1188294 "GROUP-" 1188299 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-484 1186191 1186530 1186917 "GROEBSOL" 1187519 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-483 1185019 1185379 1185430 "GRMOD" 1185959 NIL GRMOD (NIL T T) -9 NIL 1186127 NIL) (-482 1184775 1184823 1184951 "GRMOD-" 1184956 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-481 1179915 1181129 1182129 "GRIMAGE" 1183795 T GRIMAGE (NIL) -8 NIL NIL NIL) (-480 1178309 1178642 1178966 "GRDEF" 1179611 T GRDEF (NIL) -7 NIL NIL NIL) (-479 1177741 1177869 1178010 "GRAY" 1178188 T GRAY (NIL) -7 NIL NIL NIL) (-478 1176818 1177320 1177371 "GRALG" 1177524 NIL GRALG (NIL T T) -9 NIL 1177617 NIL) (-477 1176455 1176552 1176715 "GRALG-" 1176720 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-476 1172936 1176038 1176217 "GPOLSET" 1176361 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-475 1172284 1172347 1172605 "GOSPER" 1172873 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-474 1167854 1168722 1169248 "GMODPOL" 1171983 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-473 1166841 1167043 1167281 "GHENSEL" 1167666 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-472 1160913 1161840 1162860 "GENUPS" 1165925 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-471 1160604 1160661 1160750 "GENUFACT" 1160856 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-470 1160004 1160093 1160258 "GENPGCD" 1160522 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-469 1159472 1159513 1159726 "GENMFACT" 1159963 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-468 1158008 1158295 1158602 "GENEEZ" 1159215 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-467 1151180 1157619 1157781 "GDMP" 1157931 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-466 1139919 1144951 1146057 "GCNAALG" 1150163 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-465 1138046 1139094 1139122 "GCDDOM" 1139377 T GCDDOM (NIL) -9 NIL 1139534 NIL) (-464 1137486 1137643 1137858 "GCDDOM-" 1137863 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-463 1136136 1136343 1136647 "GB" 1137265 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-462 1124608 1127082 1129474 "GBINTERN" 1133827 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1122409 1122737 1123158 "GBF" 1124283 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1121166 1121355 1121622 "GBEUCLID" 1122225 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1120497 1120640 1120789 "GAUSSFAC" 1121037 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-458 1118818 1119166 1119480 "GALUTIL" 1120216 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-457 1117078 1117400 1117724 "GALPOLYU" 1118545 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-456 1114377 1114733 1115140 "GALFACTU" 1116775 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-455 1105991 1107682 1109290 "GALFACT" 1112809 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-454 1103277 1104037 1104065 "FVFUN" 1105221 T FVFUN (NIL) -9 NIL 1105941 NIL) (-453 1102507 1102725 1102753 "FVC" 1103044 T FVC (NIL) -9 NIL 1103227 NIL) (-452 1102108 1102332 1102400 "FUNDESC" 1102459 T FUNDESC (NIL) -8 NIL NIL NIL) (-451 1101681 1101905 1101986 "FUNCTION" 1102060 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-450 1099311 1100003 1100469 "FT" 1101235 T FT (NIL) -8 NIL NIL NIL) (-449 1097988 1098612 1098815 "FTEM" 1099128 T FTEM (NIL) -8 NIL NIL NIL) (-448 1096257 1096568 1096965 "FSUPFACT" 1097679 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-447 1094576 1094943 1095275 "FST" 1095945 T FST (NIL) -8 NIL NIL NIL) (-446 1093757 1093881 1094069 "FSRED" 1094458 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-445 1092446 1092712 1093059 "FSPRMELT" 1093472 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-444 1089656 1090190 1090676 "FSPECF" 1092009 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-443 1069883 1079430 1079471 "FS" 1083355 NIL FS (NIL T) -9 NIL 1085644 NIL) (-442 1057944 1061519 1065576 "FS-" 1065876 NIL FS- (NIL T T) -8 NIL NIL NIL) (-441 1057466 1057526 1057696 "FSINT" 1057885 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-440 1055602 1056459 1056762 "FSERIES" 1057245 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-439 1054626 1054760 1054984 "FSCINT" 1055482 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-438 1050490 1053570 1053611 "FSAGG" 1053981 NIL FSAGG (NIL T) -9 NIL 1054240 NIL) (-437 1048090 1048853 1049649 "FSAGG-" 1049744 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1047114 1047275 1047502 "FSAGG2" 1047943 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-435 1044774 1045072 1045620 "FS2UPS" 1046832 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-434 1044402 1044451 1044580 "FS2" 1044725 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1043268 1043451 1043753 "FS2EXPXP" 1044227 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-432 1042682 1042809 1042961 "FRUTIL" 1043148 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-431 1033599 1038177 1039535 "FR" 1041356 NIL FR (NIL T) -8 NIL NIL NIL) (-430 1028117 1031288 1031328 "FRNAALG" 1032648 NIL FRNAALG (NIL T) -9 NIL 1033246 NIL) (-429 1023598 1024866 1026141 "FRNAALG-" 1026891 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1023230 1023279 1023406 "FRNAAF2" 1023549 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1021517 1022079 1022375 "FRMOD" 1023042 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1019122 1019892 1020210 "FRIDEAL" 1021308 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-425 1018307 1018400 1018691 "FRIDEAL2" 1019029 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-424 1017398 1017854 1017895 "FRETRCT" 1017900 NIL FRETRCT (NIL T) -9 NIL 1018076 NIL) (-423 1016456 1016741 1017092 "FRETRCT-" 1017097 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1013270 1014740 1014799 "FRAMALG" 1015681 NIL FRAMALG (NIL T T) -9 NIL 1015973 NIL) (-421 1011308 1011859 1012489 "FRAMALG-" 1012712 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1004279 1010781 1011058 "FRAC" 1011063 NIL FRAC (NIL T) -8 NIL NIL NIL) (-419 1003909 1003972 1004079 "FRAC2" 1004216 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-418 1003539 1003602 1003709 "FR2" 1003846 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 997456 1000918 1000946 "FPS" 1002065 T FPS (NIL) -9 NIL 1002622 NIL) (-416 996881 997014 997178 "FPS-" 997324 NIL FPS- (NIL T) -8 NIL NIL NIL) (-415 993833 995838 995866 "FPC" 996091 T FPC (NIL) -9 NIL 996233 NIL) (-414 993614 993666 993763 "FPC-" 993768 NIL FPC- (NIL T) -8 NIL NIL NIL) (-413 992372 993102 993143 "FPATMAB" 993148 NIL FPATMAB (NIL T) -9 NIL 993300 NIL) (-412 990515 991114 991461 "FPARFRAC" 992088 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-411 985807 986407 987089 "FORTRAN" 989947 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-410 983493 984023 984562 "FORT" 985288 T FORT (NIL) -7 NIL NIL NIL) (-409 981067 981731 981759 "FORTFN" 982819 T FORTFN (NIL) -9 NIL 983443 NIL) (-408 980819 980881 980909 "FORTCAT" 980968 T FORTCAT (NIL) -9 NIL 981030 NIL) (-407 978823 979435 979825 "FORMULA" 980449 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978605 978641 978710 "FORMULA1" 978787 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-405 978122 978180 978353 "FORDER" 978547 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-404 977182 977382 977575 "FOP" 977949 T FOP (NIL) -7 NIL NIL NIL) (-403 975595 976462 976636 "FNLA" 977064 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-402 974214 974725 974753 "FNCAT" 975213 T FNCAT (NIL) -9 NIL 975473 NIL) (-401 973657 974173 974201 "FNAME" 974206 T FNAME (NIL) -8 NIL NIL NIL) (-400 971983 973156 973184 "FMTC" 973189 T FMTC (NIL) -9 NIL 973225 NIL) (-399 970531 971919 971965 "FMONOID" 971970 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-398 967120 968486 968527 "FMONCAT" 969744 NIL FMONCAT (NIL T) -9 NIL 970349 NIL) (-397 966138 966862 967011 "FM" 967016 NIL FM (NIL T T) -8 NIL NIL NIL) (-396 963460 964208 964236 "FMFUN" 965380 T FMFUN (NIL) -9 NIL 966088 NIL) (-395 962693 962910 962938 "FMC" 963228 T FMC (NIL) -9 NIL 963410 NIL) (-394 959566 960618 960672 "FMCAT" 961867 NIL FMCAT (NIL T T) -9 NIL 962362 NIL) (-393 958234 959332 959432 "FM1" 959511 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-392 955972 956424 956918 "FLOATRP" 957785 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-391 948628 953701 954322 "FLOAT" 955371 T FLOAT (NIL) -8 NIL NIL NIL) (-390 946030 946566 947144 "FLOATCP" 948095 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-389 944548 945622 945663 "FLINEXP" 945668 NIL FLINEXP (NIL T) -9 NIL 945761 NIL) (-388 943678 943937 944265 "FLINEXP-" 944270 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-387 942736 942898 943122 "FLASORT" 943530 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-386 939654 940706 940758 "FLALG" 941985 NIL FLALG (NIL T T) -9 NIL 942452 NIL) (-385 932918 937063 937104 "FLAGG" 938366 NIL FLAGG (NIL T) -9 NIL 939018 NIL) (-384 931572 931983 932473 "FLAGG-" 932478 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 930596 930757 930984 "FLAGG2" 931425 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-382 927227 928441 928500 "FINRALG" 929628 NIL FINRALG (NIL T T) -9 NIL 930136 NIL) (-381 926351 926616 926955 "FINRALG-" 926960 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-380 925657 925956 925984 "FINITE" 926180 T FINITE (NIL) -9 NIL 926287 NIL) (-379 917608 920187 920227 "FINAALG" 923894 NIL FINAALG (NIL T) -9 NIL 925347 NIL) (-378 912724 913990 915134 "FINAALG-" 916513 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-377 912002 912479 912582 "FILE" 912654 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 910562 910984 911038 "FILECAT" 911722 NIL FILECAT (NIL T T) -9 NIL 911938 NIL) (-375 907958 909792 909820 "FIELD" 909860 T FIELD (NIL) -9 NIL 909940 NIL) (-374 906500 906963 907474 "FIELD-" 907479 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-373 904182 905135 905482 "FGROUP" 906186 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-372 903254 903436 903656 "FGLMICPK" 904014 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-371 898488 903179 903236 "FFX" 903241 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-370 898083 898150 898285 "FFSLPE" 898421 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-369 893959 894855 895651 "FFPOLY" 897319 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 893457 893499 893708 "FFPOLY2" 893917 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-367 888705 893376 893439 "FFP" 893444 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-366 883505 888616 888680 "FF" 888685 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-365 878015 882848 883038 "FFNBX" 883359 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-364 872327 877150 877408 "FFNBP" 877869 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-363 866344 871611 871822 "FFNB" 872160 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-362 865164 865374 865689 "FFINTBAS" 866141 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-361 860740 863411 863439 "FFIELDC" 864059 T FFIELDC (NIL) -9 NIL 864435 NIL) (-360 859318 859773 860270 "FFIELDC-" 860275 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-359 858875 858933 859057 "FFHOM" 859260 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-358 856534 857057 857574 "FFF" 858390 NIL FFF (NIL T) -7 NIL NIL NIL) (-357 851548 856276 856377 "FFCGX" 856477 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-356 846566 851280 851387 "FFCGP" 851491 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-355 841145 846293 846401 "FFCG" 846502 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-354 819808 830877 830963 "FFCAT" 836128 NIL FFCAT (NIL T T T) -9 NIL 837579 NIL) (-353 814819 816053 817367 "FFCAT-" 818597 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-352 814224 814273 814508 "FFCAT2" 814770 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-351 802877 807196 808416 "FEXPR" 813076 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-350 801805 802274 802315 "FEVALAB" 802399 NIL FEVALAB (NIL T) -9 NIL 802660 NIL) (-349 800922 801174 801512 "FEVALAB-" 801517 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-348 799332 800305 800508 "FDIV" 800821 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-347 796194 797079 797194 "FDIVCAT" 798762 NIL FDIVCAT (NIL T T T T) -9 NIL 799199 NIL) (-346 795950 795983 796153 "FDIVCAT-" 796158 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-345 795164 795257 795534 "FDIV2" 795857 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 794072 794459 794661 "FCTRDATA" 794982 T FCTRDATA (NIL) -8 NIL NIL NIL) (-343 792728 793017 793306 "FCPAK1" 793803 T FCPAK1 (NIL) -7 NIL NIL NIL) (-342 791731 792228 792369 "FCOMP" 792619 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-341 775046 778881 782419 "FC" 788213 T FC (NIL) -8 NIL NIL NIL) (-340 766741 771367 771407 "FAXF" 773209 NIL FAXF (NIL T) -9 NIL 773901 NIL) (-339 763862 764675 765500 "FAXF-" 765965 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-338 758431 763238 763414 "FARRAY" 763719 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-337 752995 755378 755431 "FAMR" 756454 NIL FAMR (NIL T T) -9 NIL 756914 NIL) (-336 751819 752187 752622 "FAMR-" 752627 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-335 750846 751741 751794 "FAMONOID" 751799 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-334 748476 749328 749381 "FAMONC" 750322 NIL FAMONC (NIL T T) -9 NIL 750708 NIL) (-333 746950 748230 748367 "FAGROUP" 748372 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-332 744703 745064 745467 "FACUTIL" 746631 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-331 743790 743987 744209 "FACTFUNC" 744513 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-330 735548 743093 743292 "EXPUPXS" 743646 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-329 733001 733571 734157 "EXPRTUBE" 734982 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-328 729212 729864 730594 "EXPRODE" 732340 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-327 713506 727861 728290 "EXPR" 728816 NIL EXPR (NIL T) -8 NIL NIL NIL) (-326 707940 708647 709453 "EXPR2UPS" 712804 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-325 707566 707629 707738 "EXPR2" 707877 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-324 697883 706717 707008 "EXPEXPAN" 707402 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-323 697647 697840 697869 "EXIT" 697874 T EXIT (NIL) -8 NIL NIL NIL) (-322 697067 697371 697462 "EXITAST" 697576 T EXITAST (NIL) -8 NIL NIL NIL) (-321 696688 696756 696869 "EVALCYC" 696999 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-320 696205 696347 696388 "EVALAB" 696558 NIL EVALAB (NIL T) -9 NIL 696662 NIL) (-319 695662 695808 696029 "EVALAB-" 696034 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-318 692770 694318 694346 "EUCDOM" 694901 T EUCDOM (NIL) -9 NIL 695251 NIL) (-317 691109 691617 692207 "EUCDOM-" 692212 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-316 678426 681407 684157 "ESTOOLS" 688379 T ESTOOLS (NIL) -7 NIL NIL NIL) (-315 678052 678115 678224 "ESTOOLS2" 678363 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-314 677797 677845 677925 "ESTOOLS1" 678004 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-313 671498 673428 673456 "ES" 676224 T ES (NIL) -9 NIL 677634 NIL) (-312 666175 667732 669549 "ES-" 669713 NIL ES- (NIL T) -8 NIL NIL NIL) (-311 662483 663310 664090 "ESCONT" 665415 T ESCONT (NIL) -7 NIL NIL NIL) (-310 662222 662260 662342 "ESCONT1" 662445 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-309 661891 661947 662047 "ES2" 662166 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-308 661515 661579 661688 "ES1" 661827 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-307 660707 660860 661036 "ERROR" 661359 T ERROR (NIL) -7 NIL NIL NIL) (-306 653723 660566 660657 "EQTBL" 660662 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-305 645982 649037 650486 "EQ" 652307 NIL -2068 (NIL T) -8 NIL NIL NIL) (-304 645608 645671 645780 "EQ2" 645919 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-303 640851 641946 643039 "EP" 644547 NIL EP (NIL T) -7 NIL NIL NIL) (-302 639391 639742 640048 "ENV" 640565 T ENV (NIL) -8 NIL NIL NIL) (-301 638351 639025 639053 "ENTIRER" 639058 T ENTIRER (NIL) -9 NIL 639104 NIL) (-300 634763 636533 636894 "EMR" 638159 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-299 633867 634078 634132 "ELTAGG" 634512 NIL ELTAGG (NIL T T) -9 NIL 634723 NIL) (-298 633574 633648 633789 "ELTAGG-" 633794 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-297 633332 633367 633421 "ELTAB" 633505 NIL ELTAB (NIL T T) -9 NIL 633557 NIL) (-296 632434 632604 632803 "ELFUTS" 633183 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-295 632158 632232 632260 "ELEMFUN" 632365 T ELEMFUN (NIL) -9 NIL NIL NIL) (-294 632022 632049 632117 "ELEMFUN-" 632122 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-293 626439 630064 630105 "ELAGG" 631045 NIL ELAGG (NIL T) -9 NIL 631508 NIL) (-292 624616 625158 625821 "ELAGG-" 625826 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-291 623898 624065 624221 "ELABOR" 624480 T ELABOR (NIL) -8 NIL NIL NIL) (-290 622505 622838 623132 "ELABEXPR" 623624 T ELABEXPR (NIL) -8 NIL NIL NIL) (-289 615017 617142 617971 "EFUPXS" 621780 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-288 608143 610266 611077 "EFULS" 614292 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-287 605580 605986 606458 "EFSTRUC" 607775 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-286 595017 596937 598485 "EF" 604095 NIL EF (NIL T T) -7 NIL NIL NIL) (-285 593995 594502 594651 "EAB" 594888 T EAB (NIL) -8 NIL NIL NIL) (-284 593117 593954 593982 "E04UCFA" 593987 T E04UCFA (NIL) -8 NIL NIL NIL) (-283 592239 593076 593104 "E04NAFA" 593109 T E04NAFA (NIL) -8 NIL NIL NIL) (-282 591361 592198 592226 "E04MBFA" 592231 T E04MBFA (NIL) -8 NIL NIL NIL) (-281 590483 591320 591348 "E04JAFA" 591353 T E04JAFA (NIL) -8 NIL NIL NIL) (-280 589607 590442 590470 "E04GCFA" 590475 T E04GCFA (NIL) -8 NIL NIL NIL) (-279 588731 589566 589594 "E04FDFA" 589599 T E04FDFA (NIL) -8 NIL NIL NIL) (-278 587853 588690 588718 "E04DGFA" 588723 T E04DGFA (NIL) -8 NIL NIL NIL) (-277 581930 583378 584742 "E04AGNT" 586509 T E04AGNT (NIL) -7 NIL NIL NIL) (-276 580550 581231 581271 "DVARCAT" 581612 NIL DVARCAT (NIL T) -9 NIL 581775 NIL) (-275 579700 579966 580280 "DVARCAT-" 580285 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-274 571661 579499 579628 "DSMP" 579633 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-273 570012 570803 570844 "DSEXT" 571207 NIL DSEXT (NIL T) -9 NIL 571501 NIL) (-272 568201 568725 569391 "DSEXT-" 569396 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-271 562784 564146 565214 "DROPT" 567153 T DROPT (NIL) -8 NIL NIL NIL) (-270 562443 562508 562606 "DROPT1" 562719 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-269 557462 558684 559821 "DROPT0" 561326 T DROPT0 (NIL) -7 NIL NIL NIL) (-268 555771 556132 556518 "DRAWPT" 557096 T DRAWPT (NIL) -7 NIL NIL NIL) (-267 550262 551281 552360 "DRAW" 554745 NIL DRAW (NIL T) -7 NIL NIL NIL) (-266 549889 549948 550066 "DRAWHACK" 550203 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-265 548590 548889 549180 "DRAWCX" 549618 T DRAWCX (NIL) -7 NIL NIL NIL) (-264 548099 548174 548325 "DRAWCURV" 548516 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-263 538417 540529 542644 "DRAWCFUN" 546004 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-262 534888 537082 537123 "DQAGG" 537752 NIL DQAGG (NIL T) -9 NIL 538026 NIL) (-261 521471 529099 529182 "DPOLCAT" 531034 NIL DPOLCAT (NIL T T T T) -9 NIL 531579 NIL) (-260 515990 517656 519614 "DPOLCAT-" 519619 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-259 508847 515851 515949 "DPMO" 515954 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-258 501601 508627 508794 "DPMM" 508799 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-257 501123 501385 501474 "DOMTMPLT" 501532 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-256 500472 500925 501005 "DOMCTOR" 501063 T DOMCTOR (NIL) -8 NIL NIL NIL) (-255 499624 499952 500103 "DOMAIN" 500341 T DOMAIN (NIL) -8 NIL NIL NIL) (-254 492636 499259 499411 "DMP" 499525 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-253 490413 491703 491744 "DMEXT" 491749 NIL DMEXT (NIL T) -9 NIL 491925 NIL) (-252 490007 490069 490213 "DLP" 490351 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 483130 489334 489524 "DLIST" 489849 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 479668 481955 481996 "DLAGG" 482546 NIL DLAGG (NIL T) -9 NIL 482776 NIL) (-249 478180 478994 479022 "DIVRING" 479114 T DIVRING (NIL) -9 NIL 479197 NIL) (-248 477363 477607 477907 "DIVRING-" 477912 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 475405 475822 476228 "DISPLAY" 476977 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 468812 475319 475382 "DIRPROD" 475387 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 467642 467863 468128 "DIRPROD2" 468605 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 455861 462353 462406 "DIRPCAT" 462664 NIL DIRPCAT (NIL NIL T) -9 NIL 463539 NIL) (-243 453061 453829 454710 "DIRPCAT-" 455047 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 452342 452508 452694 "DIOSP" 452895 T DIOSP (NIL) -7 NIL NIL NIL) (-241 448756 451226 451267 "DIOPS" 451701 NIL DIOPS (NIL T) -9 NIL 451930 NIL) (-240 448275 448419 448610 "DIOPS-" 448615 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 447182 447954 447982 "DIFRING" 447987 T DIFRING (NIL) -9 NIL 448009 NIL) (-238 446830 446928 446956 "DIFFSPC" 447075 T DIFFSPC (NIL) -9 NIL 447150 NIL) (-237 446451 446553 446705 "DIFFSPC-" 446710 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 445387 445985 446026 "DIFFMOD" 446031 NIL DIFFMOD (NIL T) -9 NIL 446129 NIL) (-235 445083 445140 445181 "DIFFDOM" 445302 NIL DIFFDOM (NIL T) -9 NIL 445370 NIL) (-234 444930 444960 445044 "DIFFDOM-" 445049 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 442670 444134 444175 "DIFEXT" 444180 NIL DIFEXT (NIL T) -9 NIL 444333 NIL) (-232 439704 442174 442215 "DIAGG" 442220 NIL DIAGG (NIL T) -9 NIL 442240 NIL) (-231 439052 439245 439497 "DIAGG-" 439502 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-230 433902 438011 438288 "DHMATRIX" 438821 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-229 429370 430423 431433 "DFSFUN" 432912 T DFSFUN (NIL) -7 NIL NIL NIL) (-228 423604 428301 428613 "DFLOAT" 429078 T DFLOAT (NIL) -8 NIL NIL NIL) (-227 421843 422148 422537 "DFINTTLS" 423312 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-226 418662 419864 420264 "DERHAM" 421509 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-225 416198 418437 418526 "DEQUEUE" 418606 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-224 415440 415585 415768 "DEGRED" 416060 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-223 411846 412615 413461 "DEFINTRF" 414668 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-222 409383 409870 410462 "DEFINTEF" 411365 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-221 408667 409003 409118 "DEFAST" 409288 T DEFAST (NIL) -8 NIL NIL NIL) (-220 401703 408260 408410 "DECIMAL" 408537 T DECIMAL (NIL) -8 NIL NIL NIL) (-219 399161 399673 400179 "DDFACT" 401247 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-218 398751 398800 398951 "DBLRESP" 399112 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-217 397952 398521 398612 "DBASIS" 398700 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-216 395736 396182 396543 "DBASE" 397718 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 394924 395216 395362 "DATAARY" 395635 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 393982 394883 394911 "D03FAFA" 394916 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 393041 393941 393969 "D03EEFA" 393974 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 390967 391457 391946 "D03AGNT" 392572 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 390208 390926 390954 "D02EJFA" 390959 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 389449 390167 390195 "D02CJFA" 390200 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 388690 389408 389436 "D02BHFA" 389441 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 387931 388649 388677 "D02BBFA" 388682 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 381062 382717 384323 "D02AGNT" 386345 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 378812 379353 379899 "D01WGTS" 380536 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 377819 378771 378799 "D01TRNS" 378804 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 376827 377778 377806 "D01GBFA" 377811 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 375835 376786 376814 "D01FCFA" 376819 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 374843 375794 375822 "D01ASFA" 375827 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 373851 374802 374830 "D01AQFA" 374835 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 372859 373810 373838 "D01APFA" 373843 T D01APFA (NIL) -8 NIL NIL NIL) (-199 371867 372818 372846 "D01ANFA" 372851 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 370875 371826 371854 "D01AMFA" 371859 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 369883 370834 370862 "D01ALFA" 370867 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 368891 369842 369870 "D01AKFA" 369875 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 367899 368850 368878 "D01AJFA" 368883 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 361122 362747 364308 "D01AGNT" 366358 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 360441 360587 360739 "CYCLOTOM" 360990 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 357096 357889 358616 "CYCLES" 359734 T CYCLES (NIL) -7 NIL NIL NIL) (-191 356396 356542 356713 "CVMP" 356957 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 354183 354495 354864 "CTRIGMNP" 356124 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 353541 353977 354050 "CTOR" 354130 T CTOR (NIL) -8 NIL NIL NIL) (-188 353014 353272 353373 "CTORKIND" 353460 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 352219 352607 352635 "CTORCAT" 352817 T CTORCAT (NIL) -9 NIL 352930 NIL) (-186 351793 351928 352087 "CTORCAT-" 352092 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 351207 351467 351575 "CTORCALL" 351717 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 350563 350680 350833 "CSTTOOLS" 351104 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 346260 347019 347777 "CRFP" 349875 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 345675 345981 346073 "CRCEAST" 346188 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 344698 344907 345135 "CRAPACK" 345479 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 344078 344183 344387 "CPMATCH" 344574 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 343797 343831 343937 "CPIMA" 344044 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 340055 340817 341536 "COORDSYS" 343132 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 339443 339588 339730 "CONTOUR" 339933 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 334908 337446 337938 "CONTFRAC" 338983 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 334782 334809 334837 "CONDUIT" 334874 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 333736 334410 334438 "COMRING" 334443 T COMRING (NIL) -9 NIL 334495 NIL) (-173 332718 333094 333278 "COMPPROP" 333572 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 332373 332414 332542 "COMPLPAT" 332677 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 320756 332182 332291 "COMPLEX" 332296 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320386 320449 320556 "COMPLEX2" 320693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 319707 319846 320006 "COMPILER" 320246 T COMPILER (NIL) -8 NIL NIL NIL) (-168 319419 319460 319558 "COMPFACT" 319666 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 300794 313123 313163 "COMPCAT" 314167 NIL COMPCAT (NIL T) -9 NIL 315515 NIL) (-166 289682 293233 296860 "COMPCAT-" 297216 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 289405 289439 289542 "COMMUPC" 289648 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 289193 289233 289292 "COMMONOP" 289366 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 288701 288944 289031 "COMM" 289126 T COMM (NIL) -8 NIL NIL NIL) (-162 288223 288505 288580 "COMMAAST" 288646 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 287418 287666 287694 "COMBOPC" 288032 T COMBOPC (NIL) -9 NIL 288207 NIL) (-160 286272 286524 286766 "COMBINAT" 287208 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 282615 283303 283930 "COMBF" 285694 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 281277 281731 281966 "COLOR" 282400 T COLOR (NIL) -8 NIL NIL NIL) (-157 280693 280998 281090 "COLONAST" 281205 T COLONAST (NIL) -8 NIL NIL NIL) (-156 280327 280380 280505 "CMPLXRT" 280640 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 279715 280027 280126 "CLLCTAST" 280248 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 275175 276245 277325 "CLIP" 278655 T CLIP (NIL) -7 NIL NIL NIL) (-153 273348 274276 274516 "CLIF" 275002 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 269330 271466 271507 "CLAGG" 272436 NIL CLAGG (NIL T) -9 NIL 272972 NIL) (-151 267674 268209 268792 "CLAGG-" 268797 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 267212 267303 267443 "CINTSLPE" 267583 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 264677 265184 265732 "CHVAR" 266740 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 263717 264391 264419 "CHARZ" 264424 T CHARZ (NIL) -9 NIL 264439 NIL) (-147 263465 263511 263589 "CHARPOL" 263671 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 262383 263096 263124 "CHARNZ" 263171 T CHARNZ (NIL) -9 NIL 263227 NIL) (-145 260127 261037 261390 "CHAR" 262050 T CHAR (NIL) -8 NIL NIL NIL) (-144 259835 259914 259942 "CFCAT" 260053 T CFCAT (NIL) -9 NIL NIL NIL) (-143 259058 259187 259370 "CDEN" 259719 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 254655 258211 258491 "CCLASS" 258798 T CCLASS (NIL) -8 NIL NIL NIL) (-141 253876 254063 254240 "CATEGORY" 254498 T -10 (NIL) -8 NIL NIL NIL) (-140 253371 253795 253843 "CATCTOR" 253848 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 252762 253074 253172 "CATAST" 253293 T CATAST (NIL) -8 NIL NIL NIL) (-138 252178 252483 252575 "CASEAST" 252690 T CASEAST (NIL) -8 NIL NIL NIL) (-137 247076 248335 249079 "CARTEN" 251490 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 246172 246332 246553 "CARTEN2" 246923 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 244302 245322 245579 "CARD" 245935 T CARD (NIL) -8 NIL NIL NIL) (-134 243824 244106 244181 "CAPSLAST" 244247 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 243266 243522 243550 "CACHSET" 243682 T CACHSET (NIL) -9 NIL 243760 NIL) (-132 242656 243044 243072 "CABMON" 243122 T CABMON (NIL) -9 NIL 243178 NIL) (-131 242093 242360 242470 "BYTEORD" 242566 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 240944 241622 241764 "BYTE" 241927 T BYTE (NIL) -8 NIL NIL 242049) (-129 235871 240449 240621 "BYTEBUF" 240792 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 233133 235563 235670 "BTREE" 235797 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 230335 232781 232903 "BTOURN" 233043 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 227442 229777 229818 "BTCAT" 229886 NIL BTCAT (NIL T) -9 NIL 229963 NIL) (-125 227091 227189 227338 "BTCAT-" 227343 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 221982 226337 226365 "BTAGG" 226479 T BTAGG (NIL) -9 NIL 226589 NIL) (-123 221436 221597 221803 "BTAGG-" 221808 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 218172 220714 220929 "BSTREE" 221253 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 217280 217436 217620 "BRILL" 218028 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 213675 215978 216019 "BRAGG" 216668 NIL BRAGG (NIL T) -9 NIL 216926 NIL) (-119 212108 212610 213165 "BRAGG-" 213170 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 204344 211452 211637 "BPADICRT" 211955 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 202353 204281 204326 "BPADIC" 204331 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 202045 202081 202195 "BOUNDZRO" 202317 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 197027 198471 199383 "BOP" 201153 T BOP (NIL) -8 NIL NIL NIL) (-114 194754 195212 195687 "BOP1" 196585 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 194437 194516 194544 "BOOLE" 194655 T BOOLE (NIL) -9 NIL 194737 NIL) (-112 193088 194011 194160 "BOOLEAN" 194308 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 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T) ((-23) . T) ((-47 |#1| #0=(-577)) . T) ((-25) . T) ((-38 #1=(-420 (-577))) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-38 |#1|) |has| |#1| (-174)) ((-38 |#2|) |has| |#1| (-375)) ((-38 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-35) |has| |#1| (-38 (-420 (-577)))) ((-95) |has| |#1| (-38 (-420 (-577)))) ((-102) . T) ((-111 #1# #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-375)) ((-111 $ $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-132) . T) ((-146) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-146))) (|has| |#1| (-146))) ((-148) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-148))) (|has| |#1| (-148))) ((-634 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-634 (-577)) . T) ((-634 #2=(-1206)) -12 (|has| |#1| (-375)) (|has| |#2| (-1068 (-1206)))) ((-634 |#1|) |has| |#1| (-174)) ((-634 |#2|) . T) ((-634 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-631 (-885)) . T) ((-174) -2867 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-632 (-228)) -12 (|has| |#1| (-375)) (|has| |#2| (-1052))) ((-632 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-1052))) ((-632 (-549)) -12 (|has| |#1| (-375)) (|has| |#2| (-632 (-549)))) ((-632 (-916 (-391))) -12 (|has| |#1| (-375)) (|has| |#2| (-632 (-916 (-391))))) ((-632 (-916 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-632 (-916 (-577))))) ((-235 $) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-233 |#2|) |has| |#1| (-375)) ((-239) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-238) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-238))) (-12 (|has| |#1| (-375)) (|has| |#2| (-239))) (|has| |#1| (-15 * (|#1| (-577) |#1|)))) ((-273 |#2|) |has| |#1| (-375)) ((-249) |has| |#1| (-375)) ((-295) |has| |#1| (-38 (-420 (-577)))) ((-297 #0# |#1|) . T) ((-297 |#2| $) -12 (|has| |#1| (-375)) (|has| |#2| (-297 |#2| |#2|))) ((-297 $ $) |has| (-577) (-1142)) ((-301) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-320 |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-375) |has| |#1| (-375)) ((-350 |#2|) |has| |#1| (-375)) ((-389 |#2|) |has| |#1| (-375)) ((-413 |#2|) |has| |#1| (-375)) ((-465) |has| |#1| (-375)) ((-506) |has| |#1| (-38 (-420 (-577)))) ((-527 (-1206) |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-527 (-1206) |#2|))) ((-527 |#2| |#2|) -12 (|has| |#1| (-375)) (|has| |#2| (-320 |#2|))) ((-569) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-667 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-667 (-577)) . T) ((-667 |#1|) . T) ((-667 |#2|) |has| |#1| (-375)) ((-667 $) . T) ((-669 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-669 #3=(-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-659 (-577)))) ((-669 |#1|) . T) ((-669 |#2|) |has| |#1| (-375)) ((-669 $) . T) ((-661 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-661 |#1|) |has| |#1| (-174)) ((-661 |#2|) |has| |#1| (-375)) ((-661 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-659 #3#) -12 (|has| |#1| (-375)) (|has| |#2| (-659 (-577)))) ((-659 |#2|) |has| |#1| (-375)) ((-738 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-738 |#1|) |has| |#1| (-174)) ((-738 |#2|) |has| |#1| (-375)) ((-738 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375))) ((-747) . T) ((-812) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-813) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-815) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-816) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-841) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-869) -12 (|has| |#1| (-375)) (|has| |#2| (-841))) ((-870) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-870))) (-12 (|has| |#1| (-375)) (|has| |#2| (-841)))) ((-873) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-870))) (-12 (|has| |#1| (-375)) (|has| |#2| (-841)))) ((-920 $ #4=(-1206)) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-928 (-1206)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-926 (-1206)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-926 (-1206))))) ((-926 (-1206)) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-926 (-1206)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-926 (-1206))))) ((-928 #4#) -2867 (-12 (|has| |#1| (-375)) (|has| |#2| (-928 (-1206)))) (-12 (|has| |#1| (-375)) (|has| |#2| (-926 (-1206)))) (-12 (|has| |#1| (-15 * (|#1| (-577) |#1|))) (|has| |#1| (-926 (-1206))))) ((-910 (-391)) -12 (|has| |#1| (-375)) (|has| |#2| (-910 (-391)))) ((-910 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-910 (-577)))) ((-908 |#2|) |has| |#1| (-375)) ((-937) -12 (|has| |#1| (-375)) (|has| |#2| (-937))) ((-1003 |#1| #0# (-1112)) . T) ((-948) |has| |#1| (-375)) ((-1022 |#2|) |has| |#1| (-375)) ((-1032) |has| |#1| (-38 (-420 (-577)))) ((-1052) -12 (|has| |#1| (-375)) (|has| |#2| (-1052))) ((-1068 (-420 (-577))) -12 (|has| |#1| (-375)) (|has| |#2| (-1068 (-577)))) ((-1068 (-577)) -12 (|has| |#1| (-375)) (|has| |#2| (-1068 (-577)))) ((-1068 #2#) -12 (|has| |#1| (-375)) (|has| |#2| (-1068 (-1206)))) ((-1068 |#2|) . T) ((-1081 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1081 |#1|) . T) ((-1081 |#2|) |has| |#1| (-375)) ((-1081 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1086 #1#) -2867 (|has| |#1| (-375)) (|has| |#1| (-38 (-420 (-577))))) ((-1086 |#1|) . T) ((-1086 |#2|) |has| |#1| (-375)) ((-1086 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1079) . T) ((-1088) . T) ((-1142) . T) ((-1130) . T) ((-1182) -12 (|has| |#1| (-375)) (|has| |#2| (-1182))) ((-1232) |has| |#1| (-38 (-420 (-577)))) ((-1235) |has| |#1| (-38 (-420 (-577)))) ((-1247) . T) ((-1251) |has| |#1| (-375)) ((-1257 |#1|) . T) ((-1275 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-792)) . T) ((-25) . T) ((-38 #1=(-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-420 (-577)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-634 #1#) -2867 (|has| |#1| (-1068 (-420 (-577)))) (|has| |#1| (-38 (-420 (-577))))) ((-634 (-577)) . T) ((-634 #2=(-1112)) . T) ((-634 |#1|) . T) ((-634 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-631 (-885)) . T) ((-174) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-632 (-549)) -12 (|has| (-1112) (-632 (-549))) (|has| |#1| (-632 (-549)))) ((-632 (-916 (-391))) -12 (|has| (-1112) (-632 (-916 (-391)))) (|has| |#1| (-632 (-916 (-391))))) ((-632 (-916 (-577))) -12 (|has| (-1112) (-632 (-916 (-577)))) (|has| |#1| (-632 (-916 (-577))))) ((-235 $) . T) ((-233 |#1|) . T) ((-239) . T) ((-238) . T) ((-273 |#1|) . T) ((-297 (-420 $) (-420 $)) |has| |#1| (-569)) ((-297 |#1| |#1|) . T) ((-297 $ $) . T) ((-301) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-318) |has| |#1| (-375)) ((-320 $) . T) ((-337 |#1| #0#) . T) ((-389 |#1|) . T) ((-424 |#1|) . T) ((-465) -2867 (|has| |#1| (-937)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-527 #2# |#1|) . T) ((-527 #2# $) . T) ((-527 $ $) . T) ((-569) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-667 #1#) |has| |#1| (-38 (-420 (-577)))) ((-667 (-577)) . T) ((-667 |#1|) . T) ((-667 $) . T) ((-669 #1#) |has| |#1| (-38 (-420 (-577)))) ((-669 #3=(-577)) |has| |#1| (-659 (-577))) ((-669 |#1|) . T) ((-669 $) . T) ((-661 #1#) |has| |#1| (-38 (-420 (-577)))) ((-661 |#1|) |has| |#1| (-174)) ((-661 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-659 #3#) |has| |#1| (-659 (-577))) ((-659 |#1|) . T) ((-738 #1#) |has| |#1| (-38 (-420 (-577)))) ((-738 |#1|) |has| |#1| (-174)) ((-738 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375))) ((-747) . T) ((-920 $ #2#) . T) ((-920 $ #4=(-1206)) -2867 (|has| |#1| (-928 (-1206))) (|has| |#1| (-926 (-1206)))) ((-926 #2#) . T) ((-926 (-1206)) |has| |#1| (-926 (-1206))) ((-928 #2#) . T) ((-928 #4#) -2867 (|has| |#1| (-928 (-1206))) (|has| |#1| (-926 (-1206)))) ((-910 (-391)) -12 (|has| (-1112) (-910 (-391))) (|has| |#1| (-910 (-391)))) ((-910 (-577)) -12 (|has| (-1112) (-910 (-577))) (|has| |#1| (-910 (-577)))) ((-977 |#1| #0# #2#) . T) ((-937) |has| |#1| (-937)) ((-948) |has| |#1| (-375)) ((-1068 (-420 (-577))) |has| |#1| (-1068 (-420 (-577)))) ((-1068 (-577)) |has| |#1| (-1068 (-577))) ((-1068 #2#) . T) ((-1068 |#1|) . T) ((-1081 #1#) |has| |#1| (-38 (-420 (-577)))) ((-1081 |#1|) . T) ((-1081 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1086 #1#) |has| |#1| (-38 (-420 (-577)))) ((-1086 |#1|) . T) ((-1086 $) -2867 (|has| |#1| (-937)) (|has| |#1| (-569)) (|has| |#1| (-465)) (|has| |#1| (-375)) (|has| |#1| (-174))) ((-1079) . T) ((-1088) . T) ((-1142) . T) ((-1130) . T) ((-1182) |has| |#1| (-1182)) ((-1247) . T) ((-1251) |has| |#1| (-937))) +((-3891 (((-665 (-1112)) $) 34 T ELT)) (-4048 (($ $) 31 T ELT)) (-3872 (($ |#2| |#3|) NIL T ELT) (($ $ (-1112) |#3|) 28 T ELT) (($ $ (-665 (-1112)) (-665 |#3|)) 27 T ELT)) (-4014 (($ $) 14 T ELT)) (-4025 ((|#2| $) 12 T ELT)) (-1597 ((|#3| $) 10 T ELT))) +(((-1274 |#1| |#2| |#3|) (-10 -8 (-15 -3891 ((-665 (-1112)) |#1|)) (-15 -3872 (|#1| |#1| (-665 (-1112)) (-665 |#3|))) (-15 -3872 (|#1| |#1| (-1112) |#3|)) (-15 -4048 (|#1| |#1|)) (-15 -3872 (|#1| |#2| |#3|)) (-15 -1597 (|#3| |#1|)) (-15 -4014 (|#1| |#1|)) (-15 -4025 (|#2| |#1|))) (-1275 |#2| |#3|) (-1079) (-813)) (T -1274)) +NIL +(-10 -8 (-15 -3891 ((-665 (-1112)) |#1|)) (-15 -3872 (|#1| |#1| (-665 (-1112)) (-665 |#3|))) (-15 -3872 (|#1| |#1| (-1112) |#3|)) (-15 -4048 (|#1| |#1|)) (-15 -3872 (|#1| |#2| |#3|)) (-15 -1597 (|#3| |#1|)) (-15 -4014 (|#1| |#1|)) (-15 -4025 (|#2| |#1|))) +((-3586 (((-112) $ $) 7 T ELT)) (-4113 (((-112) $) 17 T ELT)) (-3891 (((-665 (-1112)) $) 86 T ELT)) (-3341 (((-1206) $) 118 T ELT)) (-1758 (((-2 (|:| -3273 $) (|:| -4486 $) (|:| |associate| $)) $) 63 (|has| |#1| (-569)) ELT)) (-2261 (($ $) 64 (|has| |#1| (-569)) ELT)) (-2538 (((-112) $) 66 (|has| |#1| (-569)) ELT)) (-3610 (($ $ |#2|) 113 T ELT) (($ $ |#2| |#2|) 112 T ELT)) (-2072 (((-1187 (-2 (|:| |k| |#2|) (|:| |c| |#1|))) $) 119 T ELT)) (-2478 (((-3 $ "failed") $ $) 20 T ELT)) (-2305 (($) 18 T CONST)) (-4048 (($ $) 72 T ELT)) (-3167 (((-3 $ "failed") $) 37 T ELT)) (-1655 (((-112) $) 85 T ELT)) (-4030 ((|#2| $) 115 T ELT) ((|#2| $ |#2|) 114 T ELT)) (-3357 (((-112) $) 35 T ELT)) (-3720 (($ $ (-949)) 116 T ELT)) (-2696 (((-112) $) 74 T ELT)) (-3872 (($ |#1| |#2|) 73 T ELT) (($ $ (-1112) |#2|) 88 T ELT) (($ $ (-665 (-1112)) (-665 |#2|)) 87 T ELT)) (-4417 (($ (-1 |#1| |#1|) $) 75 T ELT)) (-4014 (($ $) 77 T ELT)) (-4025 ((|#1| $) 78 T ELT)) (-3235 (((-1188) $) 10 T ELT)) (-1470 (((-1150) $) 11 T ELT)) (-2568 (($ $ |#2|) 110 T ELT)) (-3574 (((-3 $ "failed") $ $) 62 (|has| |#1| (-569)) ELT)) (-3373 (((-1187 |#1|) $ |#1|) 109 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) ELT)) (-2916 ((|#1| $ |#2|) 120 T ELT) (($ $ $) 96 (|has| |#2| (-1142)) ELT)) (-3641 (($ $ (-1206)) 108 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-665 (-1206))) 106 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1206) (-792)) 105 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-665 (-1206)) (-665 (-792))) 104 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 100 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-792)) 98 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-1597 ((|#2| $) 76 T ELT)) (-4165 (($ $) 84 T ELT)) (-3709 (((-885) $) 12 T ELT) (($ (-577)) 33 T ELT) (($ (-420 (-577))) 69 (|has| |#1| (-38 (-420 (-577)))) ELT) (($ $) 61 (|has| |#1| (-569)) ELT) (($ |#1|) 59 (|has| |#1| (-174)) ELT)) (-4171 ((|#1| $ |#2|) 71 T ELT)) (-2708 (((-3 $ "failed") $) 60 (|has| |#1| (-146)) ELT)) (-3331 (((-792)) 32 T CONST)) (-1343 ((|#1| $) 117 T ELT)) (-2643 (((-112) $ $) 6 T ELT)) (-4124 (((-112) $ $) 65 (|has| |#1| (-569)) ELT)) (-4215 ((|#1| $ |#2|) 111 (-12 (|has| |#1| (-15 ** (|#1| |#1| |#2|))) (|has| |#1| (-15 -3709 (|#1| (-1206))))) ELT)) (-2839 (($) 19 T CONST)) (-2853 (($) 34 T CONST)) (-2389 (($ $ (-1206)) 107 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-665 (-1206))) 103 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-1206) (-792)) 102 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $ (-665 (-1206)) (-665 (-792))) 101 (-12 (|has| |#1| (-926 (-1206))) (|has| |#1| (-15 * (|#1| |#2| |#1|)))) ELT) (($ $) 99 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT) (($ $ (-792)) 97 (|has| |#1| (-15 * (|#1| |#2| |#1|))) ELT)) (-3018 (((-112) $ $) 8 T ELT)) (-3139 (($ $ |#1|) 70 (|has| |#1| (-375)) ELT)) (-3128 (($ $) 23 T ELT) (($ $ $) 22 T ELT)) (-3114 (($ $ $) 15 T ELT)) (** (($ $ (-949)) 28 T ELT) (($ $ (-792)) 36 T ELT)) (* (($ (-949) $) 14 T ELT) (($ (-792) $) 16 T ELT) (($ (-577) $) 24 T ELT) (($ $ $) 27 T ELT) (($ $ |#1|) 80 T ELT) (($ |#1| $) 79 T ELT) (($ (-420 (-577)) $) 68 (|has| |#1| (-38 (-420 (-577)))) ELT) (($ $ (-420 (-577))) 67 (|has| |#1| (-38 (-420 (-577)))) ELT))) +(((-1275 |#1| |#2|) (-141) (-1079) (-813)) (T -1275)) +((-2072 (*1 *2 *1) (-12 (-4 *1 (-1275 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-813)) (-5 *2 (-1187 (-2 (|:| |k| *4) (|:| |c| *3)))))) (-3341 (*1 *2 *1) (-12 (-4 *1 (-1275 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-813)) (-5 *2 (-1206)))) (-1343 (*1 *2 *1) (-12 (-4 *1 (-1275 *2 *3)) (-4 *3 (-813)) (-4 *2 (-1079)))) (-3720 (*1 *1 *1 *2) (-12 (-5 *2 (-949)) (-4 *1 (-1275 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-813)))) (-4030 (*1 *2 *1) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-813)))) (-4030 (*1 *2 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-813)))) (-3610 (*1 *1 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-813)))) (-3610 (*1 *1 *1 *2 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-813)))) (-4215 (*1 *2 *1 *3) (-12 (-4 *1 (-1275 *2 *3)) (-4 *3 (-813)) (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3709 (*2 (-1206)))) (-4 *2 (-1079)))) (-2568 (*1 *1 *1 *2) (-12 (-4 *1 (-1275 *3 *2)) (-4 *3 (-1079)) (-4 *2 (-813)))) (-3373 (*1 *2 *1 *3) (-12 (-4 *1 (-1275 *3 *4)) (-4 *3 (-1079)) (-4 *4 (-813)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1187 *3))))) +(-13 (-1003 |t#1| |t#2| (-1112)) (-297 |t#2| |t#1|) (-10 -8 (-15 -2072 ((-1187 (-2 (|:| |k| |t#2|) (|:| |c| |t#1|))) $)) (-15 -3341 ((-1206) $)) (-15 -1343 (|t#1| $)) (-15 -3720 ($ $ (-949))) (-15 -4030 (|t#2| $)) (-15 -4030 (|t#2| $ |t#2|)) (-15 -3610 ($ $ |t#2|)) (-15 -3610 ($ $ |t#2| |t#2|)) (IF (|has| |t#1| (-15 -3709 (|t#1| (-1206)))) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -4215 (|t#1| $ |t#2|)) |%noBranch|) |%noBranch|) (-15 -2568 ($ $ |t#2|)) (IF (|has| |t#2| (-1142)) (-6 (-297 $ $)) |%noBranch|) (IF (|has| |t#1| (-15 * (|t#1| |t#2| |t#1|))) (PROGN (-6 (-239)) (IF (|has| |t#1| (-926 (-1206))) (-6 (-926 (-1206))) |%noBranch|)) |%noBranch|) (IF (|has| |t#1| (-15 ** (|t#1| |t#1| |t#2|))) (-15 -3373 ((-1187 |t#1|) $ |t#1|)) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-420 (-577))) |has| |#1| (-38 (-420 (-577)))) ((-38 |#1|) |has| |#1| (-174)) ((-38 $) |has| |#1| (-569)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-420 (-577)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-132) . T) ((-146) |has| |#1| (-146)) ((-148) |has| |#1| (-148)) ((-634 #0#) |has| |#1| (-38 (-420 (-577)))) ((-634 (-577)) . T) ((-634 |#1|) |has| |#1| (-174)) ((-634 $) |has| |#1| (-569)) ((-631 (-885)) . T) ((-174) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-235 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-239) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-238) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-297 |#2| |#1|) . T) ((-297 $ $) |has| |#2| (-1142)) ((-301) |has| |#1| (-569)) ((-569) |has| |#1| (-569)) ((-667 #0#) |has| |#1| (-38 (-420 (-577)))) ((-667 (-577)) . T) ((-667 |#1|) . T) ((-667 $) . T) ((-669 #0#) |has| |#1| (-38 (-420 (-577)))) ((-669 |#1|) . T) ((-669 $) . T) ((-661 #0#) |has| |#1| (-38 (-420 (-577)))) ((-661 |#1|) |has| |#1| (-174)) ((-661 $) |has| |#1| (-569)) ((-738 #0#) |has| |#1| (-38 (-420 (-577)))) ((-738 |#1|) |has| |#1| (-174)) ((-738 $) |has| |#1| (-569)) ((-747) . T) ((-920 $ #1=(-1206)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1206)))) ((-926 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1206)))) ((-928 #1#) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-926 (-1206)))) ((-1003 |#1| |#2| (-1112)) . T) ((-1081 #0#) |has| |#1| (-38 (-420 (-577)))) ((-1081 |#1|) . T) ((-1081 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1086 #0#) |has| |#1| (-38 (-420 (-577)))) ((-1086 |#1|) . T) ((-1086 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1079) . T) ((-1088) . T) ((-1142) . T) ((-1130) . T) ((-1247) . T)) +((-2612 ((|#2| |#2|) 12 T ELT)) (-3206 (((-431 |#2|) |#2|) 14 T ELT)) (-3407 (((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-577))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-577)))) 30 T ELT))) +(((-1276 |#1| |#2|) (-10 -7 (-15 -3206 ((-431 |#2|) |#2|)) (-15 -2612 (|#2| |#2|)) (-15 -3407 ((-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-577))) (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (-577)))))) (-569) (-13 (-1273 |#1|) (-569) (-10 -8 (-15 -3642 ($ $ $))))) (T -1276)) +((-3407 (*1 *2 *2) (-12 (-5 *2 (-2 (|:| |flg| (-3 "nil" "sqfr" "irred" "prime")) (|:| |fctr| *4) (|:| |xpnt| (-577)))) (-4 *4 (-13 (-1273 *3) (-569) (-10 -8 (-15 -3642 ($ $ $))))) (-4 *3 (-569)) (-5 *1 (-1276 *3 *4)))) (-2612 (*1 *2 *2) (-12 (-4 *3 (-569)) (-5 *1 (-1276 *3 *2)) (-4 *2 (-13 (-1273 *3) (-569) (-10 -8 (-15 -3642 ($ $ $))))))) (-3206 (*1 *2 *3) (-12 (-4 *4 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T) ((-1081 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1086 #1#) |has| |#1| (-38 (-420 (-577)))) ((-1086 |#1|) . T) ((-1086 $) -2867 (|has| |#1| (-569)) (|has| |#1| (-174))) ((-1079) . T) ((-1088) . T) ((-1142) . T) ((-1130) . T) ((-1232) |has| |#1| (-38 (-420 (-577)))) ((-1235) |has| |#1| (-38 (-420 (-577)))) ((-1247) . T) ((-1275 |#1| #0#) . 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NIL) (-1320 3450577 3452181 3452756 "XPR" 3453782 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1319 3447972 3449908 3450112 "XPOLY" 3450408 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1318 3445303 3446979 3447034 "XPOLYC" 3447322 NIL XPOLYC (NIL T T) -9 NIL 3447435 NIL) (-1317 3441249 3443820 3444208 "XPBWPOLY" 3444961 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1316 3436518 3439225 3439267 "XF" 3439888 NIL XF (NIL T) -9 NIL 3440288 NIL) (-1315 3436115 3436227 3436396 "XF-" 3436401 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1314 3431007 3432586 3432641 "XFALG" 3434813 NIL XFALG (NIL T T) -9 NIL 3435602 NIL) (-1313 3430122 3430244 3430449 "XEXPPKG" 3430899 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1312 3427863 3429972 3430068 "XDPOLY" 3430073 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1311 3426518 3427256 3427299 "XALG" 3427304 NIL XALG (NIL T) -9 NIL 3427415 NIL) (-1310 3419428 3424495 3424989 "WUTSET" 3426110 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1309 3417530 3418480 3418803 "WP" 3419239 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1308 3417078 3417352 3417422 "WHILEAST" 3417482 T WHILEAST (NIL) -8 NIL NIL NIL) (-1307 3416490 3416795 3416889 "WHEREAST" 3417006 T WHEREAST (NIL) -8 NIL NIL NIL) (-1306 3415364 3415574 3415869 "WFFINTBS" 3416287 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1305 3413232 3413695 3414157 "WEIER" 3414936 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1304 3412156 3412714 3412756 "VSPACE" 3412892 NIL VSPACE (NIL T) -9 NIL 3412966 NIL) (-1303 3411988 3412021 3412112 "VSPACE-" 3412117 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1302 3411785 3411839 3411907 "VOID" 3411942 T VOID (NIL) -8 NIL NIL NIL) (-1301 3409885 3410280 3410686 "VIEW" 3411401 T VIEW (NIL) -7 NIL NIL NIL) (-1300 3406153 3406948 3407685 "VIEWDEF" 3409170 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1299 3395097 3397701 3399874 "VIEW3D" 3404002 T VIEW3D (NIL) -8 NIL NIL NIL) (-1298 3387114 3389008 3390587 "VIEW2D" 3393540 T VIEW2D (NIL) -8 NIL NIL NIL) (-1297 3382020 3386884 3386976 "VECTOR" 3387057 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1296 3380573 3380856 3381174 "VECTOR2" 3381750 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1295 3373527 3378277 3378320 "VECTCAT" 3379315 NIL VECTCAT (NIL T) -9 NIL 3379902 NIL) (-1294 3372469 3372795 3373185 "VECTCAT-" 3373190 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1293 3371875 3372120 3372240 "VARIABLE" 3372384 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1292 3371808 3371813 3371843 "UTYPE" 3371848 T UTYPE (NIL) -9 NIL NIL NIL) (-1291 3370616 3370792 3371054 "UTSODETL" 3371634 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1290 3368008 3368516 3369040 "UTSODE" 3370157 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1289 3359318 3365769 3366249 "UTS" 3367586 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1288 3349325 3355251 3355294 "UTSCAT" 3356406 NIL UTSCAT (NIL T) -9 NIL 3357164 NIL) (-1287 3346451 3347395 3348384 "UTSCAT-" 3348389 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1286 3346072 3346121 3346254 "UTS2" 3346402 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1285 3339939 3342882 3342925 "URAGG" 3344995 NIL URAGG (NIL T) -9 NIL 3345718 NIL) (-1284 3336662 3337741 3338864 "URAGG-" 3338869 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1283 3332031 3335297 3335762 "UPXSSING" 3336326 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1282 3323509 3331413 3331677 "UPXS" 3331825 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1281 3315924 3323413 3323485 "UPXSCONS" 3323490 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1280 3304672 3312126 3312188 "UPXSCCA" 3312762 NIL UPXSCCA (NIL T T) -9 NIL 3312995 NIL) (-1279 3304292 3304395 3304569 "UPXSCCA-" 3304574 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1278 3292940 3300119 3300162 "UPXSCAT" 3300810 NIL UPXSCAT (NIL T) -9 NIL 3301419 NIL) (-1277 3292364 3292449 3292628 "UPXS2" 3292855 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1276 3291000 3291271 3291622 "UPSQFREE" 3292107 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1275 3283828 3287266 3287321 "UPSCAT" 3288401 NIL UPSCAT (NIL T T) -9 NIL 3289167 NIL) (-1274 3282984 3283239 3283566 "UPSCAT-" 3283571 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1273 3267118 3276111 3276154 "UPOLYC" 3278255 NIL UPOLYC (NIL T) -9 NIL 3279476 NIL) (-1272 3257966 3260872 3264019 "UPOLYC-" 3264024 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1271 3257587 3257636 3257769 "UPOLYC2" 3257917 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1270 3248162 3257270 3257399 "UP" 3257506 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1269 3247483 3247608 3247772 "UPMP" 3248051 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1268 3247030 3247117 3247256 "UPDIVP" 3247396 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1267 3245568 3245847 3246163 "UPDECOMP" 3246779 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1266 3244781 3244911 3245097 "UPCDEN" 3245452 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1265 3244294 3244369 3244518 "UP2" 3244706 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1264 3242647 3243498 3243775 "UNISEG" 3244052 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1263 3241852 3241989 3242194 "UNISEG2" 3242490 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1262 3240894 3241092 3241318 "UNIFACT" 3241668 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1261 3222704 3240206 3240448 "ULS" 3240710 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1260 3209414 3222608 3222680 "ULSCONS" 3222685 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1259 3189214 3202494 3202556 "ULSCCAT" 3203194 NIL ULSCCAT (NIL T T) -9 NIL 3203483 NIL) (-1258 3188210 3188509 3188897 "ULSCCAT-" 3188902 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1257 3176655 3183756 3183799 "ULSCAT" 3184662 NIL ULSCAT (NIL T) -9 NIL 3185393 NIL) (-1256 3176079 3176164 3176343 "ULS2" 3176570 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1255 3175090 3175708 3175815 "UINT8" 3175926 T UINT8 (NIL) -8 NIL NIL 3176011) (-1254 3174100 3174718 3174825 "UINT64" 3174936 T UINT64 (NIL) -8 NIL NIL 3175021) (-1253 3173110 3173728 3173835 "UINT32" 3173946 T UINT32 (NIL) -8 NIL NIL 3174031) (-1252 3172120 3172738 3172845 "UINT16" 3172956 T UINT16 (NIL) -8 NIL NIL 3173041) (-1251 3170199 3171366 3171396 "UFD" 3171608 T UFD (NIL) -9 NIL 3171722 NIL) (-1250 3169981 3170039 3170134 "UFD-" 3170139 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1249 3169039 3169246 3169462 "UDVO" 3169787 T UDVO (NIL) -7 NIL NIL NIL) (-1248 3166805 3167264 3167735 "UDPO" 3168603 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1247 3166738 3166743 3166773 "TYPE" 3166778 T TYPE (NIL) -9 NIL NIL NIL) (-1246 3166450 3166693 3166724 "TYPEAST" 3166729 T TYPEAST (NIL) -8 NIL NIL NIL) (-1245 3165403 3165623 3165863 "TWOFACT" 3166244 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1244 3164378 3164812 3165047 "TUPLE" 3165203 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1243 3162015 3162588 3163127 "TUBETOOL" 3163861 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1242 3160821 3161062 3161304 "TUBE" 3161808 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1241 3155000 3159793 3160076 "TS" 3160573 NIL TS (NIL T) -8 NIL NIL NIL) (-1240 3143142 3147757 3147854 "TSETCAT" 3153123 NIL TSETCAT (NIL T T T T) -9 NIL 3154655 NIL) (-1239 3137610 3139474 3141365 "TSETCAT-" 3141370 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1238 3132083 3133096 3134025 "TRMANIP" 3136746 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1237 3131512 3131587 3131750 "TRIMAT" 3132015 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1236 3129324 3129615 3129972 "TRIGMNIP" 3131261 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1235 3128808 3128957 3128987 "TRIGCAT" 3129200 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1234 3128453 3128556 3128697 "TRIGCAT-" 3128702 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1233 3125067 3127311 3127592 "TREE" 3128207 NIL TREE (NIL T) -8 NIL NIL NIL) (-1232 3124173 3124869 3124899 "TRANFUN" 3124934 T TRANFUN (NIL) -9 NIL 3125000 NIL) (-1231 3123392 3123643 3123923 "TRANFUN-" 3123928 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1230 3123190 3123228 3123289 "TOPSP" 3123353 T TOPSP (NIL) -7 NIL NIL NIL) (-1229 3122520 3122653 3122807 "TOOLSIGN" 3123071 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1228 3121034 3121697 3121936 "TEXTFILE" 3122303 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1227 3118838 3119487 3119916 "TEX" 3120627 T TEX (NIL) -8 NIL NIL NIL) (-1226 3118613 3118650 3118722 "TEX1" 3118801 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1225 3118249 3118324 3118414 "TEMUTL" 3118545 T TEMUTL (NIL) -7 NIL NIL NIL) (-1224 3116343 3116683 3117008 "TBCMPPK" 3117972 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1223 3107670 3114429 3114485 "TBAGG" 3114885 NIL TBAGG (NIL T T) -9 NIL 3115096 NIL) (-1222 3102554 3104228 3105982 "TBAGG-" 3105987 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1221 3101920 3102045 3102190 "TANEXP" 3102443 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1220 3101371 3101695 3101785 "TALGOP" 3101865 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1219 3094385 3101228 3101321 "TABLE" 3101326 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1218 3093779 3093896 3094034 "TABLEAU" 3094282 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1217 3088309 3089607 3090855 "TABLBUMP" 3092565 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1216 3087519 3087678 3087859 "SYSTEM" 3088150 T SYSTEM (NIL) -8 NIL NIL NIL) (-1215 3083924 3084677 3085460 "SYSSOLP" 3086770 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1214 3083686 3083879 3083910 "SYSPTR" 3083915 T SYSPTR (NIL) -8 NIL NIL NIL) (-1213 3082521 3083213 3083339 "SYSNNI" 3083525 NIL SYSNNI (NIL NIL) -8 NIL NIL 3083617) (-1212 3081724 3082279 3082358 "SYSINT" 3082418 NIL SYSINT (NIL NIL) -8 NIL NIL 3082463) (-1211 3077822 3079002 3079712 "SYNTAX" 3081036 T SYNTAX (NIL) -8 NIL NIL NIL) (-1210 3074902 3075582 3076214 "SYMTAB" 3077212 T SYMTAB (NIL) -8 NIL NIL NIL) (-1209 3070001 3071053 3072036 "SYMS" 3073941 T SYMS (NIL) -8 NIL NIL NIL) (-1208 3066900 3069452 3069685 "SYMPOLY" 3069803 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1207 3066405 3066492 3066615 "SYMFUNC" 3066812 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1206 3062203 3063717 3064530 "SYMBOL" 3065614 T SYMBOL (NIL) -8 NIL NIL NIL) (-1205 3055676 3057431 3059151 "SWITCH" 3060505 T SWITCH (NIL) -8 NIL NIL NIL) (-1204 3048430 3054632 3054926 "SUTS" 3055440 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1203 3039908 3047812 3048076 "SUPXS" 3048224 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1202 3030431 3039526 3039652 "SUP" 3039817 NIL SUP (NIL T) -8 NIL NIL NIL) (-1201 3029578 3029717 3029934 "SUPFRACF" 3030299 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1200 3029193 3029258 3029371 "SUP2" 3029513 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1199 3027617 3027915 3028271 "SUMRF" 3028892 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1198 3026940 3027018 3027210 "SUMFS" 3027538 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1197 3008785 3026252 3026494 "SULS" 3026756 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1196 3008333 3008607 3008677 "SUCHTAST" 3008737 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1195 3007574 3007858 3007998 "SUCH" 3008241 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1194 3001213 3002480 3003439 "SUBSPACE" 3006662 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1193 3000633 3000733 3000897 "SUBRESP" 3001101 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1192 2993827 2995298 2996609 "STTF" 2999369 NIL STTF (NIL T) -7 NIL NIL NIL) (-1191 2987838 2989120 2990267 "STTFNC" 2992727 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1190 2978955 2981020 2982814 "STTAYLOR" 2986079 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1189 2971709 2978819 2978902 "STRTBL" 2978907 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1188 2966106 2971418 2971517 "STRING" 2971632 T STRING (NIL) -8 NIL NIL NIL) (-1187 2958216 2963725 2964336 "STREAM" 2965530 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1186 2957720 2957803 2957947 "STREAM3" 2958133 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1185 2956684 2956885 2957120 "STREAM2" 2957533 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1184 2956366 2956424 2956517 "STREAM1" 2956626 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1183 2955358 2955563 2955794 "STINPROD" 2956182 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1182 2954854 2955106 2955136 "STEP" 2955216 T STEP (NIL) -9 NIL 2955294 NIL) (-1181 2953969 2954343 2954491 "STEPAST" 2954728 T STEPAST (NIL) -8 NIL NIL NIL) (-1180 2947025 2953868 2953945 "STBL" 2953950 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1179 2941583 2946188 2946231 "STAGG" 2946384 NIL STAGG (NIL T) -9 NIL 2946473 NIL) (-1178 2939135 2939887 2940759 "STAGG-" 2940764 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1177 2937107 2938905 2938997 "STACK" 2939078 NIL STACK (NIL T) -8 NIL NIL NIL) (-1176 2929114 2935248 2935704 "SREGSET" 2936737 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1175 2921461 2922908 2924421 "SRDCMPK" 2927720 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1174 2913770 2918820 2918850 "SRAGG" 2920153 T SRAGG (NIL) -9 NIL 2920761 NIL) (-1173 2912721 2913042 2913421 "SRAGG-" 2913426 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1172 2906305 2911668 2912089 "SQMATRIX" 2912347 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1171 2899717 2903023 2903750 "SPLTREE" 2905650 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1170 2895542 2896373 2897019 "SPLNODE" 2899143 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1169 2894517 2894822 2894852 "SPFCAT" 2895296 T SPFCAT (NIL) -9 NIL NIL NIL) (-1168 2893212 2893464 2893728 "SPECOUT" 2894275 T SPECOUT (NIL) -7 NIL NIL NIL) (-1167 2883858 2886176 2886206 "SPADXPT" 2890884 T SPADXPT (NIL) -9 NIL 2893050 NIL) (-1166 2883613 2883659 2883728 "SPADPRSR" 2883811 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1165 2881216 2883568 2883599 "SPADAST" 2883604 T SPADAST (NIL) -8 NIL NIL NIL) (-1164 2872817 2874920 2874963 "SPACEC" 2879336 NIL SPACEC (NIL T) -9 NIL 2881152 NIL) (-1163 2870617 2872749 2872798 "SPACE3" 2872803 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1162 2869349 2869540 2869831 "SORTPAK" 2870422 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1161 2867411 2867744 2868156 "SOLVETRA" 2869013 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1160 2866449 2866683 2866944 "SOLVESER" 2867184 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1159 2861681 2862641 2863636 "SOLVERAD" 2865501 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1158 2857406 2858105 2858834 "SOLVEFOR" 2861048 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1157 2851017 2856754 2856851 "SNTSCAT" 2856856 NIL SNTSCAT (NIL T T T T) -9 NIL 2856926 NIL) (-1156 2844561 2849340 2849731 "SMTS" 2850707 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1155 2838276 2844449 2844526 "SMP" 2844531 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1154 2836405 2836736 2837134 "SMITH" 2837973 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1153 2827937 2832984 2833087 "SMATCAT" 2834438 NIL SMATCAT (NIL NIL T T T) -9 NIL 2834988 NIL) (-1152 2824709 2825700 2826878 "SMATCAT-" 2826883 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1151 2822178 2823917 2823960 "SKAGG" 2824221 NIL SKAGG (NIL T) -9 NIL 2824356 NIL) (-1150 2817672 2821651 2821835 "SINT" 2821987 T SINT (NIL) -8 NIL NIL 2822149) (-1149 2817438 2817482 2817548 "SIMPAN" 2817628 T SIMPAN (NIL) -7 NIL NIL NIL) (-1148 2816663 2816973 2817113 "SIG" 2817320 T SIG (NIL) -8 NIL NIL NIL) (-1147 2815483 2815722 2815997 "SIGNRF" 2816422 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1146 2814298 2814467 2814751 "SIGNEF" 2815312 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1145 2813538 2813881 2814005 "SIGAST" 2814196 T SIGAST (NIL) -8 NIL NIL NIL) (-1144 2811190 2811682 2812188 "SHP" 2813079 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1143 2804563 2811091 2811167 "SHDP" 2811172 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1142 2804074 2804314 2804344 "SGROUP" 2804437 T SGROUP (NIL) -9 NIL 2804499 NIL) (-1141 2803926 2803958 2804031 "SGROUP-" 2804036 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1140 2800645 2801415 2802138 "SGCF" 2803225 T SGCF (NIL) -7 NIL NIL NIL) (-1139 2794354 2800091 2800188 "SFRTCAT" 2800193 NIL SFRTCAT (NIL T T T T) -9 NIL 2800232 NIL) (-1138 2787673 2788793 2789929 "SFRGCD" 2793337 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1137 2780691 2781872 2783058 "SFQCMPK" 2786606 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1136 2780293 2780400 2780511 "SFORT" 2780632 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1135 2779219 2780133 2780254 "SEXOF" 2780259 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1134 2778134 2779100 2779168 "SEX" 2779173 T SEX (NIL) -8 NIL NIL NIL) (-1133 2773723 2774630 2774725 "SEXCAT" 2777347 NIL SEXCAT (NIL T T T T T) -9 NIL 2777907 NIL) (-1132 2770532 2773657 2773705 "SET" 2773710 NIL SET (NIL T) -8 NIL NIL NIL) (-1131 2768654 2769245 2769550 "SETMN" 2770273 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1130 2768184 2768372 2768402 "SETCAT" 2768519 T SETCAT (NIL) -9 NIL 2768604 NIL) (-1129 2767952 2768016 2768115 "SETCAT-" 2768120 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1128 2764055 2766413 2766456 "SETAGG" 2767326 NIL SETAGG (NIL T) -9 NIL 2767666 NIL) (-1127 2763477 2763629 2763866 "SETAGG-" 2763871 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1126 2762860 2763173 2763274 "SEQAST" 2763398 T SEQAST (NIL) -8 NIL NIL NIL) (-1125 2761987 2762353 2762414 "SEGXCAT" 2762700 NIL SEGXCAT (NIL T T) -9 NIL 2762820 NIL) (-1124 2760903 2761653 2761835 "SEG" 2761840 NIL SEG (NIL T) -8 NIL NIL NIL) (-1123 2759828 2760096 2760139 "SEGCAT" 2760661 NIL SEGCAT (NIL T) -9 NIL 2760882 NIL) (-1122 2758718 2759191 2759399 "SEGBIND" 2759655 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1121 2758333 2758398 2758511 "SEGBIND2" 2758653 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1120 2757852 2758134 2758211 "SEGAST" 2758278 T SEGAST (NIL) -8 NIL NIL NIL) (-1119 2757061 2757197 2757401 "SEG2" 2757696 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1118 2756294 2756996 2757043 "SDVAR" 2757048 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1117 2747645 2756064 2756194 "SDPOL" 2756199 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1116 2746214 2746504 2746823 "SCPKG" 2747360 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1115 2745336 2745550 2745742 "SCOPE" 2746044 T SCOPE (NIL) -8 NIL NIL NIL) (-1114 2744532 2744690 2744869 "SCACHE" 2745191 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1113 2744116 2744350 2744380 "SASTCAT" 2744385 T SASTCAT (NIL) -9 NIL 2744398 NIL) (-1112 2743519 2743951 2744027 "SAOS" 2744062 T SAOS (NIL) -8 NIL NIL NIL) (-1111 2743078 2743119 2743292 "SAERFFC" 2743478 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1110 2736105 2742975 2743055 "SAE" 2743060 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2735692 2735733 2735892 "SAEFACT" 2736064 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1108 2733995 2734327 2734728 "RURPK" 2735358 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1107 2732572 2732938 2733243 "RULESET" 2733829 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1106 2729687 2730325 2730783 "RULE" 2732253 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2729257 2729481 2729564 "RULECOLD" 2729639 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1104 2729041 2729075 2729146 "RTVALUE" 2729208 T RTVALUE (NIL) -8 NIL NIL NIL) (-1103 2728452 2728758 2728852 "RSTRCAST" 2728969 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1102 2723222 2724095 2725015 "RSETGCD" 2727651 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2711793 2717530 2717627 "RSETCAT" 2721746 NIL RSETCAT (NIL T T T T) -9 NIL 2722843 NIL) (-1100 2709612 2710259 2711083 "RSETCAT-" 2711088 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1099 2701920 2703374 2704894 "RSDCMPK" 2708211 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1098 2699789 2700352 2700426 "RRCC" 2701512 NIL RRCC (NIL T T) -9 NIL 2701856 NIL) (-1097 2699110 2699314 2699593 "RRCC-" 2699598 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1096 2698493 2698806 2698907 "RPTAST" 2699031 T RPTAST (NIL) -8 NIL NIL NIL) (-1095 2670879 2681605 2681672 "RPOLCAT" 2692338 NIL RPOLCAT (NIL T T T) -9 NIL 2695498 NIL) (-1094 2661849 2664717 2667839 "RPOLCAT-" 2667844 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1093 2652302 2660060 2660542 "ROUTINE" 2661389 T ROUTINE (NIL) -8 NIL NIL NIL) (-1092 2648351 2651928 2652068 "ROMAN" 2652184 T ROMAN (NIL) -8 NIL NIL NIL) (-1091 2646463 2647211 2647471 "ROIRC" 2648156 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1090 2642181 2644952 2644982 "RNS" 2645286 T RNS (NIL) -9 NIL 2645560 NIL) (-1089 2640588 2641073 2641607 "RNS-" 2641682 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1088 2639881 2640385 2640415 "RNG" 2640420 T RNG (NIL) -9 NIL 2640441 NIL) (-1087 2638842 2639246 2639448 "RNGBIND" 2639732 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1086 2638137 2638615 2638658 "RMODULE" 2638663 NIL RMODULE (NIL T) -9 NIL 2638690 NIL) (-1085 2636961 2637067 2637403 "RMCAT2" 2638038 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1084 2633463 2636307 2636604 "RMATRIX" 2636723 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1083 2625962 2628550 2628665 "RMATCAT" 2632024 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633006 NIL) (-1082 2625301 2625484 2625791 "RMATCAT-" 2625796 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1081 2624874 2625088 2625131 "RLINSET" 2625193 NIL RLINSET (NIL T) -9 NIL 2625237 NIL) (-1080 2624435 2624516 2624644 "RINTERP" 2624793 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1079 2623359 2624033 2624063 "RING" 2624119 T RING (NIL) -9 NIL 2624211 NIL) (-1078 2623139 2623195 2623292 "RING-" 2623297 NIL RING- (NIL T) -8 NIL NIL NIL) (-1077 2621950 2622217 2622475 "RIDIST" 2622903 T RIDIST (NIL) -7 NIL NIL NIL) (-1076 2612575 2621418 2621624 "RGCHAIN" 2621798 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1075 2611833 2612317 2612358 "RGBCSPC" 2612416 NIL RGBCSPC (NIL T) -9 NIL 2612468 NIL) (-1074 2610899 2611358 2611399 "RGBCMDL" 2611631 NIL RGBCMDL (NIL T) -9 NIL 2611745 NIL) (-1073 2607839 2608507 2609177 "RF" 2610263 NIL RF (NIL T) -7 NIL NIL NIL) (-1072 2607479 2607548 2607651 "RFFACTOR" 2607770 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1071 2607198 2607239 2607336 "RFFACT" 2607438 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1070 2605249 2605679 2606061 "RFDIST" 2606838 T RFDIST (NIL) -7 NIL NIL NIL) (-1069 2604696 2604794 2604957 "RETSOL" 2605151 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1068 2604314 2604412 2604455 "RETRACT" 2604588 NIL RETRACT (NIL T) -9 NIL 2604675 NIL) (-1067 2604157 2604188 2604275 "RETRACT-" 2604280 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1066 2603705 2603979 2604049 "RETAST" 2604109 T RETAST (NIL) -8 NIL NIL NIL) (-1065 2596055 2603358 2603485 "RESULT" 2603600 T RESULT (NIL) -8 NIL NIL NIL) (-1064 2594490 2595324 2595523 "RESRING" 2595958 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1063 2594114 2594175 2594273 "RESLATC" 2594427 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1062 2593813 2593854 2593961 "REPSQ" 2594073 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1061 2591193 2591815 2592417 "REP" 2593233 T REP (NIL) -7 NIL NIL NIL) (-1060 2590884 2590925 2591036 "REPDB" 2591152 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1059 2584716 2586173 2587396 "REP2" 2589696 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1058 2581019 2581774 2582582 "REP1" 2583943 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1057 2573027 2579160 2579616 "REGSET" 2580649 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1056 2571736 2572175 2572425 "REF" 2572812 NIL REF (NIL T) -8 NIL NIL NIL) (-1055 2571101 2571216 2571383 "REDORDER" 2571620 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1054 2566465 2570314 2570541 "RECLOS" 2570929 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1053 2565499 2565698 2565913 "REALSOLV" 2566272 T REALSOLV (NIL) -7 NIL NIL NIL) (-1052 2565333 2565386 2565416 "REAL" 2565421 T REAL (NIL) -9 NIL 2565456 NIL) (-1051 2561780 2562618 2563502 "REAL0Q" 2564498 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1050 2557333 2558369 2559430 "REAL0" 2560761 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1049 2556744 2557050 2557144 "RDUCEAST" 2557261 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1048 2556143 2556221 2556428 "RDIV" 2556666 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1047 2555193 2555385 2555598 "RDIST" 2555965 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1046 2553778 2554077 2554449 "RDETRS" 2554901 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1045 2551572 2552044 2552582 "RDETR" 2553320 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1044 2550191 2550475 2550872 "RDEEFS" 2551288 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1043 2548694 2549006 2549431 "RDEEF" 2549879 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1042 2542171 2545648 2545678 "RCFIELD" 2546973 T RCFIELD (NIL) -9 NIL 2547704 NIL) (-1041 2540127 2540739 2541435 "RCFIELD-" 2541510 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1040 2536179 2538200 2538243 "RCAGG" 2539327 NIL RCAGG (NIL T) -9 NIL 2539792 NIL) (-1039 2535789 2535901 2536064 "RCAGG-" 2536069 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1038 2535106 2535236 2535401 "RATRET" 2535673 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1037 2534647 2534726 2534847 "RATFACT" 2535034 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1036 2533925 2534075 2534227 "RANDSRC" 2534517 T RANDSRC (NIL) -7 NIL NIL NIL) (-1035 2533653 2533703 2533776 "RADUTIL" 2533874 T RADUTIL (NIL) -7 NIL NIL NIL) (-1034 2525777 2532484 2532795 "RADIX" 2533376 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1033 2515371 2525619 2525749 "RADFF" 2525754 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1032 2515000 2515093 2515123 "RADCAT" 2515283 T RADCAT (NIL) -9 NIL NIL NIL) (-1031 2514770 2514830 2514930 "RADCAT-" 2514935 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1030 2512681 2514540 2514632 "QUEUE" 2514713 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1029 2508520 2512614 2512662 "QUAT" 2512667 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1028 2508145 2508194 2508325 "QUATCT2" 2508471 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1027 2500521 2504568 2504610 "QUATCAT" 2505401 NIL QUATCAT (NIL T) -9 NIL 2506167 NIL) (-1026 2496402 2497697 2499087 "QUATCAT-" 2499183 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1025 2493658 2495450 2495493 "QUAGG" 2495874 NIL QUAGG (NIL T) -9 NIL 2496049 NIL) (-1024 2493206 2493480 2493550 "QQUTAST" 2493610 T QQUTAST (NIL) -8 NIL NIL NIL) (-1023 2492117 2492719 2492884 "QFORM" 2493087 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1022 2481793 2487964 2488006 "QFCAT" 2488674 NIL QFCAT (NIL T) -9 NIL 2489675 NIL) (-1021 2477108 2478561 2480155 "QFCAT-" 2480251 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2476733 2476782 2476913 "QFCAT2" 2477059 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1019 2476164 2476298 2476430 "QEQUAT" 2476623 T QEQUAT (NIL) -8 NIL NIL NIL) (-1018 2469182 2470363 2471549 "QCMPACK" 2475097 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2466632 2467168 2467598 "QALGSET" 2468837 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465861 2466043 2466279 "QALGSET2" 2466450 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1015 2464528 2464770 2465089 "PWFFINTB" 2465634 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1014 2462673 2462871 2463227 "PUSHVAR" 2464342 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1013 2458400 2459616 2459659 "PTRANFN" 2461570 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1012 2456737 2457082 2457406 "PTPACK" 2458111 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1011 2456360 2456423 2456534 "PTFUNC2" 2456674 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1010 2450285 2455149 2455192 "PTCAT" 2455492 NIL PTCAT (NIL T) -9 NIL 2455645 NIL) (-1009 2449934 2449975 2450101 "PSQFR" 2450244 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1008 2448506 2448822 2449158 "PSEUDLIN" 2449632 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1007 2435026 2437601 2439927 "PSETPK" 2446266 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1006 2427734 2430762 2430860 "PSETCAT" 2433901 NIL PSETCAT (NIL T T T T) -9 NIL 2434715 NIL) (-1005 2425459 2426201 2427025 "PSETCAT-" 2427030 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1004 2424772 2424967 2424997 "PSCURVE" 2425269 T PSCURVE (NIL) -9 NIL 2425436 NIL) (-1003 2420488 2422262 2422329 "PSCAT" 2423181 NIL PSCAT (NIL T T T) -9 NIL 2423421 NIL) (-1002 2419482 2419764 2420167 "PSCAT-" 2420172 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1001 2417681 2418541 2418806 "PRTITION" 2419239 T PRTITION (NIL) -8 NIL NIL NIL) (-1000 2417092 2417398 2417492 "PRTDAST" 2417609 T PRTDAST (NIL) -8 NIL NIL NIL) (-999 2405974 2408396 2410584 "PRS" 2414954 NIL PRS (NIL T T) -7 NIL NIL NIL) (-998 2403594 2405296 2405336 "PRQAGG" 2405519 NIL PRQAGG (NIL T) -9 NIL 2405621 NIL) (-997 2402864 2403235 2403263 "PROPLOG" 2403402 T PROPLOG (NIL) -9 NIL 2403517 NIL) (-996 2402462 2402525 2402648 "PROPFUN2" 2402787 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-995 2401759 2401898 2402070 "PROPFUN1" 2402323 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-994 2399820 2400506 2400803 "PROPFRML" 2401495 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-993 2399265 2399396 2399524 "PROPERTY" 2399712 T PROPERTY (NIL) -8 NIL NIL NIL) (-992 2393153 2397431 2398251 "PRODUCT" 2398491 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-991 2390111 2392611 2392845 "PR" 2392964 NIL PR (NIL T T) -8 NIL NIL NIL) (-990 2389901 2389939 2389998 "PRINT" 2390072 T PRINT (NIL) -7 NIL NIL NIL) (-989 2389217 2389358 2389510 "PRIMES" 2389781 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-988 2387264 2387683 2388149 "PRIMELT" 2388796 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-987 2386981 2387042 2387070 "PRIMCAT" 2387194 T PRIMCAT (NIL) -9 NIL NIL NIL) (-986 2382703 2386919 2386964 "PRIMARR" 2386969 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-985 2381692 2381888 2382116 "PRIMARR2" 2382521 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-984 2381329 2381391 2381502 "PREASSOC" 2381630 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-983 2380780 2380937 2380965 "PPCURVE" 2381170 T PPCURVE (NIL) -9 NIL 2381306 NIL) (-982 2380327 2380575 2380658 "PORTNUM" 2380717 T PORTNUM (NIL) -8 NIL NIL NIL) (-981 2377664 2378085 2378677 "POLYROOT" 2379908 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-980 2370872 2377268 2377428 "POLY" 2377537 NIL POLY (NIL T) -8 NIL NIL NIL) (-979 2370249 2370313 2370547 "POLYLIFT" 2370808 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-978 2366470 2366973 2367602 "POLYCATQ" 2369794 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-977 2352118 2358217 2358282 "POLYCAT" 2361796 NIL POLYCAT (NIL T T T) -9 NIL 2363674 NIL) (-976 2345237 2347429 2349813 "POLYCAT-" 2349818 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-975 2344818 2344892 2345012 "POLY2UP" 2345163 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-974 2344444 2344507 2344616 "POLY2" 2344755 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-973 2343105 2343368 2343644 "POLUTIL" 2344218 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-972 2341424 2341737 2342068 "POLTOPOL" 2342827 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-971 2336420 2341358 2341405 "POINT" 2341410 NIL POINT (NIL T) -8 NIL NIL NIL) (-970 2334553 2334964 2335339 "PNTHEORY" 2336065 T PNTHEORY (NIL) -7 NIL NIL NIL) (-969 2332999 2333308 2333707 "PMTOOLS" 2334251 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-968 2332586 2332670 2332787 "PMSYM" 2332915 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-967 2332088 2332163 2332338 "PMQFCAT" 2332511 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-966 2331431 2331553 2331709 "PMPRED" 2331965 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2330812 2330910 2331072 "PMPREDFS" 2331332 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-964 2329466 2329684 2330062 "PMPLCAT" 2330574 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-963 2328992 2329077 2329229 "PMLSAGG" 2329381 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-962 2328459 2328541 2328723 "PMKERNEL" 2328910 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-961 2328070 2328151 2328264 "PMINS" 2328378 NIL PMINS (NIL T) -7 NIL NIL NIL) (-960 2327506 2327581 2327790 "PMFS" 2327995 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-959 2326722 2326852 2327057 "PMDOWN" 2327383 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-958 2325865 2326047 2326228 "PMASS" 2326561 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325114 2325248 2325411 "PMASSFS" 2325752 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-956 2324763 2324837 2324931 "PLOTTOOL" 2325040 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-955 2319184 2320574 2321722 "PLOT" 2323635 T PLOT (NIL) -8 NIL NIL NIL) (-954 2314836 2316030 2316952 "PLOT3D" 2318282 T PLOT3D (NIL) -8 NIL NIL NIL) (-953 2313724 2313925 2314160 "PLOT1" 2314640 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-952 2288899 2293790 2298641 "PLEQN" 2308990 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-951 2288205 2288339 2288519 "PINTERP" 2288764 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2287892 2287945 2288048 "PINTERPA" 2288152 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-949 2286988 2287656 2287743 "PI" 2287783 T PI (NIL) -8 NIL NIL 2287850) (-948 2285073 2286246 2286274 "PID" 2286456 T PID (NIL) -9 NIL 2286590 NIL) (-947 2284818 2284861 2284936 "PICOERCE" 2285030 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-946 2284126 2284277 2284453 "PGROEB" 2284674 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-945 2279565 2280524 2281430 "PGE" 2283240 T PGE (NIL) -7 NIL NIL NIL) (-944 2277646 2277935 2278301 "PGCD" 2279282 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-943 2276972 2277087 2277248 "PFRPAC" 2277530 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-942 2273222 2275520 2275873 "PFR" 2276651 NIL PFR (NIL T) -8 NIL NIL NIL) (-941 2271575 2271855 2272180 "PFOTOOLS" 2272969 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-940 2270090 2270347 2270698 "PFOQ" 2271332 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-939 2268573 2268803 2269159 "PFO" 2269874 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-938 2264498 2268462 2268531 "PF" 2268536 NIL PF (NIL NIL) -8 NIL NIL NIL) (-937 2261576 2263089 2263117 "PFECAT" 2263702 T PFECAT (NIL) -9 NIL 2264086 NIL) (-936 2261003 2261175 2261389 "PFECAT-" 2261394 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-935 2259576 2259858 2260159 "PFBRU" 2260752 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-934 2257406 2257794 2258226 "PFBR" 2259227 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-933 2253208 2254915 2255563 "PERM" 2256791 NIL PERM (NIL T) -8 NIL NIL NIL) (-932 2248262 2249415 2250285 "PERMGRP" 2252371 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-931 2246174 2247286 2247327 "PERMCAT" 2247727 NIL PERMCAT (NIL T) -9 NIL 2248025 NIL) (-930 2245821 2245868 2245992 "PERMAN" 2246127 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-929 2243062 2245486 2245608 "PENDTREE" 2245732 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-928 2241943 2242206 2242247 "PDSPC" 2242780 NIL PDSPC (NIL T) -9 NIL 2243025 NIL) (-927 2240998 2241264 2241626 "PDSPC-" 2241631 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-926 2239712 2240648 2240689 "PDRING" 2240694 NIL PDRING (NIL T) -9 NIL 2240722 NIL) (-925 2238455 2239217 2239271 "PDMOD" 2239276 NIL PDMOD (NIL T T) -9 NIL 2239380 NIL) (-924 2235622 2236448 2237116 "PDEPROB" 2237807 T PDEPROB (NIL) -8 NIL NIL NIL) (-923 2233131 2233671 2234226 "PDEPACK" 2235087 T PDEPACK (NIL) -7 NIL NIL NIL) (-922 2232019 2232233 2232484 "PDECOMP" 2232930 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-921 2229536 2230427 2230455 "PDECAT" 2231242 T PDECAT (NIL) -9 NIL 2231955 NIL) (-920 2229153 2229220 2229274 "PDDOM" 2229439 NIL PDDOM (NIL T T) -9 NIL 2229519 NIL) (-919 2228966 2229002 2229109 "PDDOM-" 2229114 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-918 2228711 2228750 2228840 "PCOMP" 2228927 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-917 2226751 2227512 2227809 "PBWLB" 2228440 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-916 2218930 2220824 2222162 "PATTERN" 2225434 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-915 2218556 2218619 2218728 "PATTERN2" 2218867 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-914 2216265 2216701 2217158 "PATTERN1" 2218145 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-913 2213531 2214214 2214695 "PATRES" 2215830 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2213089 2213162 2213294 "PATRES2" 2213458 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-911 2210942 2211377 2211784 "PATMATCH" 2212756 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-910 2210396 2210647 2210688 "PATMAB" 2210795 NIL PATMAB (NIL T) -9 NIL 2210878 NIL) (-909 2208842 2209250 2209508 "PATLRES" 2210201 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-908 2208380 2208511 2208552 "PATAB" 2208557 NIL PATAB (NIL T) -9 NIL 2208729 NIL) (-907 2206520 2206957 2207380 "PARTPERM" 2207977 T PARTPERM (NIL) -7 NIL NIL NIL) (-906 2206129 2206204 2206306 "PARSURF" 2206451 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-905 2205755 2205818 2205927 "PARSU2" 2206066 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-904 2205513 2205559 2205626 "PARSER" 2205708 T PARSER (NIL) -7 NIL NIL NIL) (-903 2205122 2205197 2205299 "PARSCURV" 2205444 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-902 2204748 2204811 2204920 "PARSC2" 2205059 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-901 2204375 2204445 2204542 "PARPCURV" 2204684 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-900 2204001 2204064 2204173 "PARPC2" 2204312 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-899 2202990 2203374 2203556 "PARAMAST" 2203839 T PARAMAST (NIL) -8 NIL NIL NIL) (-898 2202498 2202596 2202715 "PAN2EXPR" 2202891 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-897 2201191 2201619 2201847 "PALETTE" 2202290 T PALETTE (NIL) -8 NIL NIL NIL) (-896 2199536 2200196 2200556 "PAIR" 2200877 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-895 2192448 2198793 2198988 "PADICRC" 2199390 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-894 2184684 2191792 2191977 "PADICRAT" 2192295 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-893 2182693 2184621 2184666 "PADIC" 2184671 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2179483 2181353 2181393 "PADICCT" 2181974 NIL PADICCT (NIL NIL) -9 NIL 2182256 NIL) (-891 2178428 2178640 2178908 "PADEPAC" 2179270 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-890 2177628 2177773 2177979 "PADE" 2178290 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-889 2175861 2176836 2177116 "OWP" 2177432 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-888 2175306 2175567 2175664 "OVERSET" 2175784 T OVERSET (NIL) -8 NIL NIL NIL) (-887 2174226 2174911 2175083 "OVAR" 2175174 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-886 2173466 2173611 2173772 "OUT" 2174085 T OUT (NIL) -7 NIL NIL NIL) (-885 2161702 2164575 2166775 "OUTFORM" 2171286 T OUTFORM (NIL) -8 NIL NIL NIL) (-884 2160984 2161299 2161426 "OUTBFILE" 2161595 T OUTBFILE (NIL) -8 NIL NIL NIL) (-883 2160261 2160456 2160484 "OUTBCON" 2160802 T OUTBCON (NIL) -9 NIL 2160968 NIL) (-882 2159844 2159974 2160131 "OUTBCON-" 2160136 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-881 2159140 2159573 2159662 "OSI" 2159775 T OSI (NIL) -8 NIL NIL NIL) (-880 2158559 2158981 2159009 "OSGROUP" 2159014 T OSGROUP (NIL) -9 NIL 2159036 NIL) (-879 2157270 2157531 2157816 "ORTHPOL" 2158306 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-878 2154521 2157105 2157226 "OREUP" 2157231 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-877 2151624 2154212 2154339 "ORESUP" 2154463 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-876 2149124 2149652 2150213 "OREPCTO" 2151113 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-875 2142502 2144997 2145038 "OREPCAT" 2147386 NIL OREPCAT (NIL T) -9 NIL 2148490 NIL) (-874 2139475 2140431 2141489 "OREPCAT-" 2141494 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-873 2138668 2138945 2138973 "ORDTYPE" 2139282 T ORDTYPE (NIL) -9 NIL 2139445 NIL) (-872 2137969 2138185 2138440 "ORDTYPE-" 2138445 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-871 2137325 2137708 2137866 "ORDSTRCT" 2137871 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-870 2136823 2137193 2137221 "ORDSET" 2137226 T ORDSET (NIL) -9 NIL 2137248 NIL) (-869 2135181 2136152 2136180 "ORDRING" 2136382 T ORDRING (NIL) -9 NIL 2136507 NIL) (-868 2134802 2134920 2135064 "ORDRING-" 2135069 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-867 2134053 2134618 2134646 "ORDMON" 2134651 T ORDMON (NIL) -9 NIL 2134672 NIL) (-866 2133197 2133362 2133557 "ORDFUNS" 2133902 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-865 2132412 2132927 2132955 "ORDFIN" 2133020 T ORDFIN (NIL) -9 NIL 2133094 NIL) (-864 2128759 2130998 2131407 "ORDCOMP" 2132036 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2128013 2128152 2128338 "ORDCOMP2" 2128619 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-862 2124534 2125504 2126318 "OPTPROB" 2127219 T OPTPROB (NIL) -8 NIL NIL NIL) (-861 2121276 2121975 2122679 "OPTPACK" 2123850 T OPTPACK (NIL) -7 NIL NIL NIL) (-860 2118889 2119715 2119743 "OPTCAT" 2120562 T OPTCAT (NIL) -9 NIL 2121212 NIL) (-859 2118207 2118566 2118671 "OPSIG" 2118804 T OPSIG (NIL) -8 NIL NIL NIL) (-858 2117969 2118014 2118080 "OPQUERY" 2118161 T OPQUERY (NIL) -7 NIL NIL NIL) (-857 2114878 2116280 2116784 "OP" 2117498 NIL OP (NIL T) -8 NIL NIL NIL) (-856 2114184 2114464 2114505 "OPERCAT" 2114717 NIL OPERCAT (NIL T) -9 NIL 2114814 NIL) (-855 2113927 2113995 2114112 "OPERCAT-" 2114117 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-854 2110540 2112724 2113093 "ONECOMP" 2113591 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2109833 2109960 2110134 "ONECOMP2" 2110412 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-852 2109234 2109358 2109488 "OMSERVER" 2109723 T OMSERVER (NIL) -7 NIL NIL NIL) (-851 2105748 2108674 2108714 "OMSAGG" 2108775 NIL OMSAGG (NIL T) -9 NIL 2108839 NIL) (-850 2104323 2104634 2104916 "OMPKG" 2105486 T OMPKG (NIL) -7 NIL NIL NIL) (-849 2103729 2103856 2103884 "OM" 2104183 T OM (NIL) -9 NIL NIL NIL) (-848 2102076 2103278 2103447 "OMLO" 2103610 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-847 2101012 2101183 2101403 "OMEXPR" 2101902 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-846 2100249 2100558 2100694 "OMERR" 2100896 T OMERR (NIL) -8 NIL NIL NIL) (-845 2099334 2099670 2099830 "OMERRK" 2100109 T OMERRK (NIL) -8 NIL NIL NIL) (-844 2098725 2099011 2099119 "OMENC" 2099246 T OMENC (NIL) -8 NIL NIL NIL) (-843 2092362 2093805 2094976 "OMDEV" 2097574 T OMDEV (NIL) -8 NIL NIL NIL) (-842 2091395 2091602 2091796 "OMCONN" 2092188 T OMCONN (NIL) -8 NIL NIL NIL) (-841 2089673 2090865 2090893 "OINTDOM" 2090898 T OINTDOM (NIL) -9 NIL 2090919 NIL) (-840 2086747 2088361 2088698 "OFMONOID" 2089368 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-839 2085981 2086684 2086729 "ODVAR" 2086734 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-838 2083118 2085726 2085881 "ODR" 2085886 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-837 2074523 2082894 2083020 "ODPOL" 2083025 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-836 2067866 2074395 2074500 "ODP" 2074505 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-835 2066608 2066847 2067122 "ODETOOLS" 2067640 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-834 2063551 2064233 2064949 "ODESYS" 2065941 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-833 2058381 2059341 2060366 "ODERTRIC" 2062626 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-832 2057801 2057889 2058083 "ODERED" 2058293 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-831 2054653 2055237 2055914 "ODERAT" 2057224 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-830 2051570 2052077 2052674 "ODEPRRIC" 2054182 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-829 2049465 2050109 2050595 "ODEPROB" 2051104 T ODEPROB (NIL) -8 NIL NIL NIL) (-828 2045931 2046470 2047117 "ODEPRIM" 2048944 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-827 2045174 2045282 2045542 "ODEPAL" 2045823 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-826 2041276 2042127 2042991 "ODEPACK" 2044330 T ODEPACK (NIL) -7 NIL NIL NIL) (-825 2040319 2040444 2040666 "ODEINT" 2041165 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-824 2034384 2035845 2037292 "ODEIFTBL" 2038892 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-823 2029734 2030568 2031520 "ODEEF" 2033543 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-822 2029077 2029172 2029395 "ODECONST" 2029639 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-821 2027140 2027849 2027877 "ODECAT" 2028482 T ODECAT (NIL) -9 NIL 2029013 NIL) (-820 2023633 2026845 2026967 "OCT" 2027050 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023265 2023314 2023441 "OCTCT2" 2023584 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-818 2017534 2020308 2020348 "OC" 2021445 NIL OC (NIL T) -9 NIL 2022303 NIL) (-817 2014569 2015509 2016499 "OC-" 2016593 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2013792 2014362 2014390 "OCAMON" 2014395 T OCAMON (NIL) -9 NIL 2014416 NIL) (-815 2013212 2013637 2013665 "OASGP" 2013670 T OASGP (NIL) -9 NIL 2013690 NIL) (-814 2012338 2012935 2012963 "OAMONS" 2013003 T OAMONS (NIL) -9 NIL 2013046 NIL) (-813 2011629 2012158 2012186 "OAMON" 2012191 T OAMON (NIL) -9 NIL 2012211 NIL) (-812 2010740 2011378 2011406 "OAGROUP" 2011411 T OAGROUP (NIL) -9 NIL 2011431 NIL) (-811 2010422 2010478 2010567 "NUMTUBE" 2010684 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-810 2003941 2005513 2007049 "NUMQUAD" 2008906 T NUMQUAD (NIL) -7 NIL NIL NIL) (-809 1999661 2000685 2001710 "NUMODE" 2002936 T NUMODE (NIL) -7 NIL NIL NIL) (-808 1996942 1997882 1997910 "NUMINT" 1998833 T NUMINT (NIL) -9 NIL 1999597 NIL) (-807 1995854 1996087 1996305 "NUMFMT" 1996744 T NUMFMT (NIL) -7 NIL NIL NIL) (-806 1982037 1985158 1987690 "NUMERIC" 1993361 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-805 1975748 1981485 1981580 "NTSCAT" 1981585 NIL NTSCAT (NIL T T T T) -9 NIL 1981624 NIL) (-804 1974928 1975107 1975300 "NTPOLFN" 1975587 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-803 1961689 1971753 1972565 "NSUP" 1974149 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1961315 1961378 1961487 "NSUP2" 1961626 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-801 1950151 1961089 1961222 "NSMP" 1961227 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-800 1948559 1948884 1949241 "NREP" 1949839 NIL NREP (NIL T) -7 NIL NIL NIL) (-799 1947138 1947402 1947760 "NPCOEF" 1948302 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-798 1946186 1946319 1946535 "NORMRETR" 1947019 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-797 1944197 1944517 1944926 "NORMPK" 1945894 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-796 1943876 1943910 1944034 "NORMMA" 1944163 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-795 1943640 1943833 1943862 "NONE" 1943867 T NONE (NIL) -8 NIL NIL NIL) (-794 1943423 1943458 1943527 "NONE1" 1943604 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-793 1942914 1942982 1943161 "NODE1" 1943355 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-792 1941015 1942046 1942301 "NNI" 1942648 T NNI (NIL) -8 NIL NIL 1942883) (-791 1939411 1939748 1940112 "NLINSOL" 1940683 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-790 1935592 1936647 1937546 "NIPROB" 1938532 T NIPROB (NIL) -8 NIL NIL NIL) (-789 1934331 1934583 1934885 "NFINTBAS" 1935354 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-788 1933415 1933981 1934022 "NETCLT" 1934194 NIL NETCLT (NIL T) -9 NIL 1934276 NIL) (-787 1932087 1932354 1932635 "NCODIV" 1933183 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-786 1931843 1931886 1931961 "NCNTFRAC" 1932044 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-785 1929999 1930387 1930807 "NCEP" 1931468 NIL NCEP (NIL T) -7 NIL NIL NIL) (-784 1928662 1929609 1929637 "NASRING" 1929747 T NASRING (NIL) -9 NIL 1929827 NIL) (-783 1928445 1928501 1928595 "NASRING-" 1928600 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-782 1927412 1928063 1928091 "NARNG" 1928208 T NARNG (NIL) -9 NIL 1928299 NIL) (-781 1927086 1927171 1927305 "NARNG-" 1927310 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-780 1925923 1926172 1926407 "NAGSP" 1926871 T NAGSP (NIL) -7 NIL NIL NIL) (-779 1916967 1918879 1920552 "NAGS" 1924270 T NAGS (NIL) -7 NIL NIL NIL) (-778 1915491 1915823 1916154 "NAGF07" 1916656 T NAGF07 (NIL) -7 NIL NIL NIL) (-777 1909963 1911320 1912627 "NAGF04" 1914204 T NAGF04 (NIL) -7 NIL NIL NIL) (-776 1902835 1904545 1906178 "NAGF02" 1908350 T NAGF02 (NIL) -7 NIL NIL NIL) (-775 1897999 1899159 1900276 "NAGF01" 1901738 T NAGF01 (NIL) -7 NIL NIL NIL) (-774 1891579 1893193 1894778 "NAGE04" 1896434 T NAGE04 (NIL) -7 NIL NIL NIL) (-773 1882640 1884869 1886999 "NAGE02" 1889469 T NAGE02 (NIL) -7 NIL NIL NIL) (-772 1878533 1879540 1880504 "NAGE01" 1881696 T NAGE01 (NIL) -7 NIL NIL NIL) (-771 1876310 1876862 1877420 "NAGD03" 1877995 T NAGD03 (NIL) -7 NIL NIL NIL) (-770 1868006 1869988 1871942 "NAGD02" 1874376 T NAGD02 (NIL) -7 NIL NIL NIL) (-769 1861745 1863242 1864682 "NAGD01" 1866586 T NAGD01 (NIL) -7 NIL NIL NIL) (-768 1857882 1858776 1859613 "NAGC06" 1860928 T NAGC06 (NIL) -7 NIL NIL NIL) (-767 1856329 1856679 1857035 "NAGC05" 1857546 T NAGC05 (NIL) -7 NIL NIL NIL) (-766 1855693 1855824 1855968 "NAGC02" 1856205 T NAGC02 (NIL) -7 NIL NIL NIL) (-765 1854494 1855221 1855261 "NAALG" 1855340 NIL NAALG (NIL T) -9 NIL 1855401 NIL) (-764 1854323 1854358 1854448 "NAALG-" 1854453 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-763 1848195 1849381 1850568 "MULTSQFR" 1853219 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-762 1847502 1847589 1847773 "MULTFACT" 1848107 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-761 1839647 1844085 1844138 "MTSCAT" 1845208 NIL MTSCAT (NIL T T) -9 NIL 1845724 NIL) (-760 1839353 1839413 1839505 "MTHING" 1839587 NIL MTHING (NIL T) -7 NIL NIL NIL) (-759 1839139 1839178 1839238 "MSYSCMD" 1839313 T MSYSCMD (NIL) -7 NIL NIL NIL) (-758 1834853 1837894 1838214 "MSET" 1838852 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1831598 1834414 1834455 "MSETAGG" 1834460 NIL MSETAGG (NIL T) -9 NIL 1834494 NIL) (-756 1827190 1828977 1829722 "MRING" 1830898 NIL MRING (NIL T T) -8 NIL NIL NIL) (-755 1826750 1826823 1826954 "MRF2" 1827117 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-754 1826362 1826403 1826547 "MRATFAC" 1826709 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-753 1823932 1824269 1824700 "MPRFF" 1826067 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-752 1817259 1823786 1823883 "MPOLY" 1823888 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-751 1816743 1816784 1816992 "MPCPF" 1817218 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-750 1816251 1816300 1816484 "MPC3" 1816694 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1815434 1815527 1815748 "MPC2" 1816166 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-748 1813711 1814072 1814462 "MONOTOOL" 1815094 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-747 1812856 1813239 1813267 "MONOID" 1813486 T MONOID (NIL) -9 NIL 1813633 NIL) (-746 1812372 1812521 1812702 "MONOID-" 1812707 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-745 1801326 1808192 1808251 "MONOGEN" 1808925 NIL MONOGEN (NIL T T) -9 NIL 1809381 NIL) (-744 1798376 1799279 1800279 "MONOGEN-" 1800398 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-743 1797093 1797641 1797669 "MONADWU" 1798061 T MONADWU (NIL) -9 NIL 1798299 NIL) (-742 1796423 1796624 1796872 "MONADWU-" 1796877 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-741 1795708 1796012 1796040 "MONAD" 1796247 T MONAD (NIL) -9 NIL 1796359 NIL) (-740 1795375 1795471 1795603 "MONAD-" 1795608 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-739 1793514 1794288 1794567 "MOEBIUS" 1795128 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-738 1792682 1793182 1793222 "MODULE" 1793227 NIL MODULE (NIL T) -9 NIL 1793266 NIL) (-737 1792220 1792346 1792536 "MODULE-" 1792541 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-736 1789750 1790584 1790911 "MODRING" 1792044 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-735 1786472 1787855 1788376 "MODOP" 1789279 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-734 1784958 1785539 1785816 "MODMONOM" 1786335 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-733 1773698 1783249 1783663 "MODMON" 1784595 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-732 1770524 1772542 1772818 "MODFIELD" 1773573 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-731 1769435 1769805 1769995 "MMLFORM" 1770354 T MMLFORM (NIL) -8 NIL NIL NIL) (-730 1768955 1769004 1769183 "MMAP" 1769386 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-729 1766848 1767787 1767828 "MLO" 1768251 NIL MLO (NIL T) -9 NIL 1768493 NIL) (-728 1764196 1764730 1765332 "MLIFT" 1766329 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-727 1763575 1763671 1763825 "MKUCFUNC" 1764107 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-726 1763168 1763244 1763367 "MKRECORD" 1763498 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-725 1762191 1762377 1762605 "MKFUNC" 1762979 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-724 1761567 1761683 1761839 "MKFLCFN" 1762074 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-723 1760832 1760946 1761131 "MKBCFUNC" 1761460 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-722 1756815 1760386 1760522 "MINT" 1760716 T MINT (NIL) -8 NIL NIL NIL) (-721 1755597 1755870 1756147 "MHROWRED" 1756570 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-720 1750341 1754132 1754537 "MFLOAT" 1755212 T MFLOAT (NIL) -8 NIL NIL NIL) (-719 1749686 1749774 1749945 "MFINFACT" 1750253 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-718 1745965 1746849 1747733 "MESH" 1748822 T MESH (NIL) -7 NIL NIL NIL) (-717 1744319 1744667 1745020 "MDDFACT" 1745652 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-716 1740855 1743450 1743491 "MDAGG" 1743746 NIL MDAGG (NIL T) -9 NIL 1743889 NIL) (-715 1728557 1740148 1740355 "MCMPLX" 1740668 T MCMPLX (NIL) -8 NIL NIL NIL) (-714 1727676 1727840 1728041 "MCDEN" 1728406 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-713 1725524 1725836 1726216 "MCALCFN" 1727406 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-712 1724401 1724689 1724922 "MAYBE" 1725330 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-711 1721959 1722536 1723098 "MATSTOR" 1723872 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-710 1717381 1721331 1721579 "MATRIX" 1721744 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-709 1713081 1713854 1714590 "MATLIN" 1716738 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-708 1702427 1706138 1706215 "MATCAT" 1711247 NIL MATCAT (NIL T T T) -9 NIL 1712719 NIL) (-707 1698380 1699690 1701103 "MATCAT-" 1701108 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1696956 1697127 1697460 "MATCAT2" 1698215 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-705 1695032 1695392 1695776 "MAPPKG3" 1696631 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-704 1693989 1694186 1694408 "MAPPKG2" 1694856 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-703 1692446 1692772 1693099 "MAPPKG1" 1693695 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-702 1691447 1691852 1692029 "MAPPAST" 1692289 T MAPPAST (NIL) -8 NIL NIL NIL) (-701 1691052 1691116 1691239 "MAPHACK3" 1691383 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-700 1690632 1690705 1690819 "MAPHACK2" 1690984 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-699 1690058 1690173 1690315 "MAPHACK1" 1690523 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-698 1687981 1688758 1689062 "MAGMA" 1689786 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-697 1687400 1687705 1687796 "MACROAST" 1687910 T MACROAST (NIL) -8 NIL NIL NIL) (-696 1683643 1685639 1686100 "M3D" 1686972 NIL M3D (NIL T) -8 NIL NIL NIL) (-695 1677123 1681954 1681995 "LZSTAGG" 1682777 NIL LZSTAGG (NIL T) -9 NIL 1683072 NIL) (-694 1672805 1674254 1675711 "LZSTAGG-" 1675716 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-693 1669718 1670696 1671183 "LWORD" 1672350 NIL LWORD (NIL T) -8 NIL NIL NIL) (-692 1669240 1669522 1669597 "LSTAST" 1669663 T LSTAST (NIL) -8 NIL NIL NIL) (-691 1661168 1669011 1669145 "LSQM" 1669150 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-690 1660386 1660531 1660759 "LSPP" 1661023 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-689 1658168 1658499 1658955 "LSMP" 1660075 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1654905 1655621 1656351 "LSMP1" 1657470 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-687 1648041 1653995 1654036 "LSAGG" 1654098 NIL LSAGG (NIL T) -9 NIL 1654176 NIL) (-686 1644550 1645660 1646873 "LSAGG-" 1646878 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-685 1641845 1643694 1643943 "LPOLY" 1644345 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-684 1641421 1641512 1641635 "LPEFRAC" 1641754 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-683 1639598 1640515 1640768 "LO" 1641253 NIL LO (NIL T T T) -8 NIL NIL NIL) (-682 1639174 1639348 1639376 "LOGIC" 1639487 T LOGIC (NIL) -9 NIL 1639568 NIL) (-681 1639030 1639059 1639130 "LOGIC-" 1639135 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-680 1638205 1638363 1638556 "LODOOPS" 1638886 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-679 1635300 1638121 1638187 "LODO" 1638192 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-678 1633824 1634073 1634426 "LODOF" 1635047 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-677 1629700 1632459 1632500 "LODOCAT" 1632938 NIL LODOCAT (NIL T) -9 NIL 1633149 NIL) (-676 1629415 1629491 1629618 "LODOCAT-" 1629623 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-675 1626401 1629256 1629374 "LODO2" 1629379 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-674 1623508 1626338 1626383 "LODO1" 1626388 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-673 1622377 1622554 1622859 "LODEEF" 1623331 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-672 1617349 1620543 1620584 "LNAGG" 1621446 NIL LNAGG (NIL T) -9 NIL 1621881 NIL) (-671 1616442 1616710 1617052 "LNAGG-" 1617057 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-670 1612422 1613367 1614006 "LMOPS" 1615857 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-669 1611721 1612199 1612240 "LMODULE" 1612245 NIL LMODULE (NIL T) -9 NIL 1612271 NIL) (-668 1608676 1611366 1611489 "LMDICT" 1611631 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-667 1608252 1608466 1608507 "LLINSET" 1608568 NIL LLINSET (NIL T) -9 NIL 1608612 NIL) (-666 1607897 1608160 1608220 "LITERAL" 1608225 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-665 1600351 1606831 1607135 "LIST" 1607626 NIL LIST (NIL T) -8 NIL NIL NIL) (-664 1599870 1599950 1600089 "LIST3" 1600271 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-663 1598859 1599055 1599283 "LIST2" 1599688 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-662 1596957 1597305 1597704 "LIST2MAP" 1598506 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-661 1596540 1596776 1596817 "LINSET" 1596822 NIL LINSET (NIL T) -9 NIL 1596856 NIL) (-660 1595354 1596048 1596215 "LINFORM" 1596425 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-659 1593653 1594381 1594422 "LINEXP" 1594912 NIL LINEXP (NIL T) -9 NIL 1595185 NIL) (-658 1592229 1593133 1593314 "LINELT" 1593524 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-657 1590786 1591066 1591377 "LINDEP" 1591981 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-656 1589922 1590518 1590628 "LINBASIS" 1590716 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-655 1586659 1587408 1588185 "LIMITRF" 1589177 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-654 1584944 1585258 1585667 "LIMITPS" 1586354 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-653 1578964 1584455 1584683 "LIE" 1584765 NIL LIE (NIL T T) -8 NIL NIL NIL) (-652 1577792 1578367 1578407 "LIECAT" 1578547 NIL LIECAT (NIL T) -9 NIL 1578698 NIL) (-651 1577627 1577660 1577748 "LIECAT-" 1577753 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-650 1569814 1577167 1577323 "LIB" 1577491 T LIB (NIL) -8 NIL NIL NIL) (-649 1565383 1566332 1567267 "LGROBP" 1568931 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-648 1563321 1563655 1564005 "LF" 1565104 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1561945 1562853 1562881 "LFCAT" 1563088 T LFCAT (NIL) -9 NIL 1563227 NIL) (-646 1558805 1559477 1560165 "LEXTRIPK" 1561309 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-645 1555393 1556375 1556878 "LEXP" 1558385 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-644 1554809 1555114 1555206 "LETAST" 1555321 T LETAST (NIL) -8 NIL NIL NIL) (-643 1553195 1553520 1553921 "LEADCDET" 1554491 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-642 1552373 1552459 1552688 "LAZM3PK" 1553116 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-641 1546884 1550450 1550988 "LAUPOL" 1551885 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-640 1546457 1546507 1546668 "LAPLACE" 1546834 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-639 1544194 1545558 1545809 "LA" 1546290 NIL LA (NIL T T T) -8 NIL NIL NIL) (-638 1543042 1543758 1543799 "LALG" 1543861 NIL LALG (NIL T) -9 NIL 1543920 NIL) (-637 1542738 1542815 1542951 "LALG-" 1542956 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-636 1542567 1542597 1542638 "KVTFROM" 1542700 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-635 1541406 1541934 1542119 "KTVLOGIC" 1542402 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-634 1541235 1541265 1541306 "KRCFROM" 1541368 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-633 1540127 1540326 1540625 "KOVACIC" 1541035 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-632 1539956 1539986 1540027 "KONVERT" 1540089 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-631 1539785 1539815 1539856 "KOERCE" 1539918 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-630 1537472 1538378 1538755 "KERNEL" 1539441 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1536956 1537049 1537181 "KERNEL2" 1537386 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-628 1530427 1535433 1535487 "KDAGG" 1535864 NIL KDAGG (NIL T T) -9 NIL 1536070 NIL) (-627 1529938 1530080 1530285 "KDAGG-" 1530290 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-626 1522638 1529599 1529754 "KAFILE" 1529816 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-625 1522242 1522527 1522590 "JVMOP" 1522595 T JVMOP (NIL) -8 NIL NIL NIL) (-624 1520978 1521482 1521731 "JVMMDACC" 1522013 T JVMMDACC (NIL) -8 NIL NIL NIL) (-623 1519914 1520368 1520573 "JVMFDACC" 1520793 T JVMFDACC (NIL) -8 NIL NIL NIL) (-622 1518495 1518990 1519290 "JVMCSTTG" 1519634 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-621 1517631 1518035 1518196 "JVMCFACC" 1518354 T JVMCFACC (NIL) -8 NIL NIL NIL) (-620 1517309 1517548 1517597 "JVMBCODE" 1517602 T JVMBCODE (NIL) -8 NIL NIL NIL) (-619 1511329 1516820 1517048 "JORDAN" 1517130 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-618 1510642 1510978 1511099 "JOINAST" 1511228 T JOINAST (NIL) -8 NIL NIL NIL) (-617 1506677 1508819 1508873 "IXAGG" 1509802 NIL IXAGG (NIL T T) -9 NIL 1510261 NIL) (-616 1505530 1505902 1506321 "IXAGG-" 1506326 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-615 1500619 1505452 1505511 "IVECTOR" 1505516 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-614 1499343 1499622 1499888 "ITUPLE" 1500386 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-613 1497815 1498022 1498317 "ITRIGMNP" 1499165 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-612 1496542 1496764 1497047 "ITFUN3" 1497591 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-611 1496168 1496231 1496340 "ITFUN2" 1496479 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-610 1495273 1495648 1495822 "ITFORM" 1496014 T ITFORM (NIL) -8 NIL NIL NIL) (-609 1493042 1494293 1494571 "ITAYLOR" 1495028 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-608 1481439 1487179 1488342 "ISUPS" 1491912 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-607 1480531 1480683 1480919 "ISUMP" 1481286 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-606 1475381 1480476 1480517 "ISTRING" 1480522 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-605 1474797 1475102 1475194 "ISAST" 1475309 T ISAST (NIL) -8 NIL NIL NIL) (-604 1473994 1474088 1474304 "IRURPK" 1474711 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-603 1472906 1473131 1473371 "IRSN" 1473774 T IRSN (NIL) -7 NIL NIL NIL) (-602 1470951 1471332 1471761 "IRRF2F" 1472544 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-601 1470692 1470736 1470812 "IRREDFFX" 1470907 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-600 1469265 1469566 1469865 "IROOT" 1470425 NIL IROOT (NIL T) -7 NIL NIL NIL) (-599 1465705 1466949 1467641 "IR" 1468605 NIL IR (NIL T) -8 NIL NIL NIL) (-598 1464844 1465198 1465349 "IRFORM" 1465574 T IRFORM (NIL) -8 NIL NIL NIL) (-597 1462433 1462952 1463518 "IR2" 1464322 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-596 1461515 1461646 1461860 "IR2F" 1462316 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-595 1461300 1461340 1461400 "IPRNTPK" 1461475 T IPRNTPK (NIL) -7 NIL NIL NIL) (-594 1457253 1461189 1461258 "IPF" 1461263 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-593 1455274 1457178 1457235 "IPADIC" 1457240 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-592 1454532 1454834 1454964 "IP4ADDR" 1455164 T IP4ADDR (NIL) -8 NIL NIL NIL) (-591 1453870 1454161 1454293 "IOMODE" 1454420 T IOMODE (NIL) -8 NIL NIL NIL) (-590 1452841 1453467 1453594 "IOBFILE" 1453763 T IOBFILE (NIL) -8 NIL NIL NIL) (-589 1452251 1452745 1452773 "IOBCON" 1452778 T IOBCON (NIL) -9 NIL 1452799 NIL) (-588 1451756 1451820 1452003 "INVLAPLA" 1452187 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-587 1441326 1443758 1446144 "INTTR" 1449420 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-586 1437619 1438403 1439268 "INTTOOLS" 1440511 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-585 1437199 1437296 1437413 "INTSLPE" 1437522 T INTSLPE (NIL) -7 NIL NIL NIL) (-584 1434666 1437122 1437181 "INTRVL" 1437186 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-583 1432244 1432780 1433355 "INTRF" 1434151 NIL INTRF (NIL T) -7 NIL NIL NIL) (-582 1431637 1431752 1431894 "INTRET" 1432142 NIL INTRET (NIL T) -7 NIL NIL NIL) (-581 1429610 1430023 1430493 "INTRAT" 1431245 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-580 1426855 1427456 1428075 "INTPM" 1429095 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-579 1423572 1424199 1424937 "INTPAF" 1426241 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-578 1418673 1419713 1420764 "INTPACK" 1422541 T INTPACK (NIL) -7 NIL NIL NIL) (-577 1414861 1418470 1418579 "INT" 1418584 T INT (NIL) -8 NIL NIL NIL) (-576 1414107 1414265 1414473 "INTHERTR" 1414703 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-575 1413540 1413626 1413814 "INTHERAL" 1414021 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-574 1411308 1411829 1412286 "INTHEORY" 1413103 T INTHEORY (NIL) -7 NIL NIL NIL) (-573 1402640 1404335 1406107 "INTG0" 1409660 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-572 1383165 1388003 1392813 "INTFTBL" 1397850 T INTFTBL (NIL) -8 NIL NIL NIL) (-571 1382390 1382552 1382725 "INTFACT" 1383024 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-570 1379787 1380263 1380820 "INTEF" 1381944 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-569 1377984 1378879 1378907 "INTDOM" 1379208 T INTDOM (NIL) -9 NIL 1379415 NIL) (-568 1377323 1377527 1377769 "INTDOM-" 1377774 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-567 1373197 1375612 1375666 "INTCAT" 1376465 NIL INTCAT (NIL T) -9 NIL 1376786 NIL) (-566 1372651 1372772 1372900 "INTBIT" 1373089 T INTBIT (NIL) -7 NIL NIL NIL) (-565 1371332 1371504 1371811 "INTALG" 1372496 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-564 1370809 1370905 1371062 "INTAF" 1371236 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-563 1363776 1370619 1370759 "INTABL" 1370764 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-562 1363013 1363575 1363640 "INT8" 1363674 T INT8 (NIL) -8 NIL NIL 1363719) (-561 1362249 1362811 1362876 "INT64" 1362910 T INT64 (NIL) -8 NIL NIL 1362955) (-560 1361485 1362047 1362112 "INT32" 1362146 T INT32 (NIL) -8 NIL NIL 1362191) (-559 1360721 1361283 1361348 "INT16" 1361382 T INT16 (NIL) -8 NIL NIL 1361427) (-558 1354822 1358269 1358297 "INS" 1359231 T INS (NIL) -9 NIL 1359896 NIL) (-557 1351876 1352833 1353807 "INS-" 1353880 NIL INS- (NIL T) -8 NIL NIL NIL) (-556 1350633 1350878 1351176 "INPSIGN" 1351629 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-555 1349727 1349868 1350065 "INPRODPF" 1350513 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-554 1348597 1348738 1348975 "INPRODFF" 1349607 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-553 1347585 1347749 1348009 "INNMFACT" 1348433 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-552 1346764 1346879 1347067 "INMODGCD" 1347484 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-551 1345248 1345517 1345841 "INFSP" 1346509 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-550 1344408 1344549 1344732 "INFPROD0" 1345128 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-549 1340975 1342473 1342988 "INFORM" 1343901 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340573 1340645 1340743 "INFORM1" 1340910 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-547 1340078 1340185 1340299 "INFINITY" 1340479 T INFINITY (NIL) -7 NIL NIL NIL) (-546 1339152 1339798 1339899 "INETCLTS" 1339997 T INETCLTS (NIL) -8 NIL NIL NIL) (-545 1337750 1338018 1338339 "INEP" 1338900 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-544 1336811 1337647 1337712 "INDE" 1337717 NIL INDE (NIL T) -8 NIL NIL NIL) (-543 1336363 1336443 1336560 "INCRMAPS" 1336738 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-542 1335085 1335632 1335838 "INBFILE" 1336177 T INBFILE (NIL) -8 NIL NIL NIL) (-541 1330264 1331321 1332265 "INBFF" 1334173 NIL INBFF (NIL T) -7 NIL NIL NIL) (-540 1329118 1329441 1329469 "INBCON" 1329982 T INBCON (NIL) -9 NIL 1330248 NIL) (-539 1328328 1328593 1328869 "INBCON-" 1328874 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-538 1327747 1328052 1328143 "INAST" 1328257 T INAST (NIL) -8 NIL NIL NIL) (-537 1327114 1327426 1327532 "IMPTAST" 1327661 T IMPTAST (NIL) -8 NIL NIL NIL) (-536 1323035 1326958 1327062 "IMATRIX" 1327067 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-535 1321727 1321866 1322182 "IMATQF" 1322891 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-534 1319907 1320174 1320511 "IMATLIN" 1321483 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-533 1313822 1319831 1319889 "ILIST" 1319894 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-532 1311488 1313682 1313795 "IIARRAY2" 1313800 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-531 1306288 1311399 1311463 "IFF" 1311468 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-530 1305569 1305905 1306021 "IFAST" 1306192 T IFAST (NIL) -8 NIL NIL NIL) (-529 1300081 1304861 1305049 "IFARRAY" 1305426 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-528 1299119 1299985 1300058 "IFAMON" 1300063 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-527 1298691 1298768 1298822 "IEVALAB" 1299029 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-526 1298354 1298434 1298594 "IEVALAB-" 1298599 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-525 1297735 1298269 1298331 "IDPO" 1298336 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-524 1296799 1297624 1297699 "IDPOAMS" 1297704 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-523 1295932 1296688 1296763 "IDPOAM" 1296768 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-522 1294412 1294939 1294991 "IDPC" 1295503 NIL IDPC (NIL T T) -9 NIL 1295784 NIL) (-521 1293744 1294304 1294377 "IDPAM" 1294382 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-520 1292959 1293636 1293709 "IDPAG" 1293714 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-519 1292503 1292765 1292855 "IDENT" 1292889 T IDENT (NIL) -8 NIL NIL NIL) (-518 1288722 1289606 1290501 "IDECOMP" 1291660 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-517 1281357 1282645 1283692 "IDEAL" 1287758 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-516 1280499 1280629 1280829 "ICDEN" 1281241 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-515 1279474 1279979 1280126 "ICARD" 1280372 T ICARD (NIL) -8 NIL NIL NIL) (-514 1277504 1277847 1278252 "IBPTOOLS" 1279151 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-513 1272619 1277124 1277237 "IBITS" 1277423 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-512 1269294 1269918 1270613 "IBATOOL" 1272036 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-511 1267055 1267535 1268068 "IBACHIN" 1268829 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-510 1264645 1266901 1267004 "IARRAY2" 1267009 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-509 1260358 1264571 1264628 "IARRAY1" 1264633 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-508 1253368 1258770 1259251 "IAN" 1259897 T IAN (NIL) -8 NIL NIL NIL) (-507 1252873 1252936 1253109 "IALGFACT" 1253305 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-506 1252365 1252514 1252542 "HYPCAT" 1252749 T HYPCAT (NIL) -9 NIL NIL NIL) (-505 1251867 1252020 1252206 "HYPCAT-" 1252211 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-504 1251414 1251662 1251745 "HOSTNAME" 1251804 T HOSTNAME (NIL) -8 NIL NIL NIL) (-503 1251247 1251296 1251337 "HOMOTOP" 1251342 NIL HOMOTOP (NIL T) -9 NIL 1251375 NIL) (-502 1247680 1249179 1249220 "HOAGG" 1250201 NIL HOAGG (NIL T) -9 NIL 1250930 NIL) (-501 1246196 1246673 1247199 "HOAGG-" 1247204 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-500 1239232 1245789 1245939 "HEXADEC" 1246066 T HEXADEC (NIL) -8 NIL NIL NIL) (-499 1237944 1238202 1238465 "HEUGCD" 1239009 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-498 1236876 1237781 1237911 "HELLFDIV" 1237916 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-497 1234886 1236653 1236741 "HEAP" 1236820 NIL HEAP (NIL T) -8 NIL NIL NIL) (-496 1234083 1234438 1234572 "HEADAST" 1234772 T HEADAST (NIL) -8 NIL NIL NIL) (-495 1227470 1233998 1234060 "HDP" 1234065 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-494 1220482 1227105 1227257 "HDMP" 1227371 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-493 1219788 1219946 1220110 "HB" 1220338 T HB (NIL) -7 NIL NIL NIL) (-492 1212798 1219634 1219738 "HASHTBL" 1219743 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-491 1212214 1212519 1212611 "HASAST" 1212726 T HASAST (NIL) -8 NIL NIL NIL) (-490 1209620 1211836 1212018 "HACKPI" 1212052 T HACKPI (NIL) -8 NIL NIL NIL) (-489 1204792 1209473 1209586 "GTSET" 1209591 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-488 1197831 1204670 1204768 "GSTBL" 1204773 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-487 1189580 1196996 1197252 "GSERIES" 1197631 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-486 1188611 1189124 1189152 "GROUP" 1189355 T GROUP (NIL) -9 NIL 1189489 NIL) (-485 1187935 1188136 1188387 "GROUP-" 1188392 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-484 1186284 1186623 1187010 "GROEBSOL" 1187612 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-483 1185112 1185472 1185523 "GRMOD" 1186052 NIL GRMOD (NIL T T) -9 NIL 1186220 NIL) (-482 1184868 1184916 1185044 "GRMOD-" 1185049 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-481 1180008 1181222 1182222 "GRIMAGE" 1183888 T GRIMAGE (NIL) -8 NIL NIL NIL) (-480 1178402 1178735 1179059 "GRDEF" 1179704 T GRDEF (NIL) -7 NIL NIL NIL) (-479 1177834 1177962 1178103 "GRAY" 1178281 T GRAY (NIL) -7 NIL NIL NIL) (-478 1176911 1177413 1177464 "GRALG" 1177617 NIL GRALG (NIL T T) -9 NIL 1177710 NIL) (-477 1176548 1176645 1176808 "GRALG-" 1176813 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-476 1173029 1176131 1176310 "GPOLSET" 1176454 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-475 1172377 1172440 1172698 "GOSPER" 1172966 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-474 1167947 1168815 1169341 "GMODPOL" 1172076 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-473 1166934 1167136 1167374 "GHENSEL" 1167759 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-472 1161006 1161933 1162953 "GENUPS" 1166018 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-471 1160697 1160754 1160843 "GENUFACT" 1160949 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-470 1160097 1160186 1160351 "GENPGCD" 1160615 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-469 1159565 1159606 1159819 "GENMFACT" 1160056 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-468 1158101 1158388 1158695 "GENEEZ" 1159308 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-467 1151273 1157712 1157874 "GDMP" 1158024 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-466 1140012 1145044 1146150 "GCNAALG" 1150256 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-465 1138139 1139187 1139215 "GCDDOM" 1139470 T GCDDOM (NIL) -9 NIL 1139627 NIL) (-464 1137579 1137736 1137951 "GCDDOM-" 1137956 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-463 1136229 1136436 1136740 "GB" 1137358 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-462 1124701 1127175 1129567 "GBINTERN" 1133920 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-461 1122502 1122830 1123251 "GBF" 1124376 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-460 1121259 1121448 1121715 "GBEUCLID" 1122318 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-459 1120590 1120733 1120882 "GAUSSFAC" 1121130 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-458 1118911 1119259 1119573 "GALUTIL" 1120309 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-457 1117171 1117493 1117817 "GALPOLYU" 1118638 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-456 1114470 1114826 1115233 "GALFACTU" 1116868 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-455 1106084 1107775 1109383 "GALFACT" 1112902 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-454 1103370 1104130 1104158 "FVFUN" 1105314 T FVFUN (NIL) -9 NIL 1106034 NIL) (-453 1102600 1102818 1102846 "FVC" 1103137 T FVC (NIL) -9 NIL 1103320 NIL) (-452 1102201 1102425 1102493 "FUNDESC" 1102552 T FUNDESC (NIL) -8 NIL NIL NIL) (-451 1101774 1101998 1102079 "FUNCTION" 1102153 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-450 1099404 1100096 1100562 "FT" 1101328 T FT (NIL) -8 NIL NIL NIL) (-449 1098081 1098705 1098908 "FTEM" 1099221 T FTEM (NIL) -8 NIL NIL NIL) (-448 1096350 1096661 1097058 "FSUPFACT" 1097772 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-447 1094669 1095036 1095368 "FST" 1096038 T FST (NIL) -8 NIL NIL NIL) (-446 1093850 1093974 1094162 "FSRED" 1094551 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-445 1092539 1092805 1093152 "FSPRMELT" 1093565 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-444 1089749 1090283 1090769 "FSPECF" 1092102 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-443 1069976 1079523 1079564 "FS" 1083448 NIL FS (NIL T) -9 NIL 1085737 NIL) (-442 1058037 1061612 1065669 "FS-" 1065969 NIL FS- (NIL T T) -8 NIL NIL NIL) (-441 1057559 1057619 1057789 "FSINT" 1057978 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-440 1055695 1056552 1056855 "FSERIES" 1057338 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-439 1054719 1054853 1055077 "FSCINT" 1055575 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-438 1050583 1053663 1053704 "FSAGG" 1054074 NIL FSAGG (NIL T) -9 NIL 1054333 NIL) (-437 1048183 1048946 1049742 "FSAGG-" 1049837 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-436 1047207 1047368 1047595 "FSAGG2" 1048036 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-435 1044867 1045165 1045713 "FS2UPS" 1046925 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-434 1044495 1044544 1044673 "FS2" 1044818 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-433 1043361 1043544 1043846 "FS2EXPXP" 1044320 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-432 1042775 1042902 1043054 "FRUTIL" 1043241 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-431 1033692 1038270 1039628 "FR" 1041449 NIL FR (NIL T) -8 NIL NIL NIL) (-430 1028210 1031381 1031421 "FRNAALG" 1032741 NIL FRNAALG (NIL T) -9 NIL 1033339 NIL) (-429 1023691 1024959 1026234 "FRNAALG-" 1026984 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-428 1023323 1023372 1023499 "FRNAAF2" 1023642 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-427 1021610 1022172 1022468 "FRMOD" 1023135 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-426 1019215 1019985 1020303 "FRIDEAL" 1021401 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-425 1018400 1018493 1018784 "FRIDEAL2" 1019122 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-424 1017491 1017947 1017988 "FRETRCT" 1017993 NIL FRETRCT (NIL T) -9 NIL 1018169 NIL) (-423 1016549 1016834 1017185 "FRETRCT-" 1017190 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-422 1013363 1014833 1014892 "FRAMALG" 1015774 NIL FRAMALG (NIL T T) -9 NIL 1016066 NIL) (-421 1011401 1011952 1012582 "FRAMALG-" 1012805 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-420 1004372 1010874 1011151 "FRAC" 1011156 NIL FRAC (NIL T) -8 NIL NIL NIL) (-419 1004002 1004065 1004172 "FRAC2" 1004309 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-418 1003632 1003695 1003802 "FR2" 1003939 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-417 997549 1001011 1001039 "FPS" 1002158 T FPS (NIL) -9 NIL 1002715 NIL) (-416 996974 997107 997271 "FPS-" 997417 NIL FPS- (NIL T) -8 NIL NIL NIL) (-415 993926 995931 995959 "FPC" 996184 T FPC (NIL) -9 NIL 996326 NIL) (-414 993707 993759 993856 "FPC-" 993861 NIL FPC- (NIL T) -8 NIL NIL NIL) (-413 992465 993195 993236 "FPATMAB" 993241 NIL FPATMAB (NIL T) -9 NIL 993393 NIL) (-412 990608 991207 991554 "FPARFRAC" 992181 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-411 985900 986500 987182 "FORTRAN" 990040 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-410 983586 984116 984655 "FORT" 985381 T FORT (NIL) -7 NIL NIL NIL) (-409 981160 981824 981852 "FORTFN" 982912 T FORTFN (NIL) -9 NIL 983536 NIL) (-408 980912 980974 981002 "FORTCAT" 981061 T FORTCAT (NIL) -9 NIL 981123 NIL) (-407 978916 979528 979918 "FORMULA" 980542 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978698 978734 978803 "FORMULA1" 978880 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-405 978215 978273 978446 "FORDER" 978640 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-404 977275 977475 977668 "FOP" 978042 T FOP (NIL) -7 NIL NIL NIL) (-403 975688 976555 976729 "FNLA" 977157 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-402 974307 974818 974846 "FNCAT" 975306 T FNCAT (NIL) -9 NIL 975566 NIL) (-401 973750 974266 974294 "FNAME" 974299 T FNAME (NIL) -8 NIL NIL NIL) (-400 972076 973249 973277 "FMTC" 973282 T FMTC (NIL) -9 NIL 973318 NIL) (-399 970624 972012 972058 "FMONOID" 972063 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-398 967213 968579 968620 "FMONCAT" 969837 NIL FMONCAT (NIL T) -9 NIL 970442 NIL) (-397 966231 966955 967104 "FM" 967109 NIL FM (NIL T T) -8 NIL NIL NIL) (-396 963553 964301 964329 "FMFUN" 965473 T FMFUN (NIL) -9 NIL 966181 NIL) (-395 962786 963003 963031 "FMC" 963321 T FMC (NIL) -9 NIL 963503 NIL) (-394 959659 960711 960765 "FMCAT" 961960 NIL FMCAT (NIL T T) -9 NIL 962455 NIL) (-393 958327 959425 959525 "FM1" 959604 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-392 956065 956517 957011 "FLOATRP" 957878 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-391 948721 953794 954415 "FLOAT" 955464 T FLOAT (NIL) -8 NIL NIL NIL) (-390 946123 946659 947237 "FLOATCP" 948188 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-389 944641 945715 945756 "FLINEXP" 945761 NIL FLINEXP (NIL T) -9 NIL 945854 NIL) (-388 943771 944030 944358 "FLINEXP-" 944363 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-387 942829 942991 943215 "FLASORT" 943623 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-386 939747 940799 940851 "FLALG" 942078 NIL FLALG (NIL T T) -9 NIL 942545 NIL) (-385 933011 937156 937197 "FLAGG" 938459 NIL FLAGG (NIL T) -9 NIL 939111 NIL) (-384 931665 932076 932566 "FLAGG-" 932571 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 930689 930850 931077 "FLAGG2" 931518 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-382 927320 928534 928593 "FINRALG" 929721 NIL FINRALG (NIL T T) -9 NIL 930229 NIL) (-381 926444 926709 927048 "FINRALG-" 927053 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-380 925750 926049 926077 "FINITE" 926273 T FINITE (NIL) -9 NIL 926380 NIL) (-379 917701 920280 920320 "FINAALG" 923987 NIL FINAALG (NIL T) -9 NIL 925440 NIL) (-378 912817 914083 915227 "FINAALG-" 916606 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-377 912095 912572 912675 "FILE" 912747 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 910655 911077 911131 "FILECAT" 911815 NIL FILECAT (NIL T T) -9 NIL 912031 NIL) (-375 908051 909885 909913 "FIELD" 909953 T FIELD (NIL) -9 NIL 910033 NIL) (-374 906593 907056 907567 "FIELD-" 907572 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-373 904275 905228 905575 "FGROUP" 906279 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-372 903347 903529 903749 "FGLMICPK" 904107 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-371 898581 903272 903329 "FFX" 903334 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-370 898176 898243 898378 "FFSLPE" 898514 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-369 894052 894948 895744 "FFPOLY" 897412 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 893550 893592 893801 "FFPOLY2" 894010 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-367 888798 893469 893532 "FFP" 893537 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-366 883598 888709 888773 "FF" 888778 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-365 878108 882941 883131 "FFNBX" 883452 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-364 872420 877243 877501 "FFNBP" 877962 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-363 866437 871704 871915 "FFNB" 872253 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-362 865257 865467 865782 "FFINTBAS" 866234 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-361 860833 863504 863532 "FFIELDC" 864152 T FFIELDC (NIL) -9 NIL 864528 NIL) (-360 859411 859866 860363 "FFIELDC-" 860368 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-359 858968 859026 859150 "FFHOM" 859353 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-358 856627 857150 857667 "FFF" 858483 NIL FFF (NIL T) -7 NIL NIL NIL) (-357 851641 856369 856470 "FFCGX" 856570 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-356 846659 851373 851480 "FFCGP" 851584 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-355 841238 846386 846494 "FFCG" 846595 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-354 819901 830970 831056 "FFCAT" 836221 NIL FFCAT (NIL T T T) -9 NIL 837672 NIL) (-353 814912 816146 817460 "FFCAT-" 818690 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-352 814317 814366 814601 "FFCAT2" 814863 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-351 802970 807289 808509 "FEXPR" 813169 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-350 801898 802367 802408 "FEVALAB" 802492 NIL FEVALAB (NIL T) -9 NIL 802753 NIL) (-349 801015 801267 801605 "FEVALAB-" 801610 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-348 799425 800398 800601 "FDIV" 800914 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-347 796287 797172 797287 "FDIVCAT" 798855 NIL FDIVCAT (NIL T T T T) -9 NIL 799292 NIL) (-346 796043 796076 796246 "FDIVCAT-" 796251 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-345 795257 795350 795627 "FDIV2" 795950 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-344 794165 794552 794754 "FCTRDATA" 795075 T FCTRDATA (NIL) -8 NIL NIL NIL) (-343 792821 793110 793399 "FCPAK1" 793896 T FCPAK1 (NIL) -7 NIL NIL NIL) (-342 791824 792321 792462 "FCOMP" 792712 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-341 775139 778974 782512 "FC" 788306 T FC (NIL) -8 NIL NIL NIL) (-340 766834 771460 771500 "FAXF" 773302 NIL FAXF (NIL T) -9 NIL 773994 NIL) (-339 763955 764768 765593 "FAXF-" 766058 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-338 758524 763331 763507 "FARRAY" 763812 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-337 753088 755471 755524 "FAMR" 756547 NIL FAMR (NIL T T) -9 NIL 757007 NIL) (-336 751912 752280 752715 "FAMR-" 752720 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-335 750939 751834 751887 "FAMONOID" 751892 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-334 748569 749421 749474 "FAMONC" 750415 NIL FAMONC (NIL T T) -9 NIL 750801 NIL) (-333 747043 748323 748460 "FAGROUP" 748465 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-332 744796 745157 745560 "FACUTIL" 746724 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-331 743883 744080 744302 "FACTFUNC" 744606 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-330 735641 743186 743385 "EXPUPXS" 743739 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-329 733094 733664 734250 "EXPRTUBE" 735075 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-328 729305 729957 730687 "EXPRODE" 732433 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-327 713599 727954 728383 "EXPR" 728909 NIL EXPR (NIL T) -8 NIL NIL NIL) (-326 708033 708740 709546 "EXPR2UPS" 712897 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-325 707659 707722 707831 "EXPR2" 707970 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-324 697976 706810 707101 "EXPEXPAN" 707495 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-323 697740 697933 697962 "EXIT" 697967 T EXIT (NIL) -8 NIL NIL NIL) (-322 697160 697464 697555 "EXITAST" 697669 T EXITAST (NIL) -8 NIL NIL NIL) (-321 696781 696849 696962 "EVALCYC" 697092 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-320 696298 696440 696481 "EVALAB" 696651 NIL EVALAB (NIL T) -9 NIL 696755 NIL) (-319 695755 695901 696122 "EVALAB-" 696127 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-318 692863 694411 694439 "EUCDOM" 694994 T EUCDOM (NIL) -9 NIL 695344 NIL) (-317 691202 691710 692300 "EUCDOM-" 692305 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-316 678519 681500 684250 "ESTOOLS" 688472 T ESTOOLS (NIL) -7 NIL NIL NIL) (-315 678145 678208 678317 "ESTOOLS2" 678456 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-314 677890 677938 678018 "ESTOOLS1" 678097 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-313 671591 673521 673549 "ES" 676317 T ES (NIL) -9 NIL 677727 NIL) (-312 666268 667825 669642 "ES-" 669806 NIL ES- (NIL T) -8 NIL NIL NIL) (-311 662576 663403 664183 "ESCONT" 665508 T ESCONT (NIL) -7 NIL NIL NIL) (-310 662315 662353 662435 "ESCONT1" 662538 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-309 661984 662040 662140 "ES2" 662259 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-308 661608 661672 661781 "ES1" 661920 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-307 660800 660953 661129 "ERROR" 661452 T ERROR (NIL) -7 NIL NIL NIL) (-306 653816 660659 660750 "EQTBL" 660755 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-305 646075 649130 650579 "EQ" 652400 NIL -2130 (NIL T) -8 NIL NIL NIL) (-304 645701 645764 645873 "EQ2" 646012 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-303 640944 642039 643132 "EP" 644640 NIL EP (NIL T) -7 NIL NIL NIL) (-302 639484 639835 640141 "ENV" 640658 T ENV (NIL) -8 NIL NIL NIL) (-301 638444 639118 639146 "ENTIRER" 639151 T ENTIRER (NIL) -9 NIL 639197 NIL) (-300 634856 636626 636987 "EMR" 638252 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-299 633960 634171 634225 "ELTAGG" 634605 NIL ELTAGG (NIL T T) -9 NIL 634816 NIL) (-298 633667 633741 633882 "ELTAGG-" 633887 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-297 633425 633460 633514 "ELTAB" 633598 NIL ELTAB (NIL T T) -9 NIL 633650 NIL) (-296 632527 632697 632896 "ELFUTS" 633276 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-295 632251 632325 632353 "ELEMFUN" 632458 T ELEMFUN (NIL) -9 NIL NIL NIL) (-294 632115 632142 632210 "ELEMFUN-" 632215 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-293 626532 630157 630198 "ELAGG" 631138 NIL ELAGG (NIL T) -9 NIL 631601 NIL) (-292 624709 625251 625914 "ELAGG-" 625919 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-291 623991 624158 624314 "ELABOR" 624573 T ELABOR (NIL) -8 NIL NIL NIL) (-290 622598 622931 623225 "ELABEXPR" 623717 T ELABEXPR (NIL) -8 NIL NIL NIL) (-289 615110 617235 618064 "EFUPXS" 621873 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-288 608236 610359 611170 "EFULS" 614385 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-287 605673 606079 606551 "EFSTRUC" 607868 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-286 595110 597030 598578 "EF" 604188 NIL EF (NIL T T) -7 NIL NIL NIL) (-285 594088 594595 594744 "EAB" 594981 T EAB (NIL) -8 NIL NIL NIL) (-284 593210 594047 594075 "E04UCFA" 594080 T E04UCFA (NIL) -8 NIL NIL NIL) (-283 592332 593169 593197 "E04NAFA" 593202 T E04NAFA (NIL) -8 NIL NIL NIL) (-282 591454 592291 592319 "E04MBFA" 592324 T E04MBFA (NIL) -8 NIL NIL NIL) (-281 590576 591413 591441 "E04JAFA" 591446 T E04JAFA (NIL) -8 NIL NIL NIL) (-280 589700 590535 590563 "E04GCFA" 590568 T E04GCFA (NIL) -8 NIL NIL NIL) (-279 588824 589659 589687 "E04FDFA" 589692 T E04FDFA (NIL) -8 NIL NIL NIL) (-278 587946 588783 588811 "E04DGFA" 588816 T E04DGFA (NIL) -8 NIL NIL NIL) (-277 582023 583471 584835 "E04AGNT" 586602 T E04AGNT (NIL) -7 NIL NIL NIL) (-276 580643 581324 581364 "DVARCAT" 581705 NIL DVARCAT (NIL T) -9 NIL 581868 NIL) (-275 579793 580059 580373 "DVARCAT-" 580378 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-274 571754 579592 579721 "DSMP" 579726 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-273 570105 570896 570937 "DSEXT" 571300 NIL DSEXT (NIL T) -9 NIL 571594 NIL) (-272 568294 568818 569484 "DSEXT-" 569489 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-271 562877 564239 565307 "DROPT" 567246 T DROPT (NIL) -8 NIL NIL NIL) (-270 562536 562601 562699 "DROPT1" 562812 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-269 557555 558777 559914 "DROPT0" 561419 T DROPT0 (NIL) -7 NIL NIL NIL) (-268 555864 556225 556611 "DRAWPT" 557189 T DRAWPT (NIL) -7 NIL NIL NIL) (-267 550355 551374 552453 "DRAW" 554838 NIL DRAW (NIL T) -7 NIL NIL NIL) (-266 549982 550041 550159 "DRAWHACK" 550296 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-265 548683 548982 549273 "DRAWCX" 549711 T DRAWCX (NIL) -7 NIL NIL NIL) (-264 548192 548267 548418 "DRAWCURV" 548609 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-263 538510 540622 542737 "DRAWCFUN" 546097 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-262 534981 537175 537216 "DQAGG" 537845 NIL DQAGG (NIL T) -9 NIL 538119 NIL) (-261 521564 529192 529275 "DPOLCAT" 531127 NIL DPOLCAT (NIL T T T T) -9 NIL 531672 NIL) (-260 516083 517749 519707 "DPOLCAT-" 519712 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-259 508940 515944 516042 "DPMO" 516047 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-258 501694 508720 508887 "DPMM" 508892 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-257 501216 501478 501567 "DOMTMPLT" 501625 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-256 500565 501018 501098 "DOMCTOR" 501156 T DOMCTOR (NIL) -8 NIL NIL NIL) (-255 499717 500045 500196 "DOMAIN" 500434 T DOMAIN (NIL) -8 NIL NIL NIL) (-254 492729 499352 499504 "DMP" 499618 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-253 490506 491796 491837 "DMEXT" 491842 NIL DMEXT (NIL T) -9 NIL 492018 NIL) (-252 490100 490162 490306 "DLP" 490444 NIL DLP (NIL T) -7 NIL NIL NIL) (-251 483223 489427 489617 "DLIST" 489942 NIL DLIST (NIL T) -8 NIL NIL NIL) (-250 479761 482048 482089 "DLAGG" 482639 NIL DLAGG (NIL T) -9 NIL 482869 NIL) (-249 478273 479087 479115 "DIVRING" 479207 T DIVRING (NIL) -9 NIL 479290 NIL) (-248 477456 477700 478000 "DIVRING-" 478005 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-247 475498 475915 476321 "DISPLAY" 477070 T DISPLAY (NIL) -7 NIL NIL NIL) (-246 468905 475412 475475 "DIRPROD" 475480 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 467735 467956 468221 "DIRPROD2" 468698 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-244 455954 462446 462499 "DIRPCAT" 462757 NIL DIRPCAT (NIL NIL T) -9 NIL 463632 NIL) (-243 453154 453922 454803 "DIRPCAT-" 455140 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-242 452435 452601 452787 "DIOSP" 452988 T DIOSP (NIL) -7 NIL NIL NIL) (-241 448849 451319 451360 "DIOPS" 451794 NIL DIOPS (NIL T) -9 NIL 452023 NIL) (-240 448368 448512 448703 "DIOPS-" 448708 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-239 447275 448047 448075 "DIFRING" 448080 T DIFRING (NIL) -9 NIL 448102 NIL) (-238 446923 447021 447049 "DIFFSPC" 447168 T DIFFSPC (NIL) -9 NIL 447243 NIL) (-237 446544 446646 446798 "DIFFSPC-" 446803 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-236 445480 446078 446119 "DIFFMOD" 446124 NIL DIFFMOD (NIL T) -9 NIL 446222 NIL) (-235 445176 445233 445274 "DIFFDOM" 445395 NIL DIFFDOM (NIL T) -9 NIL 445463 NIL) (-234 445023 445053 445137 "DIFFDOM-" 445142 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-233 442763 444227 444268 "DIFEXT" 444273 NIL DIFEXT (NIL T) -9 NIL 444426 NIL) (-232 439797 442267 442308 "DIAGG" 442313 NIL DIAGG (NIL T) -9 NIL 442333 NIL) (-231 439145 439338 439590 "DIAGG-" 439595 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-230 433995 438104 438381 "DHMATRIX" 438914 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-229 429463 430516 431526 "DFSFUN" 433005 T DFSFUN (NIL) -7 NIL NIL NIL) (-228 423697 428394 428706 "DFLOAT" 429171 T DFLOAT (NIL) -8 NIL NIL NIL) (-227 421936 422241 422630 "DFINTTLS" 423405 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-226 418755 419957 420357 "DERHAM" 421602 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-225 416291 418530 418619 "DEQUEUE" 418699 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-224 415533 415678 415861 "DEGRED" 416153 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-223 411939 412708 413554 "DEFINTRF" 414761 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-222 409476 409963 410555 "DEFINTEF" 411458 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-221 408760 409096 409211 "DEFAST" 409381 T DEFAST (NIL) -8 NIL NIL NIL) (-220 401796 408353 408503 "DECIMAL" 408630 T DECIMAL (NIL) -8 NIL NIL NIL) (-219 399254 399766 400272 "DDFACT" 401340 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-218 398844 398893 399044 "DBLRESP" 399205 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-217 398045 398614 398705 "DBASIS" 398793 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-216 395829 396275 396636 "DBASE" 397811 NIL DBASE (NIL T) -8 NIL NIL NIL) (-215 395017 395309 395455 "DATAARY" 395728 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-214 394075 394976 395004 "D03FAFA" 395009 T D03FAFA (NIL) -8 NIL NIL NIL) (-213 393134 394034 394062 "D03EEFA" 394067 T D03EEFA (NIL) -8 NIL NIL NIL) (-212 391060 391550 392039 "D03AGNT" 392665 T D03AGNT (NIL) -7 NIL NIL NIL) (-211 390301 391019 391047 "D02EJFA" 391052 T D02EJFA (NIL) -8 NIL NIL NIL) (-210 389542 390260 390288 "D02CJFA" 390293 T D02CJFA (NIL) -8 NIL NIL NIL) (-209 388783 389501 389529 "D02BHFA" 389534 T D02BHFA (NIL) -8 NIL NIL NIL) (-208 388024 388742 388770 "D02BBFA" 388775 T D02BBFA (NIL) -8 NIL NIL NIL) (-207 381155 382810 384416 "D02AGNT" 386438 T D02AGNT (NIL) -7 NIL NIL NIL) (-206 378905 379446 379992 "D01WGTS" 380629 T D01WGTS (NIL) -7 NIL NIL NIL) (-205 377912 378864 378892 "D01TRNS" 378897 T D01TRNS (NIL) -8 NIL NIL NIL) (-204 376920 377871 377899 "D01GBFA" 377904 T D01GBFA (NIL) -8 NIL NIL NIL) (-203 375928 376879 376907 "D01FCFA" 376912 T D01FCFA (NIL) -8 NIL NIL NIL) (-202 374936 375887 375915 "D01ASFA" 375920 T D01ASFA (NIL) -8 NIL NIL NIL) (-201 373944 374895 374923 "D01AQFA" 374928 T D01AQFA (NIL) -8 NIL NIL NIL) (-200 372952 373903 373931 "D01APFA" 373936 T D01APFA (NIL) -8 NIL NIL NIL) (-199 371960 372911 372939 "D01ANFA" 372944 T D01ANFA (NIL) -8 NIL NIL NIL) (-198 370968 371919 371947 "D01AMFA" 371952 T D01AMFA (NIL) -8 NIL NIL NIL) (-197 369976 370927 370955 "D01ALFA" 370960 T D01ALFA (NIL) -8 NIL NIL NIL) (-196 368984 369935 369963 "D01AKFA" 369968 T D01AKFA (NIL) -8 NIL NIL NIL) (-195 367992 368943 368971 "D01AJFA" 368976 T D01AJFA (NIL) -8 NIL NIL NIL) (-194 361215 362840 364401 "D01AGNT" 366451 T D01AGNT (NIL) -7 NIL NIL NIL) (-193 360534 360680 360832 "CYCLOTOM" 361083 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-192 357189 357982 358709 "CYCLES" 359827 T CYCLES (NIL) -7 NIL NIL NIL) (-191 356489 356635 356806 "CVMP" 357050 NIL CVMP (NIL T) -7 NIL NIL NIL) (-190 354276 354588 354957 "CTRIGMNP" 356217 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-189 353634 354070 354143 "CTOR" 354223 T CTOR (NIL) -8 NIL NIL NIL) (-188 353107 353365 353466 "CTORKIND" 353553 T CTORKIND (NIL) -8 NIL NIL NIL) (-187 352312 352700 352728 "CTORCAT" 352910 T CTORCAT (NIL) -9 NIL 353023 NIL) (-186 351886 352021 352180 "CTORCAT-" 352185 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-185 351300 351560 351668 "CTORCALL" 351810 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-184 350656 350773 350926 "CSTTOOLS" 351197 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-183 346353 347112 347870 "CRFP" 349968 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-182 345768 346074 346166 "CRCEAST" 346281 T CRCEAST (NIL) -8 NIL NIL NIL) (-181 344791 345000 345228 "CRAPACK" 345572 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-180 344171 344276 344480 "CPMATCH" 344667 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-179 343890 343924 344030 "CPIMA" 344137 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-178 340148 340910 341629 "COORDSYS" 343225 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-177 339536 339681 339823 "CONTOUR" 340026 T CONTOUR (NIL) -8 NIL NIL NIL) (-176 335001 337539 338031 "CONTFRAC" 339076 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-175 334875 334902 334930 "CONDUIT" 334967 T CONDUIT (NIL) -9 NIL NIL NIL) (-174 333829 334503 334531 "COMRING" 334536 T COMRING (NIL) -9 NIL 334588 NIL) (-173 332811 333187 333371 "COMPPROP" 333665 T COMPPROP (NIL) -8 NIL NIL NIL) (-172 332466 332507 332635 "COMPLPAT" 332770 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-171 320849 332275 332384 "COMPLEX" 332389 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320479 320542 320649 "COMPLEX2" 320786 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-169 319800 319939 320099 "COMPILER" 320339 T COMPILER (NIL) -8 NIL NIL NIL) (-168 319512 319553 319651 "COMPFACT" 319759 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-167 300887 313216 313256 "COMPCAT" 314260 NIL COMPCAT (NIL T) -9 NIL 315608 NIL) (-166 289775 293326 296953 "COMPCAT-" 297309 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-165 289498 289532 289635 "COMMUPC" 289741 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-164 289286 289326 289385 "COMMONOP" 289459 T COMMONOP (NIL) -7 NIL NIL NIL) (-163 288794 289037 289124 "COMM" 289219 T COMM (NIL) -8 NIL NIL NIL) (-162 288316 288598 288673 "COMMAAST" 288739 T COMMAAST (NIL) -8 NIL NIL NIL) (-161 287511 287759 287787 "COMBOPC" 288125 T COMBOPC (NIL) -9 NIL 288300 NIL) (-160 286365 286617 286859 "COMBINAT" 287301 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-159 282708 283396 284023 "COMBF" 285787 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-158 281370 281824 282059 "COLOR" 282493 T COLOR (NIL) -8 NIL NIL NIL) (-157 280786 281091 281183 "COLONAST" 281298 T COLONAST (NIL) -8 NIL NIL NIL) (-156 280420 280473 280598 "CMPLXRT" 280733 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-155 279808 280120 280219 "CLLCTAST" 280341 T CLLCTAST (NIL) -8 NIL NIL NIL) (-154 275268 276338 277418 "CLIP" 278748 T CLIP (NIL) -7 NIL NIL NIL) (-153 273441 274369 274609 "CLIF" 275095 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-152 269423 271559 271600 "CLAGG" 272529 NIL CLAGG (NIL T) -9 NIL 273065 NIL) (-151 267767 268302 268885 "CLAGG-" 268890 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-150 267305 267396 267536 "CINTSLPE" 267676 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-149 264770 265277 265825 "CHVAR" 266833 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-148 263810 264484 264512 "CHARZ" 264517 T CHARZ (NIL) -9 NIL 264532 NIL) (-147 263558 263604 263682 "CHARPOL" 263764 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-146 262476 263189 263217 "CHARNZ" 263264 T CHARNZ (NIL) -9 NIL 263320 NIL) (-145 260220 261130 261483 "CHAR" 262143 T CHAR (NIL) -8 NIL NIL NIL) (-144 259928 260007 260035 "CFCAT" 260146 T CFCAT (NIL) -9 NIL NIL NIL) (-143 259151 259280 259463 "CDEN" 259812 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-142 254748 258304 258584 "CCLASS" 258891 T CCLASS (NIL) -8 NIL NIL NIL) (-141 253969 254156 254333 "CATEGORY" 254591 T -10 (NIL) -8 NIL NIL NIL) (-140 253464 253888 253936 "CATCTOR" 253941 T CATCTOR (NIL) -8 NIL NIL NIL) (-139 252855 253167 253265 "CATAST" 253386 T CATAST (NIL) -8 NIL NIL NIL) (-138 252271 252576 252668 "CASEAST" 252783 T CASEAST (NIL) -8 NIL NIL NIL) (-137 247169 248428 249172 "CARTEN" 251583 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 246265 246425 246646 "CARTEN2" 247016 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-135 244395 245415 245672 "CARD" 246028 T CARD (NIL) -8 NIL NIL NIL) (-134 243917 244199 244274 "CAPSLAST" 244340 T CAPSLAST (NIL) -8 NIL NIL NIL) (-133 243359 243615 243643 "CACHSET" 243775 T CACHSET (NIL) -9 NIL 243853 NIL) (-132 242749 243137 243165 "CABMON" 243215 T CABMON (NIL) -9 NIL 243271 NIL) (-131 242186 242453 242563 "BYTEORD" 242659 T BYTEORD (NIL) -8 NIL NIL NIL) (-130 240944 241701 241850 "BYTE" 242013 T BYTE (NIL) -8 NIL NIL 242142) (-129 235871 240449 240621 "BYTEBUF" 240792 T BYTEBUF (NIL) -8 NIL NIL NIL) (-128 233133 235563 235670 "BTREE" 235797 NIL BTREE (NIL T) -8 NIL NIL NIL) (-127 230335 232781 232903 "BTOURN" 233043 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-126 227442 229777 229818 "BTCAT" 229886 NIL BTCAT (NIL T) -9 NIL 229963 NIL) (-125 227091 227189 227338 "BTCAT-" 227343 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-124 221982 226337 226365 "BTAGG" 226479 T BTAGG (NIL) -9 NIL 226589 NIL) (-123 221436 221597 221803 "BTAGG-" 221808 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-122 218172 220714 220929 "BSTREE" 221253 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-121 217280 217436 217620 "BRILL" 218028 NIL BRILL (NIL T) -7 NIL NIL NIL) (-120 213675 215978 216019 "BRAGG" 216668 NIL BRAGG (NIL T) -9 NIL 216926 NIL) (-119 212108 212610 213165 "BRAGG-" 213170 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-118 204344 211452 211637 "BPADICRT" 211955 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-117 202353 204281 204326 "BPADIC" 204331 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-116 202045 202081 202195 "BOUNDZRO" 202317 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-115 197027 198471 199383 "BOP" 201153 T BOP (NIL) -8 NIL NIL NIL) (-114 194754 195212 195687 "BOP1" 196585 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-113 194437 194516 194544 "BOOLE" 194655 T BOOLE (NIL) -9 NIL 194737 NIL) (-112 193088 194011 194160 "BOOLEAN" 194308 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 192257 192757 192811 "BMODULE" 192816 NIL BMODULE (NIL T T) -9 NIL 192881 NIL) (-110 187578 192055 192128 "BITS" 192204 T BITS (NIL) -8 NIL NIL NIL) (-109 186975 187118 187258 "BINDING" 187458 T BINDING (NIL) -8 NIL NIL NIL) (-108 180014 186570 186719 "BINARY" 186846 T BINARY (NIL) -8 NIL NIL NIL) (-107 177621 179241 179282 "BGAGG" 179542 NIL BGAGG (NIL T) -9 NIL 179679 NIL) (-106 177446 177484 177575 "BGAGG-" 177580 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176469 176830 177035 "BFUNCT" 177261 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175139 175337 175625 "BEZOUT" 176293 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171337 173991 174321 "BBTREE" 174842 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170920 171016 171044 "BASTYPE" 171221 T BASTYPE (NIL) -9 NIL 171320 NIL) (-101 170578 170677 170812 "BASTYPE-" 170817 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 170000 170088 170240 "BALFACT" 170489 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168736 169415 169601 "AUTOMOR" 169845 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168462 168467 168493 "ATTREG" 168498 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166624 167159 167511 "ATTRBUT" 168128 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166178 166452 166518 "ATTRAST" 166576 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165678 165827 165853 "ATRIG" 166054 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165475 165528 165615 "ATRIG-" 165620 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165058 165292 165318 "ASTCAT" 165323 T ASTCAT (NIL) -9 NIL 165353 NIL) (-92 164767 164844 164963 "ASTCAT-" 164968 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162741 164543 164631 "ASTACK" 164710 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161230 161543 161908 "ASSOCEQ" 162423 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160154 160889 161013 "ASP9" 161137 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 159881 160102 160141 "ASP8" 160146 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 158641 159486 159628 "ASP80" 159770 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 157431 158276 158408 "ASP7" 158540 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 156277 157108 157226 "ASP78" 157344 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 155138 155957 156074 "ASP77" 156191 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 153942 154776 154907 "ASP74" 155038 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 152734 153577 153709 "ASP73" 153841 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 151730 152560 152660 "ASP6" 152665 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150569 151407 151525 "ASP55" 151643 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149410 150243 150362 "ASP50" 150481 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148390 149111 149221 "ASP4" 149331 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 147370 148091 148201 "ASP49" 148311 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 146046 146909 147077 "ASP42" 147259 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144715 145579 145749 "ASP41" 145933 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 143557 144392 144510 "ASP35" 144628 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143286 143505 143544 "ASP34" 143549 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143005 143090 143166 "ASP33" 143241 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141791 142640 142772 "ASP31" 142904 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141520 141739 141778 "ASP30" 141783 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141237 141324 141400 "ASP29" 141475 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140966 141185 141224 "ASP28" 141229 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140695 140914 140953 "ASP27" 140958 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139671 140393 140504 "ASP24" 140615 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138640 139473 139585 "ASP20" 139590 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137620 138341 138451 "ASP1" 138561 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 136455 137294 137413 "ASP19" 137532 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 136174 136259 136335 "ASP12" 136410 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 134918 135773 135917 "ASP10" 136061 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 132530 134762 134853 "ARRAY2" 134858 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 127890 132178 132292 "ARRAY1" 132447 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 126904 127095 127316 "ARRAY12" 127713 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 120949 123106 123181 "ARR2CAT" 125811 NIL ARR2CAT (NIL T T T) -9 NIL 126569 NIL) (-56 118239 119127 120081 "ARR2CAT-" 120086 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117490 117866 117991 "ARITY" 118132 T ARITY (NIL) -8 NIL NIL NIL) (-54 116248 116418 116717 "APPRULE" 117326 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115893 115947 116066 "APPLYORE" 116194 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115193 115486 115606 "ANY" 115791 T ANY (NIL) -8 NIL NIL NIL) (-51 114447 114594 114751 "ANY1" 115067 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 111773 112884 113211 "ANTISYM" 114171 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111217 111480 111576 "ANON" 111695 T ANON (NIL) -8 NIL NIL NIL) (-48 104373 109756 110210 "AN" 110781 T AN (NIL) -8 NIL NIL NIL) (-47 100029 101645 101696 "AMR" 102444 NIL AMR (NIL T T) -9 NIL 103044 NIL) (-46 99081 99362 99725 "AMR-" 99730 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82550 98998 99059 "ALIST" 99064 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78847 82144 82313 "ALGSC" 82468 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75297 75957 76564 "ALGPKG" 78287 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74562 74675 74859 "ALGMFACT" 75183 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70545 71176 71770 "ALGMANIP" 74146 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59884 70171 70321 "ALGFF" 70478 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59056 59211 59390 "ALGFACT" 59742 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57845 58583 58621 "ALGEBRA" 58626 NIL ALGEBRA (NIL T) -9 NIL 58667 NIL) (-37 57545 57622 57754 "ALGEBRA-" 57759 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38506 55382 55434 "ALAGG" 55570 NIL ALAGG (NIL T T) -9 NIL 55731 NIL) (-35 38006 38155 38181 "AHYP" 38382 T AHYP (NIL) -9 NIL NIL NIL) (-34 36891 37185 37211 "AGG" 37710 T AGG (NIL) -9 NIL 37989 NIL) (-33 36289 36487 36701 "AGG-" 36706 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34049 34518 34923 "AF" 35931 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33469 33774 33864 "ADDAST" 33977 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32701 32996 33152 "ACPLOT" 33331 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20258 29633 29671 "ACFS" 30278 NIL ACFS (NIL T) -9 NIL 30517 NIL) (-28 18165 18775 19537 "ACFS-" 19542 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13873 16198 16224 "ACF" 17103 T ACF (NIL) -9 NIL 17516 NIL) (-26 12505 12911 13404 "ACF-" 13409 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12015 12258 12284 "ABELSG" 12376 T ABELSG (NIL) -9 NIL 12441 NIL) (-24 11876 11907 11973 "ABELSG-" 11978 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11145 11492 11518 "ABELMON" 11688 T ABELMON (NIL) -9 NIL 11800 NIL) (-22 10785 10893 11031 "ABELMON-" 11036 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10035 10491 10517 "ABELGRP" 10589 T ABELGRP (NIL) -9 NIL 10664 NIL) (-20 9462 9627 9843 "ABELGRP-" 9848 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8724 8763 "A1AGG" 8768 NIL A1AGG (NIL T) -9 NIL 8808 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
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(|:| |relerr| (-228)))) (-5 *2 (-2 @@ -10629,10 +10431,10 @@ (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1182 (-228))) + (-3 (|:| |str| (-1187 (-228))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2097 + (|:| -3433 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -10640,6259 +10442,6305 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-572))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1090 *2 *3 *4)) (-4 *2 (-1074)) (-4 *3 (-809)) - (-4 *4 (-865)) (-4 *2 (-465))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1292 *1)) (-4 *1 (-379 *4)) (-4 *4 (-174)) - (-5 *2 (-705 *4)))) - ((*1 *2) - (-12 (-4 *4 (-174)) (-5 *2 (-705 *4)) (-5 *1 (-429 *3 *4)) - (-4 *3 (-430 *4)))) - ((*1 *2) (-12 (-4 *1 (-430 *3)) (-4 *3 (-174)) (-5 *2 (-705 *3))))) -(((*1 *1 *2) - (-12 (-5 *2 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\ No newline at end of file |