diff options
| -rwxr-xr-x | configure | 18 | ||||
| -rw-r--r-- | configure.ac | 2 | ||||
| -rw-r--r-- | configure.ac.pamphlet | 2 | ||||
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 14 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 14 | ||||
| -rw-r--r-- | src/algebra/boolean.spad.pamphlet | 81 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1992 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 2656 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1325 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9954 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29987 |
12 files changed, 23079 insertions, 22971 deletions
@@ -1,6 +1,6 @@ #! /bin/sh # Guess values for system-dependent variables and create Makefiles. -# Generated by GNU Autoconf 2.63 for OpenAxiom 1.4.0-2010-04-03. +# Generated by GNU Autoconf 2.63 for OpenAxiom 1.4.0-2010-04-04. # # Report bugs to <open-axiom-bugs@lists.sf.net>. # @@ -745,8 +745,8 @@ SHELL=${CONFIG_SHELL-/bin/sh} # Identity of this package. PACKAGE_NAME='OpenAxiom' PACKAGE_TARNAME='openaxiom' -PACKAGE_VERSION='1.4.0-2010-04-03' -PACKAGE_STRING='OpenAxiom 1.4.0-2010-04-03' +PACKAGE_VERSION='1.4.0-2010-04-04' +PACKAGE_STRING='OpenAxiom 1.4.0-2010-04-04' PACKAGE_BUGREPORT='open-axiom-bugs@lists.sf.net' ac_unique_file="src/Makefile.pamphlet" @@ -1511,7 +1511,7 @@ if test "$ac_init_help" = "long"; then # Omit some internal or obsolete options to make the list less imposing. # This message is too long to be a string in the A/UX 3.1 sh. cat <<_ACEOF -\`configure' configures OpenAxiom 1.4.0-2010-04-03 to adapt to many kinds of systems. +\`configure' configures OpenAxiom 1.4.0-2010-04-04 to adapt to many kinds of systems. Usage: $0 [OPTION]... [VAR=VALUE]... @@ -1581,7 +1581,7 @@ fi if test -n "$ac_init_help"; then case $ac_init_help in - short | recursive ) echo "Configuration of OpenAxiom 1.4.0-2010-04-03:";; + short | recursive ) echo "Configuration of OpenAxiom 1.4.0-2010-04-04:";; esac cat <<\_ACEOF @@ -1688,7 +1688,7 @@ fi test -n "$ac_init_help" && exit $ac_status if $ac_init_version; then cat <<\_ACEOF -OpenAxiom configure 1.4.0-2010-04-03 +OpenAxiom configure 1.4.0-2010-04-04 generated by GNU Autoconf 2.63 Copyright (C) 1992, 1993, 1994, 1995, 1996, 1998, 1999, 2000, 2001, @@ -1702,7 +1702,7 @@ cat >config.log <<_ACEOF This file contains any messages produced by compilers while running configure, to aid debugging if configure makes a mistake. -It was created by OpenAxiom $as_me 1.4.0-2010-04-03, which was +It was created by OpenAxiom $as_me 1.4.0-2010-04-04, which was generated by GNU Autoconf 2.63. Invocation command line was $ $0 $@ @@ -21165,7 +21165,7 @@ exec 6>&1 # report actual input values of CONFIG_FILES etc. instead of their # values after options handling. ac_log=" -This file was extended by OpenAxiom $as_me 1.4.0-2010-04-03, which was +This file was extended by OpenAxiom $as_me 1.4.0-2010-04-04, which was generated by GNU Autoconf 2.63. Invocation command line was CONFIG_FILES = $CONFIG_FILES @@ -21228,7 +21228,7 @@ Report bugs to <bug-autoconf@gnu.org>." _ACEOF cat >>$CONFIG_STATUS <<_ACEOF || ac_write_fail=1 ac_cs_version="\\ -OpenAxiom config.status 1.4.0-2010-04-03 +OpenAxiom config.status 1.4.0-2010-04-04 configured by $0, generated by GNU Autoconf 2.63, with options \\"`$as_echo "$ac_configure_args" | sed 's/^ //; s/[\\""\`\$]/\\\\&/g'`\\" diff --git a/configure.ac b/configure.ac index 8e8f721d..e43c585f 100644 --- a/configure.ac +++ b/configure.ac @@ -1,6 +1,6 @@ sinclude(config/open-axiom.m4) sinclude(config/aclocal.m4) -AC_INIT([OpenAxiom], [1.4.0-2010-04-03], +AC_INIT([OpenAxiom], [1.4.0-2010-04-04], [open-axiom-bugs@lists.sf.net]) AC_CONFIG_AUX_DIR(config) diff --git a/configure.ac.pamphlet b/configure.ac.pamphlet index 294d62c4..b506d533 100644 --- a/configure.ac.pamphlet +++ b/configure.ac.pamphlet @@ -1200,7 +1200,7 @@ information: <<Autoconf init>>= sinclude(config/open-axiom.m4) sinclude(config/aclocal.m4) -AC_INIT([OpenAxiom], [1.4.0-2010-04-03], +AC_INIT([OpenAxiom], [1.4.0-2010-04-04], [open-axiom-bugs@lists.sf.net]) @ diff --git a/src/ChangeLog b/src/ChangeLog index 1c04a53f..534d0b45 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2010-04-04 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/boolean.spad.pamphlet (PropositionalFormulaFunctions1): New. + (PropositionalFormulaFunctions2): Likewise. + 2010-04-03 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/sys-utility.boot ($ClosedIOMode): New. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 75bac0b7..8c99bd1e 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -497,15 +497,17 @@ axiom_algebra_layer_5_objects = \ $(addsuffix .$(FASLEXT),$(axiom_algebra_layer_5))) $(OUT)/CHARPOL.$(FASLEXT): $(OUT)/SETCAT-.$(FASLEXT) -$(OUT)PROPFRML.$(FASLEXT): $(OUT)/KERNEL.$(FASLEXT) +$(OUT)/PROPFRML.$(FASLEXT): $(OUT)/KERNEL.$(FASLEXT) $(OUT)/KTVLOGIC.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT) $(OUT)/BYTE.$(FASLEXT) +$(OUT)/PROPFUN1.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) +$(OUT)/PROPFUN2.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) axiom_algebra_layer_6 = \ - PROPFRML AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ - DIFEXT DIFEXT- ES1 ES2 GRMOD GRMOD- \ - HYPCAT HYPCAT- MODRING NASRING NASRING- \ - SORTPAK ZMOD \ - KTVLOGIC OAMONS BYTE SYSINT SYSNNI + PROPFRML PROPFUN1 AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ + DIFEXT DIFEXT- ES1 ES2 GRMOD GRMOD- \ + HYPCAT HYPCAT- MODRING NASRING NASRING- \ + SORTPAK ZMOD PROPFUN2 \ + KTVLOGIC OAMONS BYTE SYSINT SYSNNI axiom_algebra_layer_6_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_6)) diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index ddbb379c..11c6399e 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -481,15 +481,17 @@ axiom_algebra_layer_5_objects = \ <<layer6>>= $(OUT)/CHARPOL.$(FASLEXT): $(OUT)/SETCAT-.$(FASLEXT) -$(OUT)PROPFRML.$(FASLEXT): $(OUT)/KERNEL.$(FASLEXT) +$(OUT)/PROPFRML.$(FASLEXT): $(OUT)/KERNEL.$(FASLEXT) $(OUT)/KTVLOGIC.$(FASLEXT): $(OUT)/PROPLOG.$(FASLEXT) $(OUT)/BYTE.$(FASLEXT) +$(OUT)/PROPFUN1.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) +$(OUT)/PROPFUN2.$(FASLEXT): $(OUT)/PROPFRML.$(FASLEXT) axiom_algebra_layer_6 = \ - PROPFRML AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ - DIFEXT DIFEXT- ES1 ES2 GRMOD GRMOD- \ - HYPCAT HYPCAT- MODRING NASRING NASRING- \ - SORTPAK ZMOD \ - KTVLOGIC OAMONS BYTE SYSINT SYSNNI + PROPFRML PROPFUN1 AUTOMOR CARTEN2 CHARPOL COMPLEX2 \ + DIFEXT DIFEXT- ES1 ES2 GRMOD GRMOD- \ + HYPCAT HYPCAT- MODRING NASRING NASRING- \ + SORTPAK ZMOD PROPFUN2 \ + KTVLOGIC OAMONS BYTE SYSINT SYSNNI axiom_algebra_layer_6_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_6)) diff --git a/src/algebra/boolean.spad.pamphlet b/src/algebra/boolean.spad.pamphlet index 15071693..9be8f2a3 100644 --- a/src/algebra/boolean.spad.pamphlet +++ b/src/algebra/boolean.spad.pamphlet @@ -246,6 +246,81 @@ PropositionalFormula(T: SetCategory): Public == Private where @ +<<package PROPFUN1 PropositionalFormulaFunctions1>>= +)abbrev package PROPFUN1 PropositionalFormulaFunctions1 +++ Author: Gabriel Dos Reis +++ Date Created: April 03, 2010 +++ Date Last Modified: April 03, 2010 +++ Description: +++ This package collects unary functions operating on propositional +++ formulae. +PropositionalFormulaFunctions1(T): Public == Private where + T: SetCategory + Public == Type with + dual: PropositionalFormula T -> PropositionalFormula T + ++ \spad{dual f} returns the dual of the proposition \spad{f}. + terms: PropositionalFormula T -> Set T + ++ \spad{terms f} ++ returns the set of terms appearing in + ++ the formula \spad{f}. + Private == add + macro F == PropositionalFormula T + inline Pair(F,F) + dual f == + f = true$F => false$F + f = false$F => true$F + isTerm f case T => f + (f1 := isNot f) case F => not dual f1 + (f2 := isAnd f) case Pair(F,F) => + disjunction(dual first f2, dual second f2) + (f2 := isOr f) case Pair(F,F) => + conjunction(dual first f2, dual second f2) + error "formula contains `equiv' or `implies'" + terms f == + (t := isTerm f) case T => { t } + (f1 := isNot f) case F => terms f1 + (f2 := isAnd f) case Pair(F,F) => + union(terms first f2, terms second f2) + (f2 := isOr f) case Pair(F,F) => + union(terms first f2, terms second f2) + empty()$Set(T) +@ + +<<package PROPFUN2 PropositionalFormulaFunctions2>>= +)abbrev package PROPFUN2 PropositionalFormulaFunctions2 +++ Author: Gabriel Dos Reis +++ Date Created: April 03, 2010 +++ Date Last Modified: April 03, 2010 +++ Description: +++ This package collects binary functions operating on propositional +++ formulae. +PropositionalFormulaFunctions2(S,T): Public == Private where + S: SetCategory + T: SetCategory + Public == Type with + map: (S -> T, PropositionalFormula S) -> PropositionalFormula T + ++ \spad{map(f,x)} returns a propositional formula where + ++ all terms in \spad{x} have been replaced by the result + ++ of applying the function \spad{f} to them. + Private == add + macro FS == PropositionalFormula S + macro FT == PropositionalFormula T + map(f,x) == + x = true$FS => true$FT + x = false$FS => false$FT + (t := isTerm x) case S => f(t)::FT + (f1 := isNot x) case FS => not map(f,f1) + (f2 := isAnd x) case Pair(FS,FS) => + conjunction(map(f,first f2), map(f,second f2)) + (f2 := isOr x) case Pair(FS,FS) => + disjunction(map(f,first f2), map(f,second f2)) + (f2 := isImplies x) case Pair(FS,FS) => + implies(map(f,first f2), map(f,second f2)) + (f2 := isEquiv x) case Pair(FS,FS) => + equiv(map(f,first f2), map(f,second f2)) + error "invalid propositional formula" + +@ + \section{domain REF Reference} <<domain REF Reference>>= )abbrev domain REF Reference @@ -532,7 +607,7 @@ KleeneTrivalentLogic(): Public == Private where <<license>>= --Copyright (c) 1991-2002, The Numerical Algorithms Group Ltd. --All rights reserved. ---Copyright (C) 2007-2009, Gabriel Dos Reis. +--Copyright (C) 2007-2010, Gabriel Dos Reis. --All rights reserved. -- --Redistribution and use in source and binary forms, with or without @@ -571,8 +646,12 @@ KleeneTrivalentLogic(): Public == Private where <<domain BOOLEAN Boolean>> <<domain IBITS IndexedBits>> <<domain BITS Bits>> + <<category PROPLOG PropositionalLogic>> <<domain PROPFRML PropositionalFormula>> +<<package PROPFUN1 PropositionalFormulaFunctions1>> +<<package PROPFUN2 PropositionalFormulaFunctions2>> + <<domain KTVLOGIC KleeneTrivalentLogic>> @ diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 8c11e2ea..c23e3ecf 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2267652 . 3479296388) +(2268440 . 3479376211) (-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."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . 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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4441 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4437 . T) (-4442 . T) (-4436 . T)) +((-4444 . T) (-4442 . T) (-4441 . T) ((-4449 "*") . T) (-4440 . T) (-4445 . T) (-4439 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -1666) +(-32 R -1668) ((|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 -1044) (QUOTE (-569))))) +((|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (-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 -4444))) +((|HasAttribute| |#1| (QUOTE -4447))) (-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}."))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . 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"))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . 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 -1666 UP UPUP -3283) +(-40 -1668 UP UPUP -2520) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2774 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2774 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2774 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) -(-41 R -1666) +((-4440 |has| (-412 |#2|) (-367)) (-4445 |has| (-412 |#2|) (-367)) (-4439 |has| (-412 |#2|) (-367)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2776 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2776 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2776 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2776 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +(-41 R -1668) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -435) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -435) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-310)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) +((-4444 |has| |#1| (-561)) (-4442 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-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."))) -((-4444 . T) (-4445 . T)) -((-2774 (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|))))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|))))))) +((-4447 . T) (-4448 . T)) +((-2776 (-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|))))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-367)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| $ (QUOTE (-1057))) (|HasCategory| $ (LIST (QUOTE -1046) (QUOTE (-569))))) (-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}."))) -((-4441 . T)) +((-4444 . 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 -1666) +(-54 |Base| R -1668) ((|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"))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . 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}"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-61 -3570) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-61 -3573) ((|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 -3570) +(-62 -3573) ((|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 -3570) +(-63 -3573) ((|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 -3570) +(-64 -3573) ((|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 -3570) +(-65 -3573) ((|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 -3570) +(-66 -3573) ((|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 -3570) +(-67 -3573) ((|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 -3570) +(-68 -3573) ((|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 -3570) +(-69 -3573) ((|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 -3570) +(-70 -3573) ((|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 -3570) +(-71 -3573) ((|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 -3570) +(-72 -3573) ((|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 -3570) +(-73 -3573) ((|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 -3570) +(-74 -3573) ((|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 -3570) +(-77 -3573) ((|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 -3570) +(-78 -3573) ((|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 -3570) +(-79 -3573) ((|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 -3570) +(-80 -3573) ((|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 -3570) +(-81 -3573) ((|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 -3570) +(-82 -3573) ((|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 -3570) +(-83 -3573) ((|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 -3570) +(-84 -3573) ((|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 -3570) +(-85 -3573) ((|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 -3570) +(-86 -3573) ((|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 -3570) +(-87 -3573) ((|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 -3570) +(-88 -3573) ((|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 -3570) +(-89 -3573) ((|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 (-367)))) (-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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-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\"."))) -((-4444 . T)) +((-4447 . 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."))) -((-4444 . T) ((-4446 "*") . T) (-4445 . T) (-4441 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4442 . T) (-4436 . T) (-4435 . T) (-4434 . T) (-4433 . T) (-4432 . T) (-4440 . T) (-4443 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4431 . T)) +((-4447 . T) ((-4449 "*") . T) (-4448 . T) (-4444 . T) (-4442 . T) (-4441 . T) (-4440 . T) (-4445 . T) (-4439 . T) (-4438 . T) (-4437 . T) (-4436 . T) (-4435 . T) (-4443 . T) (-4446 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4434 . 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}."))) -((-4441 . T)) +((-4444 . 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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-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 (-4446 "*")))) +((|HasAttribute| |#1| (QUOTE (-4449 "*")))) (-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"))) -((-4444 . T)) +((-4447 . 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."))) -((-4445 . T)) +((-4448 . 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1030))) (|HasCategory| (-569) (QUOTE (-825))) (-2776 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1160))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|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}"))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1108))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1108))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) (-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}"))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -(-115 -1666 UP) +(-115 -1668 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-915))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-116 |#1|) (QUOTE (-1028))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-2774 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-1158))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-915))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-116 |#1|) (QUOTE (-1030))) (|HasCategory| (-116 |#1|) (QUOTE (-825))) (-2776 (|HasCategory| (-116 |#1|) (QUOTE (-825))) (|HasCategory| (-116 |#1|) (QUOTE (-855)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-1160))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-116 |#1|) (QUOTE (-234))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -519) (QUOTE (-1185)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-310))) (|HasCategory| (-116 |#1|) (QUOTE (-550))) (|HasCategory| (-116 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-915)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4445))) +((|HasAttribute| |#1| (QUOTE -4448))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -414,15 +414,15 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,v,r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|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."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-2774 (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-129) (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106)))) (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-129) (QUOTE (-1106))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1108))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-2776 (-12 (|HasCategory| (-129) (QUOTE (-1108))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-129) (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1108)))) (|HasCategory| (-129) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-129) (QUOTE (-1108))) (|HasCategory| (-129) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-129) (QUOTE (-1108))) (|HasCategory| (-129) (LIST (QUOTE -312) (QUOTE (-129)))))) (-129) ((|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 @@ -466,13 +466,13 @@ NIL NIL (-134) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0, 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-4446 "*") . T)) +(((-4449 "*") . T)) NIL -(-135 |minix| -2406 S T$) +(-135 |minix| -2409 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2406 R) +(-136 |minix| -2409 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -494,8 +494,8 @@ NIL NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4444 . T) (-4434 . T) (-4445 . T)) -((-2774 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4447 . T) (-4437 . T) (-4448 . T)) +((-2776 (-12 (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-372))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{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 @@ -510,7 +510,7 @@ NIL NIL (-145) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4441 . T)) +((-4444 . T)) NIL (-146 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -518,9 +518,9 @@ NIL NIL (-147) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4441 . T)) +((-4444 . T)) NIL -(-148 -1666 UP UPUP) +(-148 -1668 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 @@ -531,14 +531,14 @@ NIL (-150 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasAttribute| |#1| (QUOTE -4444))) +((|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasAttribute| |#1| (QUOTE -4447))) (-151 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-152 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,[i1,i2,...,iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,[i1,i2,...,iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4439 . T) (-4438 . T) (-4441 . T)) +((-4442 . T) (-4441 . T) (-4444 . T)) NIL (-153) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -560,7 +560,7 @@ 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 -(-158 R -1666) +(-158 R -1668) ((|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 @@ -591,10 +591,10 @@ NIL (-165 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1008))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4440)) (|HasAttribute| |#2| (QUOTE -4443)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561)))) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1010))) (|HasCategory| |#2| (QUOTE (-1210))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4443)) (|HasAttribute| |#2| (QUOTE -4446)) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x, r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4437 -2774 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4440 |has| |#1| (-6 -4440)) (-4443 |has| |#1| (-6 -4443)) (-3098 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 -2776 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4443 |has| |#1| (-6 -4443)) (-4446 |has| |#1| (-6 -4446)) (-3101 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -610,8 +610,8 @@ NIL NIL (-170 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}."))) -((-4437 -2774 (|has| |#1| (-561)) (-12 (|has| |#1| (-310)) (|has| |#1| (-915)))) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4440 |has| |#1| (-6 -4440)) (-4443 |has| |#1| (-6 -4443)) (-3098 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-234))) (-12 (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-372)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-833)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-1028)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-1208)))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| 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(|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185))))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-353))))) (-171 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 @@ -622,7 +622,7 @@ NIL NIL (-173) ((|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."))) -(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-174) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -630,7 +630,7 @@ NIL NIL (-175 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4446 "*") . T) (-4437 . T) (-4442 . T) (-4436 . T) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") . T) (-4440 . T) (-4445 . T) (-4439 . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-176) ((|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}."))) @@ -684,7 +684,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-189 R -1666) +(-189 R -1668) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -792,23 +792,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,start,end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-216 -1666 UP UPUP R) +(-216 -1668 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 -(-217 -1666 FP) +(-217 -1668 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 (-218) ((|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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1030))) (|HasCategory| (-569) (QUOTE (-825))) (-2776 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1160))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-219) ((|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-220 R -1666) +(-220 R -1668) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -822,19 +822,19 @@ NIL NIL (-223 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-224 |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}."))) -((-4441 . T)) +((-4444 . T)) NIL -(-225 R -1666) +(-225 R -1668) ((|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 (-226) ((|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}."))) -((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-3091 . T) (-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-227) ((|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)}.}"))) @@ -842,23 +842,23 @@ NIL NIL (-228 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}"))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4449 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-229 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 (-230 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."))) -((-4445 . T)) +((-4448 . T)) NIL (-231 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234)))) (-232 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x, deriv, n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x, deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4441 . T)) +((-4444 . T)) NIL (-233 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -866,36 +866,36 @@ NIL NIL (-234) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x, n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4441 . T)) +((-4444 . T)) NIL (-235 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4444))) +((|HasAttribute| |#1| (QUOTE -4447))) (-236 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}."))) -((-4445 . T)) +((-4448 . T)) NIL (-237) ((|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 -(-238 S -2406 R) +(-238 S -2409 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4441)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (QUOTE (-1106)))) -(-239 -2406 R) +((|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (QUOTE (-853))) (|HasAttribute| |#3| (QUOTE -4444)) (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1057))) (|HasCategory| |#3| (QUOTE (-1108)))) +(-239 -2409 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4438 |has| |#2| (-1055)) (-4439 |has| |#2| (-1055)) (-4441 |has| |#2| (-6 -4441)) ((-4446 "*") |has| |#2| (-173)) (-4444 . T)) +((-4441 |has| |#2| (-1057)) (-4442 |has| |#2| (-1057)) (-4444 |has| |#2| (-6 -4444)) ((-4449 "*") |has| |#2| (-173)) (-4447 . T)) NIL -(-240 -2406 A B) +(-240 -2409 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 -(-241 -2406 R) +(-241 -2409 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."))) -((-4438 |has| |#2| (-1055)) (-4439 |has| |#2| (-1055)) (-4441 |has| |#2| (-6 -4441)) ((-4446 "*") |has| |#2| (-173)) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (-2774 (-12 (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-1106)))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1055)))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) 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(((|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 @@ -906,7 +906,7 @@ NIL NIL (-244) ((|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}."))) -((-4437 . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-245 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."))) @@ -914,16 +914,16 @@ NIL NIL (-246 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}"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-247 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 (-248 |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"))) -(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4449 "*") |has| |#2| (-173)) (-4440 |has| |#2| (-561)) (-4445 |has| |#2| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-249) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE (-569))))) (-12 (|HasCategory| |#3| (QUOTE (-1057))) (|HasCategory| |#3| (LIST (QUOTE -906) (QUOTE (-1185)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#3| (QUOTE (-1108))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (-254 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#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 (-234)))) (-255 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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL (-256 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}."))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL (-257) ((|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."))) @@ -994,8 +994,8 @@ NIL NIL (-266 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"))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#3| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-267 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v, n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s, n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1040,11 +1040,11 @@ 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 -(-278 R -1666) +(-278 R -1668) ((|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 -(-279 R -1666) +(-279 R -1668) ((|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 @@ -1067,10 +1067,10 @@ NIL (-284 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 (-855))) (|HasCategory| |#2| (QUOTE (-1106)))) +((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108)))) (-285 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}."))) -((-4445 . T)) +((-4448 . T)) NIL (-286 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}."))) @@ -1091,18 +1091,18 @@ NIL (-290 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 -4445))) +((|HasAttribute| |#1| (QUOTE -4448))) (-291 |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 -(-292 S R |Mod| -3440 -2126 |exactQuo|) +(-292 S R |Mod| -1538 -4198 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-293) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4437 . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-294) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "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"))) @@ -1118,21 +1118,21 @@ NIL NIL (-297 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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-299) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-300 -1666 S) +(-300 -1668 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 -(-301 E -1666) +(-301 E -1668) ((|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 @@ -1147,7 +1147,7 @@ NIL (-304 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 -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1055)))) +((|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1057)))) (-305) ((|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 @@ -1170,7 +1170,7 @@ NIL NIL (-310) ((|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|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-311 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1180,7 +1180,7 @@ 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 -(-313 -1666) +(-313 -1668) ((|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 @@ -1194,8 +1194,8 @@ NIL NIL (-316 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))}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1028))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-2774 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-1158))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-234))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -312) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (LIST (QUOTE -289) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1259) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-310))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-855))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))) (-2774 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1259 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-1030))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (-2776 (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-825))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-855)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-1160))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-234))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -519) (QUOTE (-1185)) (LIST (QUOTE -1261) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -312) (LIST (QUOTE -1261) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (LIST (QUOTE -289) (LIST (QUOTE -1261) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1261) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-310))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-550))) (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-855))) (-12 (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))) (-2776 (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1261 |#1| |#2| |#3| |#4|) (QUOTE (-915))) (|HasCategory| $ (QUOTE (-145)))))) (-317 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 @@ -1206,9 +1206,9 @@ NIL NIL (-319 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."))) -((-4441 -2774 (-1756 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (-12 (|has| |#1| (-561)) (-2774 (-1756 (|has| |#1| (-1055)) (|has| |#1| (-644 (-569)))) (|has| |#1| (-1055)) (|has| |#1| (-478)))) (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) ((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4442 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(|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 @@ -1218,8 +1218,8 @@ NIL NIL (-322 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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . 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(|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 @@ -1230,7 +1230,7 @@ NIL NIL (-325 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."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-797)))) (-326 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1246,19 +1246,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) (-329 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-330 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."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-331 S -1666) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-331 S -1668) ((|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 (-372)))) -(-332 -1666) +(-332 -1668) ((|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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-333) ((|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."))) @@ -1280,54 +1280,54 @@ 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 -(-338 S -1666 UP UPUP R) +(-338 S -1668 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 -(-339 -1666 UP UPUP R) +(-339 -1668 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 -(-340 -1666 UP UPUP R) +(-340 -1668 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-341 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|)))) (-342 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-343 |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.}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -1044) (QUOTE (-383)))) (|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#3| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#3| (LIST (QUOTE -1046) (QUOTE (-383)))) (|HasCategory| $ (QUOTE (-1057))) (|HasCategory| $ (LIST (QUOTE -1046) (QUOTE (-569))))) (-344 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 -(-345 S -1666 UP UPUP) +(-345 S -1668 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 (-372))) (|HasCategory| |#2| (QUOTE (-367)))) -(-346 -1666 UP UPUP) +(-346 -1668 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."))) -((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 |has| (-412 |#2|) (-367)) (-4445 |has| (-412 |#2|) (-367)) (-4439 |has| (-412 |#2|) (-367)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-347 |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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-348 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-349 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-350 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 @@ -1342,33 +1342,33 @@ NIL NIL (-353) ((|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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-354 R UP -1666) +(-354 R UP -1668) ((|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 (-355 |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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-356 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-357 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-358 |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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| (-916 |#1|) (QUOTE (-145))) (|HasCategory| (-916 |#1|) (QUOTE (-372)))) (|HasCategory| (-916 |#1|) (QUOTE (-147))) (|HasCategory| (-916 |#1|) (QUOTE (-372))) (|HasCategory| (-916 |#1|) (QUOTE (-145)))) (-359 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) -(-360 -1666 GF) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +(-360 -1668 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 @@ -1376,21 +1376,21 @@ 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 -(-362 -1666 FP FPP) +(-362 -1668 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 (-363 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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-145)))) (-364 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 (-365 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4441 . T)) +((-4444 . T)) NIL (-366 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1398,7 +1398,7 @@ NIL NIL (-367) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-368 |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."))) @@ -1414,7 +1414,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-561)))) (-371 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) +((-4444 |has| |#1| (-561)) (-4442 . T) (-4441 . T)) NIL (-372) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1426,7 +1426,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-367)))) (-374 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| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL (-375 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1435,14 +1435,14 @@ NIL (-376 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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106)))) +((|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108)))) (-377 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4444 . T)) +((-4447 . T)) NIL (-378 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4439 . T) (-4438 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4442 . T) (-4441 . T)) NIL (-379 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."))) @@ -1454,7 +1454,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-381 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}"))) -((-4441 . T)) +((-4444 . T)) NIL (-382 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1462,7 +1462,7 @@ NIL NIL (-383) ((|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}."))) -((-4427 . T) (-4435 . T) (-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4430 . T) (-4438 . T) (-3091 . T) (-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-384 |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}."))) @@ -1470,11 +1470,11 @@ NIL NIL (-385 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}"))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-386 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}."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL (-387) ((|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}."))) @@ -1486,7 +1486,7 @@ NIL NIL (-389 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."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-173)))) (-390 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1498,7 +1498,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-392) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-393) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1510,13 +1510,13 @@ NIL NIL (-395 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL (-396) ((|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 -(-397 -1666 UP UPUP R) +(-397 -1668 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 @@ -1540,11 +1540,11 @@ 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 -(-403 -3570 |returnType| -3936 |symbols|) +(-403 -3573 |returnType| -3939 |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 -(-404 -1666 UP) +(-404 -1668 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f, n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1558,15 +1558,15 @@ NIL NIL (-407) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-408 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4427)) (|HasAttribute| |#1| (QUOTE -4435))) +((|HasAttribute| |#1| (QUOTE -4430)) (|HasAttribute| |#1| (QUOTE -4438))) (-409) ((|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\"."))) -((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-3091 . T) (-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-410 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."))) @@ -1578,20 +1578,20 @@ NIL NIL (-412 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."))) -((-4431 -12 (|has| |#1| (-6 -4442)) (|has| |#1| (-457)) (|has| |#1| (-6 -4431))) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-825))) (-2774 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4442)) (|HasAttribute| |#1| (QUOTE -4431)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4434 -12 (|has| |#1| (-6 -4445)) (|has| |#1| (-457)) (|has| |#1| (-6 -4434))) (-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (QUOTE (-825))) (-2776 (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-855)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1160))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-833)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-550))) (-12 (|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4434)) (|HasCategory| |#1| (QUOTE (-457)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-413 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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 (-414 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."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL (-415 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 -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569))))) +((|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-416 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 @@ -1600,14 +1600,14 @@ 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 -(-418 R -1666 UP A) +(-418 R -1668 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)}."))) -((-4441 . T)) +((-4444 . T)) NIL -(-419 R -1666 UP A |ibasis|) +(-419 R -1668 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|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (LIST (QUOTE -1044) (|devaluate| |#2|)))) +((|HasCategory| |#4| (LIST (QUOTE -1046) (|devaluate| |#2|)))) (-420 AR R AS S) ((|constructor| (NIL "FramedNonAssociativeAlgebraFunctions2 implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1618,12 +1618,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-422 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{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."))) -((-4441 |has| |#1| (-561)) (-4439 . T) (-4438 . T)) +((-4444 |has| |#1| (-561)) (-4442 . T) (-4441 . T)) NIL (-423 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."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1227))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1227)))) (|HasCategory| |#1| (QUOTE (-1028))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -312) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -289) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1229))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-1229)))) (|HasCategory| |#1| (QUOTE (-1030))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-457)))) (-424 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 @@ -1650,37 +1650,37 @@ NIL ((|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-430 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4444 . T) (-4434 . T) (-4445 . T)) +((-4447 . T) (-4437 . T) (-4448 . T)) NIL -(-431 R -1666) +(-431 R -1668) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-432 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4431 -12 (|has| |#1| (-6 -4431)) (|has| |#2| (-6 -4431))) (-4438 . T) (-4439 . T) (-4441 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4431)) (|HasAttribute| |#2| (QUOTE -4431)))) -(-433 R -1666) +((-4434 -12 (|has| |#1| (-6 -4434)) (|has| |#2| (-6 -4434))) (-4441 . T) (-4442 . T) (-4444 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4434)) (|HasAttribute| |#2| (QUOTE -4434)))) +(-433 R -1668) ((|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 (-434 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 -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1118))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) +((|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-1120))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (-435 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}."))) -((-4441 -2774 (|has| |#1| (-1055)) (|has| |#1| (-478))) (-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) ((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-561)) (-4436 |has| |#1| (-561))) +((-4444 -2776 (|has| |#1| (-1057)) (|has| |#1| (-478))) (-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) ((-4449 "*") |has| |#1| (-561)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-561)) (-4439 |has| |#1| (-561))) NIL -(-436 R -1666) +(-436 R -1668) ((|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 -(-437 R -1666) +(-437 R -1668) ((|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)))) -(-438 R -1666) +(-438 R -1668) ((|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 @@ -1688,10 +1688,10 @@ 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 -(-440 R -1666 UP) +(-440 R -1668 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 -1044) (QUOTE (-48))))) +((|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-48))))) (-441) ((|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 @@ -1720,7 +1720,7 @@ 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 -(-448 R UP -1666) +(-448 R UP -1668) ((|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 @@ -1758,16 +1758,16 @@ NIL NIL (-457) ((|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}."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-458 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"))) -((-4441 |has| (-412 (-958 |#1|)) (-561)) (-4439 . T) (-4438 . T)) +((-4444 |has| (-412 (-958 |#1|)) (-561)) (-4442 . T) (-4441 . T)) ((|HasCategory| (-412 (-958 |#1|)) (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-412 (-958 |#1|)) (QUOTE (-561)))) (-459 |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"))) -(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4449 "*") |has| |#2| (-173)) (-4440 |has| |#2| (-561)) (-4445 |has| |#2| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-460 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 @@ -1794,7 +1794,7 @@ NIL NIL (-466 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL (-467 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1802,8 +1802,8 @@ NIL NIL (-468 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-469 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 @@ -1832,7 +1832,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-476 |lv| -1666 R) +(-476 |lv| -1668 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1842,23 +1842,23 @@ NIL NIL (-478) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4441 . T)) +((-4444 . T)) NIL (-479 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2776 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1210))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3579) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1185))))) (|HasSignature| |#1| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#1|))))))) (-480 |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."))) -((-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106)))) +((-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108)))) (-481 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)}"))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) (-482) ((|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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-483) ((|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'."))) @@ -1866,29 +1866,29 @@ NIL NIL (-484 |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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-485) ((|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 (-486 |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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(LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-798))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-853))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))))) (|HasCategory| (-569) (QUOTE (-855))) (-12 (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (QUOTE (-1057)))) (-12 (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185))))) (-2776 (|HasCategory| |#2| (QUOTE (-1057))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-1108)))) (|HasAttribute| |#2| (QUOTE -4444)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))))) (-488) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-489 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-490 -1666 UP UPUP R) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-490 -1668 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1898,12 +1898,12 @@ NIL NIL (-492) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1030))) (|HasCategory| (-569) (QUOTE (-825))) (-2776 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1160))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) (-493 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 -4444)) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) +((|HasAttribute| |#1| (QUOTE -4447)) (|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (-494 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1924,34 +1924,34 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-499 -1666 UP |AlExt| |AlPol|) +(-499 -1668 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-500) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| $ (QUOTE (-1055))) (|HasCategory| $ (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| $ (QUOTE (-1057))) (|HasCategory| $ (LIST (QUOTE -1046) (QUOTE (-569))))) (-501 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-502 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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-503 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 -(-504 R UP -1666) +(-504 R UP -1668) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-505 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1106))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| (-112) (QUOTE (-1108))) (|HasCategory| (-112) (LIST (QUOTE -312) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-112) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-112) (QUOTE (-1108))) (|HasCategory| (-112) (LIST (QUOTE -618) (QUOTE (-867))))) (-506 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 @@ -1964,10 +1964,10 @@ 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 -(-509 -1666 |Expon| |VarSet| |DPoly|) +(-509 -1668 |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 -619) (QUOTE (-1183))))) +((|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-1185))))) (-510 |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 @@ -2014,36 +2014,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-797)))) (-521 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}"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-522) ((|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 (-523 |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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((-2774 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((-2776 (|HasCategory| (-586 |#1|) (QUOTE (-145))) (|HasCategory| (-586 |#1|) (QUOTE (-372)))) (|HasCategory| (-586 |#1|) (QUOTE (-147))) (|HasCategory| (-586 |#1|) (QUOTE (-372))) (|HasCategory| (-586 |#1|) (QUOTE (-145)))) (-524 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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-525 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."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-526 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 -4445))) +((|HasAttribute| |#3| (QUOTE -4448))) (-527 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 -4445))) +((|HasAttribute| |#7| (QUOTE -4448))) (-528 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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4449 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-529) ((|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 @@ -2076,7 +2076,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-537 K -1666 |Par|) +(-537 K -1668 |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 @@ -2100,7 +2100,7 @@ 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 -(-543 K -1666 |Par|) +(-543 K -1668 |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 @@ -2130,7 +2130,7 @@ NIL NIL (-550) ((|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."))) -((-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4445 . T) (-4446 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-551) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2150,13 +2150,13 @@ NIL NIL (-555 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) -(-556 R -1666) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +(-556 R -1668) ((|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 -(-557 R0 -1666 UP UPUP R) +(-557 R0 -1668 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 @@ -2166,7 +2166,7 @@ NIL NIL (-559 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."))) -((-3088 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-3091 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-560 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."))) @@ -2174,9 +2174,9 @@ NIL NIL (-561) ((|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."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-562 R -1666) +(-562 R -1668) ((|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 @@ -2188,7 +2188,7 @@ 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 -(-565 R -1666 L) +(-565 R -1668 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 -661) (|devaluate| |#2|)))) @@ -2196,31 +2196,31 @@ NIL ((|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 -(-567 -1666 UP UPUP R) +(-567 -1668 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 -(-568 -1666 UP) +(-568 -1668 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 (-569) ((|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."))) -((-4426 . T) (-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4429 . T) (-4435 . T) (-4439 . T) (-4434 . T) (-4445 . T) (-4446 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-570) ((|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 -(-571 R -1666 L) +(-571 R -1668 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 -661) (|devaluate| |#2|)))) -(-572 R -1666) +(-572 R -1668) ((|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 -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-634))))) -(-573 -1666 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1147)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-634))))) +(-573 -1668 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 @@ -2228,27 +2228,27 @@ 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 -(-575 -1666) +(-575 -1668) ((|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 (-576 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."))) -((-3088 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-3091 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-577) ((|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 -(-578 R -1666) +(-578 R -1668) ((|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 -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-287))) (|HasCategory| |#2| (QUOTE (-634))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-287)))) (|HasCategory| |#1| (QUOTE (-561)))) -(-579 -1666 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-287))) (|HasCategory| |#2| (QUOTE (-634))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185))))) (-12 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-287)))) (|HasCategory| |#1| (QUOTE (-561)))) +(-579 -1668 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 -(-580 R -1666) +(-580 R -1668) ((|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 @@ -2270,21 +2270,21 @@ NIL NIL (-585 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-586 |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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) (-587) ((|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 -(-588 R -1666) +(-588 R -1668) ((|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 -(-589 E -1666) +(-589 E -1668) ((|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 @@ -2292,10 +2292,10 @@ 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 -(-591 -1666) +(-591 -1668) ((|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}."))) -((-4439 . T) (-4438 . T)) -((|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-1183))))) +((-4442 . T) (-4441 . T)) +((|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-1185))))) (-592 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 @@ -2322,19 +2322,19 @@ NIL NIL (-598 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-2774 (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-2776 (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1108)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (-599 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 (-600 |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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|)))) (|HasCategory| (-569) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569)))))) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-569)) (|devaluate| |#1|)))) (|HasCategory| (-569) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-569)))))) (-601 |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|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-4446 "*") |has| |#1| (-561)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-561)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-561)))) (-602) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|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"))) @@ -2348,7 +2348,7 @@ 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 -(-605 R -1666 FG) +(-605 R -1668 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 @@ -2358,12 +2358,12 @@ NIL NIL (-607 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1057))) (-12 (|HasCategory| |#1| (QUOTE (-1010))) (|HasCategory| |#1| (QUOTE (-1057)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-608 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 -4445)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4444)) (|HasCategory| |#3| (QUOTE (-1106)))) +((|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#2| (QUOTE (-855))) (|HasAttribute| |#1| (QUOTE -4447)) (|HasCategory| |#3| (QUOTE (-1108)))) (-609 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2378,19 +2378,19 @@ NIL NIL (-612 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4441 -2774 (-1756 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4439 . T) (-4438 . T)) -((-2774 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4444 -2776 (-1759 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4442 . T) (-4441 . T)) +((-2776 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-613 |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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (QUOTE (-1167))) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| (-1167) (QUOTE (-855))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) (-614 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 (-615 |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}."))) -((-4445 . T)) +((-4448 . T)) NIL (-616 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"))) @@ -2408,7 +2408,7 @@ NIL ((|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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-620 -1666 UP) +(-620 -1668 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2430,20 +2430,20 @@ NIL NIL (-625 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."))) -((-4441 . T)) +((-4444 . T)) NIL (-626 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}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-853)))) -(-627 R -1666) +(-627 R -1668) ((|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 (-628 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"))) -((-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4437 . T) (-4441 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4442 . T) (-4441 . T) ((-4449 "*") . T) (-4440 . T) (-4444 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (-629 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 @@ -2458,7 +2458,7 @@ NIL NIL (-632 |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}}."))) -((-4441 . T)) +((-4444 . T)) NIL (-633 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}}."))) @@ -2468,30 +2468,30 @@ NIL ((|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 -(-635 R -1666) +(-635 R -1668) ((|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 -(-636 |lv| -1666) +(-636 |lv| -1668) ((|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 (-637) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-1165) (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 (-52))) (QUOTE (-1106)))) +((-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (QUOTE (-1167))) (LIST (QUOTE |:|) (QUOTE -2216) (QUOTE (-52))))))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-52) (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-1167) (QUOTE (-855))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 (-52))) (QUOTE (-1108)))) (-638 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) (-639 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4439 . T) (-4438 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4442 . T) (-4441 . T)) NIL (-640 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4441 -2774 (-1756 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4439 . T) (-4438 . T)) -((-2774 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) +((-4444 -2776 (-1759 (|has| |#2| (-371 |#1|)) (|has| |#1| (-561))) (-12 (|has| |#2| (-422 |#1|)) (|has| |#1| (-561)))) (-4442 . T) (-4441 . T)) +((-2776 (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -422) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -371) (|devaluate| |#1|)))) (-641 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 @@ -2503,10 +2503,10 @@ NIL (-643 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 -((-1745 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) +((-1749 (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-367)))) (-644 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4441 . T)) +((-4444 . T)) NIL (-645 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-linear set if it is stable by dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{Module} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet,{} RightLinearSet."))) @@ -2526,8 +2526,8 @@ NIL NIL (-649 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-833))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-650 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2538,8 +2538,8 @@ NIL NIL (-652 S) ((|substitute| (($ |#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."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-653 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 @@ -2551,39 +2551,39 @@ NIL (-655 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4445))) +((|HasAttribute| |#1| (QUOTE -4448))) (-656 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-657 R -1666 L) +(-657 R -1668 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 (-658 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}}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-659 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-660 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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 (-367)))) (-661 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}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-662 -1666 UP) +(-662 -1668 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)))) -(-663 A -2222) +(-663 A -2673) ((|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}}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) (-664 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 @@ -2598,7 +2598,7 @@ NIL NIL (-667 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}."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) ((|HasCategory| |#1| (QUOTE (-796)))) (-668 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."))) @@ -2606,7 +2606,7 @@ NIL NIL (-669 |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) (-4439 . T) (-4438 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4442 . T) (-4441 . T)) ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-173)))) (-670 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}."))) @@ -2614,13 +2614,13 @@ NIL NIL (-671 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}."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-672 -1666) +(-672 -1668) ((|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 -(-673 -1666 |Row| |Col| M) +(-673 -1668 |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 @@ -2630,8 +2630,8 @@ NIL NIL (-675 |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."))) -((-4441 . T) (-4444 . T) (-4438 . T) (-4439 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561))) (-2774 (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +((-4444 . T) (-4447 . T) (-4441 . T) (-4442 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4449 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561))) (-2776 (|HasAttribute| |#2| (QUOTE (-4449 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) (-676) ((|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 @@ -2651,7 +2651,7 @@ NIL (-680 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 -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-681) ((|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 @@ -2695,10 +2695,10 @@ NIL (-691 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| (($ (|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 (-4446 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561)))) +((|HasAttribute| |#2| (QUOTE (-4449 "*"))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-561)))) (-692 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| (($ (|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"))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL (-693 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."))) @@ -2706,8 +2706,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561)))) (-694 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."))) -((-4444 . T) (-4445 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4446 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4447 . T) (-4448 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-310))) (|HasCategory| |#1| (QUOTE (-561))) (|HasAttribute| |#1| (QUOTE (-4449 "*"))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-695 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 @@ -2716,7 +2716,7 @@ NIL ((|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 -(-697 S -1666 FLAF FLAS) +(-697 S -1668 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,xlist,kl,ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,xlist,k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2726,11 +2726,11 @@ NIL NIL (-699) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4437 . T) (-4442 |has| (-704) (-367)) (-4436 |has| (-704) (-367)) (-3098 . T) (-4443 |has| (-704) (-6 -4443)) (-4440 |has| (-704) (-6 -4440)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-2774 (|HasCategory| (-704) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-234))) (-2774 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2774 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-704) (QUOTE (-1028))) (|HasCategory| (-704) (QUOTE (-1208))) (-12 (|HasCategory| (-704) (QUOTE (-1008))) (|HasCategory| (-704) (QUOTE (-1208)))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-1208)))) (|HasCategory| (-704) (QUOTE (-1066))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367)))) (-2774 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-561)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-561))) (|HasAttribute| (-704) (QUOTE -4443)) (|HasAttribute| (-704) (QUOTE -4440)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-145)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-353))))) +((-4440 . T) (-4445 |has| (-704) (-367)) (-4439 |has| (-704) (-367)) (-3101 . T) (-4446 |has| (-704) (-6 -4446)) (-4443 |has| (-704) (-6 -4443)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-704) (QUOTE (-147))) (|HasCategory| (-704) (QUOTE (-145))) (|HasCategory| (-704) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-372))) (|HasCategory| (-704) (QUOTE (-367))) (-2776 (|HasCategory| (-704) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-704) (QUOTE (-234))) (-2776 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (LIST (QUOTE -289) (QUOTE (-704)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -312) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE (-704)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-704) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-704) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (-2776 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-353)))) (|HasCategory| (-704) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-704) (QUOTE (-1030))) (|HasCategory| (-704) (QUOTE (-1210))) (-12 (|HasCategory| (-704) (QUOTE (-1010))) (|HasCategory| (-704) (QUOTE (-1210)))) (-2776 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (-2776 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-367))) (|HasCategory| (-704) (QUOTE (-915)))) (-12 (|HasCategory| (-704) (QUOTE (-353))) (|HasCategory| (-704) (QUOTE (-915))))) (|HasCategory| (-704) (QUOTE (-550))) (-12 (|HasCategory| (-704) (QUOTE (-1068))) (|HasCategory| (-704) (QUOTE (-1210)))) (|HasCategory| (-704) (QUOTE (-1068))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915))) (-2776 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-367)))) (-2776 (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-561)))) (-12 (|HasCategory| (-704) (QUOTE (-234))) (|HasCategory| (-704) (QUOTE (-367)))) (-12 (|HasCategory| (-704) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-704) (QUOTE (-367)))) (|HasCategory| (-704) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-704) (QUOTE (-561))) (|HasAttribute| (-704) (QUOTE -4446)) (|HasAttribute| (-704) (QUOTE -4443)) (-12 (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-145)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-704) (QUOTE (-310))) (|HasCategory| (-704) (QUOTE (-915)))) (|HasCategory| (-704) (QUOTE (-353))))) (-700 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,d,n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4445 . T)) +((-4448 . T)) NIL (-701 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}."))) @@ -2740,13 +2740,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-703 OV E -1666 PG) +(-703 OV E -1668 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL (-704) ((|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}"))) -((-3088 . T) (-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-3091 . T) (-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-705 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."))) @@ -2754,7 +2754,7 @@ NIL NIL (-706) ((|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}"))) -((-4443 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4446 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-707 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"))) @@ -2772,7 +2772,7 @@ NIL ((|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 -(-711 S -2830 I) +(-711 S -2832 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 @@ -2782,7 +2782,7 @@ NIL NIL (-713 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)}.}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL (-714 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}."))) @@ -2792,25 +2792,25 @@ NIL ((|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 -(-716 R |Mod| -3440 -2126 |exactQuo|) +(-716 R |Mod| -1538 -4198 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-717 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4440 |has| |#1| (-367)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1088) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4443 |has| |#1| (-367)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1090) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1160))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (QUOTE (-234))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-718 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-719 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) +((-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-720 R |Mod| -3440 -2126 |exactQuo|) +(-720 R |Mod| -1538 -4198 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4441 . T)) +((-4444 . T)) NIL (-721 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2818,11 +2818,11 @@ NIL NIL (-722 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL -(-723 -1666) +(-723 -1668) ((|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]]}."))) -((-4441 . T)) +((-4444 . T)) NIL (-724 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."))) @@ -2846,7 +2846,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-353))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-372)))) (-729 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."))) -((-4437 |has| |#1| (-367)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 |has| |#1| (-367)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-730 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."))) @@ -2856,7 +2856,7 @@ NIL ((|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 -(-732 -1666 UP) +(-732 -1668 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 @@ -2874,8 +2874,8 @@ NIL NIL (-736 |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."))) -(((-4446 "*") |has| |#2| (-173)) (-4437 |has| |#2| (-561)) (-4442 |has| |#2| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2774 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4449 "*") |has| |#2| (-173)) (-4440 |has| |#2| (-561)) (-4445 |has| |#2| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (-2776 (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-561)))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-869 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-737 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2890,16 +2890,16 @@ NIL NIL (-740 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) +((-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) (-4444 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-855)))) (-741 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4434 . T) (-4445 . T)) +((-4437 . T) (-4448 . T)) NIL (-742 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}."))) -((-4444 . T) (-4434 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-4447 . T) (-4437 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-743) ((|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 @@ -2910,7 +2910,7 @@ NIL NIL (-745 |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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL (-746 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"))) @@ -2926,7 +2926,7 @@ NIL NIL (-749 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}."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL (-750) ((|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}."))) @@ -3008,11 +3008,11 @@ NIL ((|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 -(-770 -1666) +(-770 -1668) ((|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 -(-771 P -1666) +(-771 P -1668) ((|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 @@ -3020,7 +3020,7 @@ NIL NIL NIL NIL -(-773 UP -1666) +(-773 UP -1668) ((|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 @@ -3034,9 +3034,9 @@ NIL NIL (-776) ((|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."))) -(((-4446 "*") . T)) +(((-4449 "*") . T)) NIL -(-777 R -1666) +(-777 R -1668) ((|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 @@ -3056,7 +3056,7 @@ NIL ((|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 -(-782 -1666 |ExtF| |SUEx| |ExtP| |n|) +(-782 -1668 |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 @@ -3070,28 +3070,28 @@ NIL NIL (-785 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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . 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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 (-787 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.")) 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(|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 -412) (QUOTE (-569)))))) (-789 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.}"))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL (-790 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 (-561))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-173)))) +((-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-1057))) (|HasCategory| |#1| (QUOTE (-173)))) (-791) ((|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 @@ -3135,28 +3135,28 @@ NIL (-801 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) +((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-372)))) (-802 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-803 -2774 R OS S) +(-803 -2776 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-804 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-2774 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1005 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (-2776 (|HasCategory| (-1007 |#1|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2776 (|HasCategory| (-1007 |#1|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| (-1007 |#1|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1007 |#1|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (-805) ((|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 -(-806 R -1666 L) +(-806 R -1668 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 -(-807 R -1666) +(-807 R -1668) ((|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 @@ -3164,7 +3164,7 @@ NIL ((|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 -(-809 R -1666) +(-809 R -1668) ((|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 @@ -3172,11 +3172,11 @@ NIL ((|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 -(-811 -1666 UP UPUP R) +(-811 -1668 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 -(-812 -1666 UP L LQ) +(-812 -1668 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 @@ -3184,41 +3184,41 @@ NIL ((|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 -(-814 -1666 UP L LQ) +(-814 -1668 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 -(-815 -1666 UP) +(-815 -1668 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 -(-816 -1666 L UP A LO) +(-816 -1668 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 -(-817 -1666 UP) +(-817 -1668 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)))) -(-818 -1666 LO) +(-818 -1668 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 -(-819 -1666 LODO) +(-819 -1668 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)) +((|HasCategory| |#1| (QUOTE (-915))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-823 (-1185)) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-823 (-1185)) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-823 (-1185)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-823 (-1185)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-823 (-1185)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) (-822 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4446 "*") |has| |#2| (-367)) (-4437 |has| |#2| (-367)) (-4442 |has| |#2| (-367)) (-4436 |has| |#2| (-367)) (-4441 . T) (-4439 . T) (-4438 . T)) +(((-4449 "*") |has| |#2| (-367)) (-4440 |has| |#2| (-367)) (-4445 |has| |#2| (-367)) (-4439 |has| |#2| (-367)) (-4444 . T) (-4442 . T) (-4441 . T)) ((|HasCategory| |#2| (QUOTE (-367)))) (-823 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}))."))) @@ -3230,7 +3230,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-855)))) (-825) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-826) ((|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}"))) @@ -3258,7 +3258,7 @@ NIL NIL (-832 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}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) ((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-234)))) (-833) ((|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."))) @@ -3270,7 +3270,7 @@ NIL NIL (-835 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4444 . T) (-4434 . T) (-4445 . T)) +((-4447 . T) (-4437 . T) (-4448 . T)) NIL (-836) ((|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."))) @@ -3282,8 +3282,8 @@ NIL NIL (-838 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."))) -((-4441 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4444 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2776 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (-2776 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) (-839 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 @@ -3294,7 +3294,7 @@ NIL NIL (-841 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) +((-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-842) ((|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)."))) @@ -3322,13 +3322,13 @@ NIL NIL (-848 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4441 |has| |#1| (-853))) -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2774 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (-2774 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) +((-4444 |has| |#1| (-853))) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-21))) (-2776 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-853)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (-2776 (|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-550)))) (-849) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-850 -2406 S) +(-850 -2409 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3342,7 +3342,7 @@ NIL NIL (-853) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4441 . T)) +((-4444 . T)) NIL (-854 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3358,20 +3358,20 @@ NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173)))) (-857 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL (-858 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 (-367))) (|HasCategory| |#1| (QUOTE (-561)))) -(-859 R |sigma| -3111) +(-859 R |sigma| -3117) ((|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."))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) -(-860 |x| R |sigma| -3111) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-367)))) +(-860 |x| R |sigma| -3117) ((|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}."))) -((-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-367)))) +((-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-367)))) (-861 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 @@ -3414,7 +3414,7 @@ NIL NIL (-871 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) +((-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) (-872 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,dd,ns,ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,dd,ns,ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3426,24 +3426,24 @@ NIL NIL (-874 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-875 |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)."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-876 |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)."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-875 |#1|) (QUOTE (-915))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-147))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-875 |#1|) (QUOTE (-1028))) (|HasCategory| (-875 |#1|) (QUOTE (-825))) (-2774 (|HasCategory| (-875 |#1|) (QUOTE (-825))) (|HasCategory| (-875 |#1|) (QUOTE (-855)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-1158))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-234))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -519) (QUOTE (-1183)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -875) (|devaluate| |#1|)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (QUOTE (-310))) (|HasCategory| (-875 |#1|) (QUOTE (-550))) (|HasCategory| (-875 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-875 |#1|) (QUOTE (-915))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-147))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-875 |#1|) (QUOTE (-1030))) (|HasCategory| (-875 |#1|) (QUOTE (-825))) (-2776 (|HasCategory| (-875 |#1|) (QUOTE (-825))) (|HasCategory| (-875 |#1|) (QUOTE (-855)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-1160))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| (-875 |#1|) (QUOTE (-234))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -519) (QUOTE (-1185)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -312) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (LIST (QUOTE -289) (LIST (QUOTE -875) (|devaluate| |#1|)) (LIST (QUOTE -875) (|devaluate| |#1|)))) (|HasCategory| (-875 |#1|) (QUOTE (-310))) (|HasCategory| (-875 |#1|) (QUOTE (-550))) (|HasCategory| (-875 |#1|) (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-875 |#1|) (QUOTE (-915)))) (|HasCategory| (-875 |#1|) (QUOTE (-145))))) (-877 |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)}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-825))) (-2774 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1158))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-825))) (-2776 (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855)))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1160))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -289) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-855))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-915)))) (|HasCategory| |#2| (QUOTE (-145))))) (-878 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 (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))))) (-879) ((|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 @@ -3503,7 +3503,7 @@ NIL (-893 |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 (-1745 (|HasCategory| |#2| (QUOTE (-1055)))) (-1745 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (-12 (|HasCategory| |#2| (QUOTE (-1055))) (-1745 (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183))))) +((-12 (-1749 (|HasCategory| |#2| (QUOTE (-1057)))) (-1749 (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185)))))) (-12 (|HasCategory| |#2| (QUOTE (-1057))) (-1749 (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185)))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185))))) (-894 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 @@ -3512,7 +3512,7 @@ NIL ((|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 -(-896 R -2830) +(-896 R -2832) ((|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 @@ -3536,7 +3536,7 @@ NIL ((|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 -(-902 UP -1666) +(-902 UP -1668) ((|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 @@ -3554,19 +3554,19 @@ NIL NIL (-906 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1, n1)..., sn, nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{D(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x, [s1,...,sn], [n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x, s, n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}.") (($ $ |#1|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4441 . T)) +((-4444 . T)) NIL (-907 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 (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (-908 |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 (-909 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p, el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4441 . T)) +((-4444 . T)) NIL (-910 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3574,8 +3574,8 @@ NIL NIL (-911 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4441 . T)) -((-2774 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) +((-4444 . T)) +((-2776 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-855)))) (-912 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 @@ -3590,13 +3590,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-915) ((|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}."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-916 |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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-372)))) -(-917 R0 -1666 UP UPUP R) +(-917 R0 -1668 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 @@ -3610,7 +3610,7 @@ NIL NIL (-920 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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-921 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."))) @@ -3624,7 +3624,7 @@ NIL ((|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 -(-924 -1666) +(-924 -1668) ((|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 @@ -3634,17 +3634,17 @@ NIL NIL (-926) ((|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| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL (-927) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4446 "*") . T)) +(((-4449 "*") . T)) NIL -(-928 -1666 P) +(-928 -1668 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-929 |xx| -1666) +(-929 |xx| -1668) ((|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 @@ -3668,7 +3668,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-935 R -1666) +(-935 R -1668) ((|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 @@ -3680,7 +3680,7 @@ NIL ((|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 -(-938 S R -1666) +(-938 S R -1668) ((|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 @@ -3700,11 +3700,11 @@ NIL ((|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 -892) (|devaluate| |#1|)))) -(-943 R -1666 -2830) +(-943 R -1668 -2832) ((|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 -(-944 -2830) +(-944 -2832) ((|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 @@ -3726,8 +3726,8 @@ NIL NIL (-949 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1057))) (-12 (|HasCategory| |#1| (QUOTE (-1010))) (|HasCategory| |#1| (QUOTE (-1057)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-950 |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 @@ -3747,12 +3747,12 @@ NIL (-954 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 (-915))) (|HasAttribute| |#2| (QUOTE -4442)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) +((|HasCategory| |#2| (QUOTE (-915))) (|HasAttribute| |#2| (QUOTE -4445)) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#4| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#4| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (-955 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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL -(-956 E V R P -1666) +(-956 E V R P -1668) ((|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 @@ -3762,9 +3762,9 @@ NIL NIL (-958 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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1183) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-959 E V R P -1666) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1185) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1185) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1185) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1185) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1185) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-959 E V R P -1668) ((|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 (-457)))) @@ -3786,13 +3786,13 @@ NIL NIL (-964 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"))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-965) ((|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 -(-966 -1666) +(-966 -1668) ((|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 @@ -3806,12 +3806,12 @@ NIL NIL (-969 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}"))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4442))) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4445))) (-970 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,b)} \\undocumented"))) -((-4441 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) +((-4444 -12 (|has| |#2| (-478)) (|has| |#1| (-478)))) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731))))) (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-372)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-478))) (|HasCategory| |#2| (QUOTE (-478)))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-798))) (|HasCategory| |#2| (QUOTE (-798))))) (-12 (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-731)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-855))))) (-971) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3820,1321 +3820,1329 @@ NIL ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\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.")) (|isTerm| (((|Maybe| |#1|) $) "\\spad{isTerm f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-973) +(-973 T$) +((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|terms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{terms f} \\spad{++} returns the set of terms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) +NIL +NIL +(-974 S T$) +((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all terms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) +NIL +NIL +(-975) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-974 S) +(-976 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL -(-975 R |polR|) +(-977 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 (-457)))) -(-976) +(-978) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-977) +(-979) ((|constructor| (NIL "\\indented{1}{Partition is an OrderedCancellationAbelianMonoid which is used} as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|Integer|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{powers(li)} returns a list of 2-element lists. For each 2-element list,{} the first element is an entry of \\spad{li} and the second element is the multiplicity with which the first element occurs in \\spad{li}. There is a 2-element list for each value occurring in \\spad{l}.")) (|partition| (($ (|List| (|Integer|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-978 S |Coef| |Expon| |Var|) +(-980 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 -(-979 |Coef| |Expon| |Var|) +(-981 |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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-980) +(-982) ((|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 -(-981 S R E |VarSet| P) +(-983 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 (-561)))) -(-982 R E |VarSet| P) +(-984 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."))) -((-4444 . T)) +((-4447 . T)) NIL -(-983 R E V P) +(-985 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 (-147))) (|HasCategory| |#1| (QUOTE (-310)))) (|HasCategory| |#1| (QUOTE (-457)))) -(-984 K) +(-986 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 -(-985 |VarSet| E RC P) +(-987 |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 -(-986 R) +(-988 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}."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-987 R1 R2) +(-989 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-988 R) +(-990 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 -(-989 K) +(-991 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 -(-990 R E OV PPR) +(-992 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 -(-991 K R UP -1666) +(-993 K R UP -1668) ((|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 -(-992 |vl| |nv|) +(-994 |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 -(-993 R |Var| |Expon| |Dpoly|) +(-995 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 (-147))) (|HasCategory| |#1| (QUOTE (-310))))) -(-994 R E V P TS) +(-996 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 -(-995) +(-997) ((|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 -(-996 A B R S) +(-998 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 -(-997 A S) +(-999 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 (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1158)))) -(-998 S) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-1030))) (|HasCategory| |#2| (QUOTE (-825))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-1160)))) +(-1000 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}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-999 |n| K) +(-1001 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-1000) +(-1002) ((|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 -(-1001 S) +(-1003 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."))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL -(-1002 S R) +(-1004 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 (-550))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-293)))) -(-1003 R) +((|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1068))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-293)))) +(-1005 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}."))) -((-4437 |has| |#1| (-293)) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 |has| |#1| (-293)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1004 QR R QS S) +(-1006 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 -(-1005 R) +(-1007 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.}"))) -((-4437 |has| |#1| (-293)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1183)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-550)))) -(-1006 S) +((-4440 |has| |#1| (-293)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-293))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -519) (QUOTE (-1185)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -289) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-1068))) (|HasCategory| |#1| (QUOTE (-550)))) +(-1008 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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1007 S) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1009 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1008) +(-1010) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1009 -1666 UP UPUP |radicnd| |n|) +(-1011 -1668 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4437 |has| (-412 |#2|) (-367)) (-4442 |has| (-412 |#2|) (-367)) (-4436 |has| (-412 |#2|) (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2774 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2774 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2774 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) -(-1010 |bb|) +((-4440 |has| (-412 |#2|) (-367)) (-4445 |has| (-412 |#2|) (-367)) (-4439 |has| (-412 |#2|) (-367)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-412 |#2|) (QUOTE (-145))) (|HasCategory| (-412 |#2|) (QUOTE (-147))) (|HasCategory| (-412 |#2|) (QUOTE (-353))) (-2776 (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (|HasCategory| (-412 |#2|) (QUOTE (-367))) (|HasCategory| (-412 |#2|) (QUOTE (-372))) (-2776 (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (QUOTE (-353)))) (-2776 (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-353))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -644) (QUOTE (-569)))) (-2776 (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 |#2|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-12 (|HasCategory| (-412 |#2|) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-412 |#2|) (QUOTE (-367)))) (-12 (|HasCategory| (-412 |#2|) (QUOTE (-234))) (|HasCategory| (-412 |#2|) (QUOTE (-367))))) +(-1012 |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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-1183)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1028))) (|HasCategory| (-569) (QUOTE (-825))) (-2774 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1158))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1183)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) -(-1011) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-569) (QUOTE (-915))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-1185)))) (|HasCategory| (-569) (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-147))) (|HasCategory| (-569) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-1030))) (|HasCategory| (-569) (QUOTE (-825))) (-2776 (|HasCategory| (-569) (QUOTE (-825))) (|HasCategory| (-569) (QUOTE (-855)))) (|HasCategory| (-569) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-1160))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| (-569) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| (-569) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| (-569) (QUOTE (-234))) (|HasCategory| (-569) (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| (-569) (LIST (QUOTE -519) (QUOTE (-1185)) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -312) (QUOTE (-569)))) (|HasCategory| (-569) (LIST (QUOTE -289) (QUOTE (-569)) (QUOTE (-569)))) (|HasCategory| (-569) (QUOTE (-310))) (|HasCategory| (-569) (QUOTE (-550))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-569) (LIST (QUOTE -644) (QUOTE (-569)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-569) (QUOTE (-915)))) (|HasCategory| (-569) (QUOTE (-145))))) +(-1013) ((|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 -(-1012) +(-1014) ((|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 -(-1013 RP) +(-1015 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 -(-1014 S) +(-1016 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 -(-1015 A S) +(-1017 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 -4445)) (|HasCategory| |#2| (QUOTE (-1106)))) -(-1016 S) +((|HasAttribute| |#1| (QUOTE -4448)) (|HasCategory| |#2| (QUOTE (-1108)))) +(-1018 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 -(-1017 S) +(-1019 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 -(-1018) +(-1020) ((|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}}"))) -((-4437 . T) (-4442 . T) (-4436 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4441 . T)) +((-4440 . T) (-4445 . T) (-4439 . T) (-4442 . T) (-4441 . T) ((-4449 "*") . T) (-4444 . T)) NIL -(-1019 R -1666) +(-1021 R -1668) ((|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 -(-1020 R -1666) +(-1022 R -1668) ((|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 -(-1021 -1666 UP) +(-1023 -1668 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 -(-1022 -1666 UP) +(-1024 -1668 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 -(-1023 S) +(-1025 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 -(-1024 F1 UP UPUP R F2) +(-1026 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 -(-1025) +(-1027) ((|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 -(-1026 |Pol|) +(-1028 |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 -(-1027 |Pol|) +(-1029 |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 -(-1028) +(-1030) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-1029) +(-1031) ((|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 -(-1030 |TheField|) +(-1032 |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"))) -((-4437 . T) (-4442 . T) (-4436 . T) (-4439 . T) (-4438 . T) ((-4446 "*") . T) (-4441 . T)) -((-2774 (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1044) (QUOTE (-569))))) -(-1031 -1666 L) +((-4440 . T) (-4445 . T) (-4439 . T) (-4442 . T) (-4441 . T) ((-4449 "*") . T) (-4444 . T)) +((-2776 (|HasCategory| (-412 (-569)) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-412 (-569)) (LIST (QUOTE -1046) (QUOTE (-569))))) +(-1033 -1668 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 -(-1032 S) +(-1034 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 (-1106)))) -(-1033 R E V P) +((|HasCategory| |#1| (QUOTE (-1108)))) +(-1035 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."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1034 R) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1036 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 (-4446 "*")))) -(-1035 R) +((|HasAttribute| |#1| (QUOTE (-4449 "*")))) +(-1037 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 (-367))) (|HasCategory| |#1| (QUOTE (-372)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-310)))) -(-1036 S) +(-1038 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 -(-1037) +(-1039) ((|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 -(-1038 S) +(-1040 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 -(-1039 S) +(-1041 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 -(-1040 -1666 |Expon| |VarSet| |FPol| |LFPol|) +(-1042 -1668 |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"))) -(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1041) +(-1043) ((|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.}"))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1042) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (QUOTE (-1185))) (LIST (QUOTE |:|) (QUOTE -2216) (QUOTE (-52))))))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-52) (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-1185) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1044) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-1043 A S) +(-1045 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 -(-1044 S) +(-1046 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 -(-1045 Q R) +(-1047 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 -(-1046) +(-1048) ((|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 -(-1047 UP) +(-1049 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 -(-1048 R) +(-1050 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 -(-1049 R) +(-1051 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 -(-1050 T$) +(-1052 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| $) "\\spad{red(c)} returns the `red' component of \\spad{`c'}."))) NIL NIL -(-1051 T$) +(-1053 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 -(-1052 R |ls|) +(-1054 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}."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1106))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -785) (|devaluate| |#1|) (LIST (QUOTE -869) (|devaluate| |#2|)))))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-869 |#2|) (QUOTE (-372))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1053) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1108))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -785) (|devaluate| |#1|) (LIST (QUOTE -869) (|devaluate| |#2|)))))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-785 |#1| (-869 |#2|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| (-869 |#2|) (QUOTE (-372))) (|HasCategory| (-785 |#1| (-869 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1055) ((|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 -(-1054 S) +(-1056 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 -(-1055) +(-1057) ((|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."))) -((-4441 . T)) +((-4444 . T)) NIL -(-1056 |xx| -1666) +(-1058 |xx| -1668) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-1057 R) +(-1059 R) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{R}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the ring \\spad{R}.\\space{2}This category differs from} \\indented{2}{\\spad{RightModule} in that no other assumption (such as addition)} \\indented{2}{is made about the underlying set.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{r*x} is the left-dilation of \\spad{x} by \\spad{r}.")) (|zero?| (((|Boolean|) $) "\\spad{zero? x} holds is \\spad{x} is the origin.")) ((|Zero|) (($) "\\spad{0} represents the origin of the linear set"))) NIL NIL -(-1058 S |m| |n| R |Row| |Col|) +(-1060 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 (-310))) (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (QUOTE (-561))) (|HasCategory| |#4| (QUOTE (-173)))) -(-1059 |m| |n| R |Row| |Col|) +(-1061 |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"))) -((-4444 . T) (-4439 . T) (-4438 . T)) +((-4447 . T) (-4442 . T) (-4441 . T)) NIL -(-1060 |m| |n| R) +(-1062 |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}."))) -((-4444 . T) (-4439 . T) (-4438 . T)) -((|HasCategory| |#3| (QUOTE (-173))) (-2774 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-561))) (-12 (|HasCategory| |#3| (QUOTE (-1106))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1061 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-4447 . T) (-4442 . T) (-4441 . T)) +((|HasCategory| |#3| (QUOTE (-173))) (-2776 (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1108))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (QUOTE (-367)))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-1108))) (|HasCategory| |#3| (QUOTE (-310))) (|HasCategory| |#3| (QUOTE (-561))) (-12 (|HasCategory| |#3| (QUOTE (-1108))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1063 |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 -(-1062 R) +(-1064 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 -(-1063 S T$) +(-1065 S T$) ((|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 (-1106)))) -(-1064) +((|HasCategory| |#1| (QUOTE (-1108)))) +(-1066) ((|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 -(-1065 S) +(-1067 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|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-1066) +(-1068) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\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."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1067 |TheField| |ThePolDom|) +(-1069 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-1068) +(-1070) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4435 . T) (-4439 . T) (-4434 . T) (-4445 . T) (-4446 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1069) +(-1071) ((|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}"))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1183))) (LIST (QUOTE |:|) (QUOTE -2214) (QUOTE (-52))))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-52) (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1106))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (QUOTE (-1106))) (|HasCategory| (-1183) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1183)) (|:| -2214 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1070 S R E V) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (QUOTE (-1185))) (LIST (QUOTE |:|) (QUOTE -2216) (QUOTE (-52))))))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-52) (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| (-52) (QUOTE (-1108))) (|HasCategory| (-52) (LIST (QUOTE -312) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (QUOTE (-1108))) (|HasCategory| (-1185) (QUOTE (-855))) (|HasCategory| (-52) (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-52) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1072 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -998) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-1183))))) -(-1071 R E V) +((|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1000) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-1185))))) +(-1073 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL -(-1072) +(-1074) ((|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 -(-1073 S |TheField| |ThePols|) +(-1075 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 -(-1074 |TheField| |ThePols|) +(-1076 |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 -(-1075 R E V P TS) +(-1077 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 -(-1076 S R E V P) +(-1078 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 -(-1077 R E V P) +(-1079 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}."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1078 R E V P TS) +(-1080 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 -(-1079) +(-1081) ((|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 -(-1080) +(-1082) ((|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 -(-1081 |f|) +(-1083 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1082 |Base| R -1666) +(-1084 |Base| R -1668) ((|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 -(-1083 |Base| R -1666) +(-1085 |Base| R -1668) ((|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 -(-1084 R |ls|) +(-1086 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 -(-1085 UP SAE UPA) +(-1087 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 -(-1086 R UP M) +(-1088 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."))) -((-4437 |has| |#1| (-367)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-353)))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) -(-1087 UP SAE UPA) +((-4440 |has| |#1| (-367)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-353))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-353)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-372))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-353)))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185))))) (-12 (|HasCategory| |#1| (QUOTE (-353))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185))))) (-12 (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (QUOTE (-367))))) +(-1089 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 -(-1088) +(-1090) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-1089) +(-1091) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-1090 S) +(-1092 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 -(-1091) +(-1093) ((|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 -(-1092 R) +(-1094 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 -(-1093 R) +(-1095 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"))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1094 (-1183)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1094 S) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| (-1096 (-1185)) (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| (-1096 (-1185)) (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| (-1096 (-1185)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| (-1096 (-1185)) (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| (-1096 (-1185)) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-234))) (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-1096 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 -(-1095 R S) +(-1097 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 (-853)))) -(-1096) +(-1098) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment \\spad{`s'}. If \\spad{`s'} designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1097 R S) +(-1099 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1098 S) +(-1100 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1100 |#1|) (QUOTE (-1106)))) -(-1099 S) +((|HasCategory| (-1102 |#1|) (QUOTE (-1108)))) +(-1101 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#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 -(-1100 S) +(-1102 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-1106)))) -(-1101 S L) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-1108)))) +(-1103 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 -(-1102) +(-1104) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1103 A S) +(-1105 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1104 S) +(-1106 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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}."))) -((-4434 . T)) +((-4437 . T)) NIL -(-1105 S) +(-1107 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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 -(-1106) +(-1108) ((|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{=}}")) (|before?| (((|Boolean|) $ $) "spad{before?(\\spad{x},{}\\spad{y})} holds if \\spad{x} comes before \\spad{y} in the internal total ordering used by OpenAxiom.")) (|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 -(-1107 |m| |n|) +(-1109 |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 -(-1108 S) +(-1110 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)}}"))) -((-4444 . T) (-4434 . T) (-4445 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-1109 |Str| |Sym| |Int| |Flt| |Expr|) +((-4447 . T) (-4437 . T) (-4448 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#1| (QUOTE (-372))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-1111 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,...,an), [i1,...,im])} returns \\spad{(a_i1,...,a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,...,an), i)} returns \\spad{ai}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s, t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL NIL -(-1110) +(-1112) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1111 |Str| |Sym| |Int| |Flt| |Expr|) +(-1113 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1112 R FS) +(-1114 R FS) ((|constructor| (NIL "\\axiomType{SimpleFortranProgram(\\spad{f},{}type)} provides a simple model of some FORTRAN subprograms,{} making it possible to coerce objects of various domains into a FORTRAN subprogram called \\axiom{\\spad{f}}. These can then be translated into legal FORTRAN code.")) (|fortran| (($ (|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 -(-1113 R E V P TS) +(-1115 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 -(-1114 R E V P TS) +(-1116 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 -(-1115 R E V P) +(-1117 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.}"))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1116) +(-1118) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em 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 -(-1117 S) +(-1119 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.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1118) +(-1120) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|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 -(-1119 |dimtot| |dim1| S) +(-1121 |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}."))) -((-4438 |has| |#3| (-1055)) (-4439 |has| |#3| (-1055)) (-4441 |has| |#3| (-6 -4441)) ((-4446 "*") |has| |#3| (-173)) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-173))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-234))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-731))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-798))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-853))) (|HasCategory| |#3| (LIST (QUOTE -312) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1055))) (|HasCategory| |#3| (LIST 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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 (-457)))) -(-1121) +(-1123) ((|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 -(-1122 R -1666) +(-1124 R -1668) ((|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 -(-1123 R) +(-1125 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 -(-1124) +(-1126) ((|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 -(-1125) +(-1127) ((|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 -(-1126) +(-1128) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4432 . T) (-4436 . T) (-4431 . T) (-4442 . T) (-4443 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4435 . T) (-4439 . T) (-4434 . T) (-4445 . T) (-4446 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1127 S) +(-1129 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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4444 . T) (-4445 . T)) +((-4447 . T) (-4448 . T)) NIL -(-1128 S |ndim| R |Row| |Col|) +(-1130 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-367))) (|HasAttribute| |#3| (QUOTE (-4446 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) -(-1129 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-367))) (|HasAttribute| |#3| (QUOTE (-4449 "*"))) (|HasCategory| |#3| (QUOTE (-173)))) +(-1131 |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."))) -((-4444 . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4447 . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1130 R |Row| |Col| M) +(-1132 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 -(-1131 R |VarSet|) +(-1133 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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-915))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4442)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2774 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-1132 |Coef| |Var| SMP) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-915))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (|HasCategory| |#1| (QUOTE (-457))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-383)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-383))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -892) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -892) (QUOTE (-569))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-383)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541))))) (|HasCategory| |#1| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4445)) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (-2776 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-915)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-1134 |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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1133 R E V P) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) +(-1135 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}"))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1134 UP -1666) +(-1136 UP -1668) ((|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 -(-1135 R) +(-1137 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 -(-1136 R) +(-1138 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 -(-1137 R) +(-1139 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 -(-1138 S A) +(-1140 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 (-855)))) -(-1139 R) +(-1141 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 -(-1140 R) +(-1142 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 -(-1141) +(-1143) ((|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 -(-1142) +(-1144) ((|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 -(-1143) +(-1145) ((|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 -(-1144) +(-1146) ((|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 -(-1145) +(-1147) ((|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 -(-1146 V C) +(-1148 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 -(-1147 V C) +(-1149 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))) (-2774 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1146) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1146 |#1| |#2|) (QUOTE (-1106))))) (|HasCategory| (-1146 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1148 |ndim| R) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-1148 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1148) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1148 |#1| |#2|) (QUOTE (-1108)))) (|HasCategory| (-1148 |#1| |#2|) (QUOTE (-1108))) (-2776 (|HasCategory| (-1148 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-1148 |#1| |#2|) (LIST (QUOTE -312) (LIST (QUOTE -1148) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1148 |#1| |#2|) (QUOTE (-1108))))) (|HasCategory| (-1148 |#1| |#2|) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1150 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4441 . T) (-4433 |has| |#2| (-6 (-4446 "*"))) (-4444 . T) (-4438 . T) (-4439 . T)) -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1044) (QUOTE (-569)))) (-2774 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-367))) (-2774 (|HasAttribute| |#2| (QUOTE (-4446 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) -(-1149 S) +((-4444 . T) (-4436 |has| |#2| (-6 (-4449 "*"))) (-4447 . T) (-4441 . T) (-4442 . T)) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234))) (|HasAttribute| |#2| (QUOTE (-4449 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (LIST (QUOTE -1046) (QUOTE (-569)))) (-2776 (-12 (|HasCategory| |#2| (QUOTE (-234))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))))) (|HasCategory| |#2| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#2| (QUOTE (-310))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-367))) (-2776 (|HasAttribute| |#2| (QUOTE (-4449 "*"))) (|HasCategory| |#2| (LIST (QUOTE -644) (QUOTE (-569)))) (|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasCategory| |#2| (QUOTE (-234)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-173)))) +(-1151 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1150) +(-1152) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1151 R E V P TS) +(-1153 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 -(-1152 R E V P) +(-1154 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."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1153 S) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1155 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}."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1154 A S) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1156 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 -(-1155 S) +(-1157 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 -(-1156 |Key| |Ent| |dent|) +(-1158 |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."))) -((-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106)))) -(-1157) +((-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-855))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108)))) +(-1159) ((|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 -(-1158) +(-1160) ((|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 -(-1159 |Coef|) +(-1161 |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 -(-1160 S) +(-1162 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 -(-1161 A B) +(-1163 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 -(-1162 A B C) +(-1164 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 -(-1163 S) +(-1165 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."))) -((-4445 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1164) +((-4448 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1166) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1165) +(-1167) NIL -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1106))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) -(-1166 |Entry|) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| (-144) (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| (-144) (QUOTE (-1108))) (|HasCategory| (-144) (LIST (QUOTE -312) (QUOTE (-144)))))) +(-1168 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (QUOTE (-1165))) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#1|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (QUOTE (-1106))) (|HasCategory| (-1165) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 (-1165)) (|:| -2214 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1167 A) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (QUOTE (-1167))) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#1|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (QUOTE (-1108))) (|HasCategory| (-1167) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 (-1167)) (|:| -2216 |#1|)) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1169 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 (-367))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) -(-1168 |Coef|) +(-1170 |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 -(-1169 |Coef|) +(-1171 |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 -(-1170 R UP) +(-1172 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 (-310)))) -(-1171 |n| R) +(-1173 |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. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1176 R) +(-1178 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . 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T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1120))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1210))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3579) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1185))))) (|HasSignature| |#1| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#1|))))))) +(-1184) ((|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 -(-1183) +(-1185) ((|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 -(-1184 R) +(-1186 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 -(-1185 R) +(-1187 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-6 -4442)) (-4438 . T) (-4439 . T) (-4441 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2776 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-457))) (-12 (|HasCategory| (-979) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasAttribute| |#1| (QUOTE -4445))) +(-1188) ((|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 -(-1187) +(-1189) ((|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 -(-1188) +(-1190) ((|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|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1189 N) +(-1191 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1190 N) +(-1192 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'}."))) NIL NIL -(-1191) +(-1193) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1192 R) +(-1194 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 -(-1193) +(-1195) ((|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 -(-1194 S) +(-1196 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 -(-1195 S) +(-1197 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 -(-1196 |Key| |Entry|) +(-1198 |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}"))) -((-4444 . T) (-4445 . T)) -((-12 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2003) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2214) (|devaluate| |#2|)))))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#2| (QUOTE (-1106)))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1106))) (-2774 (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2003 |#1|) (|:| -2214 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) -(-1197 R) +((-4447 . T) (-4448 . T)) +((-12 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -312) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2006) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2216) (|devaluate| |#2|)))))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-1108)))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -619) (QUOTE (-541)))) (-12 (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (LIST (QUOTE -312) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#2| (QUOTE (-1108))) (-2776 (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#2| (LIST (QUOTE -618) (QUOTE (-867)))) (|HasCategory| (-2 (|:| -2006 |#1|) (|:| -2216 |#2|)) (LIST (QUOTE -618) (QUOTE (-867))))) +(-1199 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 -(-1198 S |Key| |Entry|) +(-1200 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 -(-1199 |Key| |Entry|) +(-1201 |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})}."))) -((-4445 . T)) +((-4448 . T)) NIL -(-1200 |Key| |Entry|) +(-1202 |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 -(-1201) +(-1203) ((|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 -(-1202 S) +(-1204 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 -(-1203) +(-1205) ((|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 -(-1204) +(-1206) ((|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 -(-1205 R) +(-1207 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 -(-1206) +(-1208) ((|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 -(-1207 S) +(-1209 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1208) +(-1210) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1209 S) +(-1211 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1106))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1210 S) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1108))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1212 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1211) +(-1213) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1212 R -1666) +(-1214 R -1668) ((|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 -(-1213 R |Row| |Col| M) +(-1215 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 -(-1214 R -1666) +(-1216 R -1668) ((|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 -619) (LIST (QUOTE -898) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -892) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -619) (LIST (QUOTE -898) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -892) (|devaluate| |#1|))))) -(-1215 S R E V P) +(-1217 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 (-372)))) -(-1216 R E V P) +(-1218 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1217 |Coef|) +(-1219 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1218 |Curve|) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-367)))) +(-1220 |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 -(-1219) +(-1221) ((|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 -(-1220 S) +(-1222 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 (-1106))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1221 -1666) +((|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1223 -1668) ((|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 -(-1222) +(-1224) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1223) +(-1225) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1224 S) +(-1226 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 (-855)))) -(-1225) +(-1227) ((|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 -(-1226 S) +(-1228 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 -(-1227) +(-1229) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1228) +(-1230) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) NIL NIL -(-1229) +(-1231) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1230) +(-1232) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 64 bits."))) NIL NIL -(-1231) +(-1233) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) NIL NIL -(-1232 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1234 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1233 |Coef|) +(-1235 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1234 S |Coef| UTS) +(-1236 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 (-367)))) -(-1235 |Coef| UTS) +(-1237 |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)}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1236 |Coef| UTS) +(-1238 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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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 -(-1239 R S) +(-1241 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) 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NIL -((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-1106)))) -(-1241 |x| R |y| S) +((|HasCategory| |#1| (QUOTE (-853))) (|HasCategory| |#1| (QUOTE (-1108)))) +(-1243 |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 -(-1242 R Q UP) +(-1244 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 -(-1243 R UP) +(-1245 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 -(-1244 R UP) +(-1246 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 -(-1245 R U) +(-1247 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."))) 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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 -(-1248 S R) +(-1250 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 -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1158)))) -(-1249 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-457))) (|HasCategory| |#2| (QUOTE (-561))) (|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (QUOTE (-1160)))) +(-1251 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}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4440 |has| |#1| (-367)) (-4442 |has| |#1| (-6 -4442)) (-4439 . T) (-4438 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4443 |has| |#1| (-367)) (-4445 |has| |#1| (-6 -4445)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL -(-1250 S |Coef| |Expon|) +(-1252 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1118))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3793) (LIST (|devaluate| |#2|) (QUOTE (-1183)))))) -(-1251 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1120))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3796) (LIST (|devaluate| |#2|) (QUOTE (-1185)))))) +(-1253 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1252 RC P) +(-1254 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1253 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1255 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1254 |Coef|) +(-1256 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1255 S |Coef| ULS) +(-1257 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 -(-1256 |Coef| ULS) +(-1258 |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)}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1257 |Coef| ULS) +(-1259 |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)}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) -(-1258 |Coef| |var| |cen|) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2776 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1210))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3579) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1185))))) (|HasSignature| |#1| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) +(-1260 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4442 |has| |#1| (-367)) (-4436 |has| |#1| (-367)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1118))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2774 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) -(-1259 R FE |var| |cen|) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4445 |has| |#1| (-367)) (-4439 |has| |#1| (-367)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#1| (QUOTE (-173))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569))) (|devaluate| |#1|)))) (|HasCategory| (-412 (-569)) (QUOTE (-1120))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-2776 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-561)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -412) (QUOTE (-569)))))) (-2776 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1210))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3579) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1185))))) (|HasSignature| |#1| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#1|))))))) +(-1261 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))}."))) -(((-4446 "*") |has| (-1258 |#2| |#3| |#4|) (-173)) (-4437 |has| (-1258 |#2| |#3| |#4|) (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-173))) (-2774 (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1258 |#2| |#3| |#4|) (LIST (QUOTE -1044) (QUOTE (-569)))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1258 |#2| |#3| |#4|) (QUOTE (-561)))) -(-1260 A S) +(((-4449 "*") |has| (-1260 |#2| |#3| |#4|) (-173)) (-4440 |has| (-1260 |#2| |#3| |#4|) (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| (-1260 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-173))) (-2776 (|HasCategory| (-1260 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1260 |#2| |#3| |#4|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569)))))) (|HasCategory| (-1260 |#2| |#3| |#4|) (LIST (QUOTE -1046) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| (-1260 |#2| |#3| |#4|) (LIST (QUOTE -1046) (QUOTE (-569)))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-367))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-457))) (|HasCategory| (-1260 |#2| |#3| |#4|) (QUOTE (-561)))) +(-1262 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4445))) -(-1261 S) +((|HasAttribute| |#1| (QUOTE -4448))) +(-1263 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1262 |Coef1| |Coef2| UTS1 UTS2) +(-1264 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1263 S |Coef|) +(-1265 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-569)))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-1208))) (|HasSignature| |#2| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2488) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1183))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367)))) -(-1264 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#2| (QUOTE (-965))) (|HasCategory| |#2| (QUOTE (-1210))) (|HasSignature| |#2| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3579) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1185))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#2| (QUOTE (-367)))) +(-1266 |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."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1265 |Coef| |var| |cen|) +(-1267 |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| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4446 "*") |has| |#1| (-173)) (-4437 |has| |#1| (-561)) (-4438 . T) (-4439 . T) (-4441 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2774 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1183)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1118))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -3793) (LIST (|devaluate| |#1|) (QUOTE (-1183)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2774 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1208))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -2488) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1183))))) (|HasSignature| |#1| (LIST (QUOTE -1710) (LIST (LIST (QUOTE -649) (QUOTE (-1183))) (|devaluate| |#1|))))))) -(-1266 |Coef| UTS) +(((-4449 "*") |has| |#1| (-173)) (-4440 |has| |#1| (-561)) (-4441 . T) (-4442 . T) (-4444 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasCategory| |#1| (QUOTE (-561))) (-2776 (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -906) (QUOTE (-1185)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-776)) (|devaluate| |#1|)))) (|HasCategory| (-776) (QUOTE (-1120))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasSignature| |#1| (LIST (QUOTE -3796) (LIST (|devaluate| |#1|) (QUOTE (-1185)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-776))))) (|HasCategory| |#1| (QUOTE (-367))) (-2776 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-569)))) (|HasCategory| |#1| (QUOTE (-965))) (|HasCategory| |#1| (QUOTE (-1210))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasSignature| |#1| (LIST (QUOTE -3579) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1185))))) (|HasSignature| |#1| (LIST (QUOTE -1712) (LIST (LIST (QUOTE -649) (QUOTE (-1185))) (|devaluate| |#1|))))))) +(-1268 |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 -(-1267 -1666 UP L UTS) +(-1269 -1668 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 (-561)))) -(-1268) +(-1270) ((|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 -(-1269 |sym|) +(-1271 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1270 S R) +(-1272 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 (-1008))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1271 R) +((|HasCategory| |#2| (QUOTE (-1010))) (|HasCategory| |#2| (QUOTE (-1057))) (|HasCategory| |#2| (QUOTE (-731))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1273 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4445 . T) (-4444 . T)) +((-4448 . T) (-4447 . T)) NIL -(-1272 A B) +(-1274 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1273 R) +(-1275 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4445 . T) (-4444 . T)) -((-2774 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2774 (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2774 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1008))) (|HasCategory| |#1| (QUOTE (-1055)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) -(-1274) +((-4448 . T) (-4447 . T)) +((-2776 (-12 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) (-2776 (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867))))) (|HasCategory| |#1| (LIST (QUOTE -619) (QUOTE (-541)))) (-2776 (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108)))) (|HasCategory| |#1| (QUOTE (-855))) (|HasCategory| (-569) (QUOTE (-855))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-731))) (|HasCategory| |#1| (QUOTE (-1057))) (-12 (|HasCategory| |#1| (QUOTE (-1010))) (|HasCategory| |#1| (QUOTE (-1057)))) (|HasCategory| |#1| (LIST (QUOTE -618) (QUOTE (-867)))) (-12 (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -312) (|devaluate| |#1|))))) +(-1276) ((|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 -(-1275) +(-1277) ((|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 -(-1276) +(-1278) ((|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 -(-1277) +(-1279) ((|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 -(-1278) +(-1280) ((|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| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1279 A S) +(-1281 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1280 S) +(-1282 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}."))) -((-4439 . T) (-4438 . T)) +((-4442 . T) (-4441 . T)) NIL -(-1281 R) +(-1283 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 -(-1282 K R UP -1666) +(-1284 K R UP -1668) ((|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 -(-1283) +(-1285) ((|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 -(-1284) +(-1286) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1285 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1287 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)"))) -((-4439 |has| |#1| (-173)) (-4438 |has| |#1| (-173)) (-4441 . T)) +((-4442 |has| |#1| (-173)) (-4441 |has| |#1| (-173)) (-4444 . T)) ((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367)))) -(-1286 R E V P) +(-1288 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}}."))) -((-4445 . T) (-4444 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) -(-1287 R) +((-4448 . T) (-4447 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#4| (LIST (QUOTE -312) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -619) (QUOTE (-541)))) (|HasCategory| |#4| (QUOTE (-1108))) (|HasCategory| |#1| (QUOTE (-561))) (|HasCategory| |#3| (QUOTE (-372))) (|HasCategory| |#4| (LIST (QUOTE -618) (QUOTE (-867))))) +(-1289 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})"))) -((-4438 . T) (-4439 . T) (-4441 . T)) +((-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1288 |vl| R) +(-1290 |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."))) -((-4441 . T) (-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4437))) -(-1289 R |VarSet| XPOLY) +((-4444 . T) (-4440 |has| |#2| (-6 -4440)) (-4442 . T) (-4441 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4440))) +(-1291 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 -(-1290 |vl| R) +(-1292 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) +((-4440 |has| |#2| (-6 -4440)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL -(-1291 S -1666) +(-1293 S -1668) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-372))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1292 -1666) +(-1294 -1668) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4436 . T) (-4442 . T) (-4437 . T) ((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +((-4439 . T) (-4445 . T) (-4440 . T) ((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL -(-1293 |VarSet| R) +(-1295 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasAttribute| |#2| (QUOTE -4437))) -(-1294 |vl| R) +((-4440 |has| |#2| (-6 -4440)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasCategory| |#2| (LIST (QUOTE -722) (LIST (QUOTE -412) (QUOTE (-569))))) (|HasAttribute| |#2| (QUOTE -4440))) +(-1296 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) +((-4440 |has| |#2| (-6 -4440)) (-4442 . T) (-4441 . T) (-4444 . T)) NIL -(-1295 R) +(-1297 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4437 |has| |#1| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4437))) -(-1296 R E) +((-4440 |has| |#1| (-6 -4440)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasAttribute| |#1| (QUOTE -4440))) +(-1298 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4441 . T) (-4442 |has| |#1| (-6 -4442)) (-4437 |has| |#1| (-6 -4437)) (-4439 . T) (-4438 . T)) -((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4441)) (|HasAttribute| |#1| (QUOTE -4442)) (|HasAttribute| |#1| (QUOTE -4437))) -(-1297 |VarSet| R) +((-4444 . T) (-4445 |has| |#1| (-6 -4445)) (-4440 |has| |#1| (-6 -4440)) (-4442 . T) (-4441 . T)) +((|HasCategory| |#1| (QUOTE (-173))) (|HasCategory| |#1| (QUOTE (-367))) (|HasAttribute| |#1| (QUOTE -4444)) (|HasAttribute| |#1| (QUOTE -4445)) (|HasAttribute| |#1| (QUOTE -4440))) +(-1299 |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."))) -((-4437 |has| |#2| (-6 -4437)) (-4439 . T) (-4438 . T) (-4441 . T)) -((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4437))) -(-1298 A) +((-4440 |has| |#2| (-6 -4440)) (-4442 . T) (-4441 . T) (-4444 . T)) +((|HasCategory| |#2| (QUOTE (-173))) (|HasAttribute| |#2| (QUOTE -4440))) +(-1300 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 -(-1299 R |ls| |ls2|) +(-1301 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 -(-1300 R) +(-1302 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 -(-1301 |p|) +(-1303 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4446 "*") . T) (-4438 . T) (-4439 . T) (-4441 . T)) +(((-4449 "*") . T) (-4441 . T) (-4442 . T) (-4444 . T)) NIL NIL NIL @@ -5152,4 +5160,4 @@ NIL NIL NIL NIL -((-3 NIL 2267632 2267637 2267642 2267647) (-2 NIL 2267612 2267617 2267622 2267627) (-1 NIL 2267592 2267597 2267602 2267607) (0 NIL 2267572 2267577 2267582 2267587) (-1301 "ZMOD.spad" 2267381 2267394 2267510 2267567) (-1300 "ZLINDEP.spad" 2266447 2266458 2267371 2267376) (-1299 "ZDSOLVE.spad" 2256392 2256414 2266437 2266442) (-1298 "YSTREAM.spad" 2255887 2255898 2256382 2256387) (-1297 "XRPOLY.spad" 2255107 2255127 2255743 2255812) (-1296 "XPR.spad" 2252902 2252915 2254825 2254924) (-1295 "XPOLY.spad" 2252457 2252468 2252758 2252827) (-1294 "XPOLYC.spad" 2251776 2251792 2252383 2252452) (-1293 "XPBWPOLY.spad" 2250213 2250233 2251556 2251625) (-1292 "XF.spad" 2248676 2248691 2250115 2250208) (-1291 "XF.spad" 2247119 2247136 2248560 2248565) (-1290 "XFALG.spad" 2244167 2244183 2247045 2247114) (-1289 "XEXPPKG.spad" 2243418 2243444 2244157 2244162) (-1288 "XDPOLY.spad" 2243032 2243048 2243274 2243343) (-1287 "XALG.spad" 2242692 2242703 2242988 2243027) (-1286 "WUTSET.spad" 2238531 2238548 2242338 2242365) (-1285 "WP.spad" 2237730 2237774 2238389 2238456) (-1284 "WHILEAST.spad" 2237528 2237537 2237720 2237725) (-1283 "WHEREAST.spad" 2237199 2237208 2237518 2237523) (-1282 "WFFINTBS.spad" 2234862 2234884 2237189 2237194) (-1281 "WEIER.spad" 2233084 2233095 2234852 2234857) (-1280 "VSPACE.spad" 2232757 2232768 2233052 2233079) (-1279 "VSPACE.spad" 2232450 2232463 2232747 2232752) (-1278 "VOID.spad" 2232127 2232136 2232440 2232445) (-1277 "VIEW.spad" 2229807 2229816 2232117 2232122) (-1276 "VIEWDEF.spad" 2225008 2225017 2229797 2229802) (-1275 "VIEW3D.spad" 2208969 2208978 2224998 2225003) (-1274 "VIEW2D.spad" 2196860 2196869 2208959 2208964) (-1273 "VECTOR.spad" 2195534 2195545 2195785 2195812) (-1272 "VECTOR2.spad" 2194173 2194186 2195524 2195529) (-1271 "VECTCAT.spad" 2192077 2192088 2194141 2194168) (-1270 "VECTCAT.spad" 2189788 2189801 2191854 2191859) (-1269 "VARIABLE.spad" 2189568 2189583 2189778 2189783) (-1268 "UTYPE.spad" 2189212 2189221 2189558 2189563) (-1267 "UTSODETL.spad" 2188507 2188531 2189168 2189173) (-1266 "UTSODE.spad" 2186723 2186743 2188497 2188502) (-1265 "UTS.spad" 2181527 2181555 2185190 2185287) (-1264 "UTSCAT.spad" 2179006 2179022 2181425 2181522) (-1263 "UTSCAT.spad" 2176129 2176147 2178550 2178555) (-1262 "UTS2.spad" 2175724 2175759 2176119 2176124) (-1261 "URAGG.spad" 2170397 2170408 2175714 2175719) (-1260 "URAGG.spad" 2165034 2165047 2170353 2170358) (-1259 "UPXSSING.spad" 2162679 2162705 2164115 2164248) (-1258 "UPXS.spad" 2159833 2159861 2160811 2160960) (-1257 "UPXSCONS.spad" 2157592 2157612 2157965 2158114) (-1256 "UPXSCCA.spad" 2156163 2156183 2157438 2157587) (-1255 "UPXSCCA.spad" 2154876 2154898 2156153 2156158) (-1254 "UPXSCAT.spad" 2153465 2153481 2154722 2154871) (-1253 "UPXS2.spad" 2153008 2153061 2153455 2153460) (-1252 "UPSQFREE.spad" 2151422 2151436 2152998 2153003) (-1251 "UPSCAT.spad" 2149033 2149057 2151320 2151417) (-1250 "UPSCAT.spad" 2146350 2146376 2148639 2148644) (-1249 "UPOLYC.spad" 2141390 2141401 2146192 2146345) (-1248 "UPOLYC.spad" 2136322 2136335 2141126 2141131) (-1247 "UPOLYC2.spad" 2135793 2135812 2136312 2136317) (-1246 "UP.spad" 2132992 2133007 2133379 2133532) (-1245 "UPMP.spad" 2131892 2131905 2132982 2132987) (-1244 "UPDIVP.spad" 2131457 2131471 2131882 2131887) (-1243 "UPDECOMP.spad" 2129702 2129716 2131447 2131452) (-1242 "UPCDEN.spad" 2128911 2128927 2129692 2129697) (-1241 "UP2.spad" 2128275 2128296 2128901 2128906) (-1240 "UNISEG.spad" 2127628 2127639 2128194 2128199) (-1239 "UNISEG2.spad" 2127125 2127138 2127584 2127589) (-1238 "UNIFACT.spad" 2126228 2126240 2127115 2127120) (-1237 "ULS.spad" 2116786 2116814 2117873 2118302) (-1236 "ULSCONS.spad" 2109182 2109202 2109552 2109701) (-1235 "ULSCCAT.spad" 2106919 2106939 2109028 2109177) (-1234 "ULSCCAT.spad" 2104764 2104786 2106875 2106880) (-1233 "ULSCAT.spad" 2102996 2103012 2104610 2104759) (-1232 "ULS2.spad" 2102510 2102563 2102986 2102991) (-1231 "UINT8.spad" 2102387 2102396 2102500 2102505) (-1230 "UINT64.spad" 2102263 2102272 2102377 2102382) (-1229 "UINT32.spad" 2102139 2102148 2102253 2102258) (-1228 "UINT16.spad" 2102015 2102024 2102129 2102134) (-1227 "UFD.spad" 2101080 2101089 2101941 2102010) (-1226 "UFD.spad" 2100207 2100218 2101070 2101075) (-1225 "UDVO.spad" 2099088 2099097 2100197 2100202) (-1224 "UDPO.spad" 2096581 2096592 2099044 2099049) (-1223 "TYPE.spad" 2096513 2096522 2096571 2096576) (-1222 "TYPEAST.spad" 2096432 2096441 2096503 2096508) (-1221 "TWOFACT.spad" 2095084 2095099 2096422 2096427) (-1220 "TUPLE.spad" 2094570 2094581 2094983 2094988) (-1219 "TUBETOOL.spad" 2091437 2091446 2094560 2094565) (-1218 "TUBE.spad" 2090084 2090101 2091427 2091432) (-1217 "TS.spad" 2088683 2088699 2089649 2089746) (-1216 "TSETCAT.spad" 2075810 2075827 2088651 2088678) (-1215 "TSETCAT.spad" 2062923 2062942 2075766 2075771) (-1214 "TRMANIP.spad" 2057289 2057306 2062629 2062634) (-1213 "TRIMAT.spad" 2056252 2056277 2057279 2057284) (-1212 "TRIGMNIP.spad" 2054779 2054796 2056242 2056247) (-1211 "TRIGCAT.spad" 2054291 2054300 2054769 2054774) (-1210 "TRIGCAT.spad" 2053801 2053812 2054281 2054286) (-1209 "TREE.spad" 2052376 2052387 2053408 2053435) (-1208 "TRANFUN.spad" 2052215 2052224 2052366 2052371) (-1207 "TRANFUN.spad" 2052052 2052063 2052205 2052210) (-1206 "TOPSP.spad" 2051726 2051735 2052042 2052047) (-1205 "TOOLSIGN.spad" 2051389 2051400 2051716 2051721) (-1204 "TEXTFILE.spad" 2049950 2049959 2051379 2051384) (-1203 "TEX.spad" 2047096 2047105 2049940 2049945) (-1202 "TEX1.spad" 2046652 2046663 2047086 2047091) (-1201 "TEMUTL.spad" 2046207 2046216 2046642 2046647) (-1200 "TBCMPPK.spad" 2044300 2044323 2046197 2046202) (-1199 "TBAGG.spad" 2043350 2043373 2044280 2044295) (-1198 "TBAGG.spad" 2042408 2042433 2043340 2043345) (-1197 "TANEXP.spad" 2041816 2041827 2042398 2042403) (-1196 "TABLE.spad" 2040227 2040250 2040497 2040524) (-1195 "TABLEAU.spad" 2039708 2039719 2040217 2040222) (-1194 "TABLBUMP.spad" 2036511 2036522 2039698 2039703) (-1193 "SYSTEM.spad" 2035739 2035748 2036501 2036506) (-1192 "SYSSOLP.spad" 2033222 2033233 2035729 2035734) (-1191 "SYSPTR.spad" 2033121 2033130 2033212 2033217) (-1190 "SYSNNI.spad" 2032303 2032314 2033111 2033116) (-1189 "SYSINT.spad" 2031707 2031718 2032293 2032298) (-1188 "SYNTAX.spad" 2027913 2027922 2031697 2031702) (-1187 "SYMTAB.spad" 2025981 2025990 2027903 2027908) (-1186 "SYMS.spad" 2022004 2022013 2025971 2025976) (-1185 "SYMPOLY.spad" 2021011 2021022 2021093 2021220) (-1184 "SYMFUNC.spad" 2020512 2020523 2021001 2021006) (-1183 "SYMBOL.spad" 2018015 2018024 2020502 2020507) (-1182 "SWITCH.spad" 2014786 2014795 2018005 2018010) (-1181 "SUTS.spad" 2011691 2011719 2013253 2013350) (-1180 "SUPXS.spad" 2008832 2008860 2009823 2009972) (-1179 "SUP.spad" 2005645 2005656 2006418 2006571) (-1178 "SUPFRACF.spad" 2004750 2004768 2005635 2005640) (-1177 "SUP2.spad" 2004142 2004155 2004740 2004745) (-1176 "SUMRF.spad" 2003116 2003127 2004132 2004137) (-1175 "SUMFS.spad" 2002753 2002770 2003106 2003111) (-1174 "SULS.spad" 1993298 1993326 1994398 1994827) (-1173 "SUCHTAST.spad" 1993067 1993076 1993288 1993293) (-1172 "SUCH.spad" 1992749 1992764 1993057 1993062) (-1171 "SUBSPACE.spad" 1984864 1984879 1992739 1992744) (-1170 "SUBRESP.spad" 1984034 1984048 1984820 1984825) (-1169 "STTF.spad" 1980133 1980149 1984024 1984029) (-1168 "STTFNC.spad" 1976601 1976617 1980123 1980128) (-1167 "STTAYLOR.spad" 1969236 1969247 1976482 1976487) (-1166 "STRTBL.spad" 1967741 1967758 1967890 1967917) (-1165 "STRING.spad" 1967150 1967159 1967164 1967191) (-1164 "STRICAT.spad" 1966938 1966947 1967118 1967145) (-1163 "STREAM.spad" 1963856 1963867 1966463 1966478) (-1162 "STREAM3.spad" 1963429 1963444 1963846 1963851) (-1161 "STREAM2.spad" 1962557 1962570 1963419 1963424) (-1160 "STREAM1.spad" 1962263 1962274 1962547 1962552) (-1159 "STINPROD.spad" 1961199 1961215 1962253 1962258) (-1158 "STEP.spad" 1960400 1960409 1961189 1961194) (-1157 "STEPAST.spad" 1959634 1959643 1960390 1960395) (-1156 "STBL.spad" 1958160 1958188 1958327 1958342) (-1155 "STAGG.spad" 1957235 1957246 1958150 1958155) (-1154 "STAGG.spad" 1956308 1956321 1957225 1957230) (-1153 "STACK.spad" 1955665 1955676 1955915 1955942) (-1152 "SREGSET.spad" 1953369 1953386 1955311 1955338) (-1151 "SRDCMPK.spad" 1951930 1951950 1953359 1953364) (-1150 "SRAGG.spad" 1947073 1947082 1951898 1951925) (-1149 "SRAGG.spad" 1942236 1942247 1947063 1947068) (-1148 "SQMATRIX.spad" 1939852 1939870 1940768 1940855) (-1147 "SPLTREE.spad" 1934404 1934417 1939288 1939315) (-1146 "SPLNODE.spad" 1930992 1931005 1934394 1934399) (-1145 "SPFCAT.spad" 1929801 1929810 1930982 1930987) (-1144 "SPECOUT.spad" 1928353 1928362 1929791 1929796) (-1143 "SPADXPT.spad" 1919948 1919957 1928343 1928348) (-1142 "spad-parser.spad" 1919413 1919422 1919938 1919943) (-1141 "SPADAST.spad" 1919114 1919123 1919403 1919408) (-1140 "SPACEC.spad" 1903313 1903324 1919104 1919109) (-1139 "SPACE3.spad" 1903089 1903100 1903303 1903308) (-1138 "SORTPAK.spad" 1902638 1902651 1903045 1903050) (-1137 "SOLVETRA.spad" 1900401 1900412 1902628 1902633) (-1136 "SOLVESER.spad" 1898929 1898940 1900391 1900396) (-1135 "SOLVERAD.spad" 1894955 1894966 1898919 1898924) (-1134 "SOLVEFOR.spad" 1893417 1893435 1894945 1894950) (-1133 "SNTSCAT.spad" 1893017 1893034 1893385 1893412) (-1132 "SMTS.spad" 1891289 1891315 1892582 1892679) (-1131 "SMP.spad" 1888764 1888784 1889154 1889281) (-1130 "SMITH.spad" 1887609 1887634 1888754 1888759) (-1129 "SMATCAT.spad" 1885719 1885749 1887553 1887604) (-1128 "SMATCAT.spad" 1883761 1883793 1885597 1885602) (-1127 "SKAGG.spad" 1882724 1882735 1883729 1883756) (-1126 "SINT.spad" 1881556 1881565 1882590 1882719) (-1125 "SIMPAN.spad" 1881284 1881293 1881546 1881551) (-1124 "SIG.spad" 1880614 1880623 1881274 1881279) (-1123 "SIGNRF.spad" 1879732 1879743 1880604 1880609) (-1122 "SIGNEF.spad" 1879011 1879028 1879722 1879727) (-1121 "SIGAST.spad" 1878396 1878405 1879001 1879006) (-1120 "SHP.spad" 1876324 1876339 1878352 1878357) (-1119 "SHDP.spad" 1866035 1866062 1866544 1866675) (-1118 "SGROUP.spad" 1865643 1865652 1866025 1866030) (-1117 "SGROUP.spad" 1865249 1865260 1865633 1865638) (-1116 "SGCF.spad" 1858412 1858421 1865239 1865244) (-1115 "SFRTCAT.spad" 1857342 1857359 1858380 1858407) (-1114 "SFRGCD.spad" 1856405 1856425 1857332 1857337) (-1113 "SFQCMPK.spad" 1851042 1851062 1856395 1856400) (-1112 "SFORT.spad" 1850481 1850495 1851032 1851037) (-1111 "SEXOF.spad" 1850324 1850364 1850471 1850476) (-1110 "SEX.spad" 1850216 1850225 1850314 1850319) (-1109 "SEXCAT.spad" 1847817 1847857 1850206 1850211) (-1108 "SET.spad" 1846141 1846152 1847238 1847277) (-1107 "SETMN.spad" 1844591 1844608 1846131 1846136) (-1106 "SETCAT.spad" 1843913 1843922 1844581 1844586) (-1105 "SETCAT.spad" 1843233 1843244 1843903 1843908) (-1104 "SETAGG.spad" 1839782 1839793 1843213 1843228) (-1103 "SETAGG.spad" 1836339 1836352 1839772 1839777) (-1102 "SEQAST.spad" 1836042 1836051 1836329 1836334) (-1101 "SEGXCAT.spad" 1835198 1835211 1836032 1836037) (-1100 "SEG.spad" 1835011 1835022 1835117 1835122) (-1099 "SEGCAT.spad" 1833936 1833947 1835001 1835006) (-1098 "SEGBIND.spad" 1833694 1833705 1833883 1833888) (-1097 "SEGBIND2.spad" 1833392 1833405 1833684 1833689) (-1096 "SEGAST.spad" 1833106 1833115 1833382 1833387) (-1095 "SEG2.spad" 1832541 1832554 1833062 1833067) (-1094 "SDVAR.spad" 1831817 1831828 1832531 1832536) (-1093 "SDPOL.spad" 1829243 1829254 1829534 1829661) (-1092 "SCPKG.spad" 1827332 1827343 1829233 1829238) (-1091 "SCOPE.spad" 1826485 1826494 1827322 1827327) (-1090 "SCACHE.spad" 1825181 1825192 1826475 1826480) (-1089 "SASTCAT.spad" 1825090 1825099 1825171 1825176) (-1088 "SAOS.spad" 1824962 1824971 1825080 1825085) (-1087 "SAERFFC.spad" 1824675 1824695 1824952 1824957) (-1086 "SAE.spad" 1822850 1822866 1823461 1823596) (-1085 "SAEFACT.spad" 1822551 1822571 1822840 1822845) (-1084 "RURPK.spad" 1820210 1820226 1822541 1822546) (-1083 "RULESET.spad" 1819663 1819687 1820200 1820205) (-1082 "RULE.spad" 1817903 1817927 1819653 1819658) (-1081 "RULECOLD.spad" 1817755 1817768 1817893 1817898) (-1080 "RTVALUE.spad" 1817490 1817499 1817745 1817750) (-1079 "RSTRCAST.spad" 1817207 1817216 1817480 1817485) (-1078 "RSETGCD.spad" 1813585 1813605 1817197 1817202) (-1077 "RSETCAT.spad" 1803521 1803538 1813553 1813580) (-1076 "RSETCAT.spad" 1793477 1793496 1803511 1803516) (-1075 "RSDCMPK.spad" 1791929 1791949 1793467 1793472) (-1074 "RRCC.spad" 1790313 1790343 1791919 1791924) (-1073 "RRCC.spad" 1788695 1788727 1790303 1790308) (-1072 "RPTAST.spad" 1788397 1788406 1788685 1788690) (-1071 "RPOLCAT.spad" 1767757 1767772 1788265 1788392) (-1070 "RPOLCAT.spad" 1746831 1746848 1767341 1767346) (-1069 "ROUTINE.spad" 1742714 1742723 1745478 1745505) (-1068 "ROMAN.spad" 1742042 1742051 1742580 1742709) (-1067 "ROIRC.spad" 1741122 1741154 1742032 1742037) (-1066 "RNS.spad" 1740025 1740034 1741024 1741117) (-1065 "RNS.spad" 1739014 1739025 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1225200 1225205) (-765 "NARNG.spad" 1223912 1223922 1224552 1224557) (-764 "NAGSP.spad" 1222989 1222997 1223902 1223907) (-763 "NAGS.spad" 1212650 1212658 1222979 1222984) (-762 "NAGF07.spad" 1211081 1211089 1212640 1212645) (-761 "NAGF04.spad" 1205483 1205491 1211071 1211076) (-760 "NAGF02.spad" 1199552 1199560 1205473 1205478) (-759 "NAGF01.spad" 1195313 1195321 1199542 1199547) (-758 "NAGE04.spad" 1189013 1189021 1195303 1195308) (-757 "NAGE02.spad" 1179673 1179681 1189003 1189008) (-756 "NAGE01.spad" 1175675 1175683 1179663 1179668) (-755 "NAGD03.spad" 1173679 1173687 1175665 1175670) (-754 "NAGD02.spad" 1166426 1166434 1173669 1173674) (-753 "NAGD01.spad" 1160719 1160727 1166416 1166421) (-752 "NAGC06.spad" 1156594 1156602 1160709 1160714) (-751 "NAGC05.spad" 1155095 1155103 1156584 1156589) (-750 "NAGC02.spad" 1154362 1154370 1155085 1155090) (-749 "NAALG.spad" 1153903 1153913 1154330 1154357) (-748 "NAALG.spad" 1153464 1153476 1153893 1153898) (-747 "MULTSQFR.spad" 1150422 1150439 1153454 1153459) (-746 "MULTFACT.spad" 1149805 1149822 1150412 1150417) (-745 "MTSCAT.spad" 1147899 1147920 1149703 1149800) (-744 "MTHING.spad" 1147558 1147568 1147889 1147894) (-743 "MSYSCMD.spad" 1146992 1147000 1147548 1147553) (-742 "MSET.spad" 1144950 1144960 1146698 1146737) (-741 "MSETAGG.spad" 1144795 1144805 1144918 1144945) (-740 "MRING.spad" 1141772 1141784 1144503 1144570) (-739 "MRF2.spad" 1141342 1141356 1141762 1141767) (-738 "MRATFAC.spad" 1140888 1140905 1141332 1141337) (-737 "MPRFF.spad" 1138928 1138947 1140878 1140883) (-736 "MPOLY.spad" 1136399 1136414 1136758 1136885) (-735 "MPCPF.spad" 1135663 1135682 1136389 1136394) (-734 "MPC3.spad" 1135480 1135520 1135653 1135658) (-733 "MPC2.spad" 1135126 1135159 1135470 1135475) (-732 "MONOTOOL.spad" 1133477 1133494 1135116 1135121) (-731 "MONOID.spad" 1132796 1132804 1133467 1133472) (-730 "MONOID.spad" 1132113 1132123 1132786 1132791) (-729 "MONOGEN.spad" 1130861 1130874 1131973 1132108) (-728 "MONOGEN.spad" 1129631 1129646 1130745 1130750) (-727 "MONADWU.spad" 1127661 1127669 1129621 1129626) (-726 "MONADWU.spad" 1125689 1125699 1127651 1127656) (-725 "MONAD.spad" 1124849 1124857 1125679 1125684) (-724 "MONAD.spad" 1124007 1124017 1124839 1124844) (-723 "MOEBIUS.spad" 1122743 1122757 1123987 1124002) (-722 "MODULE.spad" 1122613 1122623 1122711 1122738) (-721 "MODULE.spad" 1122503 1122515 1122603 1122608) (-720 "MODRING.spad" 1121838 1121877 1122483 1122498) (-719 "MODOP.spad" 1120503 1120515 1121660 1121727) (-718 "MODMONOM.spad" 1120234 1120252 1120493 1120498) (-717 "MODMON.spad" 1117029 1117045 1117748 1117901) (-716 "MODFIELD.spad" 1116391 1116430 1116931 1117024) (-715 "MMLFORM.spad" 1115251 1115259 1116381 1116386) (-714 "MMAP.spad" 1114993 1115027 1115241 1115246) (-713 "MLO.spad" 1113452 1113462 1114949 1114988) (-712 "MLIFT.spad" 1112064 1112081 1113442 1113447) (-711 "MKUCFUNC.spad" 1111599 1111617 1112054 1112059) (-710 "MKRECORD.spad" 1111203 1111216 1111589 1111594) (-709 "MKFUNC.spad" 1110610 1110620 1111193 1111198) (-708 "MKFLCFN.spad" 1109578 1109588 1110600 1110605) (-707 "MKBCFUNC.spad" 1109073 1109091 1109568 1109573) (-706 "MINT.spad" 1108512 1108520 1108975 1109068) (-705 "MHROWRED.spad" 1107023 1107033 1108502 1108507) (-704 "MFLOAT.spad" 1105543 1105551 1106913 1107018) (-703 "MFINFACT.spad" 1104943 1104965 1105533 1105538) (-702 "MESH.spad" 1102725 1102733 1104933 1104938) (-701 "MDDFACT.spad" 1100936 1100946 1102715 1102720) (-700 "MDAGG.spad" 1100227 1100237 1100916 1100931) (-699 "MCMPLX.spad" 1096238 1096246 1096852 1097053) (-698 "MCDEN.spad" 1095448 1095460 1096228 1096233) (-697 "MCALCFN.spad" 1092570 1092596 1095438 1095443) (-696 "MAYBE.spad" 1091854 1091865 1092560 1092565) (-695 "MATSTOR.spad" 1089162 1089172 1091844 1091849) (-694 "MATRIX.spad" 1087866 1087876 1088350 1088377) (-693 "MATLIN.spad" 1085210 1085234 1087750 1087755) (-692 "MATCAT.spad" 1076939 1076961 1085178 1085205) (-691 "MATCAT.spad" 1068540 1068564 1076781 1076786) (-690 "MATCAT2.spad" 1067822 1067870 1068530 1068535) (-689 "MAPPKG3.spad" 1066737 1066751 1067812 1067817) (-688 "MAPPKG2.spad" 1066075 1066087 1066727 1066732) (-687 "MAPPKG1.spad" 1064903 1064913 1066065 1066070) (-686 "MAPPAST.spad" 1064218 1064226 1064893 1064898) (-685 "MAPHACK3.spad" 1064030 1064044 1064208 1064213) (-684 "MAPHACK2.spad" 1063799 1063811 1064020 1064025) (-683 "MAPHACK1.spad" 1063443 1063453 1063789 1063794) (-682 "MAGMA.spad" 1061233 1061250 1063433 1063438) (-681 "MACROAST.spad" 1060812 1060820 1061223 1061228) (-680 "M3D.spad" 1058532 1058542 1060190 1060195) (-679 "LZSTAGG.spad" 1055770 1055780 1058522 1058527) (-678 "LZSTAGG.spad" 1053006 1053018 1055760 1055765) (-677 "LWORD.spad" 1049711 1049728 1052996 1053001) (-676 "LSTAST.spad" 1049495 1049503 1049701 1049706) (-675 "LSQM.spad" 1047725 1047739 1048119 1048170) (-674 "LSPP.spad" 1047260 1047277 1047715 1047720) (-673 "LSMP.spad" 1046110 1046138 1047250 1047255) (-672 "LSMP1.spad" 1043928 1043942 1046100 1046105) (-671 "LSAGG.spad" 1043597 1043607 1043896 1043923) (-670 "LSAGG.spad" 1043286 1043298 1043587 1043592) (-669 "LPOLY.spad" 1042240 1042259 1043142 1043211) (-668 "LPEFRAC.spad" 1041511 1041521 1042230 1042235) (-667 "LO.spad" 1040912 1040926 1041445 1041472) (-666 "LOGIC.spad" 1040514 1040522 1040902 1040907) (-665 "LOGIC.spad" 1040114 1040124 1040504 1040509) (-664 "LODOOPS.spad" 1039044 1039056 1040104 1040109) (-663 "LODO.spad" 1038428 1038444 1038724 1038763) (-662 "LODOF.spad" 1037474 1037491 1038385 1038390) (-661 "LODOCAT.spad" 1036140 1036150 1037430 1037469) (-660 "LODOCAT.spad" 1034804 1034816 1036096 1036101) (-659 "LODO2.spad" 1034077 1034089 1034484 1034523) (-658 "LODO1.spad" 1033477 1033487 1033757 1033796) (-657 "LODEEF.spad" 1032279 1032297 1033467 1033472) (-656 "LNAGG.spad" 1028111 1028121 1032269 1032274) (-655 "LNAGG.spad" 1023907 1023919 1028067 1028072) (-654 "LMOPS.spad" 1020675 1020692 1023897 1023902) (-653 "LMODULE.spad" 1020443 1020453 1020665 1020670) (-652 "LMDICT.spad" 1019730 1019740 1019994 1020021) (-651 "LLINSET.spad" 1019127 1019137 1019720 1019725) (-650 "LITERAL.spad" 1019033 1019044 1019117 1019122) (-649 "LIST.spad" 1016768 1016778 1018180 1018207) (-648 "LIST3.spad" 1016079 1016093 1016758 1016763) (-647 "LIST2.spad" 1014781 1014793 1016069 1016074) (-646 "LIST2MAP.spad" 1011684 1011696 1014771 1014776) (-645 "LINSET.spad" 1011306 1011316 1011674 1011679) (-644 "LINEXP.spad" 1010740 1010750 1011286 1011301) (-643 "LINDEP.spad" 1009549 1009561 1010652 1010657) (-642 "LIMITRF.spad" 1007477 1007487 1009539 1009544) (-641 "LIMITPS.spad" 1006380 1006393 1007467 1007472) (-640 "LIE.spad" 1004396 1004408 1005670 1005815) (-639 "LIECAT.spad" 1003872 1003882 1004322 1004391) (-638 "LIECAT.spad" 1003376 1003388 1003828 1003833) (-637 "LIB.spad" 1001426 1001434 1002035 1002050) (-636 "LGROBP.spad" 998779 998798 1001416 1001421) (-635 "LF.spad" 997734 997750 998769 998774) (-634 "LFCAT.spad" 996793 996801 997724 997729) (-633 "LEXTRIPK.spad" 992296 992311 996783 996788) (-632 "LEXP.spad" 990299 990326 992276 992291) (-631 "LETAST.spad" 989998 990006 990289 990294) (-630 "LEADCDET.spad" 988396 988413 989988 989993) (-629 "LAZM3PK.spad" 987100 987122 988386 988391) (-628 "LAUPOL.spad" 985793 985806 986693 986762) (-627 "LAPLACE.spad" 985376 985392 985783 985788) (-626 "LA.spad" 984816 984830 985298 985337) (-625 "LALG.spad" 984592 984602 984796 984811) (-624 "LALG.spad" 984376 984388 984582 984587) (-623 "KVTFROM.spad" 984111 984121 984366 984371) (-622 "KTVLOGIC.spad" 983623 983631 984101 984106) (-621 "KRCFROM.spad" 983361 983371 983613 983618) (-620 "KOVACIC.spad" 982084 982101 983351 983356) (-619 "KONVERT.spad" 981806 981816 982074 982079) (-618 "KOERCE.spad" 981543 981553 981796 981801) (-617 "KERNEL.spad" 980198 980208 981327 981332) (-616 "KERNEL2.spad" 979901 979913 980188 980193) (-615 "KDAGG.spad" 979010 979032 979881 979896) (-614 "KDAGG.spad" 978127 978151 979000 979005) (-613 "KAFILE.spad" 977090 977106 977325 977352) (-612 "JORDAN.spad" 974919 974931 976380 976525) (-611 "JOINAST.spad" 974613 974621 974909 974914) (-610 "JAVACODE.spad" 974479 974487 974603 974608) (-609 "IXAGG.spad" 972612 972636 974469 974474) (-608 "IXAGG.spad" 970600 970626 972459 972464) (-607 "IVECTOR.spad" 969370 969385 969525 969552) (-606 "ITUPLE.spad" 968531 968541 969360 969365) (-605 "ITRIGMNP.spad" 967370 967389 968521 968526) (-604 "ITFUN3.spad" 966876 966890 967360 967365) (-603 "ITFUN2.spad" 966620 966632 966866 966871) (-602 "ITFORM.spad" 965975 965983 966610 966615) (-601 "ITAYLOR.spad" 963969 963984 965839 965936) (-600 "ISUPS.spad" 956406 956421 962943 963040) (-599 "ISUMP.spad" 955907 955923 956396 956401) (-598 "ISTRING.spad" 954995 955008 955076 955103) (-597 "ISAST.spad" 954714 954722 954985 954990) (-596 "IRURPK.spad" 953431 953450 954704 954709) (-595 "IRSN.spad" 951435 951443 953421 953426) (-594 "IRRF2F.spad" 949920 949930 951391 951396) (-593 "IRREDFFX.spad" 949521 949532 949910 949915) (-592 "IROOT.spad" 947860 947870 949511 949516) (-591 "IR.spad" 945661 945675 947715 947742) (-590 "IRFORM.spad" 944985 944993 945651 945656) (-589 "IR2.spad" 944013 944029 944975 944980) (-588 "IR2F.spad" 943219 943235 944003 944008) (-587 "IPRNTPK.spad" 942979 942987 943209 943214) (-586 "IPF.spad" 942544 942556 942784 942877) (-585 "IPADIC.spad" 942305 942331 942470 942539) (-584 "IP4ADDR.spad" 941862 941870 942295 942300) (-583 "IOMODE.spad" 941384 941392 941852 941857) (-582 "IOBFILE.spad" 940745 940753 941374 941379) (-581 "IOBCON.spad" 940610 940618 940735 940740) (-580 "INVLAPLA.spad" 940259 940275 940600 940605) (-579 "INTTR.spad" 933641 933658 940249 940254) (-578 "INTTOOLS.spad" 931396 931412 933215 933220) (-577 "INTSLPE.spad" 930716 930724 931386 931391) (-576 "INTRVL.spad" 930282 930292 930630 930711) (-575 "INTRF.spad" 928706 928720 930272 930277) (-574 "INTRET.spad" 928138 928148 928696 928701) (-573 "INTRAT.spad" 926865 926882 928128 928133) (-572 "INTPM.spad" 925250 925266 926508 926513) (-571 "INTPAF.spad" 923114 923132 925182 925187) (-570 "INTPACK.spad" 913488 913496 923104 923109) (-569 "INT.spad" 912936 912944 913342 913483) (-568 "INTHERTR.spad" 912210 912227 912926 912931) (-567 "INTHERAL.spad" 911880 911904 912200 912205) (-566 "INTHEORY.spad" 908319 908327 911870 911875) (-565 "INTG0.spad" 902052 902070 908251 908256) (-564 "INTFTBL.spad" 896081 896089 902042 902047) (-563 "INTFACT.spad" 895140 895150 896071 896076) (-562 "INTEF.spad" 893525 893541 895130 895135) (-561 "INTDOM.spad" 892148 892156 893451 893520) (-560 "INTDOM.spad" 890833 890843 892138 892143) (-559 "INTCAT.spad" 889092 889102 890747 890828) (-558 "INTBIT.spad" 888599 888607 889082 889087) (-557 "INTALG.spad" 887787 887814 888589 888594) (-556 "INTAF.spad" 887287 887303 887777 887782) (-555 "INTABL.spad" 885805 885836 885968 885995) (-554 "INT8.spad" 885685 885693 885795 885800) (-553 "INT64.spad" 885564 885572 885675 885680) (-552 "INT32.spad" 885443 885451 885554 885559) (-551 "INT16.spad" 885322 885330 885433 885438) (-550 "INS.spad" 882825 882833 885224 885317) (-549 "INS.spad" 880414 880424 882815 882820) (-548 "INPSIGN.spad" 879862 879875 880404 880409) (-547 "INPRODPF.spad" 878958 878977 879852 879857) (-546 "INPRODFF.spad" 878046 878070 878948 878953) (-545 "INNMFACT.spad" 877021 877038 878036 878041) (-544 "INMODGCD.spad" 876509 876539 877011 877016) (-543 "INFSP.spad" 874806 874828 876499 876504) (-542 "INFPROD0.spad" 873886 873905 874796 874801) (-541 "INFORM.spad" 871085 871093 873876 873881) (-540 "INFORM1.spad" 870710 870720 871075 871080) (-539 "INFINITY.spad" 870262 870270 870700 870705) (-538 "INETCLTS.spad" 870239 870247 870252 870257) (-537 "INEP.spad" 868777 868799 870229 870234) (-536 "INDE.spad" 868506 868523 868767 868772) (-535 "INCRMAPS.spad" 867927 867937 868496 868501) (-534 "INBFILE.spad" 866999 867007 867917 867922) (-533 "INBFF.spad" 862793 862804 866989 866994) (-532 "INBCON.spad" 861083 861091 862783 862788) (-531 "INBCON.spad" 859371 859381 861073 861078) (-530 "INAST.spad" 859032 859040 859361 859366) (-529 "IMPTAST.spad" 858740 858748 859022 859027) (-528 "IMATRIX.spad" 857685 857711 858197 858224) (-527 "IMATQF.spad" 856779 856823 857641 857646) (-526 "IMATLIN.spad" 855384 855408 856735 856740) (-525 "ILIST.spad" 854042 854057 854567 854594) (-524 "IIARRAY2.spad" 853430 853468 853649 853676) (-523 "IFF.spad" 852840 852856 853111 853204) (-522 "IFAST.spad" 852454 852462 852830 852835) (-521 "IFARRAY.spad" 849947 849962 851637 851664) (-520 "IFAMON.spad" 849809 849826 849903 849908) (-519 "IEVALAB.spad" 849214 849226 849799 849804) (-518 "IEVALAB.spad" 848617 848631 849204 849209) (-517 "IDPO.spad" 848415 848427 848607 848612) (-516 "IDPOAMS.spad" 848171 848183 848405 848410) (-515 "IDPOAM.spad" 847891 847903 848161 848166) (-514 "IDPC.spad" 846829 846841 847881 847886) (-513 "IDPAM.spad" 846574 846586 846819 846824) (-512 "IDPAG.spad" 846321 846333 846564 846569) (-511 "IDENT.spad" 845971 845979 846311 846316) (-510 "IDECOMP.spad" 843210 843228 845961 845966) (-509 "IDEAL.spad" 838159 838198 843145 843150) (-508 "ICDEN.spad" 837348 837364 838149 838154) (-507 "ICARD.spad" 836539 836547 837338 837343) (-506 "IBPTOOLS.spad" 835146 835163 836529 836534) (-505 "IBITS.spad" 834349 834362 834782 834809) (-504 "IBATOOL.spad" 831326 831345 834339 834344) (-503 "IBACHIN.spad" 829833 829848 831316 831321) (-502 "IARRAY2.spad" 828821 828847 829440 829467) (-501 "IARRAY1.spad" 827866 827881 828004 828031) (-500 "IAN.spad" 826089 826097 827682 827775) (-499 "IALGFACT.spad" 825692 825725 826079 826084) (-498 "HYPCAT.spad" 825116 825124 825682 825687) (-497 "HYPCAT.spad" 824538 824548 825106 825111) (-496 "HOSTNAME.spad" 824346 824354 824528 824533) (-495 "HOMOTOP.spad" 824089 824099 824336 824341) (-494 "HOAGG.spad" 821371 821381 824079 824084) (-493 "HOAGG.spad" 818428 818440 821138 821143) (-492 "HEXADEC.spad" 816530 816538 816895 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187864 188125) (-165 "COMPCAT.spad" 184002 184014 185666 185671) (-164 "COMMUPC.spad" 183750 183768 183992 183997) (-163 "COMMONOP.spad" 183283 183291 183740 183745) (-162 "COMM.spad" 183094 183102 183273 183278) (-161 "COMMAAST.spad" 182857 182865 183084 183089) (-160 "COMBOPC.spad" 181772 181780 182847 182852) (-159 "COMBINAT.spad" 180539 180549 181762 181767) (-158 "COMBF.spad" 177921 177937 180529 180534) (-157 "COLOR.spad" 176758 176766 177911 177916) (-156 "COLONAST.spad" 176424 176432 176748 176753) (-155 "CMPLXRT.spad" 176135 176152 176414 176419) (-154 "CLLCTAST.spad" 175797 175805 176125 176130) (-153 "CLIP.spad" 171905 171913 175787 175792) (-152 "CLIF.spad" 170560 170576 171861 171900) (-151 "CLAGG.spad" 167065 167075 170550 170555) (-150 "CLAGG.spad" 163441 163453 166928 166933) (-149 "CINTSLPE.spad" 162772 162785 163431 163436) (-148 "CHVAR.spad" 160910 160932 162762 162767) (-147 "CHARZ.spad" 160825 160833 160890 160905) (-146 "CHARPOL.spad" 160335 160345 160815 160820) (-145 "CHARNZ.spad" 160088 160096 160315 160330) (-144 "CHAR.spad" 157962 157970 160078 160083) (-143 "CFCAT.spad" 157290 157298 157952 157957) (-142 "CDEN.spad" 156486 156500 157280 157285) (-141 "CCLASS.spad" 154635 154643 155897 155936) (-140 "CATEGORY.spad" 153677 153685 154625 154630) (-139 "CATCTOR.spad" 153568 153576 153667 153672) (-138 "CATAST.spad" 153186 153194 153558 153563) (-137 "CASEAST.spad" 152900 152908 153176 153181) (-136 "CARTEN.spad" 148187 148211 152890 152895) (-135 "CARTEN2.spad" 147577 147604 148177 148182) (-134 "CARD.spad" 144872 144880 147551 147572) (-133 "CAPSLAST.spad" 144646 144654 144862 144867) (-132 "CACHSET.spad" 144270 144278 144636 144641) (-131 "CABMON.spad" 143825 143833 144260 144265) (-130 "BYTEORD.spad" 143500 143508 143815 143820) (-129 "BYTE.spad" 142927 142935 143490 143495) (-128 "BYTEBUF.spad" 140786 140794 142096 142123) (-127 "BTREE.spad" 139859 139869 140393 140420) (-126 "BTOURN.spad" 138864 138874 139466 139493) (-125 "BTCAT.spad" 138256 138266 138832 138859) (-124 "BTCAT.spad" 137668 137680 138246 138251) (-123 "BTAGG.spad" 136796 136804 137636 137663) (-122 "BTAGG.spad" 135944 135954 136786 136791) (-121 "BSTREE.spad" 134685 134695 135551 135578) (-120 "BRILL.spad" 132882 132893 134675 134680) (-119 "BRAGG.spad" 131822 131832 132872 132877) (-118 "BRAGG.spad" 130726 130738 131778 131783) (-117 "BPADICRT.spad" 128707 128719 128962 129055) (-116 "BPADIC.spad" 128371 128383 128633 128702) (-115 "BOUNDZRO.spad" 128027 128044 128361 128366) (-114 "BOP.spad" 123209 123217 128017 128022) (-113 "BOP1.spad" 120675 120685 123199 123204) (-112 "BOOLEAN.spad" 120113 120121 120665 120670) (-111 "BMODULE.spad" 119825 119837 120081 120108) (-110 "BITS.spad" 119246 119254 119461 119488) (-109 "BINDING.spad" 118659 118667 119236 119241) (-108 "BINARY.spad" 116770 116778 117126 117219) (-107 "BGAGG.spad" 115975 115985 116750 116765) (-106 "BGAGG.spad" 115188 115200 115965 115970) (-105 "BFUNCT.spad" 114752 114760 115168 115183) (-104 "BEZOUT.spad" 113892 113919 114702 114707) (-103 "BBTREE.spad" 110737 110747 113499 113526) (-102 "BASTYPE.spad" 110409 110417 110727 110732) (-101 "BASTYPE.spad" 110079 110089 110399 110404) (-100 "BALFACT.spad" 109538 109551 110069 110074) (-99 "AUTOMOR.spad" 108989 108998 109518 109533) (-98 "ATTREG.spad" 105712 105719 108741 108984) (-97 "ATTRBUT.spad" 101735 101742 105692 105707) (-96 "ATTRAST.spad" 101452 101459 101725 101730) (-95 "ATRIG.spad" 100922 100929 101442 101447) (-94 "ATRIG.spad" 100390 100399 100912 100917) (-93 "ASTCAT.spad" 100294 100301 100380 100385) (-92 "ASTCAT.spad" 100196 100205 100284 100289) (-91 "ASTACK.spad" 99535 99544 99803 99830) (-90 "ASSOCEQ.spad" 98361 98372 99491 99496) (-89 "ASP9.spad" 97442 97455 98351 98356) (-88 "ASP8.spad" 96485 96498 97432 97437) (-87 "ASP80.spad" 95807 95820 96475 96480) (-86 "ASP7.spad" 94967 94980 95797 95802) (-85 "ASP78.spad" 94418 94431 94957 94962) (-84 "ASP77.spad" 93787 93800 94408 94413) (-83 "ASP74.spad" 92879 92892 93777 93782) (-82 "ASP73.spad" 92150 92163 92869 92874) (-81 "ASP6.spad" 91017 91030 92140 92145) (-80 "ASP55.spad" 89526 89539 91007 91012) (-79 "ASP50.spad" 87343 87356 89516 89521) (-78 "ASP4.spad" 86638 86651 87333 87338) (-77 "ASP49.spad" 85637 85650 86628 86633) (-76 "ASP42.spad" 84044 84083 85627 85632) (-75 "ASP41.spad" 82623 82662 84034 84039) (-74 "ASP35.spad" 81611 81624 82613 82618) (-73 "ASP34.spad" 80912 80925 81601 81606) (-72 "ASP33.spad" 80472 80485 80902 80907) (-71 "ASP31.spad" 79612 79625 80462 80467) (-70 "ASP30.spad" 78504 78517 79602 79607) (-69 "ASP29.spad" 77970 77983 78494 78499) (-68 "ASP28.spad" 69243 69256 77960 77965) (-67 "ASP27.spad" 68140 68153 69233 69238) (-66 "ASP24.spad" 67227 67240 68130 68135) (-65 "ASP20.spad" 66691 66704 67217 67222) (-64 "ASP1.spad" 66072 66085 66681 66686) (-63 "ASP19.spad" 60758 60771 66062 66067) (-62 "ASP12.spad" 60172 60185 60748 60753) (-61 "ASP10.spad" 59443 59456 60162 60167) (-60 "ARRAY2.spad" 58803 58812 59050 59077) (-59 "ARRAY1.spad" 57640 57649 57986 58013) (-58 "ARRAY12.spad" 56353 56364 57630 57635) (-57 "ARR2CAT.spad" 52127 52148 56321 56348) (-56 "ARR2CAT.spad" 47921 47944 52117 52122) (-55 "ARITY.spad" 47293 47300 47911 47916) (-54 "APPRULE.spad" 46553 46575 47283 47288) (-53 "APPLYORE.spad" 46172 46185 46543 46548) (-52 "ANY.spad" 45031 45038 46162 46167) (-51 "ANY1.spad" 44102 44111 45021 45026) (-50 "ANTISYM.spad" 42547 42563 44082 44097) (-49 "ANON.spad" 42240 42247 42537 42542) (-48 "AN.spad" 40549 40556 42056 42149) (-47 "AMR.spad" 38734 38745 40447 40544) (-46 "AMR.spad" 36756 36769 38471 38476) (-45 "ALIST.spad" 34168 34189 34518 34545) (-44 "ALGSC.spad" 33303 33329 34040 34093) (-43 "ALGPKG.spad" 29086 29097 33259 33264) (-42 "ALGMFACT.spad" 28279 28293 29076 29081) (-41 "ALGMANIP.spad" 25753 25768 28112 28117) (-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 2268420 2268425 2268430 2268435) (-2 NIL 2268400 2268405 2268410 2268415) (-1 NIL 2268380 2268385 2268390 2268395) (0 NIL 2268360 2268365 2268370 2268375) (-1303 "ZMOD.spad" 2268169 2268182 2268298 2268355) (-1302 "ZLINDEP.spad" 2267235 2267246 2268159 2268164) (-1301 "ZDSOLVE.spad" 2257180 2257202 2267225 2267230) (-1300 "YSTREAM.spad" 2256675 2256686 2257170 2257175) (-1299 "XRPOLY.spad" 2255895 2255915 2256531 2256600) (-1298 "XPR.spad" 2253690 2253703 2255613 2255712) (-1297 "XPOLY.spad" 2253245 2253256 2253546 2253615) (-1296 "XPOLYC.spad" 2252564 2252580 2253171 2253240) (-1295 "XPBWPOLY.spad" 2251001 2251021 2252344 2252413) (-1294 "XF.spad" 2249464 2249479 2250903 2250996) (-1293 "XF.spad" 2247907 2247924 2249348 2249353) (-1292 "XFALG.spad" 2244955 2244971 2247833 2247902) (-1291 "XEXPPKG.spad" 2244206 2244232 2244945 2244950) (-1290 "XDPOLY.spad" 2243820 2243836 2244062 2244131) (-1289 "XALG.spad" 2243480 2243491 2243776 2243815) (-1288 "WUTSET.spad" 2239319 2239336 2243126 2243153) (-1287 "WP.spad" 2238518 2238562 2239177 2239244) (-1286 "WHILEAST.spad" 2238316 2238325 2238508 2238513) (-1285 "WHEREAST.spad" 2237987 2237996 2238306 2238311) (-1284 "WFFINTBS.spad" 2235650 2235672 2237977 2237982) (-1283 "WEIER.spad" 2233872 2233883 2235640 2235645) (-1282 "VSPACE.spad" 2233545 2233556 2233840 2233867) (-1281 "VSPACE.spad" 2233238 2233251 2233535 2233540) (-1280 "VOID.spad" 2232915 2232924 2233228 2233233) (-1279 "VIEW.spad" 2230595 2230604 2232905 2232910) (-1278 "VIEWDEF.spad" 2225796 2225805 2230585 2230590) (-1277 "VIEW3D.spad" 2209757 2209766 2225786 2225791) (-1276 "VIEW2D.spad" 2197648 2197657 2209747 2209752) (-1275 "VECTOR.spad" 2196322 2196333 2196573 2196600) (-1274 "VECTOR2.spad" 2194961 2194974 2196312 2196317) (-1273 "VECTCAT.spad" 2192865 2192876 2194929 2194956) (-1272 "VECTCAT.spad" 2190576 2190589 2192642 2192647) (-1271 "VARIABLE.spad" 2190356 2190371 2190566 2190571) (-1270 "UTYPE.spad" 2190000 2190009 2190346 2190351) (-1269 "UTSODETL.spad" 2189295 2189319 2189956 2189961) (-1268 "UTSODE.spad" 2187511 2187531 2189285 2189290) (-1267 "UTS.spad" 2182315 2182343 2185978 2186075) (-1266 "UTSCAT.spad" 2179794 2179810 2182213 2182310) (-1265 "UTSCAT.spad" 2176917 2176935 2179338 2179343) (-1264 "UTS2.spad" 2176512 2176547 2176907 2176912) (-1263 "URAGG.spad" 2171185 2171196 2176502 2176507) (-1262 "URAGG.spad" 2165822 2165835 2171141 2171146) (-1261 "UPXSSING.spad" 2163467 2163493 2164903 2165036) (-1260 "UPXS.spad" 2160621 2160649 2161599 2161748) (-1259 "UPXSCONS.spad" 2158380 2158400 2158753 2158902) (-1258 "UPXSCCA.spad" 2156951 2156971 2158226 2158375) (-1257 "UPXSCCA.spad" 2155664 2155686 2156941 2156946) (-1256 "UPXSCAT.spad" 2154253 2154269 2155510 2155659) (-1255 "UPXS2.spad" 2153796 2153849 2154243 2154248) (-1254 "UPSQFREE.spad" 2152210 2152224 2153786 2153791) (-1253 "UPSCAT.spad" 2149821 2149845 2152108 2152205) (-1252 "UPSCAT.spad" 2147138 2147164 2149427 2149432) (-1251 "UPOLYC.spad" 2142178 2142189 2146980 2147133) (-1250 "UPOLYC.spad" 2137110 2137123 2141914 2141919) (-1249 "UPOLYC2.spad" 2136581 2136600 2137100 2137105) (-1248 "UP.spad" 2133780 2133795 2134167 2134320) (-1247 "UPMP.spad" 2132680 2132693 2133770 2133775) (-1246 "UPDIVP.spad" 2132245 2132259 2132670 2132675) (-1245 "UPDECOMP.spad" 2130490 2130504 2132235 2132240) (-1244 "UPCDEN.spad" 2129699 2129715 2130480 2130485) (-1243 "UP2.spad" 2129063 2129084 2129689 2129694) (-1242 "UNISEG.spad" 2128416 2128427 2128982 2128987) (-1241 "UNISEG2.spad" 2127913 2127926 2128372 2128377) (-1240 "UNIFACT.spad" 2127016 2127028 2127903 2127908) (-1239 "ULS.spad" 2117574 2117602 2118661 2119090) (-1238 "ULSCONS.spad" 2109970 2109990 2110340 2110489) (-1237 "ULSCCAT.spad" 2107707 2107727 2109816 2109965) (-1236 "ULSCCAT.spad" 2105552 2105574 2107663 2107668) (-1235 "ULSCAT.spad" 2103784 2103800 2105398 2105547) (-1234 "ULS2.spad" 2103298 2103351 2103774 2103779) (-1233 "UINT8.spad" 2103175 2103184 2103288 2103293) (-1232 "UINT64.spad" 2103051 2103060 2103165 2103170) (-1231 "UINT32.spad" 2102927 2102936 2103041 2103046) (-1230 "UINT16.spad" 2102803 2102812 2102917 2102922) (-1229 "UFD.spad" 2101868 2101877 2102729 2102798) (-1228 "UFD.spad" 2100995 2101006 2101858 2101863) (-1227 "UDVO.spad" 2099876 2099885 2100985 2100990) (-1226 "UDPO.spad" 2097369 2097380 2099832 2099837) (-1225 "TYPE.spad" 2097301 2097310 2097359 2097364) (-1224 "TYPEAST.spad" 2097220 2097229 2097291 2097296) (-1223 "TWOFACT.spad" 2095872 2095887 2097210 2097215) (-1222 "TUPLE.spad" 2095358 2095369 2095771 2095776) (-1221 "TUBETOOL.spad" 2092225 2092234 2095348 2095353) (-1220 "TUBE.spad" 2090872 2090889 2092215 2092220) (-1219 "TS.spad" 2089471 2089487 2090437 2090534) (-1218 "TSETCAT.spad" 2076598 2076615 2089439 2089466) (-1217 "TSETCAT.spad" 2063711 2063730 2076554 2076559) (-1216 "TRMANIP.spad" 2058077 2058094 2063417 2063422) (-1215 "TRIMAT.spad" 2057040 2057065 2058067 2058072) (-1214 "TRIGMNIP.spad" 2055567 2055584 2057030 2057035) (-1213 "TRIGCAT.spad" 2055079 2055088 2055557 2055562) (-1212 "TRIGCAT.spad" 2054589 2054600 2055069 2055074) (-1211 "TREE.spad" 2053164 2053175 2054196 2054223) (-1210 "TRANFUN.spad" 2053003 2053012 2053154 2053159) (-1209 "TRANFUN.spad" 2052840 2052851 2052993 2052998) (-1208 "TOPSP.spad" 2052514 2052523 2052830 2052835) (-1207 "TOOLSIGN.spad" 2052177 2052188 2052504 2052509) (-1206 "TEXTFILE.spad" 2050738 2050747 2052167 2052172) (-1205 "TEX.spad" 2047884 2047893 2050728 2050733) (-1204 "TEX1.spad" 2047440 2047451 2047874 2047879) (-1203 "TEMUTL.spad" 2046995 2047004 2047430 2047435) (-1202 "TBCMPPK.spad" 2045088 2045111 2046985 2046990) (-1201 "TBAGG.spad" 2044138 2044161 2045068 2045083) (-1200 "TBAGG.spad" 2043196 2043221 2044128 2044133) (-1199 "TANEXP.spad" 2042604 2042615 2043186 2043191) (-1198 "TABLE.spad" 2041015 2041038 2041285 2041312) (-1197 "TABLEAU.spad" 2040496 2040507 2041005 2041010) (-1196 "TABLBUMP.spad" 2037299 2037310 2040486 2040491) (-1195 "SYSTEM.spad" 2036527 2036536 2037289 2037294) (-1194 "SYSSOLP.spad" 2034010 2034021 2036517 2036522) (-1193 "SYSPTR.spad" 2033909 2033918 2034000 2034005) (-1192 "SYSNNI.spad" 2033091 2033102 2033899 2033904) (-1191 "SYSINT.spad" 2032495 2032506 2033081 2033086) (-1190 "SYNTAX.spad" 2028701 2028710 2032485 2032490) (-1189 "SYMTAB.spad" 2026769 2026778 2028691 2028696) (-1188 "SYMS.spad" 2022792 2022801 2026759 2026764) (-1187 "SYMPOLY.spad" 2021799 2021810 2021881 2022008) (-1186 "SYMFUNC.spad" 2021300 2021311 2021789 2021794) (-1185 "SYMBOL.spad" 2018803 2018812 2021290 2021295) (-1184 "SWITCH.spad" 2015574 2015583 2018793 2018798) (-1183 "SUTS.spad" 2012479 2012507 2014041 2014138) (-1182 "SUPXS.spad" 2009620 2009648 2010611 2010760) (-1181 "SUP.spad" 2006433 2006444 2007206 2007359) (-1180 "SUPFRACF.spad" 2005538 2005556 2006423 2006428) (-1179 "SUP2.spad" 2004930 2004943 2005528 2005533) (-1178 "SUMRF.spad" 2003904 2003915 2004920 2004925) (-1177 "SUMFS.spad" 2003541 2003558 2003894 2003899) (-1176 "SULS.spad" 1994086 1994114 1995186 1995615) (-1175 "SUCHTAST.spad" 1993855 1993864 1994076 1994081) (-1174 "SUCH.spad" 1993537 1993552 1993845 1993850) (-1173 "SUBSPACE.spad" 1985652 1985667 1993527 1993532) (-1172 "SUBRESP.spad" 1984822 1984836 1985608 1985613) (-1171 "STTF.spad" 1980921 1980937 1984812 1984817) (-1170 "STTFNC.spad" 1977389 1977405 1980911 1980916) (-1169 "STTAYLOR.spad" 1970024 1970035 1977270 1977275) (-1168 "STRTBL.spad" 1968529 1968546 1968678 1968705) (-1167 "STRING.spad" 1967938 1967947 1967952 1967979) (-1166 "STRICAT.spad" 1967726 1967735 1967906 1967933) (-1165 "STREAM.spad" 1964644 1964655 1967251 1967266) (-1164 "STREAM3.spad" 1964217 1964232 1964634 1964639) (-1163 "STREAM2.spad" 1963345 1963358 1964207 1964212) (-1162 "STREAM1.spad" 1963051 1963062 1963335 1963340) (-1161 "STINPROD.spad" 1961987 1962003 1963041 1963046) (-1160 "STEP.spad" 1961188 1961197 1961977 1961982) (-1159 "STEPAST.spad" 1960422 1960431 1961178 1961183) (-1158 "STBL.spad" 1958948 1958976 1959115 1959130) (-1157 "STAGG.spad" 1958023 1958034 1958938 1958943) (-1156 "STAGG.spad" 1957096 1957109 1958013 1958018) (-1155 "STACK.spad" 1956453 1956464 1956703 1956730) (-1154 "SREGSET.spad" 1954157 1954174 1956099 1956126) (-1153 "SRDCMPK.spad" 1952718 1952738 1954147 1954152) (-1152 "SRAGG.spad" 1947861 1947870 1952686 1952713) (-1151 "SRAGG.spad" 1943024 1943035 1947851 1947856) (-1150 "SQMATRIX.spad" 1940640 1940658 1941556 1941643) (-1149 "SPLTREE.spad" 1935192 1935205 1940076 1940103) (-1148 "SPLNODE.spad" 1931780 1931793 1935182 1935187) (-1147 "SPFCAT.spad" 1930589 1930598 1931770 1931775) (-1146 "SPECOUT.spad" 1929141 1929150 1930579 1930584) (-1145 "SPADXPT.spad" 1920736 1920745 1929131 1929136) (-1144 "spad-parser.spad" 1920201 1920210 1920726 1920731) (-1143 "SPADAST.spad" 1919902 1919911 1920191 1920196) (-1142 "SPACEC.spad" 1904101 1904112 1919892 1919897) (-1141 "SPACE3.spad" 1903877 1903888 1904091 1904096) (-1140 "SORTPAK.spad" 1903426 1903439 1903833 1903838) (-1139 "SOLVETRA.spad" 1901189 1901200 1903416 1903421) (-1138 "SOLVESER.spad" 1899717 1899728 1901179 1901184) (-1137 "SOLVERAD.spad" 1895743 1895754 1899707 1899712) (-1136 "SOLVEFOR.spad" 1894205 1894223 1895733 1895738) (-1135 "SNTSCAT.spad" 1893805 1893822 1894173 1894200) (-1134 "SMTS.spad" 1892077 1892103 1893370 1893467) (-1133 "SMP.spad" 1889552 1889572 1889942 1890069) (-1132 "SMITH.spad" 1888397 1888422 1889542 1889547) (-1131 "SMATCAT.spad" 1886507 1886537 1888341 1888392) (-1130 "SMATCAT.spad" 1884549 1884581 1886385 1886390) (-1129 "SKAGG.spad" 1883512 1883523 1884517 1884544) (-1128 "SINT.spad" 1882344 1882353 1883378 1883507) (-1127 "SIMPAN.spad" 1882072 1882081 1882334 1882339) (-1126 "SIG.spad" 1881402 1881411 1882062 1882067) (-1125 "SIGNRF.spad" 1880520 1880531 1881392 1881397) (-1124 "SIGNEF.spad" 1879799 1879816 1880510 1880515) (-1123 "SIGAST.spad" 1879184 1879193 1879789 1879794) (-1122 "SHP.spad" 1877112 1877127 1879140 1879145) (-1121 "SHDP.spad" 1866823 1866850 1867332 1867463) (-1120 "SGROUP.spad" 1866431 1866440 1866813 1866818) (-1119 "SGROUP.spad" 1866037 1866048 1866421 1866426) (-1118 "SGCF.spad" 1859200 1859209 1866027 1866032) (-1117 "SFRTCAT.spad" 1858130 1858147 1859168 1859195) (-1116 "SFRGCD.spad" 1857193 1857213 1858120 1858125) (-1115 "SFQCMPK.spad" 1851830 1851850 1857183 1857188) (-1114 "SFORT.spad" 1851269 1851283 1851820 1851825) (-1113 "SEXOF.spad" 1851112 1851152 1851259 1851264) (-1112 "SEX.spad" 1851004 1851013 1851102 1851107) (-1111 "SEXCAT.spad" 1848605 1848645 1850994 1850999) (-1110 "SET.spad" 1846929 1846940 1848026 1848065) (-1109 "SETMN.spad" 1845379 1845396 1846919 1846924) (-1108 "SETCAT.spad" 1844701 1844710 1845369 1845374) (-1107 "SETCAT.spad" 1844021 1844032 1844691 1844696) (-1106 "SETAGG.spad" 1840570 1840581 1844001 1844016) (-1105 "SETAGG.spad" 1837127 1837140 1840560 1840565) (-1104 "SEQAST.spad" 1836830 1836839 1837117 1837122) (-1103 "SEGXCAT.spad" 1835986 1835999 1836820 1836825) (-1102 "SEG.spad" 1835799 1835810 1835905 1835910) (-1101 "SEGCAT.spad" 1834724 1834735 1835789 1835794) (-1100 "SEGBIND.spad" 1834482 1834493 1834671 1834676) (-1099 "SEGBIND2.spad" 1834180 1834193 1834472 1834477) (-1098 "SEGAST.spad" 1833894 1833903 1834170 1834175) (-1097 "SEG2.spad" 1833329 1833342 1833850 1833855) (-1096 "SDVAR.spad" 1832605 1832616 1833319 1833324) (-1095 "SDPOL.spad" 1830031 1830042 1830322 1830449) (-1094 "SCPKG.spad" 1828120 1828131 1830021 1830026) (-1093 "SCOPE.spad" 1827273 1827282 1828110 1828115) (-1092 "SCACHE.spad" 1825969 1825980 1827263 1827268) (-1091 "SASTCAT.spad" 1825878 1825887 1825959 1825964) (-1090 "SAOS.spad" 1825750 1825759 1825868 1825873) (-1089 "SAERFFC.spad" 1825463 1825483 1825740 1825745) (-1088 "SAE.spad" 1823638 1823654 1824249 1824384) (-1087 "SAEFACT.spad" 1823339 1823359 1823628 1823633) (-1086 "RURPK.spad" 1820998 1821014 1823329 1823334) (-1085 "RULESET.spad" 1820451 1820475 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1580854) (-973 "PROPFUN1.spad" 1580075 1580086 1580472 1580477) (-972 "PROPFRML.spad" 1578643 1578654 1580065 1580070) (-971 "PROPERTY.spad" 1578131 1578139 1578633 1578638) (-970 "PRODUCT.spad" 1575813 1575825 1576097 1576152) (-969 "PR.spad" 1574205 1574217 1574904 1575031) (-968 "PRINT.spad" 1573957 1573965 1574195 1574200) (-967 "PRIMES.spad" 1572210 1572220 1573947 1573952) (-966 "PRIMELT.spad" 1570291 1570305 1572200 1572205) (-965 "PRIMCAT.spad" 1569918 1569926 1570281 1570286) (-964 "PRIMARR.spad" 1568923 1568933 1569101 1569128) (-963 "PRIMARR2.spad" 1567690 1567702 1568913 1568918) (-962 "PREASSOC.spad" 1567072 1567084 1567680 1567685) (-961 "PPCURVE.spad" 1566209 1566217 1567062 1567067) (-960 "PORTNUM.spad" 1565984 1565992 1566199 1566204) (-959 "POLYROOT.spad" 1564833 1564855 1565940 1565945) (-958 "POLY.spad" 1562168 1562178 1562683 1562810) (-957 "POLYLIFT.spad" 1561433 1561456 1562158 1562163) (-956 "POLYCATQ.spad" 1559551 1559573 1561423 1561428) (-955 "POLYCAT.spad" 1553021 1553042 1559419 1559546) (-954 "POLYCAT.spad" 1545829 1545852 1552229 1552234) (-953 "POLY2UP.spad" 1545281 1545295 1545819 1545824) (-952 "POLY2.spad" 1544878 1544890 1545271 1545276) (-951 "POLUTIL.spad" 1543819 1543848 1544834 1544839) (-950 "POLTOPOL.spad" 1542567 1542582 1543809 1543814) (-949 "POINT.spad" 1541405 1541415 1541492 1541519) (-948 "PNTHEORY.spad" 1538107 1538115 1541395 1541400) (-947 "PMTOOLS.spad" 1536882 1536896 1538097 1538102) (-946 "PMSYM.spad" 1536431 1536441 1536872 1536877) (-945 "PMQFCAT.spad" 1536022 1536036 1536421 1536426) (-944 "PMPRED.spad" 1535501 1535515 1536012 1536017) (-943 "PMPREDFS.spad" 1534955 1534977 1535491 1535496) (-942 "PMPLCAT.spad" 1534035 1534053 1534887 1534892) (-941 "PMLSAGG.spad" 1533620 1533634 1534025 1534030) (-940 "PMKERNEL.spad" 1533199 1533211 1533610 1533615) (-939 "PMINS.spad" 1532779 1532789 1533189 1533194) (-938 "PMFS.spad" 1532356 1532374 1532769 1532774) (-937 "PMDOWN.spad" 1531646 1531660 1532346 1532351) (-936 "PMASS.spad" 1530656 1530664 1531636 1531641) (-935 "PMASSFS.spad" 1529623 1529639 1530646 1530651) (-934 "PLOTTOOL.spad" 1529403 1529411 1529613 1529618) (-933 "PLOT.spad" 1524326 1524334 1529393 1529398) (-932 "PLOT3D.spad" 1520790 1520798 1524316 1524321) (-931 "PLOT1.spad" 1519947 1519957 1520780 1520785) (-930 "PLEQN.spad" 1507237 1507264 1519937 1519942) (-929 "PINTERP.spad" 1506859 1506878 1507227 1507232) (-928 "PINTERPA.spad" 1506643 1506659 1506849 1506854) (-927 "PI.spad" 1506252 1506260 1506617 1506638) (-926 "PID.spad" 1505222 1505230 1506178 1506247) (-925 "PICOERCE.spad" 1504879 1504889 1505212 1505217) (-924 "PGROEB.spad" 1503480 1503494 1504869 1504874) (-923 "PGE.spad" 1495097 1495105 1503470 1503475) (-922 "PGCD.spad" 1493987 1494004 1495087 1495092) (-921 "PFRPAC.spad" 1493136 1493146 1493977 1493982) (-920 "PFR.spad" 1489799 1489809 1493038 1493131) (-919 "PFOTOOLS.spad" 1489057 1489073 1489789 1489794) (-918 "PFOQ.spad" 1488427 1488445 1489047 1489052) (-917 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1350883 1352706 1352711) (-823 "ODVAR.spad" 1350134 1350144 1350863 1350868) (-822 "ODR.spad" 1349778 1349804 1349946 1350095) (-821 "ODPOL.spad" 1347160 1347170 1347500 1347627) (-820 "ODP.spad" 1337007 1337027 1337380 1337511) (-819 "ODETOOLS.spad" 1335656 1335675 1336997 1337002) (-818 "ODESYS.spad" 1333350 1333367 1335646 1335651) (-817 "ODERTRIC.spad" 1329359 1329376 1333307 1333312) (-816 "ODERED.spad" 1328758 1328782 1329349 1329354) (-815 "ODERAT.spad" 1326373 1326390 1328748 1328753) (-814 "ODEPRRIC.spad" 1323410 1323432 1326363 1326368) (-813 "ODEPROB.spad" 1322667 1322675 1323400 1323405) (-812 "ODEPRIM.spad" 1320001 1320023 1322657 1322662) (-811 "ODEPAL.spad" 1319387 1319411 1319991 1319996) (-810 "ODEPACK.spad" 1306053 1306061 1319377 1319382) (-809 "ODEINT.spad" 1305488 1305504 1306043 1306048) (-808 "ODEIFTBL.spad" 1302883 1302891 1305478 1305483) (-807 "ODEEF.spad" 1298374 1298390 1302873 1302878) (-806 "ODECONST.spad" 1297911 1297929 1298364 1298369) (-805 "ODECAT.spad" 1296509 1296517 1297901 1297906) (-804 "OCT.spad" 1294645 1294655 1295359 1295398) (-803 "OCTCT2.spad" 1294291 1294312 1294635 1294640) (-802 "OC.spad" 1292087 1292097 1294247 1294286) (-801 "OC.spad" 1289608 1289620 1291770 1291775) (-800 "OCAMON.spad" 1289456 1289464 1289598 1289603) (-799 "OASGP.spad" 1289271 1289279 1289446 1289451) (-798 "OAMONS.spad" 1288793 1288801 1289261 1289266) (-797 "OAMON.spad" 1288654 1288662 1288783 1288788) (-796 "OAGROUP.spad" 1288516 1288524 1288644 1288649) (-795 "NUMTUBE.spad" 1288107 1288123 1288506 1288511) (-794 "NUMQUAD.spad" 1276083 1276091 1288097 1288102) (-793 "NUMODE.spad" 1267437 1267445 1276073 1276078) (-792 "NUMINT.spad" 1265003 1265011 1267427 1267432) (-791 "NUMFMT.spad" 1263843 1263851 1264993 1264998) (-790 "NUMERIC.spad" 1255957 1255967 1263648 1263653) (-789 "NTSCAT.spad" 1254465 1254481 1255925 1255952) (-788 "NTPOLFN.spad" 1254016 1254026 1254382 1254387) (-787 "NSUP.spad" 1247062 1247072 1251602 1251755) (-786 "NSUP2.spad" 1246454 1246466 1247052 1247057) (-785 "NSMP.spad" 1242684 1242703 1242992 1243119) (-784 "NREP.spad" 1241062 1241076 1242674 1242679) (-783 "NPCOEF.spad" 1240308 1240328 1241052 1241057) (-782 "NORMRETR.spad" 1239906 1239945 1240298 1240303) (-781 "NORMPK.spad" 1237808 1237827 1239896 1239901) (-780 "NORMMA.spad" 1237496 1237522 1237798 1237803) (-779 "NONE.spad" 1237237 1237245 1237486 1237491) (-778 "NONE1.spad" 1236913 1236923 1237227 1237232) (-777 "NODE1.spad" 1236400 1236416 1236903 1236908) (-776 "NNI.spad" 1235295 1235303 1236374 1236395) (-775 "NLINSOL.spad" 1233921 1233931 1235285 1235290) (-774 "NIPROB.spad" 1232462 1232470 1233911 1233916) (-773 "NFINTBAS.spad" 1230022 1230039 1232452 1232457) (-772 "NETCLT.spad" 1229996 1230007 1230012 1230017) (-771 "NCODIV.spad" 1228212 1228228 1229986 1229991) (-770 "NCNTFRAC.spad" 1227854 1227868 1228202 1228207) (-769 "NCEP.spad" 1226020 1226034 1227844 1227849) (-768 "NASRING.spad" 1225616 1225624 1226010 1226015) (-767 "NASRING.spad" 1225210 1225220 1225606 1225611) (-766 "NARNG.spad" 1224562 1224570 1225200 1225205) (-765 "NARNG.spad" 1223912 1223922 1224552 1224557) (-764 "NAGSP.spad" 1222989 1222997 1223902 1223907) (-763 "NAGS.spad" 1212650 1212658 1222979 1222984) (-762 "NAGF07.spad" 1211081 1211089 1212640 1212645) (-761 "NAGF04.spad" 1205483 1205491 1211071 1211076) (-760 "NAGF02.spad" 1199552 1199560 1205473 1205478) (-759 "NAGF01.spad" 1195313 1195321 1199542 1199547) (-758 "NAGE04.spad" 1189013 1189021 1195303 1195308) (-757 "NAGE02.spad" 1179673 1179681 1189003 1189008) (-756 "NAGE01.spad" 1175675 1175683 1179663 1179668) (-755 "NAGD03.spad" 1173679 1173687 1175665 1175670) (-754 "NAGD02.spad" 1166426 1166434 1173669 1173674) (-753 "NAGD01.spad" 1160719 1160727 1166416 1166421) (-752 "NAGC06.spad" 1156594 1156602 1160709 1160714) (-751 "NAGC05.spad" 1155095 1155103 1156584 1156589) (-750 "NAGC02.spad" 1154362 1154370 1155085 1155090) (-749 "NAALG.spad" 1153903 1153913 1154330 1154357) (-748 "NAALG.spad" 1153464 1153476 1153893 1153898) (-747 "MULTSQFR.spad" 1150422 1150439 1153454 1153459) (-746 "MULTFACT.spad" 1149805 1149822 1150412 1150417) (-745 "MTSCAT.spad" 1147899 1147920 1149703 1149800) (-744 "MTHING.spad" 1147558 1147568 1147889 1147894) (-743 "MSYSCMD.spad" 1146992 1147000 1147548 1147553) (-742 "MSET.spad" 1144950 1144960 1146698 1146737) (-741 "MSETAGG.spad" 1144795 1144805 1144918 1144945) (-740 "MRING.spad" 1141772 1141784 1144503 1144570) (-739 "MRF2.spad" 1141342 1141356 1141762 1141767) (-738 "MRATFAC.spad" 1140888 1140905 1141332 1141337) (-737 "MPRFF.spad" 1138928 1138947 1140878 1140883) (-736 "MPOLY.spad" 1136399 1136414 1136758 1136885) (-735 "MPCPF.spad" 1135663 1135682 1136389 1136394) (-734 "MPC3.spad" 1135480 1135520 1135653 1135658) (-733 "MPC2.spad" 1135126 1135159 1135470 1135475) (-732 "MONOTOOL.spad" 1133477 1133494 1135116 1135121) (-731 "MONOID.spad" 1132796 1132804 1133467 1133472) (-730 "MONOID.spad" 1132113 1132123 1132786 1132791) (-729 "MONOGEN.spad" 1130861 1130874 1131973 1132108) (-728 "MONOGEN.spad" 1129631 1129646 1130745 1130750) (-727 "MONADWU.spad" 1127661 1127669 1129621 1129626) (-726 "MONADWU.spad" 1125689 1125699 1127651 1127656) (-725 "MONAD.spad" 1124849 1124857 1125679 1125684) (-724 "MONAD.spad" 1124007 1124017 1124839 1124844) (-723 "MOEBIUS.spad" 1122743 1122757 1123987 1124002) (-722 "MODULE.spad" 1122613 1122623 1122711 1122738) (-721 "MODULE.spad" 1122503 1122515 1122603 1122608) (-720 "MODRING.spad" 1121838 1121877 1122483 1122498) (-719 "MODOP.spad" 1120503 1120515 1121660 1121727) (-718 "MODMONOM.spad" 1120234 1120252 1120493 1120498) (-717 "MODMON.spad" 1117029 1117045 1117748 1117901) (-716 "MODFIELD.spad" 1116391 1116430 1116931 1117024) (-715 "MMLFORM.spad" 1115251 1115259 1116381 1116386) (-714 "MMAP.spad" 1114993 1115027 1115241 1115246) (-713 "MLO.spad" 1113452 1113462 1114949 1114988) (-712 "MLIFT.spad" 1112064 1112081 1113442 1113447) (-711 "MKUCFUNC.spad" 1111599 1111617 1112054 1112059) (-710 "MKRECORD.spad" 1111203 1111216 1111589 1111594) (-709 "MKFUNC.spad" 1110610 1110620 1111193 1111198) (-708 "MKFLCFN.spad" 1109578 1109588 1110600 1110605) (-707 "MKBCFUNC.spad" 1109073 1109091 1109568 1109573) (-706 "MINT.spad" 1108512 1108520 1108975 1109068) (-705 "MHROWRED.spad" 1107023 1107033 1108502 1108507) (-704 "MFLOAT.spad" 1105543 1105551 1106913 1107018) (-703 "MFINFACT.spad" 1104943 1104965 1105533 1105538) (-702 "MESH.spad" 1102725 1102733 1104933 1104938) (-701 "MDDFACT.spad" 1100936 1100946 1102715 1102720) (-700 "MDAGG.spad" 1100227 1100237 1100916 1100931) (-699 "MCMPLX.spad" 1096238 1096246 1096852 1097053) (-698 "MCDEN.spad" 1095448 1095460 1096228 1096233) (-697 "MCALCFN.spad" 1092570 1092596 1095438 1095443) (-696 "MAYBE.spad" 1091854 1091865 1092560 1092565) (-695 "MATSTOR.spad" 1089162 1089172 1091844 1091849) (-694 "MATRIX.spad" 1087866 1087876 1088350 1088377) (-693 "MATLIN.spad" 1085210 1085234 1087750 1087755) (-692 "MATCAT.spad" 1076939 1076961 1085178 1085205) (-691 "MATCAT.spad" 1068540 1068564 1076781 1076786) (-690 "MATCAT2.spad" 1067822 1067870 1068530 1068535) (-689 "MAPPKG3.spad" 1066737 1066751 1067812 1067817) (-688 "MAPPKG2.spad" 1066075 1066087 1066727 1066732) (-687 "MAPPKG1.spad" 1064903 1064913 1066065 1066070) (-686 "MAPPAST.spad" 1064218 1064226 1064893 1064898) (-685 "MAPHACK3.spad" 1064030 1064044 1064208 1064213) (-684 "MAPHACK2.spad" 1063799 1063811 1064020 1064025) (-683 "MAPHACK1.spad" 1063443 1063453 1063789 1063794) (-682 "MAGMA.spad" 1061233 1061250 1063433 1063438) (-681 "MACROAST.spad" 1060812 1060820 1061223 1061228) (-680 "M3D.spad" 1058532 1058542 1060190 1060195) (-679 "LZSTAGG.spad" 1055770 1055780 1058522 1058527) (-678 "LZSTAGG.spad" 1053006 1053018 1055760 1055765) (-677 "LWORD.spad" 1049711 1049728 1052996 1053001) (-676 "LSTAST.spad" 1049495 1049503 1049701 1049706) (-675 "LSQM.spad" 1047725 1047739 1048119 1048170) (-674 "LSPP.spad" 1047260 1047277 1047715 1047720) (-673 "LSMP.spad" 1046110 1046138 1047250 1047255) (-672 "LSMP1.spad" 1043928 1043942 1046100 1046105) (-671 "LSAGG.spad" 1043597 1043607 1043896 1043923) (-670 "LSAGG.spad" 1043286 1043298 1043587 1043592) (-669 "LPOLY.spad" 1042240 1042259 1043142 1043211) (-668 "LPEFRAC.spad" 1041511 1041521 1042230 1042235) (-667 "LO.spad" 1040912 1040926 1041445 1041472) (-666 "LOGIC.spad" 1040514 1040522 1040902 1040907) (-665 "LOGIC.spad" 1040114 1040124 1040504 1040509) (-664 "LODOOPS.spad" 1039044 1039056 1040104 1040109) (-663 "LODO.spad" 1038428 1038444 1038724 1038763) (-662 "LODOF.spad" 1037474 1037491 1038385 1038390) (-661 "LODOCAT.spad" 1036140 1036150 1037430 1037469) (-660 "LODOCAT.spad" 1034804 1034816 1036096 1036101) (-659 "LODO2.spad" 1034077 1034089 1034484 1034523) (-658 "LODO1.spad" 1033477 1033487 1033757 1033796) (-657 "LODEEF.spad" 1032279 1032297 1033467 1033472) (-656 "LNAGG.spad" 1028111 1028121 1032269 1032274) (-655 "LNAGG.spad" 1023907 1023919 1028067 1028072) (-654 "LMOPS.spad" 1020675 1020692 1023897 1023902) (-653 "LMODULE.spad" 1020443 1020453 1020665 1020670) (-652 "LMDICT.spad" 1019730 1019740 1019994 1020021) (-651 "LLINSET.spad" 1019127 1019137 1019720 1019725) (-650 "LITERAL.spad" 1019033 1019044 1019117 1019122) (-649 "LIST.spad" 1016768 1016778 1018180 1018207) (-648 "LIST3.spad" 1016079 1016093 1016758 1016763) (-647 "LIST2.spad" 1014781 1014793 1016069 1016074) (-646 "LIST2MAP.spad" 1011684 1011696 1014771 1014776) (-645 "LINSET.spad" 1011306 1011316 1011674 1011679) (-644 "LINEXP.spad" 1010740 1010750 1011286 1011301) (-643 "LINDEP.spad" 1009549 1009561 1010652 1010657) (-642 "LIMITRF.spad" 1007477 1007487 1009539 1009544) (-641 "LIMITPS.spad" 1006380 1006393 1007467 1007472) (-640 "LIE.spad" 1004396 1004408 1005670 1005815) (-639 "LIECAT.spad" 1003872 1003882 1004322 1004391) (-638 "LIECAT.spad" 1003376 1003388 1003828 1003833) (-637 "LIB.spad" 1001426 1001434 1002035 1002050) (-636 "LGROBP.spad" 998779 998798 1001416 1001421) (-635 "LF.spad" 997734 997750 998769 998774) (-634 "LFCAT.spad" 996793 996801 997724 997729) (-633 "LEXTRIPK.spad" 992296 992311 996783 996788) (-632 "LEXP.spad" 990299 990326 992276 992291) (-631 "LETAST.spad" 989998 990006 990289 990294) (-630 "LEADCDET.spad" 988396 988413 989988 989993) (-629 "LAZM3PK.spad" 987100 987122 988386 988391) (-628 "LAUPOL.spad" 985793 985806 986693 986762) (-627 "LAPLACE.spad" 985376 985392 985783 985788) (-626 "LA.spad" 984816 984830 985298 985337) (-625 "LALG.spad" 984592 984602 984796 984811) (-624 "LALG.spad" 984376 984388 984582 984587) (-623 "KVTFROM.spad" 984111 984121 984366 984371) (-622 "KTVLOGIC.spad" 983623 983631 984101 984106) (-621 "KRCFROM.spad" 983361 983371 983613 983618) (-620 "KOVACIC.spad" 982084 982101 983351 983356) (-619 "KONVERT.spad" 981806 981816 982074 982079) (-618 "KOERCE.spad" 981543 981553 981796 981801) (-617 "KERNEL.spad" 980198 980208 981327 981332) (-616 "KERNEL2.spad" 979901 979913 980188 980193) (-615 "KDAGG.spad" 979010 979032 979881 979896) (-614 "KDAGG.spad" 978127 978151 979000 979005) (-613 "KAFILE.spad" 977090 977106 977325 977352) (-612 "JORDAN.spad" 974919 974931 976380 976525) (-611 "JOINAST.spad" 974613 974621 974909 974914) (-610 "JAVACODE.spad" 974479 974487 974603 974608) (-609 "IXAGG.spad" 972612 972636 974469 974474) (-608 "IXAGG.spad" 970600 970626 972459 972464) (-607 "IVECTOR.spad" 969370 969385 969525 969552) (-606 "ITUPLE.spad" 968531 968541 969360 969365) (-605 "ITRIGMNP.spad" 967370 967389 968521 968526) (-604 "ITFUN3.spad" 966876 966890 967360 967365) (-603 "ITFUN2.spad" 966620 966632 966866 966871) (-602 "ITFORM.spad" 965975 965983 966610 966615) (-601 "ITAYLOR.spad" 963969 963984 965839 965936) (-600 "ISUPS.spad" 956406 956421 962943 963040) (-599 "ISUMP.spad" 955907 955923 956396 956401) (-598 "ISTRING.spad" 954995 955008 955076 955103) (-597 "ISAST.spad" 954714 954722 954985 954990) (-596 "IRURPK.spad" 953431 953450 954704 954709) (-595 "IRSN.spad" 951435 951443 953421 953426) (-594 "IRRF2F.spad" 949920 949930 951391 951396) (-593 "IRREDFFX.spad" 949521 949532 949910 949915) (-592 "IROOT.spad" 947860 947870 949511 949516) (-591 "IR.spad" 945661 945675 947715 947742) (-590 "IRFORM.spad" 944985 944993 945651 945656) (-589 "IR2.spad" 944013 944029 944975 944980) (-588 "IR2F.spad" 943219 943235 944003 944008) (-587 "IPRNTPK.spad" 942979 942987 943209 943214) (-586 "IPF.spad" 942544 942556 942784 942877) (-585 "IPADIC.spad" 942305 942331 942470 942539) (-584 "IP4ADDR.spad" 941862 941870 942295 942300) (-583 "IOMODE.spad" 941384 941392 941852 941857) (-582 "IOBFILE.spad" 940745 940753 941374 941379) (-581 "IOBCON.spad" 940610 940618 940735 940740) (-580 "INVLAPLA.spad" 940259 940275 940600 940605) (-579 "INTTR.spad" 933641 933658 940249 940254) (-578 "INTTOOLS.spad" 931396 931412 933215 933220) (-577 "INTSLPE.spad" 930716 930724 931386 931391) (-576 "INTRVL.spad" 930282 930292 930630 930711) (-575 "INTRF.spad" 928706 928720 930272 930277) (-574 "INTRET.spad" 928138 928148 928696 928701) (-573 "INTRAT.spad" 926865 926882 928128 928133) (-572 "INTPM.spad" 925250 925266 926508 926513) (-571 "INTPAF.spad" 923114 923132 925182 925187) (-570 "INTPACK.spad" 913488 913496 923104 923109) (-569 "INT.spad" 912936 912944 913342 913483) (-568 "INTHERTR.spad" 912210 912227 912926 912931) (-567 "INTHERAL.spad" 911880 911904 912200 912205) (-566 "INTHEORY.spad" 908319 908327 911870 911875) (-565 "INTG0.spad" 902052 902070 908251 908256) (-564 "INTFTBL.spad" 896081 896089 902042 902047) (-563 "INTFACT.spad" 895140 895150 896071 896076) (-562 "INTEF.spad" 893525 893541 895130 895135) (-561 "INTDOM.spad" 892148 892156 893451 893520) (-560 "INTDOM.spad" 890833 890843 892138 892143) (-559 "INTCAT.spad" 889092 889102 890747 890828) (-558 "INTBIT.spad" 888599 888607 889082 889087) (-557 "INTALG.spad" 887787 887814 888589 888594) (-556 "INTAF.spad" 887287 887303 887777 887782) (-555 "INTABL.spad" 885805 885836 885968 885995) (-554 "INT8.spad" 885685 885693 885795 885800) (-553 "INT64.spad" 885564 885572 885675 885680) (-552 "INT32.spad" 885443 885451 885554 885559) (-551 "INT16.spad" 885322 885330 885433 885438) (-550 "INS.spad" 882825 882833 885224 885317) (-549 "INS.spad" 880414 880424 882815 882820) (-548 "INPSIGN.spad" 879862 879875 880404 880409) (-547 "INPRODPF.spad" 878958 878977 879852 879857) (-546 "INPRODFF.spad" 878046 878070 878948 878953) (-545 "INNMFACT.spad" 877021 877038 878036 878041) (-544 "INMODGCD.spad" 876509 876539 877011 877016) (-543 "INFSP.spad" 874806 874828 876499 876504) (-542 "INFPROD0.spad" 873886 873905 874796 874801) (-541 "INFORM.spad" 871085 871093 873876 873881) (-540 "INFORM1.spad" 870710 870720 871075 871080) (-539 "INFINITY.spad" 870262 870270 870700 870705) (-538 "INETCLTS.spad" 870239 870247 870252 870257) (-537 "INEP.spad" 868777 868799 870229 870234) (-536 "INDE.spad" 868506 868523 868767 868772) (-535 "INCRMAPS.spad" 867927 867937 868496 868501) (-534 "INBFILE.spad" 866999 867007 867917 867922) (-533 "INBFF.spad" 862793 862804 866989 866994) (-532 "INBCON.spad" 861083 861091 862783 862788) (-531 "INBCON.spad" 859371 859381 861073 861078) (-530 "INAST.spad" 859032 859040 859361 859366) (-529 "IMPTAST.spad" 858740 858748 859022 859027) (-528 "IMATRIX.spad" 857685 857711 858197 858224) (-527 "IMATQF.spad" 856779 856823 857641 857646) (-526 "IMATLIN.spad" 855384 855408 856735 856740) (-525 "ILIST.spad" 854042 854057 854567 854594) (-524 "IIARRAY2.spad" 853430 853468 853649 853676) (-523 "IFF.spad" 852840 852856 853111 853204) (-522 "IFAST.spad" 852454 852462 852830 852835) (-521 "IFARRAY.spad" 849947 849962 851637 851664) (-520 "IFAMON.spad" 849809 849826 849903 849908) (-519 "IEVALAB.spad" 849214 849226 849799 849804) (-518 "IEVALAB.spad" 848617 848631 849204 849209) (-517 "IDPO.spad" 848415 848427 848607 848612) (-516 "IDPOAMS.spad" 848171 848183 848405 848410) (-515 "IDPOAM.spad" 847891 847903 848161 848166) (-514 "IDPC.spad" 846829 846841 847881 847886) (-513 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T)) -(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) +(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1108)))) ((((-412 (-569))) . T) (((-412 |#1|)) . T) ((|#1|) . T) (((-569)) . T) (($) . T)) (((|#3|) . T) (((-569)) . T) (($) . T)) ((((-412 $) (-412 $)) |has| |#1| (-561)) (($ $) . T) ((|#1| |#1|) . T)) @@ -2639,40 +2639,40 @@ ((($ $) . T)) ((($) . T)) ((((-867)) . T)) -(((|#1| (-536 (-1183))) . T)) +(((|#1| (-536 (-1185))) . T)) (((|#1|) |has| |#1| (-173))) ((((-867)) . T)) (((|#2|) . T)) -(((|#4| |#4|) -12 (|has| |#4| (-312 |#4|)) (|has| |#4| (-1106)))) +(((|#4| |#4|) -12 (|has| |#4| (-312 |#4|)) (|has| |#4| (-1108)))) (((|#2|) . 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T)) -((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2006 |#1|) (|:| -2216 |#2|))) . T)) ((((-867)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-569)) . T)) (((|#1| (-412 (-569))) . T)) (((|#1|) . T)) -(-2774 (|has| |#1| (-293)) (|has| |#1| (-367))) +(-2776 (|has| |#1| (-293)) (|has| |#1| (-367))) ((((-144)) . T)) ((((-412 |#2|)) . T) (((-412 (-569))) . T) (($) . T)) (|has| |#1| (-853)) ((((-867)) . T)) ((((-867)) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) +(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1108)))) (((|#1| |#1| |#2| (-241 |#1| |#2|) (-241 |#1| |#2|)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2682,20 +2682,20 @@ ((((-867)) . T)) ((((-867)) . T)) ((((-188)) . T) (((-867)) . T)) -((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2006 |#1|) (|:| -2216 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-867)) . T)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541))) (((-898 (-569))) |has| |#1| (-619 (-898 (-569)))) (((-898 (-383))) |has| |#1| (-619 (-898 (-383))))) -((((-1183) (-52)) . T)) +((((-1185) (-52)) . T)) (((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-649 (-144))) . T) (((-1165)) . T)) +((((-649 (-144))) . T) (((-1167)) . T)) ((((-867)) . T)) -((((-1165)) . T)) -((((-1183) |#1|) |has| |#1| (-519 (-1183) |#1|)) ((|#1| |#1|) |has| |#1| (-312 |#1|))) -((((-2 (|:| -2003 (-1165)) (|:| -2214 |#1|))) . T)) +((((-1167)) . T)) +((((-1185) |#1|) |has| |#1| (-519 (-1185) |#1|)) ((|#1| |#1|) |has| |#1| (-312 |#1|))) +((((-2 (|:| -2006 (-1167)) (|:| -2216 |#1|))) . T)) (|has| |#1| (-855)) ((((-867)) . T)) ((((-541)) |has| |#1| (-619 (-541)))) @@ -2707,16 +2707,16 @@ (((|#2|) . T)) ((((-916 |#1|)) . T) (((-412 (-569))) . T) (($) . T)) ((($) . T) (((-569)) . T) (((-412 (-569))) . T) (((-617 $)) . 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T)) (|has| |#1| (-367)) @@ -2795,12 +2795,12 @@ ((((-569)) . T) (((-116 |#1|)) . T) (($) . T) (((-412 (-569))) . T)) ((((-569)) . T)) (((|#3|) . T)) -(|has| |#1| (-1106)) +(|has| |#1| (-1108)) (((|#2|) . T)) (((|#1|) . T)) ((((-569)) . T)) -(((|#2|) . T) (((-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((|#1|) . T) (($) . T) (((-569)) . T)) -(-2774 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) +(((|#2|) . T) (((-412 (-569))) |has| |#1| (-1046 (-412 (-569)))) ((|#1|) . T) (($) . T) (((-569)) . T)) +(-2776 (|has| |#1| (-173)) (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) (((|#2|) . T) (((-569)) |has| |#2| (-644 (-569)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2810,7 +2810,7 @@ (((|#1|) . T) (($) . T)) (((|#1|) . T) (((-569)) . T)) (((|#1|) . T) (((-569)) . T)) -(((|#1| (-1273 |#1|) (-1273 |#1|)) . T)) +(((|#1| (-1275 |#1|) (-1275 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#2|) . T)) ((((-867)) . T)) @@ -2818,8 +2818,8 @@ (((|#2|) . T)) (((|#3|) . T)) (((#0=(-116 |#1|) #0#) . T) ((#1=(-412 (-569)) #1#) . T) (($ $) . T)) -((((-412 (-569))) |has| |#2| (-1044 (-412 (-569)))) (((-569)) |has| |#2| (-1044 (-569))) ((|#2|) . T) (((-869 |#1|)) . T)) -((((-1131 |#1| |#2|)) . T) ((|#3|) . T) ((|#1|) . T) (((-569)) |has| |#1| (-1044 (-569))) (((-412 (-569))) |has| |#1| (-1044 (-412 (-569)))) ((|#2|) . T)) +((((-412 (-569))) |has| |#2| (-1046 (-412 (-569)))) (((-569)) |has| |#2| (-1046 (-569))) ((|#2|) . T) (((-869 |#1|)) . T)) +((((-1133 |#1| |#2|)) . T) ((|#3|) . T) ((|#1|) . T) (((-569)) |has| |#1| (-1046 (-569))) (((-412 (-569))) |has| |#1| (-1046 (-412 (-569)))) ((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2841,10 +2841,10 @@ (|has| |#1| (-915)) (|has| |#1| (-915)) (((|#4|) . T)) -(|has| |#2| (-1028)) +(|has| |#2| (-1030)) ((($) . T)) (|has| |#1| (-915)) -((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2006 |#1|) (|:| -2216 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2853,31 +2853,31 @@ (|has| |#1| (-367)) ((((-916 |#1|)) . T)) ((($) . T) (((-569)) . T) ((|#1|) . T) (((-412 (-569))) . T)) -((($) -2774 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) -((($) |has| |#1| (-853)) (((-569)) -2774 (|has| |#1| (-21)) (|has| |#1| (-853)))) +((($) -2776 (|has| |#1| (-367)) (|has| |#1| (-457)) (|has| |#1| (-561)) (|has| |#1| (-915))) ((|#1|) |has| |#1| (-173)) (((-412 (-569))) |has| |#1| (-38 (-412 (-569))))) +((($) |has| |#1| (-853)) (((-569)) -2776 (|has| |#1| (-21)) (|has| |#1| (-853)))) ((($ $) . T) ((#0=(-412 (-569)) #0#) . T)) -(-2774 (|has| |#1| (-372)) (|has| |#1| (-855))) +(-2776 (|has| |#1| (-372)) (|has| |#1| (-855))) (((|#1|) . T)) ((((-776)) . T)) ((((-867)) . 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T)) +(((#0=(-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) #0#) |has| (-2 (|:| -2006 (-1185)) (|:| -2216 (-52))) (-312 (-2 (|:| -2006 (-1185)) (|:| -2216 (-52)))))) +((((-1167)) . T)) (|has| |#1| (-915)) (|has| |#2| (-367)) (((|#1|) . T) (($) . T) (((-569)) . T)) -(-2774 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1055))) +(-2776 (|has| |#2| (-131)) (|has| |#2| (-173)) (|has| |#2| (-367)) (|has| |#2| (-798)) (|has| |#2| (-853)) (|has| |#2| (-1057))) ((((-170 (-383))) . T) (((-226)) . T) (((-383)) . T)) ((((-867)) . T)) (((|#1|) . T)) @@ -2894,13 +2894,13 @@ (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) (|has| |#1| (-38 (-412 (-569)))) -(-2774 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353))) +(-2776 (|has| |#1| (-310)) (|has| |#1| (-367)) (|has| |#1| (-353))) (|has| |#1| (-38 (-412 (-569)))) (-12 (|has| |#1| (-550)) (|has| |#1| (-833))) ((((-867)) . T)) -((((-1183)) -2774 (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1183)))) (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1183)))))) +((((-1185)) -2776 (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1185)))) (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1185)))))) (|has| |#1| (-367)) -((((-1183)) -12 (|has| |#1| (-15 * (|#1| (-412 (-569)) |#1|))) (|has| |#1| (-906 (-1183))))) +((((-1185)) -12 (|has| |#1| (-15 * (|#1| (-412 (-569)) |#1|))) (|has| |#1| (-906 (-1185))))) (|has| |#1| (-367)) ((((-412 (-569))) . T) (($) . T)) ((((-412 |#2|)) . T) (((-412 (-569))) . T) (((-569)) . T) (($) . T)) @@ -2910,16 +2910,16 @@ (((|#2|) |has| |#1| (-367))) (((|#2|) |has| |#1| (-367))) ((((-569)) . T) (($) . T)) -((((-2 (|:| -2003 |#1|) (|:| -2214 |#2|))) . T)) +((((-2 (|:| -2006 |#1|) (|:| -2216 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-173))) (((|#1|) . T)) -(((|#2|) . 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T)) -((((-412 (-569))) |has| |#2| (-1044 (-569))) (((-569)) |has| |#2| (-1044 (-569))) (((-1183)) |has| |#2| (-1044 (-1183))) ((|#2|) . T)) +((((-412 (-569))) |has| |#2| (-1046 (-569))) (((-569)) |has| |#2| (-1046 (-569))) (((-1185)) |has| |#2| (-1046 (-1185))) ((|#2|) . T)) (((#0=(-412 |#2|) #0#) . T) ((#1=(-412 (-569)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2774 (|has| |#1| (-145)) (|has| |#1| (-353))) +(-2776 (|has| |#1| (-145)) (|has| |#1| (-353))) (|has| |#1| (-147)) ((((-867)) . T)) ((($) . T)) -((((-1146 |#1| |#2|)) . T)) +((((-1148 |#1| |#2|)) . T)) (((|#1| (-569)) . T)) (((|#1| (-412 (-569))) . T)) ((((-569)) |has| |#2| (-892 (-569))) (((-383)) |has| |#2| (-892 (-383)))) @@ -2996,24 +2996,24 @@ (((|#1| |#2| (-241 |#1| |#2|) (-241 |#1| |#2|)) . T)) (((|#2|) . T)) ((((-867)) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1106)))) -((((-1183) (-52)) . T)) +(((|#1| |#1|) -12 (|has| |#1| (-312 |#1|)) (|has| |#1| (-1108)))) +((((-1185) (-52)) . 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T)) (|has| |#1| (-367)) -(-2774 (|has| |#1| (-367)) (|has| |#1| (-561))) +(-2776 (|has| |#1| (-367)) (|has| |#1| (-561))) (|has| |#1| (-367)) (|has| |#1| (-561)) -(|has| |#1| (-1106)) +(|has| |#1| (-1108)) ((((-785 |#1| (-869 |#2|))) |has| (-785 |#1| (-869 |#2|)) (-312 (-785 |#1| (-869 |#2|))))) -(-2774 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) +(-2776 (|has| |#2| (-457)) (|has| |#2| (-561)) (|has| |#2| (-915))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3086,19 +3086,19 @@ (((|#1| (-536 |#2|)) . T)) (((|#1| (-776)) . T)) (|has| |#1| (-234)) -(((|#1| (-536 (-1094 (-1183)))) . T)) +(((|#1| (-536 (-1096 (-1185)))) . T)) (|has| |#2| (-367)) ((((-586 |#1|)) . T) (((-412 (-569))) . T) (($) . T) (((-569)) . T)) ((((-569)) . T) (((-412 (-569))) . T) (($) . T)) -((((-2 (|:| -2003 (-1165)) (|:| -2214 (-52)))) . T)) +((((-2 (|:| -2006 (-1167)) (|:| -2216 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-569)) . 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-651) 183360) ((-479 . -289) 183345) ((-1229 . -618) 183327) ((-736 . -381) 183311) ((-843 . -618) 183293) ((-663 . -1064) T) ((-1257 . -1008) 183259) ((-1236 . -1008) 183225) ((-1094 . -621) 183209) ((-1069 . -1199) 183184) ((-1082 . -621) 183161) ((-877 . -619) 182968) ((-877 . -618) 182950) ((-1196 . -494) 182887) ((-423 . -1028) 182865) ((-48 . -312) 182852) ((-1069 . -107) 182798) ((-484 . -494) 182735) ((-525 . -1223) T) ((-1174 . -342) 182687) ((-1147 . -494) 182658) ((-1174 . -381) 182610) ((-1093 . -1064) T) ((-442 . -102) T) ((-184 . -1106) T) ((-253 . -34) T) ((-252 . -34) T) ((-787 . -1064) T) ((-785 . -1064) T) ((-736 . -906) 182587) ((-459 . -1064) T) ((-59 . -494) 182571) ((-1040 . -1062) 182545) ((-524 . -494) 182529) ((-521 . -494) 182513) ((-502 . -494) 182497) ((-501 . -494) 182481) ((-246 . -519) 182414) ((-1040 . -111) 182381) ((-1181 . -906) 182294) ((-1180 . -906) 182200) ((-1174 . -906) 182033) ((-1132 . -906) 182017) ((-675 . -1118) T) ((-358 . -1158) T) ((-650 . -93) T) ((-325 . -1062) 181999) ((-253 . -796) 181978) ((-253 . -799) 181929) ((-31 . -495) 181910) ((-253 . -798) 181889) ((-252 . -796) 181868) ((-252 . -799) 181819) ((-252 . -798) 181798) ((-31 . -618) 181764) ((-50 . -1064) T) ((-253 . -731) 181674) ((-252 . -731) 181584) ((-1217 . -1106) T) ((-675 . -23) T) ((-586 . -1064) T) ((-523 . -1064) T) ((-383 . -1062) 181549) ((-325 . -111) 181524) ((-73 . -387) T) ((-73 . -400) T) ((-1030 . -38) 181461) ((-699 . -405) 181443) ((-99 . -102) T) ((-716 . -1106) T) ((-1301 . -1057) 181430) ((-1009 . -145) 181402) ((-1009 . -147) 181374) ((-875 . -651) 181346) ((-383 . -111) 181302) ((-322 . -1227) 181281) ((-479 . -1008) 181247) ((-358 . -38) 181212) ((-40 . -374) 181184) ((-878 . -618) 181056) ((-127 . -125) 181040) ((-121 . -125) 181024) ((-841 . -1062) 180994) ((-838 . -21) 180946) ((-832 . -1062) 180930) ((-838 . -25) 180882) ((-322 . -561) 180833) ((-522 . -621) 180814) ((-569 . -833) T) ((-241 . -1223) T) ((-1040 . -621) 180783) 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-25) T) ((-820 . -23) 177825) ((-1183 . -618) 177807) ((-59 . -19) 177791) ((-1183 . -619) 177713) ((-1179 . -731) T) ((-1131 . -731) T) ((-521 . -19) 177697) ((-501 . -19) 177681) ((-59 . -609) 177658) ((-1093 . -1106) T) ((-907 . -102) 177636) ((-859 . -731) T) ((-787 . -1106) T) ((-521 . -609) 177613) ((-501 . -609) 177590) ((-785 . -1106) T) ((-785 . -1071) 177557) ((-466 . -1106) T) ((-459 . -1106) T) ((-591 . -722) 177532) ((-654 . -1106) T) ((-1265 . -47) 177509) ((-1259 . -102) T) ((-1258 . -47) 177479) ((-1237 . -47) 177456) ((-1217 . -173) 177407) ((-1180 . -310) 177386) ((-1174 . -310) 177365) ((-1102 . -621) 177346) ((-1096 . -621) 177327) ((-1086 . -561) 177278) ((-1010 . -906) NIL) ((-1086 . -1227) 177229) ((-675 . -131) T) ((-632 . -1118) T) ((-1079 . -621) 177210) ((-1072 . -621) 177191) ((-1042 . -621) 177172) ((-1025 . -621) 177153) ((-704 . -651) 177103) ((-277 . -1106) T) ((-85 . -446) T) ((-85 . -400) T) ((-719 . -1062) 177073) ((-716 . -173) T) ((-50 . -1106) T) ((-600 . -47) 177050) ((-226 . -653) 177015) ((-586 . -1106) T) ((-523 . -1106) T) ((-492 . -825) T) ((-492 . -926) T) ((-363 . -1227) T) ((-357 . -1227) T) ((-349 . -1227) T) ((-322 . -1118) T) ((-319 . -1057) 176925) ((-316 . -1057) 176854) ((-108 . -1227) T) ((-631 . -621) 176835) ((-363 . -561) T) ((-218 . -926) T) ((-218 . -825) T) ((-319 . -645) 176745) ((-316 . -645) 176674) ((-357 . -561) T) ((-349 . -561) T) ((-488 . -621) 176655) ((-108 . -561) T) ((-663 . -722) 176625) ((-1174 . -1028) NIL) ((-219 . -621) 176606) ((-322 . -23) T) ((-67 . -1223) T) ((-1006 . -618) 176538) ((-699 . -232) 176520) ((-719 . -111) 176485) ((-649 . -34) T) ((-246 . -494) 176469) ((-1108 . -1104) 176453) ((-172 . -1106) T) ((-1301 . -1158) T) ((-1297 . -21) T) ((-1297 . -25) T) ((-1295 . -131) T) ((-1293 . -131) T) ((-958 . -915) 176432) ((-1286 . -102) T) ((-1269 . -618) 176398) ((-1258 . -1044) 176333) ((-520 . -621) 176317) ((-1237 . -1223) 176296) ((-1237 . -892) NIL) ((-1237 . -890) 176248) ((-486 . -915) 176227) ((-1237 . -1044) 176193) ((-1217 . -519) 176160) ((-1093 . -722) 176009) ((-1068 . -653) 175996) ((-958 . -653) 175921) ((-602 . -495) 175902) ((-590 . -495) 175883) ((-787 . -722) 175712) ((-602 . -618) 175678) ((-590 . -618) 175644) ((-541 . -618) 175626) ((-541 . -619) 175607) ((-785 . -722) 175456) ((-1083 . -102) T) ((-385 . -25) T) ((-628 . -651) 175428) ((-385 . -21) T) ((-486 . -653) 175353) ((-466 . -722) 175324) ((-459 . -722) 175173) ((-993 . -102) T) ((-1196 . -619) NIL) ((-1196 . -618) 175155) ((-1148 . -1129) 175100) ((-742 . -102) T) ((-117 . -651) 175030) ((-610 . -621) 175012) ((-1052 . -1216) 174941) ((-907 . -312) 174879) ((-536 . -25) T) ((-881 . -93) T) ((-719 . -621) 174833) ((-686 . -93) T) ((-650 . -495) 174814) ((-141 . -102) T) ((-44 . -131) T) ((-681 . -93) T) ((-669 . -618) 174796) ((-347 . -1064) T) ((-292 . -1118) T) ((-650 . -618) 174749) ((-483 . -93) T) ((-359 . -618) 174731) ((-356 . -618) 174713) ((-348 . -618) 174695) ((-266 . -619) 174443) ((-266 . -618) 174425) ((-248 . -618) 174407) ((-248 . -619) 174268) ((-133 . -93) T) ((-138 . -93) T) ((-137 . -93) T) ((-1147 . -618) 174250) ((-1126 . -645) 174237) ((-1126 . -1057) 174224) ((-824 . -731) T) ((-824 . -862) T) ((-607 . -291) 174201) ((-586 . -722) 174166) ((-484 . -619) NIL) ((-484 . -618) 174148) ((-523 . -722) 174093) ((-319 . -102) T) ((-316 . -102) T) ((-292 . -23) T) ((-152 . -131) T) ((-916 . -618) 174075) ((-916 . -619) 174057) ((-391 . -731) T) ((-877 . -1062) 174009) ((-877 . -111) 173947) ((-719 . -1055) T) ((-717 . -1249) 173931) ((-699 . -353) NIL) ((-136 . -102) T) ((-114 . -102) T) ((-139 . -102) T) ((-524 . -618) 173863) ((-383 . -800) T) ((-224 . -1106) T) ((-168 . -1223) T) ((-383 . -797) T) ((-226 . -799) T) ((-226 . -796) T) ((-59 . -619) 173824) ((-59 . -618) 173736) ((-226 . -731) T) ((-521 . -619) 173697) ((-521 . -618) 173609) ((-502 . -618) 173541) ((-501 . -619) 173502) ((-501 . -618) 173414) ((-1086 . -367) 173365) ((-40 . -416) 173342) ((-77 . -1223) T) ((-876 . -915) NIL) ((-363 . -332) 173326) ((-363 . -367) T) ((-357 . -332) 173310) ((-357 . -367) T) ((-349 . -332) 173294) ((-349 . -367) T) ((-319 . -287) 173273) ((-108 . -367) T) ((-70 . -1223) T) ((-1237 . -342) 173225) ((-876 . -653) 173170) ((-1237 . -381) 173122) ((-970 . -131) 172977) ((-820 . -131) 172847) ((-964 . -656) 172831) ((-1093 . -173) 172742) ((-964 . -377) 172726) ((-1068 . -799) T) ((-1068 . -796) T) ((-877 . -621) 172624) ((-787 . -173) 172515) ((-785 . -173) 172426) ((-821 . -47) 172388) ((-1068 . -731) T) ((-330 . -494) 172372) ((-958 . -731) T) ((-1286 . -312) 172310) ((-459 . -173) 172221) ((-246 . -289) 172198) ((-1265 . -906) 172111) ((-1258 . -906) 172017) ((-1257 . -1062) 171852) ((-486 . -731) T) ((-1237 . -906) 171685) ((-1236 . -1062) 171493) ((-1217 . -293) 171472) ((-1193 . -1223) T) ((-1190 . -372) T) ((-1189 . -372) T) ((-1152 . -151) 171456) ((-1126 . -102) T) ((-1124 . -1106) T) ((-1086 . -23) T) ((-1086 . -1118) T) ((-1081 . -102) T) ((-1063 . -618) 171423) ((-933 . -961) T) ((-742 . -312) 171361) ((-75 . -1223) T) ((-669 . -386) 171333) ((-170 . -915) 171286) ((-30 . -961) T) ((-112 . -849) T) ((-1 . -618) 171268) ((-1009 . -414) 171240) ((-128 . -656) 171222) ((-50 . -625) 171206) ((-699 . -651) 171141) ((-600 . -906) 171054) ((-443 . -102) T) ((-128 . -377) 171036) ((-141 . -312) NIL) ((-877 . -1055) T) ((-838 . -855) 171015) ((-81 . -1223) T) ((-716 . -293) T) ((-40 . -1064) T) ((-586 . -173) T) ((-523 . -173) T) ((-516 . -618) 170997) ((-170 . -653) 170907) ((-512 . -618) 170889) ((-355 . -147) 170871) ((-355 . -145) T) ((-363 . -1118) T) ((-357 . -1118) T) ((-349 . -1118) T) ((-1010 . -310) T) ((-920 . -310) T) ((-877 . -244) T) ((-108 . -1118) T) ((-877 . -234) 170850) ((-1257 . -111) 170671) ((-1236 . -111) 170460) ((-246 . -1261) 170444) ((-569 . -853) T) ((-363 . -23) T) ((-358 . -353) T) ((-319 . -312) 170431) ((-316 . -312) 170372) ((-357 . -23) T) ((-322 . -131) T) ((-349 . -23) T) ((-1010 . -1028) T) ((-31 . -621) 170353) ((-108 . -23) T) ((-659 . -1057) 170337) ((-246 . -609) 170314) ((-336 . -1106) T) ((-659 . -645) 170284) ((-1259 . -38) 170176) ((-1246 . -915) 170155) ((-112 . -1106) T) ((-1041 . -102) T) ((-1246 . -653) 170080) ((-876 . -799) NIL) ((-860 . -653) 170054) ((-876 . -796) NIL) ((-821 . -892) NIL) ((-876 . -731) T) ((-1093 . -519) 169927) ((-787 . -519) 169874) ((-785 . -519) 169826) ((-576 . -653) 169813) ((-821 . -1044) 169641) ((-459 . -519) 169584) ((-393 . -394) T) ((-1257 . -621) 169397) ((-1236 . -621) 169145) ((-60 . -1223) T) ((-626 . -855) 169124) ((-505 . -666) T) ((-1152 . -982) 169093) ((-1030 . -651) 169030) ((-1009 . -457) T) ((-704 . -853) T) ((-515 . -797) T) ((-479 . -1062) 168865) ((-347 . -1106) T) ((-316 . -1158) NIL) ((-292 . -131) T) ((-399 . -1106) T) ((-875 . -1064) T) ((-699 . -374) 168832) ((-358 . -651) 168762) ((-224 . -625) 168739) ((-330 . -289) 168716) ((-479 . -111) 168537) ((-1257 . -1055) T) ((-1236 . -1055) T) ((-821 . -381) 168521) ((-170 . -731) T) ((-659 . -102) T) ((-1257 . -244) 168500) ((-1257 . -234) 168452) ((-1236 . -234) 168357) ((-1236 . -244) 168336) ((-1009 . -407) NIL) ((-675 . -644) 168284) ((-319 . -38) 168194) ((-316 . -38) 168123) ((-69 . -618) 168105) ((-322 . -498) 168071) ((-48 . -651) 168021) ((-1196 . -291) 168000) ((-1231 . -855) T) ((-1119 . -1118) 167910) ((-83 . -1223) T) ((-61 . -618) 167892) ((-484 . -291) 167871) ((-1288 . -1044) 167848) ((-1171 . -1106) T) ((-1119 . -23) 167718) ((-821 . -906) 167654) ((-1246 . -731) T) ((-1108 . -1223) T) ((-479 . -621) 167480) ((-1093 . -293) 167411) ((-972 . -1106) T) ((-899 . -102) T) ((-787 . -293) 167322) ((-330 . -19) 167306) ((-59 . -291) 167283) ((-785 . -293) 167214) ((-860 . -731) T) ((-117 . -853) NIL) ((-521 . -291) 167191) ((-330 . -609) 167168) ((-501 . -291) 167145) ((-459 . -293) 167076) ((-1041 . -312) 166927) ((-881 . -495) 166908) ((-881 . -618) 166874) ((-686 . -495) 166855) ((-576 . -731) T) ((-681 . -495) 166836) ((-686 . -618) 166786) ((-681 . -618) 166752) ((-667 . -618) 166734) ((-483 . -495) 166715) ((-483 . -618) 166681) ((-246 . -619) 166642) ((-246 . -495) 166619) ((-138 . -495) 166600) ((-137 . -495) 166581) ((-133 . -495) 166562) ((-246 . -618) 166454) ((-214 . -102) T) ((-138 . -618) 166420) ((-137 . -618) 166386) ((-133 . -618) 166352) ((-1153 . -34) T) ((-949 . -1223) T) ((-347 . -722) 166297) ((-675 . -25) T) ((-675 . -21) T) ((-1183 . -621) 166278) ((-479 . -1055) T) ((-640 . -422) 166243) ((-612 . -422) 166208) ((-1126 . -1158) T) ((-717 . -1057) 166031) ((-586 . -293) T) ((-523 . -293) T) ((-1258 . -310) 166010) ((-479 . -234) 165962) ((-479 . -244) 165941) ((-1237 . -310) 165920) ((-717 . -645) 165749) ((-1237 . -1028) NIL) ((-1086 . -131) T) ((-877 . -800) 165728) ((-144 . -102) T) ((-40 . -1106) T) ((-877 . -797) 165707) ((-649 . -1016) 165691) ((-585 . -1064) T) ((-569 . -1064) T) ((-500 . -1064) T) ((-412 . -457) T) ((-363 . -131) T) ((-319 . -405) 165675) 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163980) ((-541 . -623) 163883) ((-347 . -173) T) ((-88 . -618) 163865) ((-152 . -21) T) ((-152 . -25) T) ((-916 . -111) 163821) ((-40 . -722) 163766) ((-875 . -1106) T) ((-669 . -621) 163743) ((-650 . -621) 163724) ((-359 . -621) 163661) ((-356 . -621) 163598) ((-552 . -1106) T) ((-348 . -621) 163535) ((-330 . -619) 163496) ((-330 . -618) 163408) ((-266 . -621) 163161) ((-248 . -621) 162946) ((-1236 . -797) 162899) ((-1236 . -800) 162852) ((-253 . -381) 162821) ((-252 . -381) 162790) ((-659 . -38) 162760) ((-613 . -34) T) ((-487 . -1118) 162670) ((-480 . -34) T) ((-1119 . -131) 162540) ((-970 . -25) 162351) ((-916 . -621) 162301) ((-879 . -618) 162283) ((-970 . -21) 162238) ((-820 . -21) 162148) ((-820 . -25) 161999) ((-1229 . -372) T) ((-628 . -1064) T) ((-1185 . -561) 161978) ((-1179 . -47) 161955) ((-359 . -1055) T) ((-356 . -1055) T) ((-487 . -23) 161825) ((-348 . -1055) T) ((-266 . -1055) T) ((-248 . -1055) T) ((-1131 . -47) 161797) ((-117 . -1064) T) ((-1040 . -653) 161771) 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156305) ((-348 . -372) 156284) ((-719 . -731) T) ((-218 . -367) T) ((-116 . -457) T) ((-1296 . -1287) 156268) ((-876 . -890) 156245) ((-876 . -892) NIL) ((-970 . -855) 156144) ((-820 . -855) 156095) ((-1230 . -102) T) ((-659 . -661) 156079) ((-1209 . -34) T) ((-172 . -618) 156061) ((-1119 . -21) 155971) ((-1119 . -25) 155822) ((-876 . -1044) 155799) ((-958 . -906) 155780) ((-1246 . -47) 155757) ((-916 . -372) T) ((-59 . -656) 155741) ((-521 . -656) 155725) ((-486 . -906) 155702) ((-71 . -446) T) ((-71 . -400) T) ((-501 . -656) 155686) ((-59 . -377) 155670) ((-628 . -173) T) ((-521 . -377) 155654) ((-501 . -377) 155638) ((-832 . -713) 155622) ((-1179 . -310) 155601) ((-1185 . -131) T) ((-1148 . -1057) 155585) ((-117 . -173) T) ((-1148 . -645) 155517) ((-1152 . -312) 155455) ((-170 . -1223) T) ((-1285 . -131) T) ((-871 . -1057) 155425) ((-640 . -749) 155409) ((-612 . -749) 155393) ((-1258 . -926) 155372) ((-1237 . -926) 155351) ((-1237 . -825) NIL) ((-871 . -645) 155321) ((-699 . -722) 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149788) ((-1273 . -494) 149772) ((-1148 . -38) 149732) ((-969 . -23) T) ((-916 . -653) 149697) ((-870 . -1106) T) ((-848 . -102) T) ((-822 . -21) T) ((-640 . -1057) 149681) ((-612 . -1057) 149665) ((-822 . -25) T) ((-740 . -23) T) ((-720 . -23) T) ((-640 . -645) 149649) ((-110 . -666) T) ((-612 . -645) 149633) ((-586 . -1062) 149598) ((-523 . -1062) 149543) ((-228 . -57) 149501) ((-458 . -23) T) ((-412 . -102) T) ((-265 . -102) T) ((-699 . -293) T) ((-871 . -38) 149471) ((-586 . -111) 149427) ((-523 . -111) 149356) ((-1093 . -621) 149092) ((-423 . -1118) T) ((-319 . -1064) 148982) ((-316 . -1064) T) ((-128 . -1223) T) ((-787 . -621) 148730) ((-785 . -621) 148496) ((-663 . -1055) T) ((-1301 . -1106) T) ((-459 . -621) 148281) ((-170 . -310) 148212) ((-423 . -23) T) ((-40 . -618) 148194) ((-40 . -619) 148178) ((-108 . -998) 148160) ((-116 . -874) 148144) ((-654 . -621) 148128) ((-48 . -519) 148094) ((-1209 . -1016) 148078) ((-1188 . -618) 148045) ((-1196 . -34) T) ((-960 . -618) 148011) 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. -1280) 133101) ((-246 . -1223) T) ((-1222 . -102) T) ((-1030 . -621) 133038) ((-1179 . -1227) 133017) ((-358 . -621) 132947) ((-1131 . -1227) 132926) ((-241 . -21) 132836) ((-241 . -25) 132687) ((-127 . -119) 132671) ((-121 . -119) 132655) ((-44 . -749) 132639) ((-1179 . -561) 132550) ((-1131 . -561) 132481) ((-1230 . -1106) T) ((-1041 . -289) 132456) ((-1173 . -1089) T) ((-1000 . -1089) T) ((-821 . -131) T) ((-117 . -800) NIL) ((-117 . -797) NIL) ((-359 . -310) T) ((-356 . -310) T) ((-348 . -310) T) ((-253 . -1118) 132366) ((-252 . -1118) 132276) ((-1030 . -1055) T) ((-1009 . -1064) T) ((-48 . -621) 132209) ((-347 . -653) 132154) ((-626 . -38) 132138) ((-1286 . -618) 132100) ((-1286 . -619) 132061) ((-1083 . -618) 132043) ((-1030 . -244) T) ((-358 . -1055) T) ((-820 . -1280) 132013) ((-253 . -23) T) ((-252 . -23) T) ((-993 . -618) 131995) ((-742 . -619) 131956) ((-742 . -618) 131938) ((-804 . -855) 131917) ((-1166 . -151) 131864) ((-1005 . -519) 131776) ((-358 . -234) T) ((-358 . 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. -645) 129471) ((-1163 . -1106) 129449) ((-876 . -1227) T) ((-1293 . -645) 129419) ((-659 . -618) 129401) ((-876 . -561) T) ((-699 . -372) NIL) ((-44 . -1057) 129385) ((-1301 . -621) 129367) ((-1296 . -1106) T) ((-675 . -102) T) ((-363 . -1280) 129351) ((-357 . -1280) 129335) ((-44 . -645) 129319) ((-349 . -1280) 129303) ((-553 . -102) T) ((-525 . -855) 129282) ((-1052 . -1106) T) ((-822 . -457) 129261) ((-152 . -1057) 129245) ((-1052 . -1077) 129174) ((-1033 . -982) 129143) ((-824 . -1118) T) ((-1009 . -722) 129088) ((-152 . -645) 129072) ((-391 . -1118) T) ((-481 . -982) 129041) ((-468 . -982) 129010) ((-110 . -151) 128992) ((-73 . -618) 128974) ((-899 . -618) 128956) ((-1086 . -729) 128935) ((-1301 . -1055) T) ((-821 . -644) 128883) ((-297 . -1064) 128825) ((-170 . -1227) 128730) ((-226 . -1118) T) ((-327 . -23) T) ((-1174 . -998) 128682) ((-848 . -1106) T) ((-1259 . -1062) 128587) ((-1132 . -745) 128566) ((-1257 . -926) 128545) ((-1236 . -926) 128524) ((-875 . -731) T) ((-170 . 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116142) ((-468 . -312) 116080) ((-355 . -293) T) ((-1163 . -1261) 116064) ((-1148 . -618) 116026) ((-1148 . -619) 115987) ((-1146 . -102) T) ((-1005 . -1062) 115883) ((-40 . -906) 115835) ((-1163 . -609) 115812) ((-1301 . -653) 115799) ((-871 . -495) 115776) ((-1069 . -151) 115722) ((-877 . -1227) T) ((-1005 . -111) 115604) ((-343 . -722) 115588) ((-871 . -618) 115550) ((-175 . -722) 115482) ((-412 . -289) 115440) ((-877 . -561) T) ((-108 . -405) 115422) ((-84 . -388) T) ((-84 . -400) T) ((-706 . -173) T) ((-622 . -618) 115404) ((-99 . -731) T) ((-487 . -102) 115194) ((-99 . -478) T) ((-116 . -173) T) ((-1295 . -651) 115153) ((-1293 . -651) 115112) ((-1119 . -38) 115082) ((-170 . -644) 115030) ((-1060 . -102) T) ((-1005 . -621) 114920) ((-876 . -25) T) ((-820 . -239) 114899) ((-876 . -21) T) ((-823 . -102) T) ((-44 . -651) 114842) ((-419 . -102) T) ((-389 . -102) T) ((-110 . -312) NIL) ((-228 . -102) 114820) ((-127 . -1223) T) ((-121 . -1223) T) ((-822 . -1057) 114771) ((-822 . -645) 114713) ((-1040 . -131) T) ((-675 . -371) 114697) ((-152 . -651) 114656) ((-1005 . -1055) T) ((-1246 . -644) 114604) ((-1110 . -618) 114586) ((-1009 . -618) 114568) ((-520 . -23) T) ((-515 . -23) T) ((-347 . -310) T) ((-513 . -23) T) ((-325 . -131) T) ((-3 . -1106) T) ((-1009 . -619) 114552) ((-1005 . -244) 114531) ((-1005 . -234) 114510) ((-1301 . -731) T) ((-1265 . -145) 114489) ((-838 . -1106) T) ((-1265 . -147) 114468) ((-1258 . -147) 114447) ((-1258 . -145) 114426) ((-1257 . -1227) 114405) ((-1237 . -145) 114312) ((-1237 . -147) 114219) ((-1236 . -1227) 114198) ((-383 . -131) T) ((-569 . -892) 114180) ((0 . -1106) T) ((-175 . -173) T) ((-170 . -21) T) ((-170 . -25) T) ((-49 . -1106) T) ((-1259 . -653) 114085) ((-1257 . -561) 114036) ((-719 . -1118) T) ((-1236 . -561) 113987) ((-569 . -1044) 113969) ((-600 . -147) 113948) ((-600 . -145) 113927) ((-500 . -1044) 113870) ((-1141 . -1143) T) ((-87 . -388) T) ((-87 . -400) T) ((-877 . -367) T) ((-841 . -131) T) ((-832 . -131) T) ((-970 . -651) 113814) ((-719 . -23) T) ((-511 . -618) 113780) ((-507 . -618) 113762) ((-820 . -651) 113512) ((-1297 . -1064) T) ((-383 . -1066) T) ((-1032 . -1106) 113490) ((-55 . -1044) 113472) ((-907 . -34) T) ((-487 . -312) 113410) ((-597 . -102) T) ((-1163 . -619) 113371) ((-1163 . -618) 113303) ((-1185 . -1057) 113186) ((-45 . -102) T) ((-822 . -102) T) ((-1185 . -645) 113083) ((-1246 . -25) T) ((-1246 . -21) T) ((-860 . -25) T) ((-44 . -371) 113067) ((-860 . -21) T) ((-736 . -457) 113018) ((-1296 . -618) 113000) ((-1285 . -1057) 112970) ((-1060 . -312) 112908) ((-676 . -1089) T) ((-611 . -1089) T) ((-395 . -1106) T) ((-576 . -25) T) ((-576 . -21) T) ((-181 . -1089) T) ((-161 . -1089) T) ((-156 . -1089) T) ((-154 . -1089) T) ((-1285 . -645) 112878) ((-626 . -1106) T) ((-704 . -892) 112860) ((-1273 . -1223) T) ((-228 . -312) 112798) ((-144 . -372) T) ((-1052 . -619) 112740) ((-1052 . -618) 112683) ((-316 . -915) NIL) ((-1231 . -849) T) ((-704 . -1044) 112628) ((-716 . -926) T) ((-479 . 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109290) ((-871 . -111) 109255) ((-1010 . -457) T) ((-699 . -1044) 109200) ((-916 . -561) T) ((-538 . -618) 109182) ((-586 . -926) T) ((-492 . -1057) 109132) ((-479 . -1118) T) ((-523 . -926) T) ((-920 . -457) T) ((-65 . -618) 109114) ((-218 . -1057) 109064) ((-492 . -645) 109014) ((-363 . -651) 108951) ((-357 . -651) 108888) ((-349 . -651) 108825) ((-637 . -230) 108771) ((-218 . -645) 108721) ((-108 . -651) 108671) ((-479 . -23) T) ((-1126 . -799) T) ((-877 . -131) T) ((-1126 . -796) T) ((-1288 . -1290) 108650) ((-1126 . -731) T) ((-659 . -653) 108624) ((-297 . -618) 108365) ((-1148 . -621) 108283) ((-1041 . -34) T) ((-820 . -853) 108262) ((-585 . -310) T) ((-569 . -310) T) ((-500 . -310) T) ((-1297 . -722) 108232) ((-699 . -381) 108214) ((-699 . -342) 108196) ((-482 . -173) T) ((-385 . -722) 108166) ((-871 . -621) 108101) ((-876 . -855) NIL) ((-569 . -1028) T) ((-500 . -1028) T) ((-1139 . -618) 108083) ((-1119 . -239) 108062) ((-215 . -102) T) ((-1156 . -102) T) ((-71 . -618) 108044) 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-1118) T) ((-1258 . -457) 106235) ((-1237 . -457) 106214) ((-528 . -618) 106146) ((-717 . -653) 106071) ((-412 . -1062) 106023) ((-509 . -618) 106005) ((-916 . -23) T) ((-492 . -312) NIL) ((-1296 . -621) 105961) ((-479 . -131) T) ((-218 . -312) NIL) ((-412 . -111) 105899) ((-820 . -1064) 105829) ((-742 . -1104) 105813) ((-1257 . -498) 105779) ((-1236 . -498) 105745) ((-553 . -849) T) ((-141 . -1104) 105727) ((-482 . -293) T) ((-1296 . -1055) T) ((-1228 . -102) T) ((-1069 . -102) T) ((-848 . -621) 105595) ((-505 . -519) NIL) ((-487 . -239) 105574) ((-412 . -621) 105472) ((-969 . -1057) 105355) ((-740 . -1057) 105325) ((-969 . -645) 105222) ((-1179 . -145) 105201) ((-740 . -645) 105171) ((-458 . -1057) 105141) ((-1179 . -147) 105120) ((-1131 . -147) 105099) ((-1131 . -145) 105078) ((-640 . -1062) 105062) ((-612 . -1062) 105046) ((-458 . -645) 105016) ((-1181 . -1264) 105000) ((-1181 . -1251) 104977) ((-675 . -1106) T) ((-675 . -1059) 104917) ((-1180 . -1256) 104878) ((-553 . -1106) T) 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T) ((-821 . -457) 103978) ((-44 . -1106) T) ((-1094 . -855) T) ((-1069 . -312) 103829) ((-669 . -131) T) ((-1060 . -651) 103798) ((-675 . -722) 103782) ((-292 . -1064) T) ((-359 . -131) T) ((-356 . -131) T) ((-348 . -131) T) ((-266 . -131) T) ((-248 . -131) T) ((-389 . -651) 103751) ((-423 . -102) T) ((-152 . -1106) T) ((-45 . -230) 103701) ((-804 . -1057) 103685) ((-964 . -855) 103664) ((-1005 . -653) 103602) ((-804 . -645) 103586) ((-241 . -1280) 103556) ((-1030 . -310) T) ((-297 . -1062) 103477) ((-916 . -131) T) ((-40 . -926) T) ((-492 . -405) 103459) ((-358 . -310) T) ((-218 . -405) 103441) ((-1086 . -416) 103425) ((-297 . -111) 103341) ((-1190 . -855) T) ((-1189 . -855) T) ((-877 . -25) T) ((-877 . -21) T) ((-343 . -618) 103323) ((-1259 . -47) 103267) ((-226 . -147) T) ((-175 . -618) 103249) ((-1119 . -853) 103228) ((-779 . -618) 103210) ((-128 . -855) T) ((-613 . -236) 103157) ((-480 . -236) 103107) ((-1295 . -722) 103077) ((-48 . -310) T) ((-1293 . -722) 103047) ((-65 . -621) 102976) ((-970 . -1106) T) ((-820 . -1106) 102766) ((-315 . -102) T) ((-907 . -1223) T) ((-48 . -1028) T) ((-1236 . -644) 102674) ((-694 . -102) 102652) ((-44 . -722) 102636) ((-555 . -102) T) ((-297 . -621) 102567) ((-67 . -387) T) ((-67 . -400) T) ((-667 . -23) T) ((-822 . -651) 102503) ((-675 . -766) T) ((-1220 . -1106) 102481) ((-355 . -1062) 102426) ((-680 . -1106) 102404) ((-1068 . -147) T) ((-958 . -147) 102383) ((-958 . -145) 102362) ((-804 . -102) T) ((-152 . -722) 102346) ((-486 . -147) 102325) ((-486 . -145) 102304) ((-355 . -111) 102233) ((-1086 . -1064) T) ((-325 . -855) 102212) ((-1265 . -979) 102181) ((-632 . -1106) T) ((-1258 . -979) 102143) ((-516 . -131) T) ((-512 . -131) T) ((-298 . -230) 102093) ((-363 . -1064) T) ((-357 . -1064) T) ((-349 . -1064) T) ((-297 . -1055) 102035) ((-1237 . -979) 102004) ((-383 . -855) T) ((-108 . -1064) T) ((-1005 . -731) T) ((-875 . -926) T) ((-848 . -800) 101983) ((-848 . -797) 101962) ((-423 . -312) 101901) ((-473 . -102) T) ((-600 . -979) 101870) ((-322 . -1106) T) ((-412 . -800) 101849) ((-412 . -797) 101828) ((-505 . -494) 101810) ((-1259 . -1044) 101776) ((-1257 . -21) T) ((-1257 . -25) T) ((-1236 . -21) T) ((-1236 . -25) T) ((-820 . -722) 101718) ((-355 . -621) 101648) ((-704 . -409) T) ((-1286 . -1223) T) ((-611 . -102) T) ((-1119 . -416) 101617) ((-1009 . -372) NIL) ((-676 . -102) T) ((-181 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-1185 . -651) 101527) ((-742 . -1223) T) ((-736 . -1057) 101370) ((-44 . -766) T) ((-736 . -645) 101219) ((-598 . -102) T) ((-77 . -401) T) ((-77 . -400) T) ((-658 . -661) 101203) ((-141 . -1223) T) ((-876 . -147) T) ((-876 . -145) NIL) ((-1222 . -93) T) ((-355 . -1055) T) ((-70 . -387) T) ((-70 . -400) T) ((-1172 . -102) T) ((-675 . -519) 101136) ((-1285 . -651) 101081) ((-694 . -312) 101019) ((-969 . -38) 100916) ((-1187 . -618) 100898) ((-740 . -38) 100868) ((-555 . -312) 100672) ((-1181 . -1057) 100555) ((-319 . -1223) T) ((-355 . -234) T) ((-355 . -244) T) ((-316 . -1223) T) ((-292 . -1106) T) ((-1180 . -1057) 100390) ((-1174 . -1057) 100180) ((-1132 . -1057) 100063) ((-1181 . -645) 99960) ((-1180 . -645) 99801) ((-716 . -1227) T) ((-1174 . -645) 99597) ((-1163 . -656) 99581) ((-1132 . -645) 99478) ((-1217 . -561) 99457) ((-824 . -390) 99441) ((-716 . -561) T) ((-319 . -890) 99425) ((-319 . -892) 99350) ((-316 . -890) 99311) ((-316 . -892) NIL) ((-804 . -312) 99276) ((-322 . -722) 99117) ((-391 . -390) 99101) ((-327 . -326) 99078) ((-490 . -102) T) ((-479 . -25) T) ((-479 . -21) T) ((-423 . -38) 99052) ((-319 . -1044) 98715) ((-226 . -1208) T) ((-226 . -1211) T) ((-3 . -618) 98697) ((-316 . -1044) 98627) ((-2 . -1106) T) ((-2 . |RecordCategory|) T) ((-838 . -618) 98609) ((-1119 . -1064) 98539) ((-585 . -926) T) ((-569 . -825) T) ((-569 . -926) T) ((-500 . -926) T) ((-136 . -1044) 98523) ((-226 . -95) T) ((-170 . -147) 98502) ((-75 . -446) T) ((0 . -618) 98484) ((-75 . -400) T) ((-170 . -145) 98435) ((-226 . -35) T) ((-49 . -618) 98417) ((-482 . -1064) T) ((-492 . -232) 98399) ((-489 . -974) 98383) ((-487 . -853) 98362) ((-218 . -232) 98344) ((-81 . -446) T) ((-81 . -400) T) ((-1152 . -34) T) ((-820 . -173) 98323) ((-736 . -102) T) ((-658 . -651) 98282) ((-1032 . -618) 98249) ((-505 . -289) 98224) ((-319 . -381) 98193) ((-316 . -381) 98154) ((-316 . -342) 98115) ((-1091 . -618) 98097) ((-821 . -955) 98044) ((-667 . -131) T) ((-1246 . -145) 98023) ((-1246 . -147) 98002) ((-1181 . -102) T) ((-1180 . -102) T) ((-1174 . -102) T) ((-1166 . -1106) T) ((-1132 . -102) T) ((-223 . -34) T) ((-292 . -722) 97989) ((-1166 . -615) 97965) ((-598 . -312) NIL) ((-489 . -1106) 97943) ((-395 . -618) 97925) ((-515 . -855) T) ((-1156 . -230) 97875) ((-1265 . -1264) 97859) ((-1265 . -1251) 97836) ((-1258 . -1256) 97797) ((-1258 . -1251) 97767) ((-1258 . -1254) 97751) ((-1237 . -1235) 97712) ((-1237 . -1251) 97689) ((-626 . -618) 97671) ((-1237 . -1233) 97655) ((-704 . -926) T) ((-1181 . -287) 97621) ((-1180 . 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T) ((-197 . -1106) T) ((-196 . -1106) T) ((-195 . -1106) T) ((-194 . -1106) T) ((-241 . -102) 94465) ((-170 . -35) 94443) ((-170 . -95) 94421) ((-659 . -1044) 94317) ((-487 . -1064) 94247) ((-1119 . -1106) 94037) ((-1148 . -34) T) ((-675 . -494) 94021) ((-73 . -1223) T) ((-105 . -618) 94003) ((-1297 . -618) 93985) ((-385 . -618) 93967) ((-343 . -621) 93919) ((-175 . -621) 93836) ((-1222 . -495) 93817) ((-736 . -38) 93666) ((-576 . -1211) T) ((-576 . -1208) T) ((-536 . -618) 93648) ((-525 . -312) 93586) ((-505 . -618) 93568) ((-505 . -619) 93550) ((-1222 . -618) 93516) ((-1174 . -1158) NIL) ((-1033 . -1077) 93485) ((-1033 . -1106) T) ((-1010 . -102) T) ((-977 . -102) T) ((-920 . -102) T) ((-899 . -1044) 93462) ((-1148 . -731) T) ((-1009 . -653) 93407) ((-481 . -1106) T) ((-468 . -1106) T) ((-591 . -23) T) ((-576 . -35) T) ((-576 . -95) T) ((-432 . -102) T) ((-1069 . -230) 93353) ((-1181 . -38) 93250) ((-871 . -731) T) ((-699 . -926) T) ((-516 . -25) T) ((-512 . -21) T) ((-512 . -25) T) 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T) ((-1093 . -23) T) ((-822 . -1064) T) ((-787 . -23) T) ((-785 . -23) T) ((-486 . -457) 92105) ((-1166 . -519) 91888) ((-385 . -386) 91867) ((-1185 . -416) 91851) ((-466 . -23) T) ((-459 . -23) T) ((-96 . -1106) T) ((-489 . -519) 91784) ((-1265 . -1057) 91667) ((-1265 . -645) 91564) ((-1258 . -645) 91405) ((-1258 . -1057) 91240) ((-292 . -293) T) ((-1237 . -1057) 91030) ((-1088 . -618) 91012) ((-1088 . -619) 90993) ((-412 . -915) 90972) ((-1237 . -645) 90768) ((-50 . -1118) T) ((-1217 . -131) T) ((-1030 . -926) T) ((-1009 . -731) T) ((-848 . -653) 90741) ((-717 . -892) NIL) ((-601 . -1057) 90701) ((-586 . -1118) T) ((-523 . -1118) T) ((-600 . -1057) 90584) ((-1174 . -405) 90536) ((-1010 . -312) NIL) ((-820 . -494) 90520) ((-601 . -645) 90493) ((-358 . -926) T) ((-600 . -645) 90390) ((-1163 . -34) T) ((-412 . -653) 90342) ((-50 . -23) T) ((-716 . -131) T) ((-717 . -1044) 90222) ((-586 . -23) T) ((-108 . -519) NIL) ((-523 . -23) T) ((-170 . -414) 90193) ((-1146 . -1106) T) ((-1288 . -1287) 90177) ((-706 . -800) T) ((-706 . -797) T) ((-1126 . -310) T) ((-383 . -147) T) ((-283 . -618) 90159) ((-282 . -618) 90141) ((-1236 . -998) 90111) ((-48 . -926) T) ((-680 . -494) 90095) ((-253 . -1280) 90065) ((-252 . -1280) 90035) ((-1183 . -855) T) ((-1119 . -173) 90014) ((-1126 . -1028) T) ((-1052 . -34) T) ((-841 . -147) 89993) ((-841 . -145) 89972) ((-742 . -107) 89956) ((-617 . -132) T) ((-487 . -1106) 89746) ((-1185 . -1064) T) ((-876 . -457) T) ((-85 . -1223) T) ((-241 . -38) 89716) ((-141 . -107) 89698) ((-717 . -381) 89682) ((-838 . -621) 89550) ((-1296 . -731) T) ((-1285 . -1064) T) ((-1126 . -550) T) ((-584 . -102) T) ((-129 . -495) 89532) ((-1265 . -102) T) ((-395 . -1062) 89516) ((-1258 . -102) T) ((-1179 . -955) 89485) ((-129 . -618) 89452) ((-52 . -618) 89434) ((-1131 . -955) 89401) ((-658 . -416) 89385) ((-1237 . -102) T) ((-1165 . -519) NIL) ((-667 . -25) T) ((-626 . -1062) 89369) ((-667 . -21) T) ((-969 . -651) 89279) ((-740 . -651) 89224) ((-720 . -651) 89196) ((-395 . -111) 89175) ((-223 . -256) 89159) ((-1060 . -1059) 89099) ((-1060 . -1106) T) ((-1010 . -1158) T) ((-823 . -1106) T) ((-458 . -651) 89014) ((-347 . -1227) T) ((-640 . -653) 88998) ((-626 . -111) 88977) ((-612 . -653) 88961) ((-601 . -102) T) ((-314 . -495) 88942) ((-591 . -131) T) ((-600 . -102) T) ((-419 . -1106) T) ((-389 . -1106) T) ((-314 . -618) 88908) ((-228 . -1106) 88886) ((-652 . -519) 88819) ((-637 . -519) 88663) ((-838 . -1055) 88642) ((-649 . -151) 88626) ((-347 . -561) T) ((-717 . -906) 88569) ((-555 . -230) 88519) ((-1265 . -287) 88485) ((-1258 . -287) 88451) ((-1086 . -293) 88402) ((-492 . -853) T) ((-224 . -1118) T) ((-1237 . -287) 88368) ((-1217 . -498) 88334) ((-1010 . -38) 88284) ((-218 . -853) T) ((-423 . -651) 88243) ((-920 . -38) 88195) ((-848 . -799) 88174) ((-848 . -796) 88153) ((-848 . -731) 88132) ((-363 . -293) T) ((-357 . -293) T) ((-349 . -293) T) ((-170 . -457) 88063) ((-432 . -38) 88047) ((-108 . -293) T) ((-224 . -23) T) ((-412 . -799) 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T) ((-1005 . -1044) 86514) ((-50 . -131) T) ((-586 . -131) T) ((-523 . -131) T) ((-297 . -653) 86374) ((-347 . -332) 86351) ((-347 . -367) T) ((-325 . -326) 86328) ((-322 . -289) 86313) ((-40 . -561) T) ((-383 . -1208) T) ((-383 . -1211) T) ((-1041 . -1199) 86288) ((-1196 . -236) 86238) ((-1174 . -232) 86190) ((-333 . -1106) T) ((-383 . -95) T) ((-383 . -35) T) ((-1041 . -107) 86136) ((-482 . -1055) T) ((-1297 . -1062) 86120) ((-484 . -236) 86070) ((-1166 . -494) 86004) ((-1288 . -1057) 85988) ((-385 . -1062) 85972) ((-1288 . -645) 85942) ((-482 . -244) T) ((-821 . -102) T) ((-719 . -147) 85921) ((-719 . -145) 85900) ((-489 . -494) 85884) ((-490 . -339) 85853) ((-1297 . -111) 85832) ((-517 . -1106) T) ((-487 . -173) 85811) ((-1005 . -381) 85795) ((-418 . -102) T) ((-385 . -111) 85774) ((-1005 . -342) 85758) ((-281 . -989) 85742) ((-280 . -989) 85726) ((-1295 . -618) 85708) ((-1293 . -618) 85690) ((-110 . -519) NIL) ((-1179 . -1249) 85674) ((-859 . -857) 85658) ((-1185 . -1106) T) 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-312) 81150) ((-969 . -416) 81134) ((-704 . -1227) T) ((-637 . -289) 81109) ((-1093 . -644) 81057) ((-787 . -644) 81005) ((-785 . -644) 80953) ((-347 . -131) T) ((-292 . -618) 80935) ((-911 . -1106) T) ((-704 . -561) T) ((-129 . -621) 80917) ((-875 . -1118) T) ((-459 . -644) 80865) ((-911 . -909) 80849) ((-383 . -457) T) ((-492 . -1106) T) ((-949 . -312) 80787) ((-706 . -653) 80774) ((-554 . -849) T) ((-218 . -1106) T) ((-319 . -926) 80753) ((-316 . -926) T) ((-316 . -825) NIL) ((-395 . -725) T) ((-875 . -23) T) ((-116 . -653) 80740) ((-479 . -145) 80719) ((-423 . -416) 80703) ((-479 . -147) 80682) ((-110 . -494) 80664) ((-314 . -621) 80645) ((-2 . -618) 80627) ((-187 . -102) T) ((-1165 . -19) 80609) ((-1165 . -609) 80584) ((-663 . -21) T) ((-663 . -25) T) ((-598 . -1150) T) ((-1119 . -289) 80561) ((-340 . -25) T) ((-340 . -21) T) ((-241 . -651) 80311) ((-500 . -367) T) ((-1288 . -38) 80281) ((-1179 . -1057) 80104) ((-1148 . -1223) T) ((-1131 . -1057) 79947) ((-859 . -1057) 79931) 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. -145) 76867) ((-266 . -145) 76846) ((-266 . -147) 76825) ((-253 . -38) 76795) ((-248 . -147) 76774) ((-117 . -367) T) ((-248 . -145) 76753) ((-252 . -38) 76723) ((-152 . -111) 76702) ((-1009 . -1044) 76590) ((-1174 . -853) NIL) ((-699 . -1227) T) ((-804 . -1064) T) ((-704 . -1118) T) ((-1293 . -1055) T) ((-1163 . -1223) T) ((-1009 . -381) 76567) ((-916 . -145) T) ((-916 . -147) 76549) ((-875 . -131) T) ((-820 . -1062) 76446) ((-704 . -23) T) ((-699 . -561) T) ((-226 . -1057) 76411) ((-652 . -618) 76343) ((-652 . -619) 76304) ((-637 . -619) NIL) ((-637 . -618) 76286) ((-492 . -173) T) ((-226 . -645) 76251) ((-224 . -21) T) ((-218 . -173) T) ((-224 . -25) T) ((-479 . -1211) 76217) ((-479 . -1208) 76183) ((-276 . -618) 76165) ((-275 . -618) 76147) ((-274 . -618) 76129) ((-273 . -618) 76111) ((-272 . -618) 76093) ((-505 . -656) 76075) ((-271 . -618) 76057) ((-343 . -731) T) ((-270 . -618) 76039) ((-110 . -19) 76021) ((-175 . -731) T) ((-505 . -377) 76003) ((-213 . -618) 75985) ((-525 . -1155) 75969) ((-505 . -123) T) ((-110 . -609) 75944) ((-212 . -618) 75926) ((-479 . -35) 75892) ((-479 . -95) 75858) ((-210 . -618) 75840) ((-209 . -618) 75822) ((-208 . -618) 75804) ((-207 . -618) 75786) ((-204 . -618) 75768) ((-203 . -618) 75750) ((-202 . -618) 75732) ((-201 . -618) 75714) ((-200 . -618) 75696) ((-199 . -618) 75678) ((-198 . -618) 75660) ((-541 . -1109) 75612) ((-197 . -618) 75594) ((-196 . -618) 75576) ((-45 . -494) 75513) ((-195 . -618) 75495) ((-194 . -618) 75477) ((-152 . -621) 75446) ((-1121 . -102) T) ((-820 . -111) 75336) ((-649 . -102) 75286) ((-487 . -289) 75263) ((-1119 . -618) 74994) ((-1107 . -1106) T) ((-1052 . -1223) T) ((-1296 . -1044) 74978) ((-1068 . -1057) 74965) ((-1179 . -312) 74952) ((-958 . -1057) 74795) ((-1141 . -1106) T) ((-1131 . -312) 74782) ((-628 . -1118) T) ((-1068 . -645) 74769) ((-1102 . -1089) T) ((-958 . -645) 74618) ((-1096 . -1089) T) ((-486 . -1057) 74461) ((-1079 . -1089) T) ((-1072 . -1089) T) ((-1042 . -1089) T) ((-1025 . -1089) T) ((-117 . -1118) T) ((-486 . -645) 74310) ((-824 . -102) T) ((-631 . -1089) T) ((-628 . -23) T) ((-1156 . -519) 74102) ((-488 . -1089) T) ((-391 . -102) T) ((-327 . -102) T) ((-219 . -1089) T) ((-969 . -1106) T) ((-152 . -1055) T) ((-736 . -416) 74086) ((-117 . -23) T) ((-1009 . -906) 74038) ((-740 . -1106) T) ((-720 . -1106) T) ((-458 . -1106) T) ((-412 . -1223) T) ((-319 . -435) 74022) ((-597 . -93) T) ((-1265 . -651) 73932) ((-1033 . -619) 73893) ((-1030 . -1227) T) ((-226 . -102) T) ((-1033 . -618) 73855) ((-1258 . -651) 73737) ((-821 . -232) 73721) ((-820 . -621) 73451) ((-1237 . -651) 73288) ((-1030 . -561) T) ((-838 . -653) 73261) ((-358 . -1227) T) ((-481 . -618) 73223) ((-481 . -619) 73184) ((-468 . -619) 73145) ((-468 . -618) 73107) ((-601 . -651) 73066) ((-412 . -890) 73050) ((-322 . -1062) 72885) ((-412 . -892) 72810) ((-600 . -651) 72720) ((-848 . -1044) 72616) ((-492 . -519) NIL) ((-487 . -609) 72593) ((-358 . -561) T) ((-218 . -519) NIL) ((-877 . -457) T) ((-423 . -1106) T) ((-412 . -1044) 72457) ((-322 . -111) 72278) ((-699 . -367) T) ((-226 . -287) T) ((-1220 . -621) 72255) ((-48 . -1227) T) ((-820 . -1055) 72185) ((-1179 . -1158) 72163) ((-585 . -131) T) ((-569 . -131) T) ((-500 . -131) T) ((-1166 . -291) 72139) ((-48 . -561) T) ((-1068 . -102) T) ((-958 . -102) T) ((-876 . -1057) 72084) ((-319 . -27) 72063) ((-820 . -234) 72015) ((-250 . -840) 71997) ((-241 . -853) 71976) ((-188 . -840) 71958) ((-718 . -102) T) ((-298 . -494) 71895) ((-876 . -645) 71840) ((-486 . -102) T) ((-736 . -1064) T) ((-617 . -618) 71822) ((-617 . -619) 71683) ((-412 . -381) 71667) ((-412 . -342) 71651) ((-322 . -621) 71477) ((-1179 . -38) 71306) ((-1131 . -38) 71155) ((-859 . -38) 71125) ((-395 . -653) 71109) ((-649 . -312) 71047) ((-1157 . -495) 71028) ((-1157 . -618) 70994) ((-969 . -722) 70891) ((-740 . -722) 70861) ((-223 . -107) 70845) ((-45 . -289) 70770) ((-626 . -653) 70744) ((-315 . -1106) T) ((-292 . -1062) 70731) ((-110 . -618) 70713) ((-110 . -619) 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-457) T) ((-363 . -131) T) ((-319 . -405) 165675) ((-316 . -405) 165636) ((-357 . -131) T) ((-349 . -131) T) ((-1190 . -1108) T) ((-1128 . -38) 165623) ((-1102 . -618) 165590) ((-108 . -131) T) ((-960 . -1108) T) ((-927 . -1108) T) ((-776 . -1108) T) ((-677 . -1108) T) ((-706 . -147) T) ((-116 . -147) T) ((-1297 . -21) T) ((-1297 . -25) T) ((-1295 . -21) T) ((-1295 . -25) T) ((-669 . -1064) 165574) ((-536 . -855) T) ((-505 . -855) T) ((-359 . -1064) 165526) ((-356 . -1064) 165478) ((-348 . -1064) 165430) ((-253 . -1225) T) ((-252 . -1225) T) ((-266 . -1064) 165273) ((-248 . -1064) 165116) ((-669 . -111) 165095) ((-552 . -849) T) ((-359 . -111) 165033) ((-356 . -111) 164971) ((-348 . -111) 164909) ((-266 . -111) 164738) ((-248 . -111) 164567) ((-822 . -1229) 164546) ((-628 . -416) 164530) ((-44 . -21) T) ((-44 . -25) T) ((-820 . -644) 164436) ((-822 . -561) 164415) ((-253 . -1046) 164242) ((-252 . -1046) 164069) ((-126 . -119) 164053) ((-916 . -1064) 164018) ((-717 . -102) T) ((-704 . 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160920) ((-585 . -1108) T) ((-569 . -1108) T) ((-500 . -1108) T) ((-246 . -291) 160897) ((-316 . -232) 160858) ((-1181 . -892) NIL) ((-55 . -1108) T) ((-1133 . -892) 160717) ((-129 . -855) T) ((-1181 . -1046) 160597) ((-1133 . -1046) 160480) ((-184 . -618) 160462) ((-859 . -1046) 160358) ((-787 . -289) 160285) ((-822 . -1120) T) ((-1042 . -731) T) ((-607 . -656) 160269) ((-1054 . -984) 160198) ((-1007 . -102) T) ((-822 . -23) T) ((-717 . -1160) 160176) ((-699 . -1066) T) ((-607 . -377) 160160) ((-355 . -457) T) ((-347 . -293) T) ((-1276 . -1108) T) ((-249 . -1108) T) ((-404 . -102) T) ((-292 . -21) T) ((-292 . -25) T) ((-365 . -731) T) ((-715 . -1108) T) ((-704 . -1108) T) ((-365 . -478) T) ((-1219 . -618) 160142) ((-1181 . -381) 160126) ((-1133 . -381) 160110) ((-1032 . -416) 160072) ((-141 . -230) 160054) ((-383 . -799) T) ((-383 . -796) T) ((-875 . -173) T) ((-383 . -731) T) ((-716 . -618) 160036) ((-717 . -38) 159865) ((-1275 . -1273) 159849) ((-355 . -407) T) ((-1275 . -1108) 159799) ((-585 . -722) 159786) ((-569 . -722) 159773) ((-500 . -722) 159738) ((-1261 . -651) 159628) ((-319 . -634) 159607) ((-841 . -731) T) ((-832 . -731) T) ((-649 . -1225) T) ((-1088 . -644) 159555) ((-1181 . -906) 159498) ((-1133 . -906) 159482) ((-667 . -1064) 159466) ((-108 . -644) 159448) ((-487 . -131) 159318) ((-1187 . -1120) T) ((-958 . -47) 159287) ((-628 . -1108) T) ((-667 . -111) 159266) ((-496 . -618) 159232) ((-330 . -291) 159209) ((-486 . -47) 159166) ((-1187 . -23) T) ((-117 . -1108) T) ((-103 . -102) 159144) ((-1287 . -1120) T) ((-553 . -855) T) ((-1062 . -131) T) ((-1032 . -1066) T) ((-824 . -1046) 159128) ((-1011 . -729) 159100) ((-1287 . -23) T) ((-704 . -722) 159065) ((-591 . -618) 159047) ((-391 . -1046) 159031) ((-358 . -1066) T) ((-389 . -131) T) ((-327 . -1046) 159015) ((-1205 . -618) 158997) ((-1128 . -833) T) ((-1113 . -1108) T) ((-226 . -892) 158979) ((-1012 . -926) T) ((-91 . -34) T) ((-1012 . -825) T) ((-920 . -926) T) ((-1088 . -21) T) ((-1088 . -25) T) 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-23) T) ((-486 . -1046) 157781) ((-1095 . -619) NIL) ((-1095 . -618) 157763) ((-787 . -619) NIL) ((-787 . -618) 157724) ((-785 . -619) 157358) ((-785 . -618) 157272) ((-1121 . -644) 157178) ((-466 . -618) 157160) ((-459 . -618) 157142) ((-459 . -619) 157003) ((-1043 . -230) 156949) ((-877 . -915) 156928) ((-126 . -34) T) ((-822 . -131) T) ((-654 . -618) 156910) ((-583 . -102) T) ((-359 . -1294) 156894) ((-356 . -1294) 156878) ((-348 . -1294) 156862) ((-127 . -519) 156795) ((-121 . -519) 156728) ((-516 . -797) T) ((-516 . -800) T) ((-515 . -799) T) ((-103 . -312) 156666) ((-223 . -102) 156644) ((-704 . -173) T) ((-699 . -1108) T) ((-877 . -653) 156596) ((-65 . -388) T) ((-277 . -618) 156578) ((-65 . -400) T) ((-958 . -381) 156562) ((-875 . -293) T) ((-50 . -618) 156544) ((-1007 . -38) 156492) ((-1128 . -651) 156464) ((-586 . -618) 156446) ((-486 . -381) 156430) ((-586 . -619) 156412) ((-523 . -618) 156394) ((-916 . -1294) 156381) ((-876 . -1225) T) ((-706 . -457) T) ((-500 . -519) 156347) ((-492 . -367) T) ((-359 . -372) 156326) ((-356 . -372) 156305) ((-348 . -372) 156284) ((-719 . -731) T) ((-218 . -367) T) ((-116 . -457) T) ((-1298 . -1289) 156268) ((-876 . -890) 156245) ((-876 . -892) NIL) ((-970 . -855) 156144) ((-820 . -855) 156095) ((-1232 . -102) T) ((-659 . -661) 156079) ((-1211 . -34) T) ((-172 . -618) 156061) ((-1121 . -21) 155971) ((-1121 . -25) 155822) ((-876 . -1046) 155799) ((-958 . -906) 155780) ((-1248 . -47) 155757) ((-916 . -372) T) ((-59 . -656) 155741) ((-521 . -656) 155725) ((-486 . -906) 155702) ((-71 . -446) T) ((-71 . -400) T) ((-501 . -656) 155686) ((-59 . -377) 155670) ((-628 . -173) T) ((-521 . -377) 155654) ((-501 . -377) 155638) ((-832 . -713) 155622) ((-1181 . -310) 155601) ((-1187 . -131) T) ((-1150 . -1059) 155585) ((-117 . -173) T) ((-1150 . -645) 155517) ((-1154 . -312) 155455) ((-170 . -1225) T) ((-1287 . -131) T) ((-871 . -1059) 155425) ((-640 . -749) 155409) ((-612 . -749) 155393) ((-1260 . -926) 155372) ((-1239 . -926) 155351) ((-1239 . -825) NIL) ((-871 . -645) 155321) ((-699 . -722) 155271) ((-1238 . -915) 155224) ((-1032 . -1108) T) ((-876 . -381) 155201) ((-876 . -342) 155178) ((-911 . -1120) T) ((-170 . -890) 155162) ((-170 . -892) 155087) ((-492 . -1120) T) ((-358 . -1108) T) ((-218 . -1120) T) ((-76 . -446) T) ((-76 . -400) T) ((-170 . -1046) 154983) ((-322 . -855) T) ((-1275 . -519) 154916) ((-1259 . -653) 154813) ((-1238 . -653) 154683) ((-877 . -799) 154662) ((-877 . -796) 154641) ((-877 . -731) T) ((-492 . -23) T) ((-224 . -618) 154623) ((-175 . -457) T) ((-223 . -312) 154561) ((-86 . -446) T) ((-86 . -400) T) ((-218 . -23) T) ((-1299 . -1292) 154540) ((-682 . -1046) 154524) ((-585 . -293) T) ((-569 . -293) T) ((-500 . -293) T) ((-136 . -475) 154479) ((-659 . -651) 154438) ((-48 . -1108) T) ((-717 . -232) 154422) ((-876 . -906) NIL) ((-1248 . -892) NIL) ((-895 . -102) T) ((-891 . -102) T) ((-393 . -1108) T) ((-170 . -381) 154406) ((-170 . -342) 154390) ((-1248 . -1046) 154270) ((-860 . -1046) 154166) ((-1150 . -102) T) ((-667 . -797) 154145) ((-658 . -131) T) ((-117 . -519) 154053) ((-667 . -800) 154032) ((-576 . -1046) 154014) ((-297 . -1282) 153984) ((-871 . -102) T) ((-969 . -561) 153963) ((-1219 . -1064) 153846) ((-1011 . -1059) 153791) ((-487 . -644) 153697) ((-910 . -1108) T) ((-1032 . -722) 153634) ((-716 . -1064) 153599) ((-1011 . -645) 153544) ((-622 . -102) T) ((-607 . -34) T) ((-1155 . -1225) T) ((-1219 . -111) 153413) ((-479 . -653) 153310) ((-358 . -722) 153255) ((-170 . -906) 153214) ((-704 . -293) T) ((-699 . -173) T) ((-716 . -111) 153170) ((-1303 . -1066) T) ((-1248 . -381) 153154) ((-423 . -1229) 153132) ((-1126 . -618) 153114) ((-316 . -853) NIL) ((-423 . -561) T) ((-226 . -310) T) ((-1238 . -796) 153067) ((-1238 . -799) 153020) ((-1259 . -731) T) ((-1238 . -731) T) ((-48 . -722) 152985) ((-226 . -1030) T) ((-355 . -1282) 152962) ((-1261 . -416) 152928) ((-723 . -731) T) ((-336 . -618) 152910) ((-1248 . -906) 152853) ((-1219 . -621) 152735) ((-112 . -618) 152717) ((-112 . -619) 152699) ((-723 . -478) T) ((-716 . -621) 152649) ((-1298 . -1059) 152633) ((-487 . -21) 152543) ((-127 . -494) 152527) ((-121 . -494) 152511) ((-487 . -25) 152362) ((-1298 . -645) 152332) ((-628 . -293) T) ((-591 . -1064) 152307) ((-442 . -1108) T) ((-1070 . -310) T) ((-117 . -293) T) ((-1112 . -102) T) ((-1011 . -102) T) ((-591 . -111) 152275) ((-1150 . -312) 152213) ((-1219 . -1057) T) ((-1070 . -1030) T) ((-66 . -1225) T) ((-1062 . -25) T) ((-1062 . -21) T) ((-716 . -1057) T) ((-389 . -21) T) ((-389 . -25) T) ((-699 . -519) NIL) ((-1032 . -173) T) ((-716 . -244) T) ((-1070 . -550) T) ((-717 . -651) 152123) ((-511 . -102) T) ((-507 . -102) T) ((-358 . -173) T) ((-347 . -618) 152105) ((-412 . -1059) 152057) ((-399 . -618) 152039) ((-1128 . -853) T) ((-479 . -731) T) ((-898 . -1046) 152007) ((-412 . -645) 151959) ((-108 . -855) T) ((-663 . -1064) 151943) ((-492 . -131) T) ((-1261 . -1066) T) ((-218 . -131) T) ((-1165 . -102) 151921) ((-99 . -1108) T) 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140784) ((-223 . -1129) 140768) ((-1275 . -291) 140745) ((-1219 . -653) 140670) ((-1011 . -651) 140600) ((-969 . -21) T) ((-969 . -25) T) ((-740 . -21) T) ((-740 . -25) T) ((-720 . -21) T) ((-720 . -25) T) ((-716 . -653) 140565) ((-458 . -21) T) ((-458 . -25) T) ((-343 . -102) T) ((-175 . -102) T) ((-1007 . -1066) T) ((-875 . -1057) T) ((-779 . -102) T) ((-1260 . -367) 140544) ((-1259 . -906) 140450) ((-1239 . -367) 140429) ((-1238 . -906) 140280) ((-1032 . -618) 140262) ((-412 . -833) 140215) ((-1183 . -498) 140181) ((-170 . -926) 140112) ((-1182 . -498) 140078) ((-1176 . -498) 140044) ((-717 . -1108) T) ((-1134 . -498) 140010) ((-585 . -1064) 139997) ((-569 . -1064) 139984) ((-500 . -1064) 139949) ((-319 . -293) 139928) ((-316 . -293) T) ((-358 . -618) 139910) ((-423 . -25) T) ((-423 . -21) T) ((-99 . -289) 139889) ((-585 . -111) 139874) ((-569 . -111) 139859) ((-500 . -111) 139815) ((-1185 . -892) 139782) ((-907 . -494) 139766) ((-48 . -618) 139748) ((-48 . -619) 139693) ((-241 . 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. -38) 136184) ((-218 . -1000) 136166) ((-117 . -621) 136096) ((-175 . -38) 136028) ((-1259 . -310) 136007) ((-1238 . -310) 135986) ((-663 . -731) T) ((-99 . -618) 135968) ((-482 . -1059) 135933) ((-1176 . -644) 135885) ((-482 . -645) 135850) ((-490 . -25) T) ((-490 . -21) T) ((-1238 . -1030) 135802) ((-1065 . -1225) T) ((-628 . -1057) T) ((-383 . -409) T) ((-395 . -102) T) ((-1113 . -623) 135717) ((-266 . -906) 135663) ((-248 . -906) 135640) ((-117 . -1057) T) ((-821 . -1120) T) ((-1095 . -731) T) ((-628 . -234) 135619) ((-626 . -102) T) ((-787 . -731) T) ((-785 . -731) T) ((-418 . -1120) T) ((-117 . -244) T) ((-40 . -372) NIL) ((-117 . -234) NIL) ((-1230 . -855) T) ((-459 . -731) T) ((-821 . -23) T) ((-736 . -25) T) ((-736 . -21) T) ((-1085 . -289) 135598) ((-78 . -401) T) ((-78 . -400) T) ((-538 . -772) 135580) ((-699 . -1064) 135530) ((-1267 . -131) T) ((-1260 . -131) T) ((-1239 . -131) T) ((-1183 . -25) T) ((-1150 . -416) 135514) ((-640 . -371) 135446) ((-612 . -371) 135378) 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131061) ((-933 . -618) 131043) ((-347 . -731) T) ((-30 . -618) 131025) ((-871 . -1108) T) ((-848 . -1066) 131004) ((-40 . -653) 130949) ((-226 . -1229) T) ((-412 . -1066) T) ((-1167 . -151) 130931) ((-1007 . -293) 130882) ((-622 . -1108) T) ((-226 . -561) T) ((-322 . -1256) 130866) ((-322 . -1253) 130836) ((-706 . -651) 130808) ((-1198 . -1201) 130787) ((-1083 . -618) 130769) ((-1198 . -107) 130719) ((-652 . -151) 130703) ((-637 . -151) 130649) ((-116 . -651) 130621) ((-484 . -1201) 130600) ((-492 . -147) T) ((-492 . -145) NIL) ((-1128 . -619) 130515) ((-443 . -618) 130497) ((-218 . -147) T) ((-218 . -145) NIL) ((-1128 . -618) 130479) ((-129 . -102) T) ((-52 . -102) T) ((-1239 . -644) 130431) ((-484 . -107) 130381) ((-1001 . -23) T) ((-1299 . -38) 130351) ((-1181 . -1120) T) ((-1133 . -1120) T) ((-1070 . -1229) T) ((-314 . -102) T) ((-859 . -1120) T) ((-958 . -1229) 130330) ((-486 . -1229) 130309) ((-1070 . -561) T) ((-958 . -561) 130240) ((-1181 . -23) T) ((-1159 . -1091) T) ((-1133 . -23) T) ((-859 . -23) T) ((-486 . -561) 130171) ((-1150 . -722) 130103) ((-675 . -1059) 130087) ((-1154 . -519) 130020) ((-675 . -645) 130004) ((-1043 . -619) NIL) ((-1043 . -618) 129986) ((-96 . -1091) T) ((-871 . -722) 129956) ((-1219 . -47) 129925) ((-253 . -131) T) ((-252 . -131) T) ((-1112 . -1108) T) ((-1011 . -1108) T) ((-62 . -618) 129907) ((-1176 . -855) NIL) ((-1032 . -797) T) ((-1032 . -800) T) ((-1303 . -1064) 129894) ((-1303 . -111) 129879) ((-1267 . -25) T) ((-1267 . -21) T) ((-875 . -653) 129866) ((-1260 . -21) T) ((-1260 . -25) T) ((-1239 . -21) T) ((-1239 . -25) T) ((-1035 . -151) 129850) ((-877 . -825) 129829) ((-877 . -926) T) ((-717 . -289) 129756) ((-601 . -21) T) ((-343 . -651) 129715) ((-601 . -25) T) ((-600 . -21) T) ((-175 . -651) 129632) ((-40 . -731) T) ((-223 . -519) 129565) ((-600 . -25) T) ((-481 . -151) 129549) ((-468 . -151) 129533) ((-927 . -799) T) ((-927 . -731) T) ((-776 . -798) T) ((-776 . -799) T) ((-511 . -1108) T) ((-507 . -1108) T) ((-776 . -731) T) ((-226 . -367) T) ((-1297 . -1059) 129517) ((-1295 . -1059) 129501) ((-1297 . -645) 129471) ((-1165 . -1108) 129449) ((-876 . -1229) T) ((-1295 . -645) 129419) ((-659 . -618) 129401) ((-876 . -561) T) ((-699 . -372) NIL) ((-44 . -1059) 129385) ((-1303 . -621) 129367) ((-1298 . -1108) T) ((-675 . -102) T) ((-363 . -1282) 129351) ((-357 . -1282) 129335) ((-44 . -645) 129319) ((-349 . -1282) 129303) ((-553 . -102) T) ((-525 . -855) 129282) ((-1054 . -1108) T) ((-822 . -457) 129261) ((-152 . -1059) 129245) ((-1054 . -1079) 129174) ((-1035 . -984) 129143) ((-824 . -1120) T) ((-1011 . -722) 129088) ((-152 . -645) 129072) ((-391 . -1120) T) ((-481 . -984) 129041) ((-468 . -984) 129010) ((-110 . -151) 128992) ((-73 . -618) 128974) ((-899 . -618) 128956) ((-1088 . -729) 128935) ((-1303 . -1057) T) ((-821 . -644) 128883) ((-297 . -1066) 128825) ((-170 . -1229) 128730) ((-226 . -1120) T) ((-327 . -23) T) ((-1176 . -1000) 128682) ((-848 . -1108) T) ((-1261 . -1064) 128587) ((-1134 . -745) 128566) ((-1259 . -926) 128545) ((-1238 . -926) 128524) ((-875 . -731) T) ((-170 . -561) 128435) ((-585 . -653) 128422) ((-569 . -653) 128409) ((-412 . -1108) T) ((-265 . -1108) T) ((-214 . -618) 128391) ((-500 . -653) 128356) ((-226 . -23) T) ((-1238 . -825) 128309) ((-1297 . -102) T) ((-358 . -1294) 128286) ((-1295 . -102) T) ((-1261 . -111) 128178) ((-820 . -1059) 128075) ((-820 . -645) 128017) ((-144 . -618) 127999) ((-1001 . -131) T) ((-44 . -102) T) ((-241 . -855) 127950) ((-1248 . -1229) 127929) ((-103 . -494) 127913) ((-1298 . -722) 127883) ((-1095 . -47) 127844) ((-1070 . -1120) T) ((-958 . -1120) T) ((-127 . -34) T) ((-121 . -34) T) ((-787 . -47) 127821) ((-785 . -47) 127793) ((-1248 . -561) 127704) ((-358 . -372) T) ((-486 . -1120) T) ((-1181 . -131) T) ((-1133 . -131) T) ((-459 . -47) 127683) ((-876 . -367) T) ((-859 . -131) T) ((-152 . -102) T) ((-1070 . -23) T) ((-958 . -23) T) ((-576 . -561) T) ((-821 . -25) T) ((-821 . -21) T) ((-1150 . -519) 127616) ((-597 . -1091) T) 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-1296) 125872) ((-1295 . -1296) 125851) ((-787 . -892) NIL) ((-785 . -892) 125710) ((-1290 . -25) T) ((-1290 . -21) T) ((-1222 . -102) 125688) ((-1114 . -400) T) ((-628 . -653) 125675) ((-459 . -892) NIL) ((-680 . -102) 125653) ((-1095 . -1046) 125480) ((-876 . -23) T) ((-787 . -1046) 125339) ((-785 . -1046) 125196) ((-117 . -653) 125141) ((-459 . -1046) 125017) ((-319 . -621) 124581) ((-316 . -621) 124464) ((-395 . -651) 124433) ((-654 . -1046) 124417) ((-632 . -102) T) ((-223 . -494) 124401) ((-1275 . -34) T) ((-626 . -651) 124360) ((-292 . -1059) 124347) ((-136 . -621) 124331) ((-292 . -645) 124318) ((-640 . -722) 124302) ((-612 . -722) 124286) ((-675 . -38) 124246) ((-322 . -102) T) ((-85 . -618) 124228) ((-50 . -1046) 124212) ((-1128 . -1064) 124199) ((-1095 . -381) 124183) ((-787 . -381) 124167) ((-704 . -731) T) ((-704 . -799) T) ((-704 . -796) T) ((-586 . -1046) 124154) ((-523 . -1046) 124131) ((-60 . -57) 124093) ((-327 . -131) T) ((-319 . -1057) 123983) ((-316 . -1057) T) 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((-1054 . -519) 122838) ((-486 . -131) T) ((-576 . -23) T) ((-680 . -312) 122776) ((-640 . -766) T) ((-612 . -766) T) ((-1239 . -855) NIL) ((-1088 . -1059) 122686) ((-1011 . -293) T) ((-699 . -653) 122636) ((-253 . -21) T) ((-355 . -1108) T) ((-253 . -25) T) ((-252 . -21) T) ((-252 . -25) T) ((-152 . -38) 122620) ((-2 . -102) T) ((-916 . -926) T) ((-1088 . -645) 122488) ((-487 . -1282) 122458) ((-1128 . -1057) T) ((-716 . -310) T) ((-363 . -1059) 122410) ((-357 . -1059) 122362) ((-349 . -1059) 122314) ((-363 . -645) 122266) ((-224 . -1046) 122243) ((-357 . -645) 122195) ((-108 . -1059) 122145) ((-349 . -645) 122097) ((-297 . -722) 122039) ((-706 . -1066) T) ((-492 . -457) T) ((-412 . -519) 121951) ((-108 . -645) 121901) ((-218 . -457) T) ((-1128 . -234) T) ((-298 . -151) 121851) ((-1007 . -619) 121812) ((-1007 . -618) 121794) ((-997 . -618) 121776) ((-116 . -1066) T) ((-659 . -1064) 121760) ((-226 . -498) T) ((-404 . -618) 121742) ((-404 . -619) 121719) ((-1062 . -1282) 121689) ((-659 . -111) 121668) ((-1150 . -494) 121652) ((-1299 . -651) 121611) ((-385 . -651) 121580) ((-820 . -38) 121550) ((-63 . -446) T) ((-63 . -400) T) ((-1168 . -102) T) ((-876 . -131) T) ((-489 . -102) 121528) ((-1303 . -372) T) ((-1088 . -102) T) ((-1069 . -102) T) ((-355 . -722) 121473) ((-736 . -147) 121452) ((-736 . -145) 121431) ((-659 . -621) 121349) ((-1032 . -653) 121286) ((-528 . -1108) 121264) ((-363 . -102) T) ((-357 . -102) T) ((-349 . -102) T) ((-108 . -102) T) ((-509 . -1108) T) ((-358 . -653) 121209) ((-1181 . -644) 121157) ((-1133 . -644) 121105) ((-389 . -514) 121084) ((-838 . -853) 121063) ((-383 . -1229) T) ((-699 . -731) T) ((-343 . -1066) T) ((-1239 . -1000) 121015) ((-175 . -1066) T) ((-103 . -618) 120947) ((-1183 . -145) 120926) ((-1183 . -147) 120905) ((-383 . -561) T) ((-1182 . -147) 120884) ((-1182 . -145) 120863) ((-1176 . -145) 120770) ((-412 . -293) T) ((-1176 . -147) 120677) ((-1134 . -147) 120656) ((-1134 . -145) 120635) ((-322 . -38) 120476) ((-170 . -131) T) 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T) ((-213 . -102) T) ((-212 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-208 . -102) T) ((-207 . -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) ((-194 . -102) T) ((-358 . -731) T) ((-717 . -111) 119301) ((-675 . -232) 119285) ((-586 . -310) T) ((-523 . -310) T) ((-297 . -519) 119234) ((-108 . -312) NIL) ((-72 . -400) T) ((-1121 . -102) 119024) ((-838 . -416) 119008) ((-1128 . -800) T) ((-1128 . -797) T) ((-706 . -1108) T) ((-583 . -618) 118990) ((-383 . -367) T) ((-170 . -498) 118968) ((-223 . -618) 118900) ((-134 . -1108) T) ((-116 . -1108) T) ((-48 . -731) T) ((-1054 . -494) 118865) ((-141 . -430) 118847) ((-141 . -372) T) ((-1035 . -102) T) ((-517 . -514) 118826) ((-717 . -621) 118582) ((-481 . -102) T) ((-468 . -102) T) ((-1042 . -1120) T) ((-1232 . -618) 118564) ((-1190 . -1046) 118500) ((-1183 . -35) 118466) ((-1183 . -95) 118432) ((-1183 . -1213) 118398) ((-1183 . -1210) 118364) ((-1167 . -312) NIL) ((-89 . -401) T) ((-89 . -400) T) ((-1088 . -1160) 118343) ((-1182 . -1210) 118309) ((-1182 . -1213) 118275) ((-1042 . -23) T) ((-1182 . -95) 118241) ((-576 . -498) T) ((-1182 . -35) 118207) ((-1176 . -1210) 118173) ((-1176 . -1213) 118139) ((-1176 . -95) 118105) ((-365 . -1120) T) ((-363 . -1160) 118084) ((-357 . -1160) 118063) ((-349 . -1160) 118042) ((-1176 . -35) 118008) ((-1134 . -35) 117974) ((-1134 . -95) 117940) ((-108 . -1160) T) ((-1134 . -1213) 117906) ((-838 . -1066) 117885) ((-652 . -312) 117823) ((-637 . -312) 117674) ((-1134 . -1210) 117640) ((-717 . -1057) T) ((-1070 . -644) 117622) ((-1088 . -38) 117490) ((-958 . -644) 117438) ((-1012 . -147) T) ((-1012 . -145) NIL) ((-383 . -1120) T) ((-327 . -25) T) ((-325 . -23) T) ((-949 . -855) 117417) ((-717 . -329) 117394) ((-486 . -644) 117342) ((-40 . -1046) 117230) ((-717 . -234) T) ((-706 . -722) 117217) ((-343 . -1108) T) ((-175 . -1108) T) ((-334 . -855) T) ((-423 . -457) 117167) ((-383 . -23) T) ((-363 . -38) 117132) ((-357 . -38) 117097) ((-349 . -38) 117062) ((-80 . -446) T) ((-80 . -400) T) ((-226 . -25) T) ((-226 . -21) T) ((-841 . -1120) T) ((-108 . -38) 117012) ((-832 . -1120) T) ((-779 . -1108) T) ((-116 . -722) 116999) ((-677 . -1046) 116983) ((-617 . -102) T) ((-841 . -23) T) ((-832 . -23) T) ((-1165 . -289) 116960) ((-1121 . -312) 116898) ((-487 . -1059) 116795) ((-1110 . -236) 116779) ((-64 . -401) T) ((-64 . -400) T) ((-1159 . -102) T) ((-110 . -102) T) ((-487 . -645) 116721) ((-40 . -381) 116698) ((-96 . -102) T) ((-658 . -857) 116682) ((-1143 . -1091) T) ((-1070 . -21) T) ((-1070 . -25) T) ((-1062 . -1059) 116666) ((-820 . -232) 116635) ((-958 . -25) T) ((-958 . -21) T) ((-1062 . -645) 116577) ((-626 . -1066) T) ((-1128 . -372) T) ((-1035 . -312) 116515) ((-675 . -651) 116474) ((-486 . -25) T) ((-486 . -21) T) ((-389 . -1059) 116458) ((-895 . -618) 116440) ((-891 . -618) 116422) ((-528 . -519) 116355) ((-253 . -855) 116306) ((-252 . -855) 116257) ((-389 . -645) 116227) ((-876 . -644) 116204) ((-481 . -312) 116142) ((-468 . -312) 116080) ((-355 . -293) T) ((-1165 . -1263) 116064) ((-1150 . -618) 116026) ((-1150 . -619) 115987) ((-1148 . -102) T) ((-1007 . -1064) 115883) ((-40 . -906) 115835) ((-1165 . -609) 115812) ((-1303 . -653) 115799) ((-871 . -495) 115776) ((-1071 . -151) 115722) ((-877 . -1229) T) ((-1007 . -111) 115604) ((-343 . -722) 115588) ((-871 . -618) 115550) ((-175 . -722) 115482) ((-412 . -289) 115440) ((-877 . -561) T) ((-108 . -405) 115422) ((-84 . -388) T) ((-84 . -400) T) ((-706 . -173) T) ((-622 . -618) 115404) ((-99 . -731) T) ((-487 . -102) 115194) ((-99 . -478) T) ((-116 . -173) T) ((-1297 . -651) 115153) ((-1295 . -651) 115112) ((-1121 . -38) 115082) ((-170 . -644) 115030) ((-1062 . -102) T) ((-1007 . -621) 114920) ((-876 . -25) T) ((-820 . -239) 114899) ((-876 . -21) T) ((-823 . -102) T) ((-44 . -651) 114842) ((-419 . -102) T) ((-389 . -102) T) ((-110 . -312) NIL) 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-618) 112683) ((-316 . -915) NIL) ((-1233 . -849) T) ((-704 . -1046) 112628) ((-716 . -926) T) ((-479 . -1229) 112607) ((-1182 . -457) 112586) ((-1176 . -457) 112565) ((-333 . -102) T) ((-877 . -1120) T) ((-322 . -651) 112447) ((-319 . -653) 112268) ((-316 . -653) 112197) ((-479 . -561) 112148) ((-343 . -519) 112114) ((-555 . -151) 112064) ((-40 . -310) T) ((-848 . -618) 112046) ((-706 . -293) T) ((-877 . -23) T) ((-383 . -498) T) ((-1088 . -232) 112016) ((-517 . -102) T) ((-412 . -619) 111823) ((-412 . -618) 111805) ((-265 . -618) 111787) ((-116 . -293) T) ((-1261 . -731) T) ((-1259 . -367) 111766) ((-1238 . -367) 111745) ((-1288 . -34) T) ((-1233 . -1108) T) ((-117 . -1225) T) ((-108 . -232) 111727) ((-1187 . -102) T) ((-482 . -1108) T) ((-528 . -494) 111711) ((-742 . -34) T) ((-658 . -1059) 111695) ((-487 . -38) 111665) ((-658 . -645) 111635) ((-141 . -34) T) ((-117 . -890) 111612) ((-117 . -892) NIL) ((-628 . -1046) 111495) ((-649 . -855) 111474) ((-1287 . -102) T) ((-298 . -102) T) ((-717 . -372) 111453) ((-117 . -1046) 111430) ((-395 . -722) 111414) ((-626 . -722) 111398) ((-45 . -312) 111202) ((-821 . -145) 111181) ((-821 . -147) 111160) ((-292 . -651) 111132) ((-1298 . -386) 111111) ((-824 . -855) T) ((-1277 . -1108) T) ((-1168 . -230) 111058) ((-391 . -855) 111037) ((-1267 . -1213) 111003) ((-1267 . -1210) 110969) ((-1260 . -1210) 110935) ((-520 . -131) T) ((-1260 . -1213) 110901) ((-1239 . -1210) 110867) ((-1239 . -1213) 110833) ((-1267 . -35) 110799) ((-1267 . -95) 110765) ((-640 . -618) 110734) ((-612 . -618) 110703) ((-226 . -855) T) ((-1260 . -95) 110669) ((-1260 . -35) 110635) ((-1259 . -1120) T) ((-1128 . -653) 110622) ((-1239 . -95) 110588) ((-1238 . -1120) T) ((-598 . -151) 110570) ((-1088 . -353) 110549) ((-175 . -293) T) ((-117 . -381) 110526) ((-117 . -342) 110503) ((-1239 . -35) 110469) ((-875 . -310) T) ((-316 . -799) NIL) ((-316 . -796) NIL) ((-319 . -731) 110318) ((-316 . -731) T) ((-479 . -367) 110297) ((-363 . -353) 110276) ((-357 . -353) 110255) ((-349 . -353) 110234) ((-319 . -478) 110213) ((-1259 . -23) T) ((-1238 . -23) T) ((-723 . -1120) T) ((-719 . -131) T) ((-658 . -102) T) ((-482 . -722) 110178) ((-45 . -285) 110128) ((-105 . -1108) T) ((-68 . -618) 110110) ((-978 . -102) T) ((-869 . -102) T) ((-628 . -906) 110069) ((-1299 . -1108) T) ((-385 . -1108) T) ((-82 . -1225) T) ((-1224 . -1108) T) ((-1070 . -855) T) ((-117 . -906) NIL) ((-787 . -926) 110048) ((-718 . -855) T) ((-536 . -1108) T) ((-505 . -1108) T) ((-359 . -1229) T) ((-356 . -1229) T) ((-348 . -1229) T) ((-266 . -1229) 110027) ((-248 . -1229) 110006) ((-538 . -865) T) ((-1121 . -232) 109975) ((-1167 . -833) T) ((-1150 . -1064) 109959) ((-395 . -766) T) ((-699 . -1225) T) ((-696 . -1046) 109943) ((-359 . -561) T) ((-356 . -561) T) ((-348 . -561) T) ((-266 . -561) 109874) ((-248 . -561) 109805) ((-530 . -1091) T) ((-1150 . -111) 109784) ((-458 . -749) 109754) ((-871 . -1064) 109724) ((-822 . -38) 109666) ((-699 . -890) 109648) ((-699 . -892) 109630) 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106307) ((-1165 . -621) 106284) ((-1011 . -234) 106256) ((-1011 . -244) T) ((-117 . -1030) NIL) ((-916 . -1120) T) ((-1260 . -457) 106235) ((-1239 . -457) 106214) ((-528 . -618) 106146) ((-717 . -653) 106071) ((-412 . -1064) 106023) ((-509 . -618) 106005) ((-916 . -23) T) ((-492 . -312) NIL) ((-1298 . -621) 105961) ((-479 . -131) T) ((-218 . -312) NIL) ((-412 . -111) 105899) ((-820 . -1066) 105829) ((-742 . -1106) 105813) ((-1259 . -498) 105779) ((-1238 . -498) 105745) ((-553 . -849) T) ((-141 . -1106) 105727) ((-482 . -293) T) ((-1298 . -1057) T) ((-1230 . -102) T) ((-1071 . -102) T) ((-848 . -621) 105595) ((-505 . -519) NIL) ((-487 . -239) 105574) ((-412 . -621) 105472) ((-969 . -1059) 105355) ((-740 . -1059) 105325) ((-969 . -645) 105222) ((-1181 . -145) 105201) ((-740 . -645) 105171) ((-458 . -1059) 105141) ((-1181 . -147) 105120) ((-1133 . -147) 105099) ((-1133 . -145) 105078) ((-640 . -1064) 105062) ((-612 . -1064) 105046) ((-458 . -645) 105016) ((-1183 . -1266) 105000) ((-1183 . -1253) 104977) ((-675 . -1108) T) ((-675 . -1061) 104917) ((-1182 . -1258) 104878) ((-553 . -1108) T) ((-492 . -1160) T) ((-1182 . -1253) 104848) ((-1182 . -1256) 104832) ((-1176 . -1237) 104793) ((-218 . -1160) T) ((-347 . -926) T) ((-823 . -268) 104777) ((-640 . -111) 104756) ((-612 . -111) 104735) ((-1176 . -1253) 104712) ((-848 . -1057) 104691) ((-1176 . -1235) 104675) ((-520 . -25) T) ((-500 . -305) T) ((-516 . -23) T) ((-515 . -25) T) ((-513 . -25) T) ((-512 . -23) T) ((-423 . -1059) 104649) ((-412 . -1057) T) ((-322 . -1066) T) ((-699 . -310) T) ((-423 . -645) 104623) ((-108 . -853) T) ((-717 . -731) T) ((-412 . -244) T) ((-412 . -234) 104602) ((-492 . -38) 104552) ((-218 . -38) 104502) ((-479 . -498) 104468) ((-1232 . -372) T) ((-1167 . -1152) T) ((-1109 . -102) T) ((-706 . -618) 104450) ((-706 . -619) 104365) ((-719 . -21) T) ((-719 . -25) T) ((-1143 . -102) T) ((-487 . -651) 104115) ((-134 . -618) 104097) ((-116 . -618) 104079) ((-157 . -25) T) ((-1297 . -1108) T) ((-877 . -644) 104027) ((-1295 . -1108) T) ((-969 . -102) T) ((-740 . -102) T) ((-720 . -102) T) ((-458 . -102) T) ((-821 . -457) 103978) ((-44 . -1108) T) ((-1096 . -855) T) ((-1071 . -312) 103829) ((-669 . -131) T) ((-1062 . -651) 103798) ((-675 . -722) 103782) ((-292 . -1066) T) ((-359 . -131) T) ((-356 . -131) T) ((-348 . -131) T) ((-266 . -131) T) ((-248 . -131) T) ((-389 . -651) 103751) ((-423 . -102) T) ((-152 . -1108) T) ((-45 . -230) 103701) ((-804 . -1059) 103685) ((-964 . -855) 103664) ((-1007 . -653) 103602) ((-804 . -645) 103586) ((-241 . -1282) 103556) ((-1032 . -310) T) ((-297 . -1064) 103477) ((-916 . -131) T) ((-40 . -926) T) ((-492 . -405) 103459) ((-358 . -310) T) ((-218 . -405) 103441) ((-1088 . -416) 103425) ((-297 . -111) 103341) ((-1192 . -855) T) ((-1191 . -855) T) ((-877 . -25) T) ((-877 . -21) T) ((-343 . -618) 103323) ((-1261 . -47) 103267) ((-226 . -147) T) ((-175 . -618) 103249) ((-1121 . -853) 103228) ((-779 . -618) 103210) ((-128 . -855) T) ((-613 . -236) 103157) 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-926) T) ((-848 . -800) 101983) ((-848 . -797) 101962) ((-423 . -312) 101901) ((-473 . -102) T) ((-600 . -981) 101870) ((-322 . -1108) T) ((-412 . -800) 101849) ((-412 . -797) 101828) ((-505 . -494) 101810) ((-1261 . -1046) 101776) ((-1259 . -21) T) ((-1259 . -25) T) ((-1238 . -21) T) ((-1238 . -25) T) ((-820 . -722) 101718) ((-355 . -621) 101648) ((-704 . -409) T) ((-1288 . -1225) T) ((-611 . -102) T) ((-1121 . -416) 101617) ((-1011 . -372) NIL) ((-676 . -102) T) ((-181 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-1187 . -651) 101527) ((-742 . -1225) T) ((-736 . -1059) 101370) ((-44 . -766) T) ((-736 . -645) 101219) ((-598 . -102) T) ((-77 . -401) T) ((-77 . -400) T) ((-658 . -661) 101203) ((-141 . -1225) T) ((-876 . -147) T) ((-876 . -145) NIL) ((-1224 . -93) T) ((-355 . -1057) T) ((-70 . -387) T) ((-70 . -400) T) ((-1174 . -102) T) ((-675 . -519) 101136) ((-1287 . -651) 101081) ((-694 . -312) 101019) ((-969 . -38) 100916) ((-1189 . -618) 100898) ((-740 . -38) 100868) ((-555 . -312) 100672) ((-1183 . -1059) 100555) ((-319 . -1225) T) ((-355 . -234) T) ((-355 . -244) T) ((-316 . -1225) T) ((-292 . -1108) T) ((-1182 . -1059) 100390) ((-1176 . -1059) 100180) ((-1134 . -1059) 100063) ((-1183 . -645) 99960) ((-1182 . -645) 99801) ((-716 . -1229) T) ((-1176 . -645) 99597) ((-1165 . -656) 99581) ((-1134 . -645) 99478) ((-1219 . -561) 99457) ((-824 . -390) 99441) ((-716 . -561) T) ((-319 . -890) 99425) ((-319 . -892) 99350) ((-316 . -890) 99311) ((-316 . -892) NIL) ((-804 . -312) 99276) ((-322 . -722) 99117) ((-391 . -390) 99101) ((-327 . -326) 99078) ((-490 . -102) T) ((-479 . -25) T) ((-479 . -21) T) ((-423 . -38) 99052) ((-319 . -1046) 98715) ((-226 . -1210) T) ((-226 . -1213) T) ((-3 . -618) 98697) ((-316 . -1046) 98627) ((-2 . -1108) T) ((-2 . |RecordCategory|) T) ((-838 . -618) 98609) ((-1121 . -1066) 98539) ((-585 . -926) T) ((-569 . -825) T) ((-569 . -926) T) ((-500 . -926) T) ((-136 . -1046) 98523) ((-226 . -95) T) 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97689) ((-626 . -618) 97671) ((-1239 . -1235) 97655) ((-704 . -926) T) ((-1183 . -287) 97621) ((-1182 . -287) 97587) ((-1176 . -287) 97553) ((-1088 . -1108) T) ((-1069 . -1108) T) ((-48 . -305) T) ((-319 . -906) 97519) ((-316 . -906) NIL) ((-1069 . -1076) 97498) ((-1128 . -892) 97480) ((-804 . -38) 97464) ((-266 . -644) 97412) ((-248 . -644) 97360) ((-706 . -1064) 97347) ((-600 . -1253) 97324) ((-1134 . -287) 97290) ((-322 . -173) 97221) ((-363 . -1108) T) ((-357 . -1108) T) ((-349 . -1108) T) ((-505 . -19) 97203) ((-1128 . -1046) 97185) ((-1110 . -151) 97169) ((-108 . -1108) T) ((-116 . -1064) 97156) ((-716 . -367) T) ((-505 . -609) 97131) ((-706 . -111) 97116) ((-441 . -102) T) ((-881 . -1270) T) ((-251 . -102) T) ((-45 . -1157) 97066) ((-116 . -111) 97051) ((-640 . -725) T) ((-612 . -725) T) ((-1277 . -618) 97033) ((-1233 . -618) 97015) ((-1231 . -855) T) ((-820 . -519) 96948) ((-1043 . -1225) T) ((-241 . -1059) 96845) ((-1219 . -1120) T) ((-1219 . -23) T) ((-949 . -151) 96829) 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95487) ((-949 . -988) 95471) ((-920 . -645) 95423) ((-920 . -1059) 95375) ((-916 . -21) T) ((-916 . -25) T) ((-877 . -855) 95326) ((-871 . -653) 95286) ((-716 . -1120) T) ((-716 . -23) T) ((-292 . -173) T) ((-706 . -1057) T) ((-314 . -93) T) ((-706 . -234) T) ((-652 . -1108) 95264) ((-637 . -615) 95239) ((-637 . -1108) T) ((-586 . -1229) T) ((-586 . -561) T) ((-523 . -1229) T) ((-523 . -561) T) ((-492 . -651) 95189) ((-432 . -1059) 95173) ((-432 . -645) 95157) ((-363 . -722) 95109) ((-357 . -722) 95061) ((-343 . -1064) 95045) ((-349 . -722) 94997) ((-343 . -111) 94976) ((-175 . -1064) 94908) ((-218 . -651) 94858) ((-175 . -111) 94769) ((-108 . -722) 94719) ((-276 . -1108) T) ((-275 . -1108) T) ((-274 . -1108) T) ((-273 . -1108) T) ((-272 . -1108) T) ((-271 . -1108) T) ((-270 . -1108) T) ((-213 . -1108) T) ((-212 . -1108) T) ((-170 . -1213) 94697) ((-170 . -1210) 94675) ((-210 . -1108) T) ((-209 . -1108) T) ((-116 . -1057) T) ((-208 . -1108) T) ((-207 . -1108) T) ((-204 . -1108) T) 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93353) ((-1183 . -38) 93250) ((-871 . -731) T) ((-699 . -926) T) ((-516 . -25) T) ((-512 . -21) T) ((-512 . -25) T) ((-1182 . -38) 93091) ((-343 . -1057) T) ((-1176 . -38) 92887) ((-1088 . -173) T) ((-175 . -1057) T) ((-1134 . -38) 92784) ((-717 . -47) 92761) ((-363 . -173) T) ((-357 . -173) T) ((-524 . -57) 92735) ((-502 . -57) 92685) ((-355 . -1294) 92662) ((-226 . -457) T) ((-322 . -293) 92613) ((-349 . -173) T) ((-175 . -244) T) ((-1238 . -855) 92512) ((-108 . -173) T) ((-877 . -1000) 92496) ((-663 . -1120) T) ((-586 . -367) T) ((-586 . -332) 92483) ((-523 . -332) 92460) ((-523 . -367) T) ((-319 . -310) 92439) ((-316 . -310) T) ((-607 . -855) 92418) ((-1121 . -722) 92360) ((-525 . -285) 92344) ((-663 . -23) T) ((-423 . -232) 92328) ((-316 . -1030) NIL) ((-340 . -23) T) ((-103 . -1018) 92312) ((-45 . -36) 92291) ((-617 . -1108) T) ((-355 . -372) T) ((-529 . -102) T) ((-500 . -27) T) ((-241 . -312) 92229) ((-1095 . -1120) T) ((-1298 . -653) 92203) ((-787 . -1120) T) ((-785 . -1120) 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84358) ((-877 . -145) 84337) ((-1167 . -494) 84319) ((-1299 . -1057) T) ((-487 . -519) 84252) ((-1154 . -1225) T) ((-970 . -618) 84234) ((-652 . -494) 84218) ((-637 . -494) 84149) ((-820 . -618) 83880) ((-48 . -27) T) ((-1187 . -722) 83777) ((-658 . -1108) T) ((-866 . -865) T) ((-441 . -368) 83751) ((-736 . -651) 83661) ((-1110 . -102) T) ((-978 . -1108) T) ((-869 . -1108) T) ((-821 . -312) 83648) ((-538 . -532) T) ((-538 . -581) T) ((-1295 . -386) 83620) ((-1062 . -519) 83553) ((-1168 . -289) 83529) ((-241 . -232) 83498) ((-253 . -1059) 83395) ((-252 . -1059) 83292) ((-1287 . -722) 83262) ((-1175 . -93) T) ((-1002 . -93) T) ((-822 . -173) 83241) ((-253 . -645) 83183) ((-252 . -645) 83125) ((-1222 . -495) 83102) ((-228 . -519) 83035) ((-626 . -800) 83014) ((-626 . -797) 82993) ((-1222 . -618) 82905) ((-223 . -1225) T) ((-680 . -618) 82837) ((-1183 . -651) 82747) ((-1165 . -1018) 82731) ((-949 . -102) 82681) ((-355 . -731) T) ((-866 . -618) 82663) ((-1182 . -651) 82545) ((-1176 . -651) 82382) ((-1134 . -651) 82292) ((-1239 . -405) 82244) ((-1121 . -494) 82228) ((-60 . -312) 82166) ((-334 . -102) T) ((-1219 . -21) T) ((-1219 . -25) T) ((-40 . -1120) T) ((-716 . -21) T) ((-632 . -618) 82148) ((-520 . -326) 82127) ((-716 . -25) T) ((-444 . -102) T) ((-108 . -289) NIL) ((-927 . -1120) T) ((-40 . -23) T) ((-776 . -1120) T) ((-569 . -1229) T) ((-500 . -1229) T) ((-322 . -618) 82109) ((-1012 . -232) 82091) ((-170 . -166) 82075) ((-585 . -561) T) ((-569 . -561) T) ((-500 . -561) T) ((-776 . -23) T) ((-1259 . -147) 82054) ((-1168 . -609) 82030) ((-1259 . -145) 82009) ((-1035 . -494) 81993) ((-1238 . -145) 81918) ((-1238 . -147) 81843) ((-1290 . -1296) 81822) ((-481 . -494) 81806) ((-468 . -494) 81790) ((-528 . -34) T) ((-658 . -722) 81760) ((-112 . -975) T) ((-667 . -855) 81739) ((-1187 . -173) 81690) ((-369 . -102) T) ((-241 . -239) 81669) ((-253 . -102) T) ((-252 . -102) T) ((-1248 . -955) 81638) ((-246 . -855) 81617) ((-821 . -38) 81466) ((-45 . -519) 81258) ((-1167 . 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T) ((-1290 . -38) 80281) ((-1181 . -1059) 80104) ((-1150 . -1225) T) ((-1133 . -1059) 79947) ((-859 . -1059) 79931) ((-637 . -609) 79906) ((-1297 . -1064) 79890) ((-1181 . -645) 79719) ((-1133 . -645) 79568) ((-859 . -645) 79538) ((-1295 . -1064) 79522) ((-1259 . -1210) 79488) ((-554 . -1108) T) ((-1095 . -25) T) ((-1095 . -21) T) ((-536 . -797) T) ((-536 . -800) T) ((-117 . -1229) T) ((-969 . -1066) T) ((-628 . -561) T) ((-787 . -25) T) ((-787 . -21) T) ((-785 . -21) T) ((-785 . -25) T) ((-740 . -1066) T) ((-720 . -1066) T) ((-675 . -1064) 79472) ((-522 . -1091) T) ((-466 . -25) T) ((-117 . -561) T) ((-466 . -21) T) ((-459 . -25) T) ((-459 . -21) T) ((-1259 . -1213) 79438) ((-1159 . -93) T) ((-1150 . -1046) 79334) ((-822 . -293) 79313) ((-1259 . -95) 79279) ((-828 . -1108) T) ((-1242 . -102) 79257) ((-972 . -975) T) ((-675 . -111) 79236) ((-298 . -519) 79028) ((-1239 . -232) 78980) ((-1238 . -1210) 78946) ((-1238 . -1213) 78912) ((-253 . -312) 78850) ((-252 . -312) 78788) ((-1233 . -372) T) ((-1168 . -619) NIL) ((-1168 . -618) 78770) ((-1230 . -849) T) ((-1150 . -381) 78754) ((-1128 . -825) T) ((-96 . -93) T) ((-1128 . -926) T) ((-1121 . -609) 78731) ((-1088 . -619) 78715) ((-1012 . -651) 78665) ((-920 . -651) 78602) ((-820 . -291) 78579) ((-489 . -618) 78511) ((-613 . -151) 78458) ((-492 . -722) 78408) ((-423 . -1066) T) ((-487 . -494) 78392) ((-432 . -651) 78351) ((-330 . -855) 78330) ((-343 . -653) 78304) ((-50 . -21) T) ((-50 . -25) T) ((-218 . -722) 78254) ((-170 . -729) 78225) ((-175 . -653) 78157) ((-586 . -21) T) ((-586 . -25) T) ((-523 . -25) T) ((-523 . -21) T) ((-480 . -151) 78107) ((-1088 . -618) 78089) ((-1069 . -618) 78071) ((-1001 . -102) T) ((-867 . -102) T) ((-804 . -416) 78034) ((-40 . -131) T) ((-704 . -367) T) ((-706 . -731) T) ((-706 . -799) T) ((-706 . -796) T) ((-213 . -901) T) ((-585 . -1120) T) ((-569 . -1120) T) ((-500 . -1120) T) ((-363 . -618) 78016) ((-357 . -618) 77998) ((-349 . -618) 77980) ((-66 . -401) T) ((-66 . -400) T) ((-108 . -619) 77910) ((-108 . -618) 77852) ((-212 . -901) T) ((-964 . -151) 77836) ((-776 . -131) T) ((-675 . -621) 77754) ((-134 . -731) T) ((-116 . -731) T) ((-1259 . -35) 77720) ((-1062 . -494) 77704) ((-585 . -23) T) ((-569 . -23) T) ((-500 . -23) T) ((-1238 . -95) 77670) ((-1238 . -35) 77636) ((-1181 . -102) T) ((-1133 . -102) T) ((-859 . -102) T) ((-228 . -494) 77620) ((-1297 . -111) 77599) ((-1295 . -111) 77578) ((-44 . -1064) 77562) ((-1297 . -621) 77508) ((-1248 . -1251) 77492) ((-860 . -857) 77476) ((-1297 . -1057) T) ((-1187 . -293) 77455) ((-110 . -289) 77430) ((-1295 . -621) 77359) ((-128 . -151) 77341) ((-1150 . -906) 77300) ((-44 . -111) 77279) ((-1230 . -1108) T) ((-1190 . -1270) T) ((-1175 . -495) 77260) ((-1175 . -618) 77226) ((-675 . -1057) T) ((-1167 . -619) NIL) ((-1167 . -618) 77208) ((-1071 . -615) 77183) ((-1071 . -1108) T) ((-1002 . -495) 77164) ((-74 . -446) T) ((-74 . -400) T) ((-1002 . -618) 77130) ((-152 . -1064) 77114) ((-675 . -234) 77093) ((-576 . -559) 77077) 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. -102) T) ((-266 . -102) T) ((-248 . -102) T) ((-482 . -310) T) ((-1070 . -1066) T) ((-958 . -1066) T) ((-319 . -644) 43350) ((-316 . -644) 43311) ((-1181 . -1108) T) ((-486 . -1066) T) ((-484 . -102) T) ((-441 . -618) 43293) ((-1133 . -1108) T) ((-251 . -618) 43275) ((-859 . -1108) T) ((-1149 . -102) T) ((-821 . -293) 43206) ((-969 . -1064) 43089) ((-482 . -1030) T) ((-740 . -1064) 43059) ((-1042 . -651) 43018) ((-458 . -1064) 42988) ((-1155 . -1129) 42972) ((-1110 . -519) 42905) ((-969 . -111) 42774) ((-916 . -102) T) ((-740 . -111) 42739) ((-530 . -495) 42720) ((-530 . -618) 42686) ((-59 . -102) 42636) ((-525 . -619) 42597) ((-525 . -618) 42509) ((-524 . -102) 42487) ((-521 . -102) 42437) ((-502 . -102) 42415) ((-501 . -102) 42365) ((-458 . -111) 42328) ((-253 . -173) 42307) ((-252 . -173) 42286) ((-325 . -651) 42268) ((-423 . -1064) 42242) ((-1219 . -981) 42204) ((-1007 . -1120) T) ((-383 . -651) 42154) ((-1143 . -621) 42135) ((-949 . -519) 42068) ((-492 . -800) T) ((-479 . -38) 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. -519) 18964) ((-969 . -731) T) ((-740 . -731) T) ((-720 . -731) T) ((-355 . -1120) T) ((-1188 . -618) 18946) ((-224 . -102) T) ((-487 . -381) 18915) ((-520 . -1108) T) ((-515 . -1108) T) ((-513 . -1108) T) ((-804 . -653) 18889) ((-1032 . -457) T) ((-964 . -519) 18822) ((-355 . -23) T) ((-640 . -131) T) ((-612 . -131) T) ((-358 . -457) T) ((-241 . -372) 18801) ((-383 . -173) T) ((-1259 . -1066) T) ((-1238 . -1066) T) ((-226 . -1010) T) ((-821 . -621) 18538) ((-704 . -392) T) ((-423 . -731) T) ((-706 . -1229) T) ((-1150 . -644) 18486) ((-585 . -874) 18470) ((-1290 . -1064) 18454) ((-1168 . -1201) 18430) ((-706 . -561) T) ((-126 . -1108) 18408) ((-719 . -1108) T) ((-487 . -906) 18340) ((-250 . -1108) T) ((-188 . -1108) T) ((-663 . -38) 18310) ((-358 . -407) T) ((-319 . -147) 18289) ((-319 . -145) 18268) ((-128 . -519) NIL) ((-116 . -561) T) ((-316 . -147) 18224) ((-316 . -145) 18180) ((-48 . -457) T) ((-162 . -1108) T) ((-157 . -1108) T) ((-1168 . -107) 18127) ((-787 . -1160) 18105) 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. -1225) T) ((-846 . -618) 11914) ((-813 . -618) 11896) ((-774 . -618) 11878) ((-682 . -618) 11860) ((-241 . -653) 11708) ((-1185 . -1108) T) ((-1181 . -1064) 11531) ((-1158 . -1225) T) ((-1133 . -1064) 11374) ((-859 . -1064) 11358) ((-1242 . -623) 11342) ((-1181 . -111) 11151) ((-1133 . -111) 10980) ((-859 . -111) 10959) ((-1232 . -855) T) ((-1248 . -619) NIL) ((-1248 . -618) 10941) ((-347 . -1160) T) ((-860 . -618) 10923) ((-1084 . -289) 10902) ((-80 . -1225) T) ((-1012 . -915) NIL) ((-613 . -289) 10878) ((-1211 . -519) 10811) ((-492 . -1225) T) ((-576 . -618) 10793) ((-480 . -289) 10772) ((-1219 . -651) 10682) ((-522 . -93) T) ((-1095 . -232) 10666) ((-218 . -1225) T) ((-1012 . -653) 10616) ((-964 . -289) 10593) ((-292 . -926) T) ((-822 . -310) 10572) ((-875 . -102) T) ((-787 . -232) 10556) ((-920 . -653) 10508) ((-716 . -651) 10458) ((-699 . -729) 10425) ((-640 . -21) T) ((-640 . -25) T) ((-612 . -21) T) ((-552 . -102) T) ((-347 . -38) 10390) ((-492 . -890) 10372) ((-492 . -892) 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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 d754c03e..6040b2ff 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3479296386) -(4447 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3479376209) +(4450 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -356,7 +356,8 @@ |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| |PrintPackage| |PolynomialRing| |Product| - |Property| |PropositionalFormula| |PropositionalLogic| + |Property| |PropositionalFormula| |PropositionalFormulaFunctions1| + |PropositionalFormulaFunctions2| |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| |PretendAst| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| @@ -483,667 +484,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |c06fpf| |outputArgs| |lifting1| |showClipRegion| - |pi| |rational| |primitiveElement| |complexForm| |cot2tan| |part?| - |preprocess| |dualSignature| |overlabel| |infinity| |quasiComponent| - |fillPascalTriangle| |rk4qc| |imaginary| |divideIfCan!| - |noncommutativeJordanAlgebra?| |rquo| |component| |deepestInitial| - |cond| |bipolarCylindrical| |measure| |lazyIntegrate| |minGbasis| - |setAdaptive| |freeOf?| |principalIdeal| |OMencodingUnknown| - |generate| |modifyPointData| |log10| |outputSpacing| |tablePow| - |e01bef| |map| |s17def| |bivariateSLPEBR| |expextendedint| - |explicitlyEmpty?| |iicosh| |f04mbf| |bitand| |kernel| - |partialFraction| |elRow2!| |branchIfCan| |e02def| |besselY| - |previous| |isQuotient| |incrementBy| |BasicMethod| - |squareFreeFactors| |column| |lllp| |outerProduct| - |complexEigenvectors| |bitior| |draw| |f02agf| - |dimensionOfIrreducibleRepresentation| |arity| - |tableForDiscreteLogarithm| |numberOfImproperPartitions| - |inverseIntegralMatrix| |clearTable!| |setfirst!| |nextsousResultant2| - |expand| |algebraicDecompose| |mapSolve| |acotIfCan| |changeMeasure| - |ran| |OMputEndAtp| |associatedEquations| |currentEnv| - |shanksDiscLogAlgorithm| |polyRicDE| |filterWhile| |printHeader| - |multiEuclidean| |rootKerSimp| |clipBoolean| |UpTriBddDenomInv| |cCot| - |linearDependence| |sylvesterMatrix| |fortranCarriageReturn| - |generalizedInverse| |LyndonCoordinates| |filterUntil| |symbol| - |cCsch| |attributeData| |safeCeiling| |setStatus| UP2UTS |convert| - |completeEchelonBasis| |radicalSimplify| |factors| |c06fqf| - |monomRDEsys| |legendre| |select| |expression| |asinhIfCan| - |makeObject| |setright!| |minIndex| |charpol| |e01bff| - |brillhartIrreducible?| |ord| |height| |bigEndian| - |wordsForStrongGenerators| |normInvertible?| |addMatchRestricted| - |overbar| |integer| |dominantTerm| |coef| |rational?| |tanh2coth| - |coerceImages| |nextPrime| |noKaratsuba| |coth2tanh| |lowerPolynomial| - |before?| |internalZeroSetSplit| |coerceP| |exprex| |iipow| - |setProperty| |initials| |rk4f| |startTableGcd!| |elaborateFile| - |expenseOfEvaluationIF| |jordanAdmissible?| |lquo| |ranges| - |iteratedInitials| |redPol| |toroidal| |weight| |nlde| ** |lepol| - |leastPower| |operators| |omError| |showRegion| |subspace| |permanent| - |solveid| |outputGeneral| |irreducibleRepresentation| |adaptive?| - |solveLinearPolynomialEquationByRecursion| |primlimitedint| - |explicitEntries?| |iitanh| |LagrangeInterpolation| - |extendedEuclidean| |gcdPrimitive| |getDatabase| |asecIfCan| |e02dff| - |s17dgf| |PollardSmallFactor| |makeRecord| |univariatePolynomialsGcds| - |row| |f04mcf| |lo| |cSech| |f02ajf| |elColumn2!| |LowTriBddDenomInv| - |besselI| |subSet| |resultantnaif| |usingTable?| |cycleSplit!| |incr| - |lllip| |acoshIfCan| |acsch| |label| |quadratic| |safeFloor| - |changeThreshhold| |highCommonTerms| |factorsOfCyclicGroupSize| - |initial| |arrayStack| |reflect| |integralMatrix| |returnType!| - |limitPlus| |leftRank| |e01bgf| UTS2UP |cTan| |OMputEndAttr| - |fortranLiteral| |imports| |bezoutMatrix| |ricDsolve| |iidsum| - |domainTemplate| |style| |fixedPoints| |solveLinear| |denominator| - |insertMatch| |dmpToHdmp| |nilFactor| |LyndonBasis| |gbasis| - |brillhartTrials| |maxIndex| |solve1| |stopTableGcd!| - |createRandomElement| Y |c06frf| |normFactors| |prime| |baseRDEsys| - |cycles| |rationalIfCan| |makeVariable| |prevPrime| |karatsubaOnce| - |removeCosSq| |latex| |internalAugment| |littleEndian| |coerceL| - |e02agf| |basicSet| |checkRur| |aromberg| |elaborate| |accuracyIF| - |comparison| |mindegTerm| |derivative| |deepestTail| - |stoseInvertible?reg| |critM| |tail| |conical| |acscIfCan| |powern| - |prinshINFO| |idealiser| |constructor| |rules| |mainKernel| - |lieAdmissible?| |powerSum| |makeViewport3D| |euclideanSize| - |initializeGroupForWordProblem| |testModulus| |outputFixed| |simplify| - |setScreenResolution| |factorByRecursion| |explimitedint| |nothing| - |errorInfo| |iicoth| |pointLists| |cCoth| |e02ajf| |option| - |symmetricGroup| |safetyMargin| |numericalOptimization| |e02gaf| - |s17dhf| |showSummary| |matrixDimensions| - |removeRoughlyRedundantFactorsInContents| |showTheFTable| |psolve| - |atanhIfCan| |stoseInvertible?| |f02akf| |fractionFreeGauss!| |odd?| - |besselK| |maxColIndex| |printingInfo?| |f04qaf| - |resultantEuclideannaif| |split!| |simplifyPower| |cubic| |e01bhf| - |selectMultiDimensionalRoutines| |sizeMultiplication| |showAttributes| - |fortranLiteralLine| |concat!| |mesh?| |argumentList!| |iidprod| - |cCosh| |unknown| |rightRank| |startTableInvSet!| LODO2FUN - |reducedSystem| |macroExpand| |reify| |reduceBasisAtInfinity| - |addMatch| |regularRepresentation| |rightTrim| |critT| |asechIfCan| - |lSpaceBasis| |inspect| |finiteBound| |OMputEndBind| |sequence| - |c06fuf| |triangulate| |quote| |leftTrim| |cycle| |factorial| |entry?| - |toScale| |cAcsch| |cyclicSubmodule| |hdmpToDmp| |member?| - |zeroDimensional?| |coerceS| |e02ahf| |critB| |setvalue!| - |innerEigenvectors| |sinhIfCan| |karatsuba| |say| |npcoef| F |product| - |weighted| |head| |stoseInvertibleSetreg| |e02akf| |infRittWu?| - |primes| |htrigs| |intermediateResultsIF| |distribute| - |possiblyInfinite?| |subtractIfCan| |viewport3D| |sizeLess?| - |movedPoints| |HenselLift| |e01daf| |asimpson| |idealiserMatrix| - |equality| |primextintfrac| |iisech| |more?| |cTanh| |function| - |stoseInvertibleSet| |alternatingGroup| |stopTableInvSet!| |mapdiv| - |remove| |multivariate| |screenResolution| |jacobiIdentity?| - |removeRedundantFactorsInContents| |constantOperator| |clearTheFTable| - |acothIfCan| |number?| |fortran| |sortConstraints| |f02awf| - |outputFloating| |s17dlf| |variables| |result| |errorKind| - |makingStats?| |elementary| |semiResultantEuclideannaif| |setlast!| - |open| |cSinh| |cAsech| |quartic| |goodnessOfFit| |last| |eval| - |airyAi| |reset| |processTemplate| |matrixConcat3D| |makeGraphImage| - |endSubProgram| |assoc| |acschIfCan| |doubleRank| |null| |invertIfCan| - |coshIfCan| |getMultiplicationMatrix| |c06gbf| |minColIndex| - |traceMatrix| |wrregime| |finiteBasis| |sec2cos| |pattern| - |selectNonFiniteRoutines| |not| |simplifyExp| |duplicates?| |write| - |getMatch| |cycleTail| |frobenius| |f07adf| |multinomial| |hclf| - |indices| |and| RF2UTS |OMputEndBVar| |save| |functorData| |enumerate| - |supersub| |mesh| |extract!| |critBonD| |operations| |setchildren!| - |rightRemainder| |or| |taylor| |standardBasisOfCyclicSubmodule| - |readBytes!| |LiePolyIfCan| |normalizeAtInfinity| |mdeg| - |wordInGenerators| |pointColorPalette| |getCurve| |e01saf| |xor| - |laurent| |separate| |functionIsFracPolynomial?| |listexp| - |solveInField| |viewDeltaYDefault| |completeHensel| |e02baf| - |parseString| |message| |stosePrepareSubResAlgo| |case| - |subscriptedVariables| |puiseux| |primlimintfrac| |pToHdmp| |iicsch| - |fglmIfCan| |stoseSquareFreePart| |sumOfSquares| |f02axf| - |selectsecond| |Zero| |moduleSum| |fTable| - |removeRedundantFactorsInPols| |explicitlyFinite?| |rdHack1| |hi| - |seriesSolve| |cAcoth| |atrapezoidal| |One| |inv| |setMaxPoints| - |powerAssociative?| |extractIfCan| |setPosition| |pdct| |cAcsc| - |rewriteSetWithReduction| |tanhIfCan| |lazyGintegrate| |ground?| - |s18acf| |makeFR| |OMReadError?| |currentSubProgram| - |setVariableOrder| |parabolic| |pushdown| |exp1| |ground| - |simplifyLog| |lcm| |airyBi| |setelt!| |failed?| |alternating| - |randomLC| |permutation| |genericLeftTrace| |writable?| |whatInfinity| - |getMultiplicationTable| |leadingMonomial| |graphImage| - |computePowers| |padicFraction| |sech2cosh| |append| |copy!| - |rightQuotient| |mapGen| |leadingCoefficient| |rightUnit| |shuffle| - |presuper| |rdregime| |critMTonD1| |e01sbf| |f01rdf| - |primitiveMonomials| |gcd| |selectSumOfSquaresRoutines| |elt| |output| - |OMputEndError| |lyndon| |c05adf| |cCsc| |f07aef| |mvar| |e02bbf| - |hermite| |false| |stoseInternalLastSubResultant| |magnitude| - |reductum| |areEquivalent?| |OMgetVariable| |bounds| |polygon?| - |viewDeltaXDefault| |knownInfBasis| |wordInStrongGenerators| - |pseudoDivide| |factorAndSplit| |poisson| |iiasinh| - |complementaryBasis| |forLoop| |coleman| |setClipValue| |satisfy?| - |central?| |removeConstantTerm| |medialSet| |palgint0| - |wronskianMatrix| |constantToUnaryFunction| GF2FG |basis| |d02gaf| - |mapUnivariate| |dictionary| |removeRoughlyRedundantFactorsInPols| - |groebner| |powers| |cAsec| |fractRagits| |ScanRoman| - |internalSubPolSet?| |maxPoints| |leadingSupport| |tanSum| - |autoReduced?| |pushup| |vedf2vef| |rroot| |s18adf| |fortranComplex| - |bernoulli| |iFTable| |subscript| |parabolicCylindrical| |sin2csc| - |perfectNthRoot| |oddintegers| |categories| |subNode?| |shufflein| - |inverse| |unit| |addPoint2| |stirling1| - |genericLeftMinimalPolynomial| |copyInto!| |cosIfCan| |primitive?| - |has?| |c05nbf| |integralDerivationMatrix| |semicolonSeparate| - |critMonD1| |padicallyExpand| |makeop| |cyclicEntries| |leftUnit| - |high| |binaryFunction| |constantCoefficientRicDE| |e02bcf| |f01ref| - |shiftRoots| |swapColumns!| |exprHasLogarithmicWeights| |OMgetString| - |inGroundField?| |binaryTournament| |mainMonomials| |completeHermite| - |orbits| |addBadValue| |roman| |host| |rightOne| |lyndon?| - |getPickedPoints| |axes| |plusInfinity| |rootSplit| |inverseColeman| - |d02gbf| |stFuncN| |redmat| |mkPrim| |geometric| |bfEntry| - |startPolynomial| |minusInfinity| |sin?| |option?| - |internalInfRittWu?| |s17agf| |removeRoughlyRedundantFactorsInPol| - |Hausdorff| |iiacos| |drawToScale| |hasSolution?| FG2F |df2st| - |normalElement| |Beta| |dioSolve| |tanAn| |unitNormal| |rubiksGroup| - |green| |approxNthRoot| |wholeRagits| |ScanFloatIgnoreSpaces| |key| - |createMultiplicationMatrix| |fortranLogical| |shrinkable| - |showIntensityFunctions| |resultantReduit| |terms| |initiallyReduced?| - |qroot| |tanIfCan| |OMputBind| |sequences| |chebyshevT| |addPoint| - |scripted?| |clipParametric| |paraboloidal| |filename| |mapmult| - |cyclicCopy| |transform| |rightMinimalPolynomial| |c05pbf| - |integralRepresents| |flagFactor| |type| |dimensionsOf| - |leftRankPolynomial| |sorted?| |degreePartition| - |antisymmetricTensors| |OMgetSymbol| |low| |trailingCoefficient| - |commaSeparate| |upperCase!| |opeval| |numberOfFractionalTerms| - |badValues| |parse| |lowerCase?| |numberOfComputedEntries| - |transcendent?| |makeFloatFunction| |changeVar| |pdf2ef| |f02aaf| - |swapRows!| |d02kef| |next| |rightFactorIfCan| |leftOne| |ridHack1| - |rischDE| |mainCoefficients| |linSolve| |smith| |recoverAfterFail| - |internalSubQuasiComponent?| |combineFeatureCompatibility| - |intPatternMatch| |Frobenius| |binaryTree| |controlPanel| |red| - |ratDenom| |f2st| |fixedPointExquo| |trueEqual| |bfKeys| |cycleElt| - |newLine| |interReduce| |checkPrecision| |reducedDiscriminant| - |squareFreePart| |zeroVector| |range| |perfectSquare?| |regime| - |iiatan| |adaptive| |physicalLength!| |tanNa| EQ |sinh2csch| - |clipWithRanges| F2FG |minimalPolynomial| |cotIfCan| |s17ahf| - |fortranInteger| |chebyshevU| |lfextendedint| |colorDef| |sumSquares| - |froot| |radix| |lhs| |cyclic?| |digamma| |isConnected?| - |permutations| |youngGroup| |resetNew| |even?| |factorOfDegree| - |headReduced?| |ScanFloatIgnoreSpacesIfCan| |rhs| - |createLowComplexityTable| |c06eaf| |transcendentalDecompose| |expint| - |resultantReduitEuclidean| |restorePrecision| |ellipticCylindrical| - |retractable?| |deriv| |OMputBVar| |leftMinimalPolynomial| |subset?| - |sqfrFactor| |merge| |upperCase| |generic| |LiePoly| |d02raf| |pack!| - |OMgetType| |algebraic?| |integralCoordinates| |pile| |pdf2df| |rule| - |nthFractionalTerm| |evaluateInverse| |subQuasiComponent?| - |createGenericMatrix| |rightZero| |rst| |unaryFunction| |ratDsolve| - |LyndonWordsList| |ldf2lst| |f02abf| |vertConcat| |index| |upperCase?| - |primintegrate| |interpolate| |normalizeIfCan| |leastMonomial| - |whitePoint| |completeSmith| |perfectSqrt| |showTheRoutinesTable| - |leftFactorIfCan| |roughBasicSet| |transcendenceDegree| |rischDEsys| - |viewpoint| |BumInSepFFE| |ratPoly| |center| |secIfCan| |ode1| - |sparsityIF| |copies| |initTable!| |setLength!| |iiacot| - |numberOfHues| |colorFunction| |zeroSquareMatrix| |pair| - |complexNormalize| |factorList| |computeCycleLength| |fortranDouble| - |physicalLength| |lflimitedint| |value| |euclideanNormalForm| |closed| - |explogs2trigs| |factorsOfDegree| |position!| |sqfree| |atoms| - |cyclotomic| |semiResultantReduitEuclidean| |intensity| - |numberOfCycles| |randnum| |ListOfTerms| |nthr| |s17ajf| |c06ebf| - |connectTo| |figureUnits| |symFunc| |antiCommutator| - |stronglyReduced?| |d03edf| |numericalIntegration| |polygamma| - |symmetricDifference| |internalDecompose| |primeFactor| |lexGroebner| - |entry| |lowerCase!| |prolateSpheroidal| - |removeSuperfluousQuasiComponents| |gderiv| - |createLowComplexityNormalBasis| |associatorDependence| |sh| |diff| - |paren| |df2ef| |rightUnits| |sdf2lst| |quickSort| |OMputError| - |leftZero| |OMencodingBinary| |compiledFunction| |deepCopy| - |LyndonWordsList1| |firstNumer| |approxSqrt| |horizConcat| - |complexLimit| |expintegrate| |frst| |yCoordinates| |mainMonomial| - |uniform| |f02adf| |evaluate| |cscIfCan| |symmetricTensors| |sn| - |reverse| |crushedSet| |nullSpace| |indicialEquationAtInfinity| - |dimensions| |multiplyExponents| |diophantineSystem| |deleteRoutine!| - |complexElementary| |alphabetic?| |printInfo!| |extensionDegree| - |iiasec| |polCase| |yellow| |rootPower| |call| |pascalTriangle| |ode2| - |monicDecomposeIfCan| |sayLength| |fortranReal| |lfinfieldint| - |monomRDE| |euclideanGroebner| |leaves| |identitySquareMatrix| |tree| - |curveColor| |PDESolve| |stiffnessAndStabilityFactor| |flexibleArray| - |makeResult| |capacity| |divide| |cyclePartition| |trigs2explogs| - |eof?| |d03eef| |listConjugateBases| |c06ecf| |euler| |symbolTableOf| - |lighting| |commutator| |reseed| |firstUncouplingMatrix| |subCase?| - |inconsistent?| |normalizedAssociate| |difference| |computeCycleEntry| - |nthFlag| |lowerCase| |getlo| |reduced?| |rk4| |init| |s17akf| - |decompose| |mirror| |putColorInfo| |bracket| |fi2df| - |oblateSpheroidal| |generateIrredPoly| |compose| |Gamma| |setRow!| - |lieAlgebra?| |corrPoly| |totalGroebner| |laurentIfCan| |leftUnits| - |heapSort| |asinIfCan| |representationType| |swap| |OMencodingSGML| - |inverseIntegralMatrixAtInfinity| |quasiMonic?| |iifact| |generator| - |firstDenom| |squareTop| |trigs| |OMputObject| |tanintegrate| - |lazyEvaluate| |distFact| |resize| |factorGroebnerBasis| |f02aef| - |rangePascalTriangle| |conjug| |limit| - |rewriteSetByReducingWithParticularGenerators| |nullity| |iiacsc| - |reduceLODE| |coerceListOfPairs| |csubst| |leftFactor| - |getExplanations| |tensorProduct| |setnext!| |lfintegrate| - |startStats!| |search| |baseRDE| |associator| |d03faf| |ode| - |hexDigit?| |stack| |byteBuffer| |external?| |elseBranch| |rem| - |Lazard| |KrullNumber| |inrootof| |pointColor| - |removeSuperfluousCases| |monicCompleteDecompose| |quo| |is?| - |fixedDivisor| |argumentListOf| |clipSurface| |mat| |printStatement| - |gethi| |inputBinaryFile| |stiffnessAndStabilityOfODEIF| |condition| - |c06ekf| |normalize| |findConstructor| |nthExponent| |cAcosh| - |makeSeries| |complexExpand| |integral| |matrixGcd| |appendPoint| - |div| |prod| |sechIfCan| |queue| |rk4a| |acosIfCan| |numFunEvals| - |getProperty| |integralBasis| |lifting| |expressIdealMember| |exquo| - |dim| |laurentRep| |collectQuasiMonic| |addiag| |real?| |s17dcf| - |checkForZero| |infieldIntegrate| |f04maf| ~= |monic?| |iibinom| - |bindings| |shellSort| |sizePascalTriangle| |besselJ| |extendedint| - |quasiMonicPolynomials| |llprop| |move| |#| |groebnerFactorize| - |matrix| |genericRightNorm| |createPrimitiveElement| |dec| - |probablyZeroDim?| |less?| |iisinh| |integralMatrixAtInfinity| ~ - |coercePreimagesImages| |logpart| |getGoodPrime| |delay| |concat| - |OMputEndApp| |double?| |untab| |lfextlimint| |identification| - |complexEigenvalues| |f01mcf| |rightNorm| |color| |linearlyDependent?| - |rootOfIrreduciblePoly| |dark| |singRicDE| |Lazard2| |printInfo| - |numberOfVariables| |determinant| |curryLeft| |writeLine!| - |clearCache| |permutationRepresentation| |coefChoose| |OMgetEndBind| - |level| |neglist| |droot| |beauzamyBound| |OMsupportsCD?| |escape| - |univcase| |currentScope| |graeffe| |contains?| |cAsinh| |putProperty| - |multiple?| |floor| |divideIfCan| |applyRules| |powmod| |rur| - |subResultantGcdEuclidean| |substring?| |cschIfCan| |block| |d01gaf| - |integrate| |char| |systemSizeIF| |scopes| |failed| - |localIntegralBasis| |implies| |internal?| |rationalPower| - |mappingMode| |recolor| |stopTable!| |logGamma| |primeFrobenius| - |limitedIntegrate| |octon| |suffix?| |iiperm| |nthRoot| |repSq| - |squareFree| |vspace| |hasHi| |univariate?| |bat1| |maximumExponent| - |traverse| |credPol| |removeZero| |edf2efi| |monomials| - |functionIsContinuousAtEndPoints| |derivationCoordinates| - |rationalPoints| |compile| |write!| |userOrdered?| |writeUInt8!| - |prefix?| |status| |listRepresentation| |cartesian| |ratpart| - |numericIfCan| |gcdcofactprim| |invertibleElseSplit?| |ffactor| - |OMgetEndBVar| |denomLODE| |lazyPquo| |genericRightTrace| |hue| - |findCycle| |minrank| |viewWriteAvailable| |consnewpol| - |getSyntaxFormsFromFile| |noLinearFactor?| |perspective| |chiSquare1| - |second| |callForm?| |f01qcf| |leftNorm| |sign| |erf| |s15aef| |float| - |myDegree| |create| |iicos| |bandedHessian| |unary?| |third| |badNum| - |bombieriNorm| |OMsupportsSymbol?| |sumOfDivisors| - |numberOfComponents| |pushNewContour| |qualifier| |inf| - |LazardQuotient2| |unmakeSUP| |diagonalProduct| |constantRight| - |generic?| |absolutelyIrreducible?| |roughBase?| |void| |localUnquote| - |hypergeometric0F1| |semiSubResultantGcdEuclidean2| |graphs| - |mkIntegral| |iroot| |dilog| |d01gbf| |ceiling| |OMclose| - |getOperator| |pleskenSplit| |eigenvalues| |zeroDimPrime?| |root?| - |infix?| |generalPosition| |putProperties| |exprToGenUPS| - |supDimElseRittWu?| |multiplyCoefficients| |computeBasis| |sin| - |discreteLog| |extendedIntegrate| |pointPlot| |mulmod| |mask| - |maxPoints3D| |drawComplex| |returns| |cos| |linearlyDependentOverZ?| - |hspace| |radicalEigenvalues| |univariatePolynomials| |bat| - |writeInt8!| |merge!| |s21bbf| |alphabetic| |dfRange| |categoryMode| - |expPot| |expr| |one?| |tan| |read!| |largest| |rowEch| |ODESolve| - |extractSplittingLeaf| |mkAnswer| |fractRadix| |cot| |isPlus| - |purelyAlgebraicLeadingMonomial?| |fmecg| |qfactor| |OMgetEndError| - |lazyPrem| |defineProperty| |nextNormalPrimitivePoly| - |functionIsOscillatory| |initiallyReduce| |complexNumericIfCan| - |shade| |sec| |var1StepsDefault| GE |nonSingularModel| |nsqfree| - |surface| |double| |zoom| |OMgetObject| |polar| |getIdentifier| - |lintgcd| |repeating?| |nonQsign| |csc| |log| GT |normDeriv2| - |enterInCache| |iitan| |indicialEquations| |factor1| |rightTrace| - |rootBound| |genericRightMinimalPolynomial| |sumOfKthPowerDivisors| - |variable| |minset| |asin| LE |findBinding| |mainExpression| - |insertRoot!| |qinterval| |exponential| |f01qdf| |s17acf| |iterators| - BY |OMunhandledSymbol| |quoted?| |trivialIdeal?| |acos| LT |arbitrary| - |rotatez| |jacobian| |semiSubResultantGcdEuclidean1| |nullary?| - |constantLeft| |mix| |d02bbf| |create3Space| |nil?| |atan| - |eigenvector| |zeroDimPrimary?| |LazardQuotient| |leaf?| |makeSUP| - |hexDigit| |diagonal| |norm| |algebraicSort| |localAbs| |acot| - |varselect| |calcRanges| |decreasePrecision| |graphStates| |radPoly| - |size?| |genus| |quoByVar| |linearDependenceOverZ| |superHeight| - |asec| |linear?| |tab1| |reciprocalPolynomial| |writeByte!| |quotient| - |drawComplexVectorField| |goto| |dflist| |splitSquarefree| - |OMsetEncoding| |acsc| |iomode| |UP2ifCan| |rowEchLocal| |constDsolve| - |declare!| |setMinPoints3D| |qPot| |voidMode| |irDef| |coord| - |algebraicCoefficients?| |sinh| |makeYoungTableau| |OMgetEndObject| - |coordinate| |pquo| |closeComponent| |s21bcf| |wholeRadix| - |eigenMatrix| |isTimes| |nthRootIfCan| |var2StepsDefault| |cosh| - |algSplitSimple| |permutationGroup| |intChoose| |plenaryPower| NOT - |rotate| |squareMatrix| |variable?| |headReduce| |FormatArabic| - |direction| |commonDenominator| |tanh| |iicot| |currentCategoryFrame| - |contours| |indicialEquation| OR |nextPrimitiveNormalPoly| - |cylindrical| |changeName| |singleFactorBound| |repeating| - |HermiteIntegrate| |coth| |setColumn!| |binarySearchTree| - |changeWeightLevel| |interval| AND |OMgetEndApp| |rightRankPolynomial| - |leftTrace| |inR?| |hex| |collectUpper| |rotatey| - |generalizedEigenvector| |bandedJacobian| |keys| - |discriminantEuclidean| |symmetricProduct| |d02bhf| |doubleDisc| - |OMreceive| |depth| |s17adf| |buildSyntax| |primaryDecomp| |kmax| - |subResultantChain| |outputForm| |chiSquare| |f01qef| |twist| - |moreAlgebraic?| |universe| |nextSublist| |increasePrecision| - |fixPredicate| |linearPolynomials| |debug| |segment| |graphState| - |parents| |vectorise| |diagonalMatrix| |mightHaveRoots| - |solveLinearlyOverQ| |subHeight| |outputAsScript| |tab| |maxrow| D - |rootRadius| |isOpen?| |rootPoly| |eq?| |df2mf| |coefficients| - |getZechTable| |normalDenom| |close!| |anfactor| |nextSubsetGray| - |rowEchelonLocal| |zeroDim?| |repeatUntilLoop| |setRealSteps| |irCtor| - |OMputApp| |purelyTranscendental?| |OMgetInteger| |partitions| - |mathieu23| |prem| |s21bdf| |noValueMode| |lookup| |expIfCan| - |anticoord| |tubePointsDefault| |c02aff| |characteristicSerie| - |showTheIFTable| |drawStyle| |minPoints3D| |cycleRagits| |isExpt| - |createThreeSpace| |setleaves!| |normalise| |rotatex| - |structuralConstants| |iisec| |modifyPoint| |transpose| - |stronglyReduce| |quadraticNorm| |ScanArabic| |digit| |getConstant| - |generalizedEigenvectors| |parts| |hyperelliptic| |contract| |unit?| * - |symmetricPower| |spherical| |isList| |recip| |palgint| - |clearDenominator| |ksec| |patternMatch| |denomRicDE| - |semiDiscriminantEuclidean| |factorFraction| |genericLeftNorm| - |someBasis| |d02cjf| |exprHasWeightCosWXorSinWX| |collect| - |properties| |optimize| |bivariate?| |lex| |nor| |argscript| |extend| - |polyred| |OMsend| |subTriSet?| |every?| |solve| |translate| |reopen!| - |tableau| |bits| |duplicates| |goodPoint| = |f01rcf| |ldf2vmf| - |setsubMatrix!| |complement| |s17aef| |fortranCharacter| |OMgetFloat| - |print| |outputBinaryFile| |halfExtendedSubResultantGcd2| |inRadical?| - |scalarMatrix| |irVar| |refine| |doubleFloatFormat| |overset?| - |schwerpunkt| |resolve| |lyndonIfCan| |conjugates| |operation| - |normalizedDivide| < |tValues| |doublyTransitive?| |logIfCan| - |stFunc1| |totalfract| |outputAsTex| |c02agf| |binomial| |supRittWu?| - |makeViewport2D| |fortranCompilerName| > |whileLoop| |setImagSteps| - |cyclicParents| |createZechTable| |purelyAlgebraic?| |coordinates| - |characteristicSet| |firstSubsetGray| |outlineRender| <= |trim| - |jokerMode| |infinityNorm| |normal?| |OMputAtp| |tubeRadiusDefault| - |identity| |eigenvectors| |iicsc| |mathieu24| |measure2Result| >= - |hMonic| |prefixRagits| |isOp| |isPower| |balancedBinaryTree| - |intcompBasis| |gensym| |vark| |associates?| |clearTheIFTable| - |directSum| |e02bef| |d02ejf| |FormatRoman| |environment| - |gramschmidt| |patternMatchTimes| |bivariatePolynomials| - |chainSubResultants| |addPointLast| |componentUpperBound| - |seriesToOutputForm| |subPolSet?| |integers| |charClass| |palgextint| - |interpret| |slex| |listOfLists| |elliptic| |superscript| |truncate| + - |enqueue!| |edf2ef| |sort!| |collectUnder| |splitDenominator| |true| - |deleteProperty!| |fortranDoubleComplex| |unitNormalize| - |leadingCoefficientRicDE| |chvar| - |cn| |coHeight| |perfectNthPower?| - |OMserve| |exprHasAlgebraicWeight| |triangularSystems| |nand| |in?| - |maxint| |mantissa| / |reducedForm| |subMatrix| |sinIfCan| - |cardinality| |any?| |e02bdf| |constantIfCan| |members| - |removeDuplicates!| |blankSeparate| |fortranLinkerArgs| - |virtualDegree| |middle| |cyclicEqual?| |messagePrint| |ParCond| - |category| |orbit| |pushucoef| |mainValue| |nil| - |halfExtendedSubResultantGcd1| |RittWuCompare| |tRange| - |factorSquareFreePolynomial| |scaleRoots| |stFunc2| |pushdterm| - |s17aff| |domain| |internalLastSubResultant| |cosSinInfo| |viewport2D| - |diagonals| |split| |e04naf| |prepareSubResAlgo| |abs| |package| - |iiabs| |crest| |setErrorBound| |iiasin| |att2Result| - |SturmHabichtMultiple| |definingInequation| |generalLambert| |maxdeg| - |shift| |createMultiplicationTable| |dimension| |palgRDE| - |quotientByP| |clipPointsDefault| |unitCanonical| |approximate| - |solveLinearPolynomialEquationByFractions| |extractTop!| - |linearAssociatedExp| |ocf2ocdf| |tanh2trigh| |irForm| |OMputAttr| - |f04arf| |mainVariables| |complex| |janko2| |schema| |blue| |varList| - |iCompose| |readInt8!| |bothWays| |palglimint| |choosemon| - |decomposeFunc| |hostByteOrder| |order| |delta| |quatern| - |boundOfCauchy| |xCoord| |show| |mainVariable?| |orthonormalBasis| - |basisOfMiddleNucleus| |makeCos| |trapezoidalo| - |indiceSubResultantEuclidean| |property| |find| |extendIfCan| - |extendedResultant| |prologue| |alphanumeric?| |nativeModuleExtension| - |sncndn| |padecf| |pointData| |csch2sinh| |element?| - |partialQuotients| |useEisensteinCriterion?| |trace| - |evenInfiniteProduct| |internalIntegrate0| |monicRightFactorIfCan| - |kovacic| |pushuconst| |realRoots| |topFortranOutputStack| |plot| - |increase| |conditionsForIdempotents| |d01anf| |retract| |leader| - |mainDefiningPolynomial| |integralLastSubResultant| |leftLcm| - |monicRightDivide| |units| |aspFilename| |leviCivitaSymbol| - |factorPolynomial| |associative?| |patternVariable| |typeForm| - |rightDiscriminant| |loopPoints| |cfirst| |power!| |separateFactors| - |replace| |e04ucf| |OMread| |string?| |zag| |taylorIfCan| - |totalDifferential| |bringDown| |routines| |exactQuotient| - |iflist2Result| |formula| |countRealRootsMultiple| |recur| - |RemainderList| |SFunction| |exQuo| |palgLODE| |moduloP| |Nul| |scale| - |socf2socdf| |createNormalElement| |lambda| |rectangularMatrix| - |reorder| |zero?| |f04asf| |removeSquaresIfCan| |modularGcdPrimitive| - |algintegrate| |numFunEvals3D| |taylorQuoByVar| |bytes| |evenlambert| - |uncouplingMatrices| |ParCondList| |code| |unvectorise| |hostPlatform| - |isOr| |semiIndiceSubResultantEuclidean| |s19abf| |imagK| - |insertBottom!| |yCoord| |s13adf| |unitsColorDefault| |basisOfNucleus| - |makeSin| |setFormula!| |sup| |empty?| |readByte!| - |algebraicVariables| |nrows| |epilogue| |localReal?| |point?| - |datalist| |categoryFrame| |pade| |exptMod| |parent| - |createNormalPoly| |partialDenominators| |useEisensteinCriterion| - |sturmVariationsOf| |ncols| |singular?| |eulerPhi| |laplace| - |numberOfMonomials| |leadingTerm| |leftDivide| |OMgetApp| |plus| - |genericRightDiscriminant| |subResultantsChain| |withPredicates| - |OMconnOutDevice| |rewriteIdealWithHeadRemainder| |mainForm| - |toseLastSubResultant| |rightExtendedGcd| |primPartElseUnitCanonical!| - |nthFactor| |squareFreePolynomial| |d01apf| |oddInfiniteProduct| |Ei| - |typeList| |dom| |generalTwoFactor| |sts2stst| |exponents| |just| - |solveRetract| |antiCommutative?| |e04ycf| |leftDiscriminant| |list?| - |setref| |sum| |homogeneous?| |newReduc| |palgintegrate| - |mainSquareFreePart| |shiftLeft| |polynomial| |kroneckerDelta| - |signatureAst| |OMreadFile| |unexpand| |postfix| |point| - |splitConstant| |modulus| |degreeSubResultant| |connect| - |irreducible?| |times| |zeroOf| |df2fi| |const| |moebius| - |removeZeroes| |modTree| |f04atf| |unprotectedRemoveRedundantFactors| - |shallowCopy| |symbolTable| |groebner?| |skewSFunction| - |setLabelValue| |ip4Address| |characteristic| |cAtan| |augment| - |stirling2| |factorials| |top| |bubbleSort!| |rootDirectory| - |linkToFortran| |modularGcd| |setAdaptive3D| |lp| |headAst| - |systemCommand| |iExquo| |series| |zCoord| |oddlambert| - |pointSizeDefault| |idealSimplify| |basisOfCenter| - |resetAttributeButtons| |pushFortranOutputStack| |redPo| |rightDivide| - |isAnd| |title| |comp| |s19acf| |insertTop!| |imagJ| |updatF| - |endOfFile?| |rischNormalize| |s14aaf| |interactiveEnv| - |listYoungTableaus| |popFortranOutputStack| |iiGamma| |meshPar2Var| - |imagE| |splitNodeOf!| |node| |monom| - |zeroSetSplitIntoTriangularSystems| |options| |eisensteinIrreducible?| - |setFieldInfo| |fibonacci| |redpps| |exponentialOrder| |continue| - |root| |sort| |generalSqFr| |primPartElseUnitCanonical| - |outputAsFortran| |extractProperty| |createNormalPrimitivePoly| - |normal| |partialNumerators| |setPredicates| |lazyVariations| - |remainder| |enterPointData| |e| |logical?| |multiset| |iisqrt2| - |overlap| |nthExpon| |singularAtInfinity?| |genericRightTraceForm| - |d01aqf| |lazyPseudoQuotient| |min| |parametersOf| |list| |digits| - |toseInvertible?| |palginfieldint| |rightGcd| |OMgetAtp| |common| - |gcdPolynomial| |string| |pair?| |generalInfiniteProduct| |represents| - |OMconnectTCP| |car| |f04axf| |clikeUniv| |gradient| - |degreeSubResultantEuclidean| |mainVariable| |f01brf| |commutative?| - |triangSolve| |linGenPos| |infix| |random| |cdr| |leadingBasisTerm| - |insertionSort!| |mainPrimitivePart| |numberOfChildren| |shiftRight| - |pop!| |edf2fi| |curry| |rightRecip| |deref| |setDifference| - |basisOfLeftNucloid| |pmComplexintegrate| - |setLegalFortranSourceExtensions| |region| |decimal| |rootsOf| - |iprint| |OMreadStr| |reindex| |lastSubResultant| |setIntersection| - |limitedint| |removeRedundantFactors| |multiEuclideanTree| |hermiteH| - |groebnerIdeal| |getCode| |rCoord| |round| |taylorRep| - |viewPosDefault| |setUnion| |selectPolynomials| |bumprow| |reduction| - |meshFun2Var| |adaptive3D?| |getStream| |readIfCan!| |lambert| - |cyclotomicDecomposition| |realElementary| |apply| |getButtonValue| - |twoFactor| |isNot| |lazyResidueClass| |s19adf| |imagI| |bottom!| - |tryFunctionalDecomposition?| |heap| |harmonic| |character?| - |mergeDifference| |iisqrt3| |imagk| |remove!| |zero| |zeroSetSplit| - |pol| |predicates| |s14abf| |headRemainder| |size| |continuedFraction| - |toseInvertibleSet| |bitLength| |extractClosed| - |createPrimitiveNormalPoly| |numeric| |reducedContinuedFraction| - |d01asf| |content| |width| |B1solve| |fortranTypeOf| |f04faf| - |weierstrass| |hcrf| |semiDegreeSubResultantEuclidean| |OMgetAttr| - |radical| |And| |mergeFactors| |genericLeftDiscriminant| - |lazyPseudoRemainder| |atom?| |equation| |composites| |ignore?| - |precision| |check| |rightExactQuotient| |children| |vector| - |makeMulti| |Or| |torsion?| |showAll?| |univariateSolve| - |branchPoint?| |leftRecip| |basisOfRightNucloid| |first| |fracPart| - |pmintegrate| |divergence| |differentiate| |uniform01| |Not| |f01bsf| - |edf2df| |rightCharacteristicPolynomial| |groebgen| |vconcat| |rest| - |getProperties| |certainlySubVariety?| |laguerreL| |mainContent| - |tubePlot| |karatsubaDivide| |push!| |elem?| |OMlistCDs| |OMbindTCP| - |lastSubResultantElseSplit| |substitute| |integerIfCan| |bumptab| - |meshPar1Var| |points| |innerint| |cAcot| |makeSketch| |diag| - |thetaCoord| |ref| |hash| |viewSizeDefault| |removeDuplicates| - |leastAffineMultiple| |selectOrPolynomials| |complexZeros| - |monicModulo| |ideal| |principalAncestors| |printCode| |fractionPart| - |readLineIfCan!| |validExponential| |count| |mapDown!| |OMgetEndAtp| - |setOrder| |iiexp| |mr| |setScreenResolution3D| - |tryFunctionalDecomposition| |jacobi| |getRef| |super| |lagrange| - |name| |optional| |factorSquareFree| |doubleComplex?| |squareFreePrim| - |signAround| |bitCoef| |s20acf| |cyclotomicFactorization| |top!| - |conjugate| |hasPredicate?| |lift| |body| |roughUnitIdeal?| |light| - |toseSquareFreePart| |isTerm| |lastSubResultantEuclidean| |inc| - |subNodeOf?| |gcdprim| |e02daf| |reduceByQuasiMonic| |xn| |d01bbf| - |reduce| |empty| |f04jgf| |qqq| |imagj| |child| |nextIrreduciblePoly| - |push| |nextColeman| |totalDegree| |null?| |isMult| |factorset| - |computeInt| |lprop| |polyPart| |extractIndex| |OMgetBind| - |genericLeftTraceForm| |bernoulliB| |realSolve| |s14baf| |hconcat| - |basisOfCentroid| |infieldint| |laplacian| |legendreP| |makeTerm| - |torsionIfCan| |expenseOfEvaluation| |showAllElements| |leftPower| - |components| |internalIntegrate| |possiblyNewVariety?| |ptFunc| - |primitivePart!| |normal01| |f01maf| |leftCharacteristicPolynomial| - |notelem| |branchPointAtInfinity?| |invertibleSet| - |selectAndPolynomials| |bumptab1| |lazyPseudoDivide| SEGMENT - |getGraph| |nary?| |error| |OMlistSymbols| |minordet| |phiCoord| - |port| |OMopenFile| |viewDefaults| |raisePolynomial| |any| - |reducedQPowers| |getOrder| |mapUp!| |hitherPlane| |assert| - |monicDivide| |tower| |curryRight| |readLine!| |rootNormalize| - |totolex| |complex?| |OMgetEndAttr| |divisorCascade| |iilog| - |exteriorDifferential| |unrankImproperPartitions0| |btwFact| - |moebiusMu| |wholePart| |t| |radicalEigenvectors| |compdegd| |pastel| - |invmod| |bitTruth| |leadingIdeal| |mapCoef| |optional?| - |univariatePolynomial| |exportedOperators| |roughEqualIdeals?| - |radicalOfLeftTraceForm| |loadNativeModule| |quotedOperators| |equiv| - |semiLastSubResultantEuclidean| |screenResolution3D| |cCos| |dequeue| - |d01fcf| |compound?| |henselFact| |imagi| |birth| |s20adf| |numerator| - |dAndcExp| |startTable!| |rangeIsFinite| |exprToXXP| |abelianGroup| - |constant| |fullPartialFraction| |extractPoint| |nodeOf?| - |complexNumeric| |removeSinSq| |minimumDegree| |positiveSolve| - |tan2trig| |gcdcofact| |rspace| |aLinear| |useNagFunctions| - |writeBytes!| |nextPrimitivePoly| |byte| |solid| |summation| - |predicate| |numberOfOperations| |eulerE| |rightPower| |maxrank| - |weakBiRank| |minimumExponent| |algDsolve| |listOfMonoms| |kernels| - |prindINFO| |s15adf| |invertible?| |principal?| |hessian| - |lazyPremWithDefault| |c06gcf| |OMgetBVar| |e02zaf| |operator| - |maxRowIndex| |cons| |numberOfComposites| |viewWriteDefault| |index?| - |nextsubResultant2| |eyeDistance| |exponential1| - |factorSquareFreeByRecursion| |setOfMinN| |cycleLength| |tanQ| - |completeEval| |rationalPoint?| |step| |node?| |iisin| |putGraph| - |divideExponents| |univariate| |unrankImproperPartitions1| |separant| - |trunc| |numberOfDivisors| |cAcos| |OMopenString| |listLoops| - |comment| |backOldPos| |qelt| |nthCoef| |problemPoints| |readUInt32!| - |minPol| |roughSubIdeal?| |multMonom| |curveColorPalette| - |splitLinear| |qsetelt| |setMaxPoints3D| |cSin| |primintfldpoly| - |hdmpToP| |radicalEigenvector| |linear| |getOperands| |unparse| - |cyclicGroup| |cAtanh| |coerce| |s21baf| |xRange| |factor| - |quadraticForm| |characteristicPolynomial| |irreducibleFactors| - |alphanumeric| |exprToUPS| |int| |f02bbf| |selectfirst| |cothIfCan| - |construct| |sqrt| |yRange| |updateStatus!| |source| |removeCoshSq| - |nextItem| |insert!| |cAsin| |aQuadratic| |romberg| |expandPower| - |solid?| |nextNormalPoly| |zRange| |alternative?| |real| - |musserTrials| |parameters| |midpoint| |newSubProgram| - |definingEquations| |biRank| |readable?| |power| |map!| |OMgetError| - |fprindINFO| |imag| |OMUnknownSymbol?| |optpair| - |generalizedContinuumHypothesisAssumed| |minimize| |divisor| |log2| - |rightLcm| |length| |qsetelt!| |symmetricSquare| |directProduct| - |e04dgf| |identityMatrix| |c06gqf| |pow| |getVariableOrder| |entries| - |e01sef| |infinite?| |scripts| |randomR| |minRowIndex| |elements| - |cyclic| |presub| |child?| |plus!| |stoseIntegralLastSubResultant| - |mapExpon| |brace| |target| |cycleEntry| |subresultantSequence| - |degree| |ptree| |groebSolve| |relativeApprox| |closed?| - |simpleBounds?| |selectFiniteRoutines| |OMputEndObject| |isobaric?| - |binomThmExpt| |destruct| |zerosOf| |strongGenerators| |bsolve| - |viewZoomDefault| |build| |bezoutResultant| |cross| - |isAbsolutelyIrreducible?| |readInt32!| |cLog| |expintfldpoly| - |nextLatticePermutation| |iiacosh| |f07fdf| |kind| |dihedralGroup| - |var1Steps| |expandLog| |pseudoQuotient| |back| |dmpToP| - |lazyIrreducibleFactors| |palgextint0| |polygon| |op| |f02bjf| - |exists?| |binary| |elliptic?| |removeSinhSq| |realEigenvalues| - |interpretString| |integral?| |partition| |tan2cot| |aCubic| - |leftExtendedGcd| |makeprod| |mapUnivariateIfCan| |ravel| - |denominators| |monomial| |stopMusserTrials| |upperBound| - |variationOfParameters| |clearTheSymbolTable| |setProperties| - |basisOfCommutingElements| |e01sff| |simpson| |s18aef| |flexible?| - |prinpolINFO| |module| |getBadValues| |lexTriangular| |reshape| - |arguments| |key?| |stoseLastSubResultant| |sincos| |setelt| - |setMinPoints| |factorSFBRlcUnit| |c06gsf| |OMUnknownCD?| |An| - |midpoints| |distance| |linearMatrix| |rationalApproximation| - |infLex?| |e04fdf| |zeroMatrix| |replaceKthElement| - |generalizedContinuumHypothesisAssumed?| |sub| |submod| |open?| - |finite?| |copy| |numberOfIrreduciblePoly| |SturmHabichtSequence| - |antisymmetric?| |quasiRegular| |rootOf| |resetVariableOrder| |union| - |leadingIndex| |minus!| |max| |commutativeEquality| |dihedral| - |pomopo!| |singularitiesOf| |invmultisect| |rank| |viewPhiDefault| - |mathieu11| |bezoutDiscriminant| |selectODEIVPRoutines| |OMputInteger| - |morphism| |cExp| |iiatanh| |monomialIntegrate| |testDim| |update| - |f02fjf| |autoCoerce| |cos2sec| |dot| |meatAxe| |front| |weights| - |removeIrreducibleRedundantFactors| |palglimint0| |dmp2rfi| |aQuartic| - |var2Steps| |extension| |composite| |expandTrigProducts| |readUInt16!| - |stripCommentsAndBlanks| |f07fef| |complete| |basisOfLeftAnnihilator| - |packageCall| |leftGcd| |doubleResultant| |numerators| - |numberOfFactors| |pToDmp| |closedCurve?| |showTheSymbolTable| - |elaboration| |e02adf| |disjunction| |mapMatrixIfCan| |prinb| - |realEigenvectors| |resetBadValues| |integralAtInfinity?| - |rightRegularRepresentation| |symbolIfCan| |trapezoidal| - |stoseInvertible?sqfreg| |digit?| |minPoints| |d01ajf| |charthRoot| - |lowerBound| |lexico| |rarrow| |position| |nodes| |linearPart| - |sinhcosh| |s18aff| |setButtonValue| |squareFreeLexTriangular| - |e04gcf| |incrementKthElement| |match?| |UnVectorise| |lists| - |setClosed| |relerror| |addmod| |setEmpty!| |SturmHabichtCoefficients| - |rightAlternative?| |quasiRegular?| |realZeros| |allRootsOf| - |leadingExponent| |leftScalarTimes!| |resultantEuclidean| - |numberOfPrimitivePoly| |mapExponents| |polynomialZeros| - |OMParseError?| |countable?| |viewThetaDefault| |mathieu12| |pureLex| - |cosh2sech| |OMputFloat| |iiacoth| |cRationalPower| |monomialIntPoly| - |mappingAst| |declare| |prime?| |f02wef| |shallowExpand| - |selectPDERoutines| |leftMult| |rotate!| |normalForm| |symmetric?| - |cap| |palgRDE0| |radicalSolve| |leftExactQuotient| |scan| - |scanOneDimSubspaces| |fintegrate| |setPrologue!| |multisect| - |genericPosition| |pole?| |basisOfRightAnnihilator| |space| |e02aef| - |subResultantGcd| |convergents| |balancedFactorisation| - |modularFactor| |se2rfi| |printTypes| |select!| |arg1| |innerSolve1| - |stoseInvertibleSetsqfreg| |distdfact| |critpOrder| - |differentialVariables| |hasTopPredicate?| |leftRegularRepresentation| - |s01eaf| |nonLinearPart| |argument| |arg2| |sech| |conjunction| - |mapBivariate| |conditionP| |readInt16!| |d01akf| |assign| - |closedCurve| |symmetricRemainder| |rename| |csch| |rombergo| - |parametric?| |e04jaf| |sylvesterSequence| |float?| |close| - |integralBasisAtInfinity| |Vectorise| |asinh| |conditions| |tube| - |semiResultantEuclidean2| |subresultantVector| |s18dcf| |SturmHabicht| - |halfExtendedResultant2| |constant?| |belong?| |definingPolynomial| - |constantOpIfCan| |GospersMethod| |match| |acosh| |cot2trig| - |setStatus!| |f2df| |linearAssociatedLog| |stop| |OMmakeConn| - |iterationVar| |display| |pointColorDefault| |bright| |complexSolve| - |mathieu22| |deepExpand| |atanh| |numberOfNormalPoly| |cPower| - |setAttributeButtonStep| |inverseLaplace| |iiasech| - |mainCharacterization| |li| |f02xef| |acoth| |totalLex| - |leftRemainder| |rightMult| |dequeue!| |leftAlternative?| |changeBase| - |Aleph| |palgLODE0| |quadratic?| |radicalRoots| |rightScalarTimes!| - |asech| |OMputVariable| |coefficient| |nullary| |setTex!| - |listBranches| |sample| |basisOfLeftNucleus| |positiveRemainder| - |selectOptimizationRoutines| |expt| |approximants| - |useSingleFactorBound?| |OMwrite| |cup| |newTypeLists| |delete!| - |multiple| |semiResultantEuclidean1| |graphCurves| |resultant| - |makeCrit| |input| |topPredicate| |diagonal?| |rightTraceMatrix| - |lfunc| |bag| |constantKernel| |box| |applyQuote| |coth2trigh| - |separateDegrees| |library| |solveLinearPolynomialEquation| |d01alf| - |revert| |slash| |pr2dmp| |rename!| |tubePoints| - |clearFortranOutputStack| |fullDisplay| |e04mbf| |extractBottom!| - |integer?| |setPoly| |s13aaf| |unitVector| |innerSolve| |leftQuotient| - |plotPolar| |countRealRoots| |readUInt8!| |mindeg| |positive?| - |curve?| |integerBound| |linears| |ruleset| |isEquiv| |s18def| - |linearAssociatedOrder| |ef2edf| |sturmSequence| |ramified?| - |lineColorDefault| |f04adf| |simpsono| |extendedSubResultantGcd| - |setCondition!| |inputOutputBinaryFile| |halfExtendedResultant1| |set| - |iiacsch| |OMcloseConn| |contractSolve| |changeNameToObjf| - |primitivePart| |mkcomm| |createIrreduciblePoly| |test| |id| - |companionBlocks| |infiniteProduct| |chineseRemainder| |Ci| - |basisOfRightNucleus| |complexRoots| |bit?| |suchThat| |OMputString| - |decrease| |setEpilogue!| |triangular?| |algebraicOf| |dn| - |reverseLex| |indiceSubResultant| |sPol| |makeUnit| |ipow| - |antiAssociative?| |useSingleFactorBound| |table| |unravel| - |typeLists| |times!| |csc2sin| |e02dcf| |showArrayValues| |subst| - |insert| |new| |po| |setTopPredicate| |leftTraceMatrix| - |rationalFunction| |rootProduct| |obj| |showFortranOutputStack| - |selectIntegrationRoutines| |discriminant| |wreath| |fixedPoint| - |d01amf| |over| |eq| |lookupFunction| |prefix| |ddFact| |cache| - |drawCurves| |trace2PowMod| |inHallBasis?| |square?| |symbol?| |iter| - |exponent| |swap!| |binding| |monicLeftDivide| |relationsIdeal| - |delete| |hasoln| |negative?| |signature| |seed| |tubeRadius| - |exactQuotient!| |debug3D| |intersect| |upDateBranches| - |associatedSystem| |s13acf| |normalized?| |polarCoordinates| - |optAttributes| |makeEq| |s19aaf| |jordanAlgebra?| |monomial?| |curve| - |axesColorDefault| |bipolar| |updatD| |algint| |isImplies| |setValue!| - |objects| |oneDimensionalArray| |OMencodingXML| |specialTrigs| - |ramifiedAtInfinity?| |compBound| |generators| |createPrimitivePoly| - |directory| |base| |script| |minPoly| |lazy?| |divisors| |Si| - |compactFraction| |adjoint| |rightFactorCandidate| |e02ddf| - |OMputSymbol| |primextendedint| |rowEchelon| |OMconnInDevice| - |rewriteIdealWithRemainder| |elRow1!| |f02aff| |e01baf| |retractIfCan| - |nextPartition| |reverse!| |rewriteIdealWithQuasiMonicGenerators| - |setrest!| |flatten| |ReduceOrder| |externalList| |exp| - |particularSolution| |getMeasure| |prepareDecompose| |normalDeriv| - |showScalarValues| |tex| |setprevious!| |printStats!| |left| |numer| - |rootSimp| |outputMeasure| |mpsode| |cSec| |pseudoRemainder| - |scalarTypeOf| |thenBranch| |/\\| |polyRDE| |returnTypeOf| |right| - |outputList| |denom| |encodingDirectory| |clip| |complexIntegrate| - |quasiAlgebraicSet| |tracePowMod| |unknownEndian| |Is| |laguerre| - |irreducibleFactor| |\\/| |fill!| |increment| |atanIfCan| |setleft!| - |saturate| |nil| |infinite| |arbitraryExponent| |approximate| + |Record| |Union| |leftRankPolynomial| |OMputAttr| |principal?| + |defineProperty| |pi| |makingStats?| |swap| |region| |charpol| + |sorted?| |f04arf| |nextNormalPrimitivePoly| |hessian| |infinity| + |elementary| |decimal| |OMencodingSGML| |polynomialZeros| |e01bff| + |degreePartition| |mainVariables| |functionIsOscillatory| + |lazyPremWithDefault| |cond| |semiResultantEuclideannaif| |rootsOf| + |inverseIntegralMatrixAtInfinity| |brillhartIrreducible?| + |OMParseError?| |c06gcf| |janko2| |antisymmetricTensors| |generate| + |initiallyReduce| |log10| |iprint| |setlast!| |quasiMonic?| |map| + |countable?| |ord| |OMgetSymbol| |schema| |complexNumericIfCan| + |OMgetBVar| |bitand| |kernel| |cSinh| |iifact| |OMreadStr| |bigEndian| + |viewThetaDefault| |previous| |isQuotient| |incrementBy| |e02zaf| + |blue| |low| |shade| |outerProduct| |bitior| |ReduceOrder| |draw| + |cAsech| |reindex| |firstDenom| |mathieu12| |wordsForStrongGenerators| + |iCompose| |trailingCoefficient| |maxRowIndex| |var1StepsDefault| + |expand| |externalList| |quartic| |squareTop| |lastSubResultant| + |normInvertible?| |pureLex| |currentEnv| |nonSingularModel| + |readInt8!| |commaSeparate| |numberOfComposites| |filterWhile| + |particularSolution| |goodnessOfFit| |limitedint| |trigs| |cosh2sech| + |addMatchRestricted| |bothWays| |nsqfree| |filterUntil| |upperCase!| + |viewWriteDefault| |symbol| |getMeasure| |attributeData| |airyAi| + |OMputObject| |removeRedundantFactors| |convert| |OMputFloat| + |overbar| |palglimint| |index?| |surface| |opeval| |select| + |expression| |prepareDecompose| |makeObject| |multiEuclideanTree| + |processTemplate| |iiacoth| |tanintegrate| |safeCeiling| + |dominantTerm| |height| |choosemon| |polyRicDE| |nextsubResultant2| + |numberOfFractionalTerms| |zoom| |integer| |normalDeriv| |coef| + |cRationalPower| |matrixConcat3D| |lazyEvaluate| |hermiteH| + |setStatus| |rational?| |printHeader| |badValues| |decomposeFunc| + |OMgetObject| |eyeDistance| |showScalarValues| |makeGraphImage| + |groebnerIdeal| |monomialIntPoly| |distFact| UP2UTS |tanh2coth| + |lowerCase?| |hostByteOrder| |polar| |exponential1| |setprevious!| + |getCode| |endSubProgram| |resize| ** |mappingAst| |coerceImages| + |numberOfComputedEntries| |order| |getIdentifier| + |factorSquareFreeByRecursion| |printStats!| |acschIfCan| + |factorGroebnerBasis| |rCoord| |prime?| |nextPrime| |quatern| + |transcendent?| |lintgcd| |setOfMinN| |rootSimp| |doubleRank| |f02aef| + |round| |f02wef| |noKaratsuba| |makeFloatFunction| |makeRecord| |lo| + |boundOfCauchy| |repeating?| |cycleLength| |outputMeasure| + |invertIfCan| |rangePascalTriangle| |taylorRep| |shallowExpand| + |coth2tanh| |tanQ| |changeVar| |xCoord| |incr| |nonQsign| |mpsode| + |acsch| |label| |coshIfCan| |conjug| |viewPosDefault| + |lowerPolynomial| |selectPDERoutines| |initial| |pdf2ef| + |mainVariable?| |completeEval| |normDeriv2| |cSec| + |getMultiplicationMatrix| |limit| |selectPolynomials| |leftMult| + |before?| |f02aaf| |orthonormalBasis| |rationalPoint?| |enterInCache| + |pseudoRemainder| |c06gbf| + |rewriteSetByReducingWithParticularGenerators| |bumprow| |rotate!| + |internalZeroSetSplit| |basisOfMiddleNucleus| |swapRows!| |iitan| + |node?| |scalarTypeOf| |coerceP| |minColIndex| |reduction| |nullity| + |normalForm| Y |makeCos| |d02kef| |iisin| |indicialEquations| + |thenBranch| |traceMatrix| |iiacsc| |meshFun2Var| |exprex| + |symmetric?| |trapezoidalo| |rightFactorIfCan| |factor1| |putGraph| + |polyRDE| |wrregime| |reduceLODE| |adaptive3D?| |iipow| |cap| + |leftOne| |indiceSubResultantEuclidean| |rightTrace| |divideExponents| + |returnTypeOf| |outputArgs| |tail| |finiteBasis| |getStream| + |coerceListOfPairs| |setProperty| |palgRDE0| |find| |rules| + |constructor| |ridHack1| |rootBound| |unrankImproperPartitions1| + |encodingDirectory| |lifting1| |sec2cos| |csubst| |readIfCan!| + |radicalSolve| |initials| |nothing| |rischDE| |extendIfCan| |separant| + |genericRightMinimalPolynomial| |clip| |showClipRegion| |option| + |selectNonFiniteRoutines| |leftFactor| |lambert| |leftExactQuotient| + |rk4f| |showSummary| |extendedResultant| |mainCoefficients| + |sumOfKthPowerDivisors| |trunc| |complexIntegrate| |rational| + |simplifyExp| |cyclotomicDecomposition| |getExplanations| |scan| + |linSolve| |prologue| |numberOfDivisors| |minset| |quasiAlgebraicSet| + |primitiveElement| |duplicates?| |realElementary| |tensorProduct| + |scanOneDimSubspaces| |showAttributes| |alphanumeric?| |smith| |cAcos| + |findBinding| |tracePowMod| |unknown| |complexForm| |getMatch| + |getButtonValue| |setnext!| |fintegrate| |macroExpand| |OMopenString| + |recoverAfterFail| |nativeModuleExtension| |rightTrim| + |mainExpression| |unknownEndian| |cot2tan| |cycleTail| |lfintegrate| + |twoFactor| |setPrologue!| |insertRoot!| |sncndn| + |internalSubQuasiComponent?| |leftTrim| |listLoops| |Is| |part?| + |frobenius| |isNot| |startStats!| |multisect| + |combineFeatureCompatibility| |padecf| |backOldPos| |qinterval| + |laguerre| |preprocess| |f07adf| |baseRDE| |lazyResidueClass| + |genericPosition| |say| |intPatternMatch| F |pointData| |nthCoef| + |exponential| |irreducibleFactor| |dualSignature| |multinomial| + |s19adf| |associator| |pole?| |csch2sinh| |Frobenius| |problemPoints| + |f01qdf| |fill!| |overlabel| |hclf| |d03faf| |imagI| + |basisOfRightAnnihilator| |binaryTree| |element?| |readUInt32!| + |s17acf| |increment| |bottom!| |quasiComponent| |space| |indices| + |ode| |remove| |function| |multivariate| |partialQuotients| + |controlPanel| |minPol| |OMunhandledSymbol| |atanIfCan| + |fillPascalTriangle| |fortran| |hexDigit?| RF2UTS + |tryFunctionalDecomposition?| |e02aef| |variables| |result| + |useEisensteinCriterion?| |red| |quoted?| |roughSubIdeal?| |setleft!| + |byteBuffer| |rk4qc| |open| |OMputEndBVar| |heap| |last| |eval| + |subResultantGcd| |reset| |ratDenom| |evenInfiniteProduct| |multMonom| + |trivialIdeal?| |saturate| |assoc| |imaginary| |functorData| + |external?| |harmonic| |null| |convergents| |f2st| + |internalIntegrate0| |arbitrary| |curveColorPalette| |character?| + |divideIfCan!| |pattern| |enumerate| |elseBranch| |not| + |balancedFactorisation| |write| |monicRightFactorIfCan| + |fixedPointExquo| |rotatez| |splitLinear| + |noncommutativeJordanAlgebra?| |mergeDifference| |supersub| |and| + |Lazard| |modularFactor| |save| |trueEqual| |kovacic| |jacobian| + |setMaxPoints3D| |operations| |rquo| |iisqrt3| |mesh| |or| + |KrullNumber| |taylor| |se2rfi| |bfKeys| |pushuconst| |cSin| + |semiSubResultantGcdEuclidean1| |component| |inrootof| |extract!| + |imagk| |xor| |laurent| |printTypes| |cycleElt| |realRoots| |nullary?| + |primintfldpoly| |pointColor| |deepestInitial| |critBonD| |message| + |remove!| |case| |select!| |puiseux| |newLine| |topFortranOutputStack| + |constantLeft| |hdmpToP| |bipolarCylindrical| |setchildren!| |Zero| + |removeSuperfluousCases| |zeroSetSplit| |innerSolve1| |plot| + |interReduce| |mix| |radicalEigenvector| |hi| |measure| |pol| |One| + |monicCompleteDecompose| |inv| |stoseInvertibleSetsqfreg| |increase| + |reducedDiscriminant| |d02bbf| |getOperands| |addMatch| + |lazyIntegrate| |is?| |predicates| |distdfact| |ground?| + |conditionsForIdempotents| |squareFreePart| |unparse| |create3Space| + |regularRepresentation| |minGbasis| |ground| |s14abf| |fixedDivisor| + |critpOrder| |lcm| |zeroVector| |d01anf| |cyclicGroup| |nil?| |critT| + |setAdaptive| |headRemainder| |argumentListOf| |differentialVariables| + |leadingMonomial| |eigenvector| |cAtanh| |freeOf?| |asechIfCan| + |append| |continuedFraction| |clipSurface| |leadingCoefficient| + |hasTopPredicate?| |binaryTournament| |chvar| |zeroDimPrimary?| + |s21baf| |mat| |lSpaceBasis| |principalIdeal| + |leftRegularRepresentation| |primitiveMonomials| |toseInvertibleSet| + |elt| |gcd| |output| |mainMonomials| |coHeight| |cCsch| + |quadraticForm| |LazardQuotient| |inspect| |OMencodingUnknown| + |printStatement| |bitLength| |s01eaf| |false| |reductum| + |perfectNthPower?| |completeHermite| |characteristicPolynomial| + |leaf?| |finiteBound| |modifyPointData| |nonLinearPart| |OMserve| + |orbits| |irreducibleFactors| |makeSUP| |outputSpacing| |OMputEndBind| + |meshPar2Var| |extensionDegree| |argument| |exprHasAlgebraicWeight| + |addBadValue| |alphanumeric| |hexDigit| |tablePow| |sequence| |iiasec| + |imagE| |conjunction| |roman| |triangularSystems| |exprToUPS| + |diagonal| |c06fuf| |e01bef| |polCase| |splitNodeOf!| |mapBivariate| + |nand| |host| |s17def| |triangulate| |yellow| + |zeroSetSplitIntoTriangularSystems| |conditionP| |rightOne| |in?| + |moebiusMu| |diagonalProduct| |quote| |bivariateSLPEBR| |rootPower| + |eisensteinIrreducible?| |readInt16!| |categories| |lyndon?| |maxint| + |constantRight| |wholePart| |expextendedint| |cycle| |pascalTriangle| + |setFieldInfo| |d01akf| |reducedForm| |getPickedPoints| |generic?| + |radicalEigenvectors| |factorial| |explicitlyEmpty?| |fibonacci| + |ode2| |subMatrix| |axes| |absolutelyIrreducible?| |compdegd| |iicosh| + |entry?| |redpps| |monicDecomposeIfCan| |composite| |rootSplit| + |sinIfCan| |pastel| |roughBase?| |toScale| |f04mbf| |sayLength| + |exponentialOrder| |expandTrigProducts| |cardinality| |inverseColeman| + |localUnquote| |invmod| |plusInfinity| |cAcsch| |partialFraction| + |fortranReal| |root| |readUInt16!| |any?| |d02gbf| |hypergeometric0F1| + |bitTruth| |minusInfinity| |cyclicSubmodule| |lfinfieldint| + |generalSqFr| |stripCommentsAndBlanks| |e02bdf| |stFuncN| + |leadingIdeal| |semiSubResultantGcdEuclidean2| |exponent| |hdmpToDmp| + |monomRDE| |primPartElseUnitCanonical| |f07fef| |constantIfCan| + |redmat| |mapCoef| |graphs| |swap!| |euclideanGroebner| |member?| + |extractProperty| |key| |complete| |mkPrim| |members| |mkIntegral| + |optional?| |binding| |zeroDimensional?| |identitySquareMatrix| + |createNormalPrimitivePoly| |basisOfLeftAnnihilator| + |removeDuplicates!| |geometric| |iroot| |univariatePolynomial| + |monicLeftDivide| |partialNumerators| |coerceS| |curveColor| + |filename| |packageCall| |bfEntry| |blankSeparate| |exportedOperators| + |d01gbf| |type| |relationsIdeal| |e02ahf| |setPredicates| |PDESolve| + |leftGcd| |startPolynomial| |fortranLinkerArgs| |roughEqualIdeals?| + |ceiling| |hasoln| |stiffnessAndStabilityFactor| |critB| + |lazyVariations| |parse| |doubleResultant| |sin?| |virtualDegree| + |radicalOfLeftTraceForm| |OMclose| |negative?| |setvalue!| + |flexibleArray| |remainder| |numerators| |next| |option?| |middle| + |quotedOperators| |getOperator| |seed| |innerEigenvectors| + |makeResult| |enterPointData| |numberOfFactors| |internalInfRittWu?| + |cyclicEqual?| |pleskenSplit| |equiv| |tubeRadius| |sinhIfCan| + |capacity| |logical?| |pToDmp| |eigenvalues| |e02def| |s17agf| + |messagePrint| |checkPrecision| |semiLastSubResultantEuclidean| + |exactQuotient!| |karatsuba| |multiset| |divide| |closedCurve?| + |zeroDimPrime?| |ParCond| |removeRoughlyRedundantFactorsInPol| + |screenResolution3D| |besselY| EQ |debug3D| |npcoef| |iisqrt2| + |cyclePartition| |showTheSymbolTable| |orbit| |Hausdorff| |cCos| + |root?| |intersect| |overlap| |product| |trigs2explogs| |lhs| + |elaboration| |iiacos| |pushucoef| |dequeue| |generalPosition| + |upDateBranches| |eof?| |weighted| |nthExpon| |rhs| |e02adf| + |drawToScale| |mainValue| |putProperties| |d01fcf| |associatedSystem| + |head| |singularAtInfinity?| |d03eef| |disjunction| |hasSolution?| + |halfExtendedSubResultantGcd1| |exprToGenUPS| |compound?| |s13acf| + |stoseInvertibleSetreg| |genericRightTraceForm| |listConjugateBases| + |mapMatrixIfCan| FG2F |RittWuCompare| |supDimElseRittWu?| |henselFact| + |rule| |normalized?| |e02akf| |c06ecf| |d01aqf| |prinb| |df2st| + |tRange| |imagi| |multiplyCoefficients| |polarCoordinates| |index| + |infRittWu?| |lazyPseudoQuotient| |euler| |realEigenvectors| + |normalElement| |factorSquareFreePolynomial| |computeBasis| |birth| + |optAttributes| |primes| |symbolTableOf| |parametersOf| + |resetBadValues| |scaleRoots| |Beta| |discreteLog| |s20adf| |makeEq| + |htrigs| |center| |digits| |lighting| |integralAtInfinity?| |dioSolve| + |stFunc2| |extendedIntegrate| |numerator| |s19aaf| + |intermediateResultsIF| |commutator| |pair| |toseInvertible?| + |rightRegularRepresentation| |dAndcExp| |pushdterm| |tanAn| + |pointPlot| |value| |jordanAlgebra?| |distribute| |palginfieldint| + |reseed| |symbolIfCan| |unitNormal| |s17aff| |mulmod| |startTable!| + |monomial?| |possiblyInfinite?| |rightGcd| |firstUncouplingMatrix| + |trapezoidal| |rubiksGroup| |internalLastSubResultant| |rangeIsFinite| + |maxPoints3D| |curve| |subtractIfCan| |OMgetAtp| |subCase?| + |stoseInvertible?sqfreg| |green| |cosSinInfo| |drawComplex| + |exprToXXP| |entry| |axesColorDefault| |viewport3D| |gcdPolynomial| + |inconsistent?| |minPoints| |approxNthRoot| |viewport2D| |returns| + |abelianGroup| |bipolar| |sizeLess?| |normalizedAssociate| |pair?| + |d01ajf| |wholeRagits| |diagonals| |fullPartialFraction| + |linearlyDependentOverZ?| |updatD| |movedPoints| |difference| + |generalInfiniteProduct| |charthRoot| |ScanFloatIgnoreSpaces| |split| + |hspace| |extractPoint| |algint| |HenselLift| |computeCycleEntry| + |represents| |lowerBound| |sn| |createMultiplicationMatrix| |reverse| + |e04naf| |radicalEigenvalues| |nodeOf?| |isImplies| |e01daf| |nthFlag| + |OMconnectTCP| |lexico| |fortranLogical| |prepareSubResAlgo| + |univariatePolynomials| |removeSinSq| |setValue!| |call| |asimpson| + |f04axf| |lowerCase| |rarrow| |shrinkable| |abs| |minimumDegree| |bat| + |oneDimensionalArray| |leaves| |idealiserMatrix| |tree| |getlo| + |clikeUniv| |nodes| |iiabs| |showIntensityFunctions| |writeInt8!| + |positiveSolve| |OMencodingXML| |equality| |gradient| |reduced?| + |linearPart| |resultantReduit| |crest| |merge!| |tan2trig| + |specialTrigs| |primextintfrac| |rk4| |degreeSubResultantEuclidean| + |sinhcosh| |setErrorBound| |terms| |gcdcofact| |s21bbf| + |ramifiedAtInfinity?| |iisech| |s17akf| |mainVariable| |init| |s18aff| + |iiasin| |initiallyReduced?| |alphabetic| |rspace| |compBound| |more?| + |f01brf| |decompose| |setButtonValue| |att2Result| |qroot| |dfRange| + |aLinear| |generators| |cTanh| |commutative?| |mirror| + |squareFreeLexTriangular| |tanIfCan| |SturmHabichtMultiple| + |useNagFunctions| |categoryMode| |createPrimitivePoly| |generator| + |stoseInvertibleSet| |putColorInfo| |triangSolve| |e04gcf| |OMputBind| + |definingInequation| |expPot| |writeBytes!| |minPoly| + |alternatingGroup| |linGenPos| |bracket| |incrementKthElement| + |sequences| |generalLambert| |nextPrimitivePoly| |one?| |lazy?| + |stopTableInvSet!| |fi2df| |infix| |UnVectorise| |solid| |chebyshevT| + |maxdeg| |read!| |search| |divisors| |oblateSpheroidal| + |leadingBasisTerm| |setClosed| |stack| |summation| + |createMultiplicationTable| |addPoint| |rem| |largest| |Si| + |prinshINFO| |generateIrredPoly| |insertionSort!| |relerror| + |numberOfOperations| |scripted?| |dimension| |rowEch| |quo| + |compactFraction| |idealiser| |mainPrimitivePart| |compose| |addmod| + |condition| |clipParametric| |palgRDE| |eulerE| |ODESolve| |adjoint| + |mainKernel| |Gamma| |numberOfChildren| |setEmpty!| |rightPower| |div| + |extractSplittingLeaf| |rightFactorCandidate| |lieAdmissible?| + |setRow!| |shiftRight| |SturmHabichtCoefficients| |basis| + |purelyAlgebraic?| |mkAnswer| |maxrank| |exquo| |e02ddf| |dim| + |powerSum| |lieAlgebra?| |pop!| |rightAlternative?| |d02gaf| + |coordinates| |weakBiRank| ~= |fractRadix| |OMputSymbol| + |makeViewport3D| |edf2fi| |corrPoly| |quasiRegular?| |mapUnivariate| + |characteristicSet| |minimumExponent| |isPlus| |#| |primextendedint| + |matrix| |euclideanSize| |dec| |realZeros| |dictionary| + |firstSubsetGray| ~ |algDsolve| |purelyAlgebraicLeadingMonomial?| + |rowEchelon| |s17ajf| |initializeGroupForWordProblem| + |mainSquareFreePart| |concat| |allRootsOf| + |removeRoughlyRedundantFactorsInPols| |outlineRender| |listOfMonoms| + |fmecg| |OMconnInDevice| |testModulus| |c06ebf| |shiftLeft| + |leadingExponent| |groebner| |trim| |qfactor| |prindINFO| |printInfo| + |rewriteIdealWithRemainder| |outputFixed| |kroneckerDelta| |connectTo| + |leftScalarTimes!| |clearCache| |jokerMode| |powers| |level| |elRow1!| + |simplify| |figureUnits| |signatureAst| |resultantEuclidean| + |infinityNorm| |cAsec| |vspace| |lprop| |f02aff| |setScreenResolution| + |OMreadFile| |symFunc| |numberOfPrimitivePoly| |polyPart| |normal?| + |fractRagits| |hasHi| |substring?| |e01baf| |factorByRecursion| + |antiCommutator| |unexpand| |char| |mapExponents| |ScanRoman| + |OMputAtp| |failed| |univariate?| |extractIndex| |nextPartition| + |explimitedint| |postfix| |stronglyReduced?| |OMgetBind| + |internalSubPolSet?| |tubeRadiusDefault| |bat1| |suffix?| |reverse!| + |errorInfo| |splitConstant| |d03edf| |stoseLastSubResultant| + |coefficients| |identity| |maxPoints| |genericLeftTraceForm| + |maximumExponent| |rewriteIdealWithQuasiMonicGenerators| |iicoth| + |numericalIntegration| |modulus| |getZechTable| |sincos| + |eigenvectors| |compile| |leadingSupport| |bernoulliB| |traverse| + |prefix?| |status| |setrest!| |pointLists| |degreeSubResultant| + |polygamma| |normalDenom| |setMinPoints| |iicsc| |tanSum| |credPol| + |realSolve| |cCoth| |symmetricDifference| |connect| |close!| + |factorSFBRlcUnit| |mathieu24| |autoReduced?| |s14baf| |removeZero| + |extendedSubResultantGcd| |second| |irreducible?| |e02ajf| |anfactor| + |internalDecompose| |erf| |c06gsf| |float| |measure2Result| |pushup| + |edf2efi| |hconcat| |setCondition!| |third| |symmetricGroup| |zeroOf| + |primeFactor| |nextSubsetGray| |OMUnknownCD?| |vedf2vef| |hMonic| + |basisOfCentroid| |monomials| |inputOutputBinaryFile| |safetyMargin| + |df2fi| |lexGroebner| |rowEchelonLocal| |An| |void| |rroot| + |prefixRagits| |functionIsContinuousAtEndPoints| |infieldint| + |halfExtendedResultant1| |zeroDim?| |numericalOptimization| |const| + |lowerCase!| |dilog| |midpoints| |laplacian| |s18adf| |isOp| + |derivationCoordinates| |infix?| |iiacsch| |prolateSpheroidal| + |e02gaf| |repeatUntilLoop| |moebius| |sin| |distance| |rationalPoints| + |fortranComplex| |isPower| |mask| |legendreP| |OMcloseConn| + |setRealSteps| |s17dhf| |removeSuperfluousQuasiComponents| + |removeZeroes| |linearMatrix| |cos| |balancedBinaryTree| |bernoulli| + |write!| |makeTerm| |contractSolve| |modTree| |rationalApproximation| + |matrixDimensions| |gderiv| |expr| |irCtor| |tan| |intcompBasis| + |iFTable| |torsionIfCan| |userOrdered?| |changeNameToObjf| + |createLowComplexityNormalBasis| + |removeRoughlyRedundantFactorsInContents| |f04atf| |cot| |OMputApp| + |infLex?| |gensym| |subscript| |expenseOfEvaluation| |writeUInt8!| + |primitivePart| |associatorDependence| |showTheFTable| |e04fdf| + |unprotectedRemoveRedundantFactors| |sec| |purelyTranscendental?| GE + |parabolicCylindrical| |vark| |listRepresentation| |double| + |showAllElements| |mkcomm| |zeroMatrix| |psolve| |OMgetInteger| + |shallowCopy| |sh| |csc| |log| GT |associates?| |sin2csc| |cartesian| + |leftPower| |createIrreduciblePoly| |groebner?| |atanhIfCan| + |partitions| |variable| |diff| |replaceKthElement| |asin| LE + |perfectNthRoot| |clearTheIFTable| |ratpart| |components| + |companionBlocks| |generalizedContinuumHypothesisAssumed?| + |skewSFunction| |stoseInvertible?| |iterators| BY |paren| |mathieu23| + |acos| LT |directSum| |oddintegers| |internalIntegrate| |numericIfCan| + |infiniteProduct| |df2ef| |f02akf| |setLabelValue| |sub| |prem| |atan| + |e02bef| |subNode?| |gcdcofactprim| |possiblyNewVariety?| + |chineseRemainder| |rightUnits| |fractionFreeGauss!| |submod| + |ip4Address| |s21bdf| |acot| |d02ejf| |shufflein| |ptFunc| + |invertibleElseSplit?| |Ci| |sdf2lst| |odd?| |noValueMode| + |characteristic| |open?| |asec| |FormatRoman| |inverse| |ffactor| + |primitivePart!| |basisOfRightNucleus| |quickSort| |besselK| |lookup| + |cAtan| |finite?| |acsc| |environment| |unit| |OMgetEndBVar| + |normal01| |declare!| |complexRoots| |numberOfIrreduciblePoly| + |maxColIndex| |OMputError| |augment| |expIfCan| |sinh| |setfirst!| + |gramschmidt| |addPoint2| |f01maf| |denomLODE| |bit?| |stirling2| + |printingInfo?| |leftZero| |anticoord| |SturmHabichtSequence| |cosh| + |stirling1| |nextsousResultant2| |leftCharacteristicPolynomial| + |patternMatchTimes| |lazyPquo| NOT |OMputString| |factorials| |f04qaf| + |antisymmetric?| |OMencodingBinary| |tubePointsDefault| |tanh| + |genericRightTrace| |genericLeftMinimalPolynomial| + |bivariatePolynomials| |notelem| OR |decrease| |compiledFunction| + |resultantEuclideannaif| |c02aff| |bubbleSort!| |quasiRegular| |coth| + |branchPointAtInfinity?| |copyInto!| |chainSubResultants| |hue| AND + |setEpilogue!| |split!| |deepCopy| |rootDirectory| |rootOf| + |characteristicSerie| |keys| |cosIfCan| |addPointLast| |invertibleSet| + |findCycle| |triangular?| |simplifyPower| |linkToFortran| + |LyndonWordsList1| |depth| |showTheIFTable| |resetVariableOrder| + |primitive?| |componentUpperBound| |minrank| |selectAndPolynomials| + |algebraicOf| |cubic| |modularGcd| |firstNumer| |leadingIndex| + |drawStyle| |has?| |seriesToOutputForm| |bumptab1| |debug| |segment| + |viewWriteAvailable| |parents| |dn| |e01bhf| |approxSqrt| + |setAdaptive3D| |minus!| |minPoints3D| |c05nbf| |subPolSet?| D + |consnewpol| |lazyPseudoDivide| |reverseLex| + |selectMultiDimensionalRoutines| |headAst| |horizConcat| |max| + |cycleRagits| |integralDerivationMatrix| |integers| + |getSyntaxFormsFromFile| |getGraph| |indiceSubResultant| + |sizeMultiplication| |iExquo| |complexLimit| |commutativeEquality| + |isExpt| |charClass| |semicolonSeparate| |nary?| |noLinearFactor?| + |sPol| |fortranLiteralLine| |expintegrate| |zCoord| |dihedral| + |createThreeSpace| |critMonD1| |palgextint| |OMlistSymbols| + |perspective| |makeUnit| |concat!| |frst| |oddlambert| |setleaves!| + |pomopo!| |padicallyExpand| |slex| |chiSquare1| |minordet| |ipow| + |mesh?| |yCoordinates| |pointSizeDefault| |singularitiesOf| + |normalise| |callForm?| |parts| |makeop| |listOfLists| |phiCoord| * + |antiAssociative?| |argumentList!| |idealSimplify| |mainMonomial| + |rotatex| |invmultisect| |elliptic| |cyclicEntries| |f01qcf| + |OMopenFile| |useSingleFactorBound| |iidprod| |basisOfCenter| + |uniform| |structuralConstants| |viewPhiDefault| |properties| + |leftUnit| |optimize| |superscript| |leftNorm| |viewDefaults| + |unravel| |cCosh| |resetAttributeButtons| |f02adf| |iisec| |mathieu11| + |translate| |high| |truncate| |raisePolynomial| |sign| = |typeLists| + |rightRank| |redPo| |evaluate| |bezoutDiscriminant| |modifyPoint| + |binaryFunction| |enqueue!| |print| |reducedQPowers| |s15aef| |times!| + |startTableInvSet!| |rightDivide| |cscIfCan| |selectODEIVPRoutines| + |transpose| |edf2ef| |operation| |resolve| |constantCoefficientRicDE| + |myDegree| |getOrder| < |csc2sin| LODO2FUN |isAnd| |symmetricTensors| + |OMputInteger| |stronglyReduce| |sort!| |e02bcf| |mapUp!| |create| + |e02dcf| > |reducedSystem| |s19acf| |crushedSet| |morphism| + |quadraticNorm| |f01ref| |collectUnder| |iicos| |hitherPlane| <= + |showArrayValues| |reify| |insertTop!| |nullSpace| |cExp| |ScanArabic| + |shiftRoots| |splitDenominator| |bandedHessian| |monicDivide| |po| >= + |inverseIntegralMatrix| |reduceBasisAtInfinity| + |indicialEquationAtInfinity| |imagJ| |digit| |iiatanh| + |deleteProperty!| |swapColumns!| |unary?| |curryRight| + |setTopPredicate| |clearTable!| |updatF| |dimensions| |getConstant| + |monomialIntegrate| |exprHasLogarithmicWeights| |fortranDoubleComplex| + |badNum| |readLine!| |leftTraceMatrix| |returnType!| |dual| + |endOfFile?| |multiplyExponents| |generalizedEigenvectors| |testDim| + |interpret| |unitNormalize| |OMgetString| |rootNormalize| + |bombieriNorm| |rationalFunction| + |limitPlus| |rischNormalize| + |hyperelliptic| |diophantineSystem| |f02fjf| |true| + |leadingCoefficientRicDE| |inGroundField?| |totolex| + |OMsupportsSymbol?| |rootProduct| - |leftRank| |cn| |s14aaf| + |deleteRoutine!| |contract| |cos2sec| |showFortranOutputStack| + |complex?| |sumOfDivisors| |mantissa| / |e01bgf| |interactiveEnv| + |complexElementary| |unit?| |dot| |column| |failed?| + |semiDiscriminantEuclidean| |OMgetEndAttr| |numberOfComponents| + |selectIntegrationRoutines| UTS2UP |alphabetic?| |listYoungTableaus| + |symmetricPower| |meatAxe| |category| |lllp| |alternating| + |factorFraction| |divisorCascade| |nil| |pushNewContour| + |discriminant| |cTan| |iiGamma| |printInfo!| |spherical| |front| + |domain| |randomLC| |genericLeftNorm| |iilog| |qualifier| |wreath| + |OMputEndAttr| |weights| |isList| |permutation| |package| |someBasis| + |exteriorDifferential| |inf| |fixedPoint| |fortranLiteral| |yCoord| + |acotIfCan| |subQuasiComponent?| |shift| + |removeIrreducibleRedundantFactors| |recip| |genericLeftTrace| + |d02cjf| |LazardQuotient2| |unrankImproperPartitions0| |approximate| + |d01amf| |imports| |s13adf| |createGenericMatrix| |changeMeasure| + |palglimint0| |palgint| |exprHasWeightCosWXorSinWX| |writable?| + |complex| |btwFact| |unmakeSUP| |over| |varList| |bezoutMatrix| + |rightZero| |unitsColorDefault| |dmp2rfi| |clearDenominator| + |whatInfinity| |collect| |basisOfNucleus| |lookupFunction| |rst| + |ricDsolve| |delta| |show| |ksec| |aQuartic| |getMultiplicationTable| + |identification| |bivariate?| |thetaCoord| |property| |ddFact| + |iidsum| |makeSin| |unaryFunction| |var2Steps| |patternMatch| + |graphImage| |lex| |complexEigenvalues| |ref| |drawCurves| + |domainTemplate| |setFormula!| |ratDsolve| |trace| |extension| + |denomRicDE| |nor| |computePowers| |f01mcf| |viewSizeDefault| + |trace2PowMod| |style| |LyndonWordsList| |retract| |sup| |leader| + |leastAffineMultiple| |padicFraction| |argscript| |rightNorm| |units| + |inHallBasis?| |typeForm| |fixedPoints| |ldf2lst| |empty?| + |OMputEndObject| |currentCategoryFrame| |sech2cosh| |extend| + |selectOrPolynomials| |color| |square?| |solveLinear| |readByte!| + |f02abf| |isobaric?| |contours| |copy!| |polyred| |complexZeros| + |linearlyDependent?| |symbol?| |formula| |denominator| |vertConcat| + |algebraicVariables| |binomThmExpt| |indicialEquation| |OMsend| + |rightQuotient| |rootOfIrreduciblePoly| |monicModulo| |upperCase?| + |insertMatch| |lambda| |epilogue| |zerosOf| |nextPrimitiveNormalPoly| + |mapGen| |subTriSet?| |ideal| |dark| |basisOfLeftNucleus| |dmpToHdmp| + |localReal?| |primintegrate| |cylindrical| |strongGenerators| + |principalAncestors| |rightUnit| |every?| |code| |singRicDE| + |positiveRemainder| |nilFactor| |interpolate| |point?| |changeName| + |bsolve| |shuffle| |solve| |printCode| |Lazard2| + |selectOptimizationRoutines| |categoryFrame| |LyndonBasis| + |normalizeIfCan| |nrows| |singleFactorBound| |viewZoomDefault| + |datalist| |reopen!| |presuper| |fractionPart| |numberOfVariables| + |expt| |gbasis| |pade| |ncols| |leastMonomial| |build| |repeating| + |rdregime| |tableau| |determinant| |readLineIfCan!| |approximants| + |plus| |brillhartTrials| |exptMod| |whitePoint| |bezoutResultant| + |HermiteIntegrate| |bits| |critMTonD1| |validExponential| |curryLeft| + |useSingleFactorBound?| |maxIndex| |completeSmith| |parent| + |setColumn!| |cross| |dom| |duplicates| |e01sbf| |mapDown!| + |writeLine!| |OMwrite| |binarySearchTree| |solve1| |createNormalPoly| + |perfectSqrt| |isAbsolutelyIrreducible?| |sum| |goodPoint| |f01rdf| + |OMgetEndAtp| |permutationRepresentation| |cup| |polynomial| + |partialDenominators| |stopTableGcd!| |readInt32!| + |showTheRoutinesTable| |point| |changeWeightLevel| |f01rcf| + |selectSumOfSquaresRoutines| |coefChoose| |setOrder| |newTypeLists| + |times| |createRandomElement| |useEisensteinCriterion| + |leftFactorIfCan| |interval| |cLog| |iiexp| |ldf2vmf| |OMputEndError| + |OMgetEndBind| |symbolTable| |delete!| |expintfldpoly| |c06frf| + |sturmVariationsOf| |roughBasicSet| + |dimensionOfIrreducibleRepresentation| |OMgetEndApp| |neglist| + |BasicMethod| |top| |lyndon| |setsubMatrix!| |ran| + |setScreenResolution3D| |semiResultantEuclidean1| |lp| |singular?| + |systemCommand| |rightRankPolynomial| |normFactors| + |nextLatticePermutation| |transcendenceDegree| |series| |arity| + |droot| |pushFortranOutputStack| |complement| |c05adf| + |squareFreeFactors| |tryFunctionalDecomposition| |title| |comp| + |graphCurves| |eulerPhi| |prime| |OMputEndAtp| |rischDEsys| |iiacosh| + |leftTrace| |popFortranOutputStack| |complexEigenvectors| |cCsc| + |s17aef| |beauzamyBound| |jacobi| |resultant| |node| |monom| + |baseRDEsys| |options| |laplace| |viewpoint| |f07fdf| |inR?| + |continue| |fortranCharacter| |f02agf| |sort| |getRef| |f07aef| + |OMsupportsCD?| |outputAsFortran| |makeCrit| |normal| |cycles| + |numberOfMonomials| |BumInSepFFE| |hex| |dihedralGroup| |escape| + |OMgetFloat| |mvar| |e| |lagrange| |topPredicate| |ratPoly| + |rationalIfCan| |var1Steps| |leadingTerm| |min| |collectUpper| |list| + |e02bbf| |outputBinaryFile| |univcase| |factorSquareFree| |diagonal?| + |common| |makeVariable| |string| |leftDivide| |secIfCan| |rotatey| + |expandLog| |car| |halfExtendedSubResultantGcd2| |hermite| + |doubleComplex?| |currentScope| |rightTraceMatrix| |prevPrime| + |OMgetApp| |ode1| |generalizedEigenvector| |pseudoQuotient| |random| + |cdr| |inRadical?| |stoseInternalLastSubResultant| |graeffe| + |squareFreePrim| |lfunc| |karatsubaOnce| |sparsityIF| + |genericRightDiscriminant| |bandedJacobian| |back| |setDifference| + |scalarMatrix| |magnitude| |signAround| |contains?| |bag| + |removeCosSq| |copies| |subResultantsChain| |dmpToP| + |discriminantEuclidean| |setIntersection| |irVar| |areEquivalent?| + |bitCoef| |cAsinh| |constantKernel| |latex| |withPredicates| + |initTable!| |symmetricProduct| |lazyIrreducibleFactors| |setUnion| + |OMgetVariable| |refine| |putProperty| |s20acf| |coth2trigh| + |internalAugment| |setLength!| |OMconnOutDevice| |palgextint0| + |d02bhf| |apply| |doubleFloatFormat| |bounds| + |cyclotomicFactorization| |multiple?| |separateDegrees| |littleEndian| + |iiacot| |rewriteIdealWithHeadRemainder| |doubleDisc| |polygon| + |overset?| |polygon?| |top!| |floor| |solveLinearPolynomialEquation| + |zero| |coerceL| |numberOfHues| |mainForm| |f02bjf| |OMreceive| |size| + |schwerpunkt| |viewDeltaXDefault| |conjugate| |divideIfCan| |d01alf| + |numeric| |colorFunction| |e02agf| |exists?| |toseLastSubResultant| + |s17adf| |width| |knownInfBasis| |lyndonIfCan| |applyRules| + |hasPredicate?| |revert| |radical| |And| |zeroSquareMatrix| |basicSet| + |binary| |rightExtendedGcd| |equation| |buildSyntax| |powmod| + |precision| |conjugates| |wordInStrongGenerators| |roughUnitIdeal?| + |vector| |slash| |Or| |checkRur| |primPartElseUnitCanonical!| + |complexNormalize| |elliptic?| |primaryDecomp| |normalizedDivide| + |first| |pseudoDivide| |light| |rur| |differentiate| |pr2dmp| |Not| + |aromberg| |factorList| |nthFactor| |kmax| |removeSinhSq| |rest| + |factorAndSplit| |tValues| |subResultantGcdEuclidean| + |toseSquareFreePart| |elRow2!| |rename!| |elaborate| + |computeCycleLength| |squareFreePolynomial| |realEigenvalues| + |subResultantChain| |substitute| |doublyTransitive?| |poisson| + |isTerm| |cschIfCan| |tubePoints| |branchIfCan| |accuracyIF| + |fortranDouble| |d01apf| |hash| |outputForm| |interpretString| + |removeDuplicates| |iiasinh| |logIfCan| |block| + |lastSubResultantEuclidean| |clearFortranOutputStack| |comparison| + |integral?| |physicalLength| |oddInfiniteProduct| |count| |chiSquare| + |complementaryBasis| |d01gaf| |stFunc1| |mr| |subNodeOf?| + |fullDisplay| |lflimitedint| |Ei| |super| |mindegTerm| |f01qef| |name| + |optional| |partition| |forLoop| |totalfract| |gcdprim| |integrate| + |e04mbf| |derivative| |euclideanNormalForm| |twist| |typeList| |lift| + |body| |tan2cot| |coleman| |outputAsTex| |systemSizeIF| |e02daf| + |extractBottom!| |inc| |associatedEquations| |closed| |deepestTail| + |generalTwoFactor| |reduce| |moreAlgebraic?| |aCubic| |setClipValue| + |c02agf| |scopes| |reduceByQuasiMonic| |integer?| + |shanksDiscLogAlgorithm| |stoseInvertible?reg| |explogs2trigs| + |sts2stst| |universe| |leftExtendedGcd| |satisfy?| |binomial| |xn| + |localIntegralBasis| |setPoly| |critM| |exponents| |factorsOfDegree| + |nextSublist| |makeprod| |central?| |supRittWu?| |d01bbf| |implies| + |s13aaf| |conical| |position!| |just| |increasePrecision| + |mapUnivariateIfCan| |removeConstantTerm| |makeViewport2D| |internal?| + |empty| |unitVector| |acscIfCan| |sqfree| |solveRetract| + |denominators| |fixPredicate| |f04jgf| |fortranCompilerName| + |medialSet| SEGMENT |rationalPower| |error| |innerSolve| + |antiCommutative?| |powern| |stopMusserTrials| |atoms| |port| + |linearPolynomials| |LyndonCoordinates| |any| |whileLoop| |palgint0| + |mappingMode| |qqq| |assert| |leftQuotient| |tower| |e04ycf| + |cyclotomic| |upperBound| |graphState| |setImagSteps| + |wronskianMatrix| |recolor| |imagj| |plotPolar| |startTableGcd!| + |leftDiscriminant| |semiResultantReduitEuclidean| |t| + |variationOfParameters| |vectorise| |constantToUnaryFunction| + |cyclicParents| |stopTable!| |child| |countRealRoots| |elaborateFile| + |list?| |intensity| |diagonalMatrix| |clearTheSymbolTable| + |createZechTable| GF2FG |loadNativeModule| |logGamma| + |nextIrreduciblePoly| |readUInt8!| |expenseOfEvaluationIF| + |numberOfCycles| |setref| |setProperties| |mightHaveRoots| |push| + |primeFrobenius| |mindeg| |jordanAdmissible?| |homogeneous?| |randnum| + |basisOfCommutingElements| |solveLinearlyOverQ| |rightRemainder| + |constant| |limitedIntegrate| |nextColeman| |positive?| + |complexNumeric| |lquo| |tableForDiscreteLogarithm| |newReduc| + |ListOfTerms| |e01sff| |subHeight| |standardBasisOfCyclicSubmodule| + |octon| |totalDegree| |curve?| |byte| |ranges| |palgintegrate| + |predicate| |nthr| |numberOfImproperPartitions| |simpson| + |outputAsScript| |readBytes!| |iiperm| |null?| |integerBound| + |kernels| |iteratedInitials| |s18aef| |tab| |LiePolyIfCan| |isMult| + |nthRoot| |range| |linears| |redPol| |operator| + |mainDefiningPolynomial| |cons| |flexible?| |maxrow| + |normalizeAtInfinity| |repSq| |factorset| |isEquiv| |toroidal| + |perfectSquare?| |integralLastSubResultant| |rootRadius| |prinpolINFO| + |algebraicDecompose| |step| |mdeg| |computeInt| |squareFree| |s18def| + |weight| |univariate| |leftLcm| |regime| |module| |isOpen?| |mapSolve| + |wordInGenerators| |comment| |linearAssociatedOrder| |qelt| |nlde| + |iiatan| |monicRightDivide| |rootPoly| |getBadValues| + |pointColorPalette| |gethi| |extractClosed| |qsetelt| |ef2edf| |lepol| + |adaptive| |aspFilename| |eq?| |lexTriangular| |linear| + |createPrimitiveNormalPoly| |getCurve| |inputBinaryFile| |coerce| + |sturmSequence| |xRange| |leastPower| |factor| |leviCivitaSymbol| + |physicalLength!| |df2mf| |key?| |int| |reducedContinuedFraction| + |e01saf| |stiffnessAndStabilityOfODEIF| |construct| |operators| + |ramified?| |yRange| |sqrt| |factorPolynomial| |source| |tanNa| + |multiEuclidean| |separate| |c06ekf| |d01asf| |associative?| |zRange| + |lineColorDefault| |real| |omError| |parameters| |sinh2csch| |f02bbf| + |norm| |rootKerSimp| |functionIsFracPolynomial?| |normalize| |content| + |map!| |f04adf| |imag| |showRegion| |clipWithRanges| |patternVariable| + |selectfirst| |algebraicSort| |findConstructor| |listexp| |B1solve| + |length| |qsetelt!| |simpsono| |directProduct| |subspace| + |rightDiscriminant| F2FG |localAbs| |cothIfCan| |nthExponent| + |solveInField| |fortranTypeOf| |scripts| |permanent| + |minimalPolynomial| |loopPoints| |varselect| |updateStatus!| + |viewDeltaYDefault| |cAcosh| |f04faf| |assign| |solveid| |brace| + |cotIfCan| |target| |cfirst| |ptree| |calcRanges| |removeCoshSq| + |completeHensel| |makeSeries| |weierstrass| |closedCurve| + |outputGeneral| |fortranCarriageReturn| |destruct| |power!| |s17ahf| + |decreasePrecision| |nextItem| |e02baf| |hcrf| |complexExpand| + |symmetricRemainder| |fortranInteger| |irreducibleRepresentation| + |generalizedInverse| |separateFactors| |insert!| |graphStates| |kind| + |parseString| |integral| |semiDegreeSubResultantEuclidean| |rename| + |adaptive?| |chebyshevU| |replace| |radPoly| |cAsin| |op| + |stosePrepareSubResAlgo| |matrixGcd| |OMgetAttr| |rombergo| + |solveLinearPolynomialEquationByRecursion| |lfextendedint| |e04ucf| + |size?| |aQuadratic| |clipBoolean| |subscriptedVariables| + |mergeFactors| |appendPoint| |parametric?| |ravel| |primlimitedint| + |monomial| |OMread| |colorDef| |genus| |romberg| |UpTriBddDenomInv| + |primlimintfrac| |genericLeftDiscriminant| |prod| |e04jaf| + |sumSquares| |explicitEntries?| |reshape| |string?| |expandPower| + |quoByVar| |arguments| |lazyPseudoRemainder| |pToHdmp| |sechIfCan| + |setelt| |sylvesterSequence| |iitanh| |zag| |froot| |solid?| + |linearDependenceOverZ| |iicsch| |queue| |atom?| |float?| + |LagrangeInterpolation| |radix| |taylorIfCan| |nextNormalPoly| + |superHeight| |fglmIfCan| |rk4a| |composites| |copy| + |integralBasisAtInfinity| |extendedEuclidean| |totalDifferential| + |cyclic?| |alternative?| |linear?| |union| |stoseSquareFreePart| + |ignore?| |acosIfCan| |Vectorise| |bringDown| |gcdPrimitive| + |musserTrials| |digamma| |rank| |tab1| |sumOfSquares| |numFunEvals| + |check| |tube| |reciprocalPolynomial| |getDatabase| |isConnected?| + |routines| |midpoint| |update| |getProperty| |f02axf| + |rightExactQuotient| |autoCoerce| |semiResultantEuclidean2| + |asecIfCan| |permutations| |exactQuotient| |writeByte!| + |newSubProgram| |selectsecond| |children| |integralBasis| + |subresultantVector| |e02dff| |iflist2Result| |youngGroup| |quotient| + |definingEquations| |moduleSum| |makeMulti| |lifting| |s18dcf| + |s17dgf| |countRealRootsMultiple| |resetNew| |biRank| + |drawComplexVectorField| |fTable| |torsion?| |expressIdealMember| + |SturmHabicht| |PollardSmallFactor| |recur| |even?| |goto| |readable?| + |removeRedundantFactorsInPols| |showAll?| |laurentRep| |digit?| + |halfExtendedResultant2| |dflist| |univariatePolynomialsGcds| + |factorOfDegree| |RemainderList| |position| |power| + |explicitlyFinite?| |collectQuasiMonic| |univariateSolve| |constant?| + |SFunction| |splitSquarefree| |row| |match?| |headReduced?| |lists| + |OMgetError| |rdHack1| |branchPoint?| |addiag| |belong?| |f04mcf| + |exQuo| |ScanFloatIgnoreSpacesIfCan| |fprindINFO| |OMsetEncoding| + |seriesSolve| |leftRecip| |real?| |definingPolynomial| |cSech| + |createLowComplexityTable| |palgLODE| |iomode| |OMUnknownSymbol?| + |cAcoth| |basisOfRightNucloid| |s17dcf| |constantOpIfCan| |UP2ifCan| + |f02ajf| |c06eaf| |moduloP| |declare| |optpair| |atrapezoidal| + |checkForZero| |fracPart| |GospersMethod| |elColumn2!| |Nul| + |transcendentalDecompose| |generalizedContinuumHypothesisAssumed| + |rowEchLocal| |setMaxPoints| |pmintegrate| |infieldIntegrate| + |cot2trig| |LowTriBddDenomInv| |expint| |scale| |minimize| + |constDsolve| |powerAssociative?| |divergence| |f04maf| |setStatus!| + |besselI| |socf2socdf| |resultantReduitEuclidean| |divisor| + |setMinPoints3D| |arg1| |extractIfCan| |uniform01| |monic?| |f2df| + |subSet| |createNormalElement| |restorePrecision| |log2| |qPot| + |setPosition| |iibinom| |arg2| |f01bsf| |sech| |linearAssociatedLog| + |resultantnaif| |ellipticCylindrical| |rectangularMatrix| |voidMode| + |rightLcm| |bindings| |pdct| |edf2df| |csch| |OMmakeConn| |reorder| + |usingTable?| |retractable?| |close| |irDef| |symmetricSquare| + |rightCharacteristicPolynomial| |cAcsc| |conditions| |shellSort| + |asinh| |iterationVar| |cycleSplit!| |zero?| |deriv| |coord| |e04dgf| + |sizePascalTriangle| |match| |rewriteSetWithReduction| |groebgen| + |acosh| |pointColorDefault| |stop| |identityMatrix| |f04asf| |lllip| + |OMputBVar| |display| |algebraicCoefficients?| |bright| |atanh| + |tanhIfCan| |vconcat| |besselJ| |complexSolve| |acoshIfCan| + |leftMinimalPolynomial| |removeSquaresIfCan| |c06gqf| + |makeYoungTableau| |li| |getProperties| |lazyGintegrate| |extendedint| + |acoth| |mathieu22| |quadratic| |modularGcdPrimitive| |subset?| |pow| + |OMgetEndObject| |s18acf| |asech| |certainlySubVariety?| + |quasiMonicPolynomials| |deepExpand| |safeFloor| |sqfrFactor| + |algintegrate| |coordinate| |getVariableOrder| |makeFR| |laguerreL| + |llprop| |numberOfNormalPoly| |changeThreshhold| |numFunEvals3D| + |merge| |entries| |pquo| |multiple| |OMReadError?| |mainContent| + |move| |cPower| |highCommonTerms| |input| |taylorQuoByVar| |upperCase| + |e01sef| |closeComponent| |tubePlot| |box| |currentSubProgram| + |applyQuote| |groebnerFactorize| |setAttributeButtonStep| + |factorsOfCyclicGroupSize| |generic| |bytes| |library| |s21bcf| + |infinite?| |setVariableOrder| |genericRightNorm| |karatsubaDivide| + |inverseLaplace| |arrayStack| |LiePoly| |evenlambert| |randomR| + |wholeRadix| |parabolic| |createPrimitiveElement| |push!| |iiasech| + |reflect| |uncouplingMatrices| |d02raf| |eigenMatrix| |minRowIndex| + |elem?| |pushdown| |ruleset| |probablyZeroDim?| |mainCharacterization| + |integralMatrix| |pack!| |ParCondList| |isTimes| |elements| |exp1| + |OMlistCDs| |less?| |f02xef| |OMgetType| |set| |unvectorise| |cyclic| + |nthRootIfCan| |simplifyLog| |iisinh| |OMbindTCP| |cCot| |totalLex| + |test| |id| |hostPlatform| |algebraic?| |presub| |var2StepsDefault| + |integralMatrixAtInfinity| |airyBi| |suchThat| + |lastSubResultantElseSplit| |leftRemainder| |integralCoordinates| + |isOr| |algSplitSimple| |child?| |setelt!| |integerIfCan| + |coercePreimagesImages| |linearDependence| |rightMult| |c06fpf| + |table| |pile| |semiIndiceSubResultantEuclidean| |plus!| + |permutationGroup| |logpart| |bumptab| |sylvesterMatrix| |dequeue!| + |subst| |pdf2df| |insert| |s19abf| |new| |intChoose| + |stoseIntegralLastSubResultant| |mapdiv| |obj| |meshPar1Var| + |getGoodPrime| |leftAlternative?| |mapExpon| |nthFractionalTerm| + |imagK| |plenaryPower| |eq| |prefix| |screenResolution| |cache| + |delay| |points| |changeBase| |insertBottom!| |iter| |evaluateInverse| + |cycleEntry| |rotate| |jacobiIdentity?| |innerint| |OMputEndApp| + |Aleph| |delete| |subresultantSequence| |squareMatrix| |signature| + |removeRedundantFactorsInContents| |double?| |cAcot| |palgLODE0| + |paraboloidal| |quotientByP| |variable?| |degree| |constantOperator| + |makeSketch| |completeEchelonBasis| |untab| |quadratic?| + |clipPointsDefault| |mapmult| |groebSolve| |headReduce| + |clearTheFTable| |lfextlimint| |diag| |radicalSimplify| |radicalRoots| + |objects| |unitCanonical| |cyclicCopy| |FormatArabic| |relativeApprox| + |acothIfCan| |factors| |directory| |rightScalarTimes!| |base| |script| + |transform| |solveLinearPolynomialEquationByFractions| |direction| + |closed?| |number?| |curry| |totalGroebner| |c06fqf| |OMputVariable| + |extractTop!| |rightMinimalPolynomial| |simpleBounds?| + |commonDenominator| |sortConstraints| |rightRecip| |laurentIfCan| + |retractIfCan| |monomRDEsys| |coefficient| |linearAssociatedExp| + |c05pbf| |iicot| |flatten| |selectFiniteRoutines| |exp| |f02awf| + |leftUnits| |deref| |legendre| |nullary| |tex| |ocf2ocdf| + |integralRepresents| |left| |numer| |outputFloating| + |basisOfLeftNucloid| |heapSort| |asinhIfCan| |setTex!| |flagFactor| + |/\\| |s15adf| |tanh2trigh| |OMgetEndError| |right| |outputList| + |denom| |s17dlf| |pmComplexintegrate| |asinIfCan| |setright!| + |listBranches| |irForm| |\\/| |dimensionsOf| |lazyPrem| |invertible?| + |errorKind| |representationType| |setLegalFortranSourceExtensions| + |minIndex| |sample| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 45739c74..377029a4 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5369 +1,5377 @@ -(3226997 . 3479296411) -((-2031 (((-112) (-1 (-112) |#2| |#2|) $) 87) (((-112) $) NIL)) (-3012 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3940 ((|#2| $ (-569) |#2|) NIL) ((|#2| $ (-1240 (-569)) |#2|) 44)) (-4380 (($ $) 81)) (-3596 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 52) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 50) ((|#2| (-1 |#2| |#2| |#2|) $) 49)) (-4034 (((-569) (-1 (-112) |#2|) $) 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are infinite") (|:| |notEvaluated| "Range not yet evaluated"))) (-5 *1 (-193))))) +(-10 -7 (-15 -2205 ((-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")) (-2 (|:| |var| (-1185)) (|:| |fn| (-319 (-226))) (|:| -3743 (-1102 (-848 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))) (-15 -2582 ((-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")) (-2 (|:| |var| (-1185)) (|:| |fn| (-319 (-226))) (|:| -3743 (-1102 (-848 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226))))) (-15 -2278 ((-226) (-1102 (-848 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T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #0=(-412 (-569))) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-621 (-569)) -2774 (|has| |#2| (-1055)) (-12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -2774 (|has| |#2| (-1106)) (|has| |#2| (-173))) ((-618 (-867)) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-867))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1273 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1055)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1055))) ((-289 #1=(-569) |#2|) . T) ((-291 #1# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1055)) ((-416 |#2|) |has| |#2| (-1106)) ((-494 |#2|) . T) ((-609 #1# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1106))) ((-651 (-569)) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -2774 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-569)) -12 (|has| |#2| (-644 (-569))) (|has| |#2| (-1055))) ((-644 |#2|) |has| |#2| (-1055)) ((-722 |#2|) -2774 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-800) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -2774 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1183)) -12 (|has| |#2| (-906 (-1183))) (|has| |#2| (-1055))) ((-1044 #0#) -12 (|has| |#2| (-1044 (-412 (-569)))) (|has| |#2| (-1106))) ((-1044 (-569)) -12 (|has| |#2| (-1044 (-569))) (|has| |#2| (-1106))) ((-1044 |#2|) |has| |#2| (-1106)) ((-1057 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1057 $) |has| |#2| (-173)) ((-1062 |#2|) -2774 (|has| |#2| (-1055)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1062 $) |has| |#2| (-173)) ((-1055) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1064) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1118) -2774 (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1106) -2774 (|has| |#2| (-1106)) (|has| |#2| (-1055)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1223) . T) ((-1280 |#2|) |has| |#2| (-367))) -((-4085 (((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 21)) (-3596 ((|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 23)) (-1344 (((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)) 18))) -(((-240 |#1| |#2| |#3|) (-10 -7 (-15 -4085 ((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -3596 (|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -1344 ((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)))) (-776) (-1223) (-1223)) (T -240)) -((-1344 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1223)) (-4 *7 (-1223)) (-5 *2 (-241 *5 *7)) (-5 *1 (-240 *5 *6 *7)))) (-3596 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1223)) (-4 *2 (-1223)) (-5 *1 (-240 *5 *6 *2)))) (-4085 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-241 *6 *7)) (-14 *6 (-776)) (-4 *7 (-1223)) (-4 *5 (-1223)) (-5 *2 (-241 *6 *5)) (-5 *1 (-240 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-173)) ((-102) -2776 (|has| |#2| (-1108)) (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2776 (|has| |#2| (-1057)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-111 $ $) |has| |#2| (-173)) ((-131) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131))) ((-621 #0=(-412 (-569))) -12 (|has| |#2| (-1046 (-412 (-569)))) (|has| |#2| (-1108))) ((-621 (-569)) -2776 (|has| |#2| (-1057)) (-12 (|has| |#2| (-1046 (-569))) (|has| |#2| (-1108))) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-621 |#2|) -2776 (|has| |#2| (-1108)) (|has| |#2| (-173))) ((-618 (-867)) -2776 (|has| |#2| (-1108)) (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-618 (-867))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-618 (-1275 |#2|)) . T) ((-173) |has| |#2| (-173)) ((-232 |#2|) |has| |#2| (-1057)) ((-234) -12 (|has| |#2| (-234)) (|has| |#2| (-1057))) ((-289 #1=(-569) |#2|) . T) ((-291 #1# |#2|) . T) ((-312 |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1108))) ((-372) |has| |#2| (-372)) ((-381 |#2|) |has| |#2| (-1057)) ((-416 |#2|) |has| |#2| (-1108)) ((-494 |#2|) . T) ((-609 #1# |#2|) . T) ((-519 |#2| |#2|) -12 (|has| |#2| (-312 |#2|)) (|has| |#2| (-1108))) ((-651 (-569)) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 |#2|) -2776 (|has| |#2| (-1057)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-651 $) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-653 |#2|) -2776 (|has| |#2| (-1057)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-653 $) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-645 |#2|) -2776 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-644 (-569)) -12 (|has| |#2| (-644 (-569))) (|has| |#2| (-1057))) ((-644 |#2|) |has| |#2| (-1057)) ((-722 |#2|) -2776 (|has| |#2| (-367)) (|has| |#2| (-173))) ((-731) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-796) |has| |#2| (-853)) ((-797) -2776 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-798) |has| |#2| (-798)) ((-799) -2776 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-800) -2776 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-853) |has| |#2| (-853)) ((-855) -2776 (|has| |#2| (-853)) (|has| |#2| (-798))) ((-906 (-1185)) -12 (|has| |#2| (-906 (-1185))) (|has| |#2| (-1057))) ((-1046 #0#) -12 (|has| |#2| (-1046 (-412 (-569)))) (|has| |#2| (-1108))) ((-1046 (-569)) -12 (|has| |#2| (-1046 (-569))) (|has| |#2| (-1108))) ((-1046 |#2|) |has| |#2| (-1108)) ((-1059 |#2|) -2776 (|has| |#2| (-1057)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1059 $) |has| |#2| (-173)) ((-1064 |#2|) -2776 (|has| |#2| (-1057)) (|has| |#2| (-367)) (|has| |#2| (-173))) ((-1064 $) |has| |#2| (-173)) ((-1057) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1066) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-173))) ((-1120) -2776 (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-731)) (|has| |#2| (-173))) ((-1108) -2776 (|has| |#2| (-1108)) (|has| |#2| (-1057)) (|has| |#2| (-853)) (|has| |#2| (-798)) (|has| |#2| (-731)) (|has| |#2| (-372)) (|has| |#2| (-367)) (|has| |#2| (-173)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1225) . T) ((-1282 |#2|) |has| |#2| (-367))) +((-1610 (((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 21)) (-3598 ((|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|) 23)) (-1346 (((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)) 18))) +(((-240 |#1| |#2| |#3|) (-10 -7 (-15 -1610 ((-241 |#1| |#3|) (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -3598 (|#3| (-1 |#3| |#2| |#3|) (-241 |#1| |#2|) |#3|)) (-15 -1346 ((-241 |#1| |#3|) (-1 |#3| |#2|) (-241 |#1| |#2|)))) (-776) (-1225) (-1225)) (T -240)) +((-1346 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1225)) (-4 *7 (-1225)) (-5 *2 (-241 *5 *7)) (-5 *1 (-240 *5 *6 *7)))) (-3598 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-241 *5 *6)) (-14 *5 (-776)) (-4 *6 (-1225)) (-4 *2 (-1225)) (-5 *1 (-240 *5 *6 *2)))) (-1610 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-241 *6 *7)) (-14 *6 (-776)) (-4 *7 (-1225)) (-4 *5 (-1225)) (-5 *2 (-241 *6 *5)) (-5 *1 (-240 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-412 (-569))) -2776 (|has| |#1| (-353)) (|has| |#1| (-367))) ((-38 |#1|) . T) ((-38 $) -2776 (|has| |#1| (-353)) (|has| |#1| (-367))) ((-102) . T) ((-111 #0# #0#) -2776 (|has| |#1| (-353)) (|has| |#1| (-367))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2776 (|has| |#1| (-353)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-621 #0#) -2776 (|has| |#1| (-1046 (-412 (-569)))) (|has| |#1| (-353)) (|has| |#1| (-367))) ((-621 (-569)) . T) ((-621 |#1|) . T) ((-621 $) -2776 (|has| |#1| (-353)) (|has| |#1| (-367))) ((-618 (-867)) . T) ((-173) . T) ((-619 |#2|) . 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T) ((-23) . T) ((-47 |#1| #0=(-569)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-569)))) ((-95) |has| |#1| (-38 (-412 (-569)))) ((-102) . T) ((-111 #1# #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -2774 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2774 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1183)) -12 (|has| |#1| (-367)) (|has| |#2| (-1044 (-1183)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-644 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-569)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #1#) -2774 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -2774 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-731) . 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"SUPFRACF" 2818476 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1177 2817388 2817447 2817560 "SUP2" 2817702 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1176 2815836 2816110 2816466 "SUMRF" 2817087 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1175 2815171 2815237 2815429 "SUMFS" 2815757 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1174 2799138 2814348 2814599 "SULS" 2814978 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1173 2798740 2798960 2799030 "SUCHTAST" 2799090 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1172 2798035 2798265 2798405 "SUCH" 2798648 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1171 2791901 2792941 2793900 "SUBSPACE" 2797123 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1170 2791331 2791421 2791585 "SUBRESP" 2791789 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1169 2784697 2785996 2787307 "STTF" 2790067 NIL STTF (NIL T) -7 NIL NIL NIL) (-1168 2778870 2779990 2781137 "STTFNC" 2783597 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1167 2770181 2772052 2773846 "STTAYLOR" 2777111 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1166 2763311 2770045 2770128 "STRTBL" 2770133 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1165 2758675 2763266 2763297 "STRING" 2763302 T STRING (NIL) -8 NIL NIL NIL) (-1164 2753536 2758048 2758078 "STRICAT" 2758137 T STRICAT (NIL) -9 NIL 2758199 NIL) (-1163 2746289 2751155 2751766 "STREAM" 2752960 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1162 2745799 2745876 2746020 "STREAM3" 2746206 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1161 2744781 2744964 2745199 "STREAM2" 2745612 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1160 2744469 2744521 2744614 "STREAM1" 2744723 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1159 2743485 2743666 2743897 "STINPROD" 2744285 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1158 2743037 2743247 2743277 "STEP" 2743357 T STEP (NIL) -9 NIL 2743435 NIL) (-1157 2742224 2742526 2742674 "STEPAST" 2742911 T STEPAST (NIL) -8 NIL NIL NIL) (-1156 2735656 2742123 2742200 "STBL" 2742205 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1155 2730782 2734877 2734920 "STAGG" 2735073 NIL STAGG (NIL T) -9 NIL 2735162 NIL) (-1154 2728484 2729086 2729958 "STAGG-" 2729963 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1153 2726631 2728254 2728346 "STACK" 2728427 NIL STACK (NIL T) -8 NIL NIL NIL) (-1152 2719326 2724772 2725228 "SREGSET" 2726261 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1151 2711751 2713120 2714633 "SRDCMPK" 2717932 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1150 2704668 2709191 2709221 "SRAGG" 2710524 T SRAGG (NIL) -9 NIL 2711132 NIL) (-1149 2703685 2703940 2704319 "SRAGG-" 2704324 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1148 2698145 2702632 2703053 "SQMATRIX" 2703311 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1147 2691830 2694863 2695590 "SPLTREE" 2697490 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1146 2687793 2688486 2689132 "SPLNODE" 2691256 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1145 2686840 2687073 2687103 "SPFCAT" 2687547 T SPFCAT (NIL) -9 NIL NIL NIL) (-1144 2685577 2685787 2686051 "SPECOUT" 2686598 T SPECOUT (NIL) -7 NIL NIL NIL) (-1143 2676687 2678559 2678589 "SPADXPT" 2683265 T SPADXPT (NIL) -9 NIL 2685429 NIL) (-1142 2676448 2676488 2676557 "SPADPRSR" 2676640 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1141 2674497 2676403 2676434 "SPADAST" 2676439 T SPADAST (NIL) -8 NIL NIL NIL) (-1140 2666442 2668215 2668258 "SPACEC" 2672631 NIL SPACEC (NIL T) -9 NIL 2674447 NIL) (-1139 2664572 2666374 2666423 "SPACE3" 2666428 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1138 2663324 2663495 2663786 "SORTPAK" 2664377 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1137 2661416 2661719 2662131 "SOLVETRA" 2662988 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1136 2660466 2660688 2660949 "SOLVESER" 2661189 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1135 2655770 2656658 2657653 "SOLVERAD" 2659518 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1134 2651585 2652194 2652923 "SOLVEFOR" 2655137 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1133 2645855 2650934 2651031 "SNTSCAT" 2651036 NIL SNTSCAT (NIL T T T T) -9 NIL 2651106 NIL) (-1132 2639961 2644178 2644569 "SMTS" 2645545 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1131 2634646 2639849 2639926 "SMP" 2639931 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1130 2632805 2633106 2633504 "SMITH" 2634343 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1129 2625518 2629714 2629817 "SMATCAT" 2631168 NIL SMATCAT (NIL NIL T T T) -9 NIL 2631718 NIL) (-1128 2622458 2623281 2624459 "SMATCAT-" 2624464 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1127 2620124 2621694 2621737 "SKAGG" 2621998 NIL SKAGG (NIL T) -9 NIL 2622133 NIL) (-1126 2616435 2619540 2619735 "SINT" 2619922 T SINT (NIL) -8 NIL NIL 2620095) (-1125 2616207 2616245 2616311 "SIMPAN" 2616391 T SIMPAN (NIL) -7 NIL NIL NIL) (-1124 2615486 2615742 2615882 "SIG" 2616089 T SIG (NIL) -8 NIL NIL NIL) (-1123 2614324 2614545 2614820 "SIGNRF" 2615245 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1122 2613157 2613308 2613592 "SIGNEF" 2614153 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1121 2612463 2612740 2612864 "SIGAST" 2613055 T SIGAST (NIL) -8 NIL NIL NIL) (-1120 2610153 2610607 2611113 "SHP" 2612004 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1119 2604005 2610054 2610130 "SHDP" 2610135 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1118 2603578 2603770 2603800 "SGROUP" 2603893 T SGROUP (NIL) -9 NIL 2603955 NIL) (-1117 2603436 2603462 2603535 "SGROUP-" 2603540 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1116 2600271 2600969 2601692 "SGCF" 2602735 T SGCF (NIL) -7 NIL NIL NIL) (-1115 2594639 2599718 2599815 "SFRTCAT" 2599820 NIL SFRTCAT (NIL T T T T) -9 NIL 2599859 NIL) (-1114 2588060 2589078 2590214 "SFRGCD" 2593622 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1113 2581186 2582259 2583445 "SFQCMPK" 2586993 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1112 2580806 2580895 2581006 "SFORT" 2581127 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1111 2579924 2580646 2580767 "SEXOF" 2580772 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1110 2579031 2579805 2579873 "SEX" 2579878 T SEX (NIL) -8 NIL NIL NIL) (-1109 2574544 2575259 2575354 "SEXCAT" 2578291 NIL SEXCAT (NIL T T T T T) -9 NIL 2578869 NIL) (-1108 2571697 2574478 2574526 "SET" 2574531 NIL SET (NIL T) -8 NIL NIL NIL) (-1107 2569921 2570410 2570715 "SETMN" 2571438 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1106 2569417 2569569 2569599 "SETCAT" 2569775 T SETCAT (NIL) -9 NIL 2569885 NIL) (-1105 2569109 2569187 2569317 "SETCAT-" 2569322 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1104 2565470 2567570 2567613 "SETAGG" 2568483 NIL SETAGG (NIL T) -9 NIL 2568823 NIL) (-1103 2564928 2565044 2565281 "SETAGG-" 2565286 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1102 2564371 2564624 2564725 "SEQAST" 2564849 T SEQAST (NIL) -8 NIL NIL NIL) (-1101 2563570 2563864 2563925 "SEGXCAT" 2564211 NIL SEGXCAT (NIL T T) -9 NIL 2564331 NIL) (-1100 2562576 2563236 2563418 "SEG" 2563423 NIL SEG (NIL T) -8 NIL NIL NIL) (-1099 2561555 2561769 2561812 "SEGCAT" 2562334 NIL SEGCAT (NIL T) -9 NIL 2562555 NIL) (-1098 2560487 2560918 2561126 "SEGBIND" 2561382 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1097 2560108 2560167 2560280 "SEGBIND2" 2560422 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1096 2559681 2559909 2559986 "SEGAST" 2560053 T SEGAST (NIL) -8 NIL NIL NIL) (-1095 2558900 2559026 2559230 "SEG2" 2559525 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1094 2558310 2558835 2558882 "SDVAR" 2558887 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1093 2550837 2558080 2558210 "SDPOL" 2558215 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1092 2549430 2549696 2550015 "SCPKG" 2550552 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1091 2548594 2548766 2548958 "SCOPE" 2549260 T SCOPE (NIL) -8 NIL NIL NIL) (-1090 2547814 2547948 2548127 "SCACHE" 2548449 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1089 2547460 2547646 2547676 "SASTCAT" 2547681 T SASTCAT (NIL) -9 NIL 2547694 NIL) (-1088 2546947 2547295 2547371 "SAOS" 2547406 T SAOS (NIL) -8 NIL NIL NIL) (-1087 2546512 2546547 2546720 "SAERFFC" 2546906 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1086 2540451 2546409 2546489 "SAE" 2546494 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1085 2540044 2540079 2540238 "SAEFACT" 2540410 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1084 2538365 2538679 2539080 "RURPK" 2539710 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1083 2537002 2537308 2537613 "RULESET" 2538199 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1082 2534225 2534755 2535213 "RULE" 2536683 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1081 2533837 2534019 2534102 "RULECOLD" 2534177 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1080 2533627 2533655 2533726 "RTVALUE" 2533788 T RTVALUE (NIL) -8 NIL NIL NIL) (-1079 2533098 2533344 2533438 "RSTRCAST" 2533555 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1078 2527946 2528741 2529661 "RSETGCD" 2532297 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1077 2517176 2522255 2522352 "RSETCAT" 2526471 NIL RSETCAT (NIL T T T T) -9 NIL 2527568 NIL) (-1076 2515103 2515642 2516466 "RSETCAT-" 2516471 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1075 2507489 2508865 2510385 "RSDCMPK" 2513702 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1074 2505468 2505935 2506009 "RRCC" 2507095 NIL RRCC (NIL T T) -9 NIL 2507439 NIL) (-1073 2504819 2504993 2505272 "RRCC-" 2505277 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1072 2504262 2504515 2504616 "RPTAST" 2504740 T RPTAST (NIL) -8 NIL NIL NIL) (-1071 2478113 2487470 2487537 "RPOLCAT" 2498201 NIL RPOLCAT (NIL T T T) -9 NIL 2501360 NIL) (-1070 2469611 2471951 2475073 "RPOLCAT-" 2475078 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1069 2460542 2467822 2468304 "ROUTINE" 2469151 T ROUTINE (NIL) -8 NIL NIL NIL) (-1068 2457340 2460168 2460308 "ROMAN" 2460424 T ROMAN (NIL) -8 NIL NIL NIL) (-1067 2455584 2456200 2456460 "ROIRC" 2457145 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1066 2451816 2454100 2454130 "RNS" 2454434 T RNS (NIL) -9 NIL 2454708 NIL) (-1065 2450325 2450708 2451242 "RNS-" 2451317 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1064 2449728 2450136 2450166 "RNG" 2450171 T RNG (NIL) -9 NIL 2450192 NIL) (-1063 2448731 2449093 2449295 "RNGBIND" 2449579 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1062 2448130 2448518 2448561 "RMODULE" 2448566 NIL RMODULE (NIL T) -9 NIL 2448593 NIL) (-1061 2446966 2447060 2447396 "RMCAT2" 2448031 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1060 2443816 2446312 2446609 "RMATRIX" 2446728 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1059 2436643 2438903 2439018 "RMATCAT" 2442377 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2443359 NIL) (-1058 2436018 2436165 2436472 "RMATCAT-" 2436477 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1057 2435419 2435640 2435683 "RLINSET" 2435877 NIL RLINSET (NIL T) -9 NIL 2435968 NIL) (-1056 2434986 2435061 2435189 "RINTERP" 2435338 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1055 2434044 2434598 2434628 "RING" 2434684 T RING (NIL) -9 NIL 2434776 NIL) (-1054 2433836 2433880 2433977 "RING-" 2433982 NIL RING- (NIL T) -8 NIL NIL NIL) (-1053 2432677 2432914 2433172 "RIDIST" 2433600 T RIDIST (NIL) -7 NIL NIL NIL) (-1052 2423966 2432145 2432351 "RGCHAIN" 2432525 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1051 2423316 2423722 2423763 "RGBCSPC" 2423821 NIL RGBCSPC (NIL T) -9 NIL 2423873 NIL) (-1050 2422474 2422855 2422896 "RGBCMDL" 2423128 NIL RGBCMDL (NIL T) -9 NIL 2423242 NIL) (-1049 2419468 2420082 2420752 "RF" 2421838 NIL RF (NIL T) -7 NIL NIL NIL) (-1048 2419114 2419177 2419280 "RFFACTOR" 2419399 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1047 2418839 2418874 2418971 "RFFACT" 2419073 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1046 2416956 2417320 2417702 "RFDIST" 2418479 T RFDIST (NIL) -7 NIL NIL NIL) (-1045 2416409 2416501 2416664 "RETSOL" 2416858 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1044 2416045 2416125 2416168 "RETRACT" 2416301 NIL RETRACT (NIL T) -9 NIL 2416388 NIL) (-1043 2415894 2415919 2416006 "RETRACT-" 2416011 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1042 2415496 2415716 2415786 "RETAST" 2415846 T RETAST (NIL) -8 NIL NIL NIL) (-1041 2408234 2415149 2415276 "RESULT" 2415391 T RESULT (NIL) -8 NIL NIL NIL) (-1040 2406825 2407503 2407702 "RESRING" 2408137 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1039 2406461 2406510 2406608 "RESLATC" 2406762 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1038 2406166 2406201 2406308 "REPSQ" 2406420 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1037 2403588 2404168 2404770 "REP" 2405586 T REP (NIL) -7 NIL NIL NIL) (-1036 2403285 2403320 2403431 "REPDB" 2403547 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1035 2397185 2398574 2399797 "REP2" 2402097 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1034 2393562 2394243 2395051 "REP1" 2396412 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1033 2386258 2391703 2392159 "REGSET" 2393192 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1032 2385023 2385406 2385656 "REF" 2386043 NIL REF (NIL T) -8 NIL NIL NIL) (-1031 2384400 2384503 2384670 "REDORDER" 2384907 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1030 2380368 2383613 2383840 "RECLOS" 2384228 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1029 2379420 2379601 2379816 "REALSOLV" 2380175 T REALSOLV (NIL) -7 NIL NIL NIL) (-1028 2379266 2379307 2379337 "REAL" 2379342 T REAL (NIL) -9 NIL 2379377 NIL) (-1027 2375749 2376551 2377435 "REAL0Q" 2378431 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1026 2371350 2372338 2373399 "REAL0" 2374730 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1025 2370821 2371067 2371161 "RDUCEAST" 2371278 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1024 2370226 2370298 2370505 "RDIV" 2370743 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1023 2369294 2369468 2369681 "RDIST" 2370048 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1022 2367891 2368178 2368550 "RDETRS" 2369002 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1021 2365703 2366157 2366695 "RDETR" 2367433 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1020 2364328 2364606 2365003 "RDEEFS" 2365419 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1019 2362837 2363143 2363568 "RDEEF" 2364016 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1018 2356898 2359818 2359848 "RCFIELD" 2361143 T RCFIELD (NIL) -9 NIL 2361874 NIL) (-1017 2354962 2355466 2356162 "RCFIELD-" 2356237 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1016 2351231 2353063 2353106 "RCAGG" 2354190 NIL RCAGG (NIL T) -9 NIL 2354655 NIL) (-1015 2350859 2350953 2351116 "RCAGG-" 2351121 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1014 2350194 2350306 2350471 "RATRET" 2350743 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1013 2349747 2349814 2349935 "RATFACT" 2350122 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1012 2349055 2349175 2349327 "RANDSRC" 2349617 T RANDSRC (NIL) -7 NIL NIL NIL) (-1011 2348789 2348833 2348906 "RADUTIL" 2349004 T RADUTIL (NIL) -7 NIL NIL NIL) (-1010 2341905 2347622 2347932 "RADIX" 2348513 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1009 2333524 2341747 2341877 "RADFF" 2341882 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1008 2333171 2333246 2333276 "RADCAT" 2333436 T RADCAT (NIL) -9 NIL NIL NIL) (-1007 2332953 2333001 2333101 "RADCAT-" 2333106 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1006 2331051 2332723 2332815 "QUEUE" 2332896 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1005 2327588 2330984 2331032 "QUAT" 2331037 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1004 2327219 2327262 2327393 "QUATCT2" 2327539 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1003 2320668 2324013 2324055 "QUATCAT" 2324846 NIL QUATCAT (NIL T) -9 NIL 2325612 NIL) (-1002 2316807 2317844 2319234 "QUATCAT-" 2319330 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1001 2314272 2315883 2315926 "QUAGG" 2316307 NIL QUAGG (NIL T) -9 NIL 2316482 NIL) (-1000 2313874 2314094 2314164 "QQUTAST" 2314224 T QQUTAST (NIL) -8 NIL NIL NIL) (-999 2312772 2313272 2313444 "QFORM" 2313746 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-998 2303777 2309016 2309056 "QFCAT" 2309714 NIL QFCAT (NIL T) -9 NIL 2310715 NIL) (-997 2299349 2300550 2302141 "QFCAT-" 2302235 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-996 2298987 2299030 2299157 "QFCAT2" 2299300 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-995 2298447 2298557 2298687 "QEQUAT" 2298877 T QEQUAT (NIL) -8 NIL NIL NIL) (-994 2291593 2292666 2293850 "QCMPACK" 2297380 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-993 2289142 2289590 2290018 "QALGSET" 2291248 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-992 2288387 2288561 2288793 "QALGSET2" 2288962 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-991 2287077 2287301 2287618 "PWFFINTB" 2288160 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-990 2285259 2285427 2285781 "PUSHVAR" 2286891 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-989 2281177 2282231 2282272 "PTRANFN" 2284156 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-988 2279579 2279870 2280192 "PTPACK" 2280888 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-987 2279211 2279268 2279377 "PTFUNC2" 2279516 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-986 2273688 2278083 2278124 "PTCAT" 2278420 NIL PTCAT (NIL T) -9 NIL 2278573 NIL) (-985 2273346 2273381 2273505 "PSQFR" 2273647 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-984 2271941 2272239 2272573 "PSEUDLIN" 2273044 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-983 2258704 2261075 2263399 "PSETPK" 2269701 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-982 2251722 2254462 2254558 "PSETCAT" 2257579 NIL PSETCAT (NIL T T T T) -9 NIL 2258393 NIL) (-981 2249558 2250192 2251013 "PSETCAT-" 2251018 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-980 2248907 2249072 2249100 "PSCURVE" 2249368 T PSCURVE (NIL) -9 NIL 2249535 NIL) (-979 2244905 2246421 2246486 "PSCAT" 2247330 NIL PSCAT (NIL T T T) -9 NIL 2247570 NIL) (-978 2243968 2244184 2244584 "PSCAT-" 2244589 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2242673 2243333 2243538 "PRTITION" 2243783 T PRTITION (NIL) -8 NIL NIL NIL) (-976 2242148 2242394 2242486 "PRTDAST" 2242601 T PRTDAST (NIL) -8 NIL NIL NIL) (-975 2231238 2233452 2235640 "PRS" 2240010 NIL PRS (NIL T T) -7 NIL NIL NIL) (-974 2229049 2230588 2230628 "PRQAGG" 2230811 NIL PRQAGG (NIL T) -9 NIL 2230913 NIL) (-973 2228253 2228558 2228586 "PROPLOG" 2228833 T PROPLOG (NIL) -9 NIL 2228999 NIL) (-972 2226434 2227000 2227297 "PROPFRML" 2227989 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2225903 2226010 2226138 "PROPERTY" 2226326 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2219961 2224069 2224889 "PRODUCT" 2225129 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2217239 2219419 2219653 "PR" 2219772 NIL PR (NIL T T) -8 NIL NIL NIL) (-968 2217035 2217067 2217126 "PRINT" 2217200 T PRINT (NIL) -7 NIL NIL NIL) (-967 2216375 2216492 2216644 "PRIMES" 2216915 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-966 2214440 2214841 2215307 "PRIMELT" 2215954 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-965 2214169 2214218 2214246 "PRIMCAT" 2214370 T PRIMCAT (NIL) -9 NIL NIL NIL) (-964 2210284 2214107 2214152 "PRIMARR" 2214157 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2209291 2209469 2209697 "PRIMARR2" 2210102 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-962 2208934 2208990 2209101 "PREASSOC" 2209229 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-961 2208409 2208542 2208570 "PPCURVE" 2208775 T PPCURVE (NIL) -9 NIL 2208911 NIL) (-960 2208004 2208204 2208287 "PORTNUM" 2208346 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2205363 2205762 2206354 "POLYROOT" 2207585 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2199545 2204967 2205127 "POLY" 2205236 NIL POLY (NIL T) -8 NIL NIL NIL) (-957 2198928 2198986 2199220 "POLYLIFT" 2199481 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-956 2195203 2195652 2196281 "POLYCATQ" 2198473 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-955 2181915 2187043 2187108 "POLYCAT" 2190622 NIL POLYCAT (NIL T T T) -9 NIL 2192500 NIL) (-954 2175364 2177226 2179610 "POLYCAT-" 2179615 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-953 2174951 2175019 2175139 "POLY2UP" 2175290 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-952 2174583 2174640 2174749 "POLY2" 2174888 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-951 2173268 2173507 2173783 "POLUTIL" 2174357 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2171623 2171900 2172231 "POLTOPOL" 2172990 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2167088 2171559 2171605 "POINT" 2171610 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2165275 2165632 2166007 "PNTHEORY" 2166733 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2163733 2164030 2164429 "PMTOOLS" 2164973 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2163326 2163404 2163521 "PMSYM" 2163649 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2162836 2162905 2163079 "PMQFCAT" 2163251 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2162191 2162301 2162457 "PMPRED" 2162713 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-943 2161584 2161670 2161832 "PMPREDFS" 2162092 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-942 2160248 2160456 2160834 "PMPLCAT" 2161346 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2159780 2159859 2160011 "PMLSAGG" 2160163 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2159253 2159329 2159511 "PMKERNEL" 2159698 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2158870 2158945 2159058 "PMINS" 2159172 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2158312 2158381 2158590 "PMFS" 2158795 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2157540 2157658 2157863 "PMDOWN" 2158189 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2156707 2156865 2157046 "PMASS" 2157379 T PMASS (NIL) -7 NIL NIL NIL) (-935 2155980 2156090 2156253 "PMASSFS" 2156594 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-934 2155635 2155703 2155797 "PLOTTOOL" 2155906 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2150242 2151446 2152594 "PLOT" 2154507 T PLOT (NIL) -8 NIL NIL NIL) (-932 2146046 2147090 2148011 "PLOT3D" 2149341 T PLOT3D (NIL) -8 NIL NIL NIL) (-931 2144958 2145135 2145370 "PLOT1" 2145850 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-930 2120347 2125024 2129875 "PLEQN" 2140224 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2119665 2119787 2119967 "PINTERP" 2120212 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-928 2119358 2119405 2119508 "PINTERPA" 2119612 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-927 2118579 2119127 2119214 "PI" 2119254 T PI (NIL) -8 NIL NIL 2119321) (-926 2116876 2117851 2117879 "PID" 2118061 T PID (NIL) -9 NIL 2118195 NIL) (-925 2116627 2116664 2116739 "PICOERCE" 2116833 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-924 2115947 2116086 2116262 "PGROEB" 2116483 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2111534 2112348 2113253 "PGE" 2115062 T PGE (NIL) -7 NIL NIL NIL) (-922 2109657 2109904 2110270 "PGCD" 2111251 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2108995 2109098 2109259 "PFRPAC" 2109541 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2105635 2107543 2107896 "PFR" 2108674 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2104024 2104268 2104593 "PFOTOOLS" 2105382 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2102557 2102796 2103147 "PFOQ" 2103781 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2101058 2101270 2101626 "PFO" 2102341 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2097611 2100947 2101016 "PF" 2101021 NIL PF (NIL NIL) -8 NIL NIL NIL) (-915 2094945 2096216 2096244 "PFECAT" 2096829 T PFECAT (NIL) -9 NIL 2097213 NIL) (-914 2094390 2094544 2094758 "PFECAT-" 2094763 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-913 2092993 2093245 2093546 "PFBRU" 2094139 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-912 2090859 2091211 2091643 "PFBR" 2092644 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-911 2086741 2088235 2088911 "PERM" 2090216 NIL PERM (NIL T) -8 NIL NIL NIL) (-910 2081975 2082948 2083818 "PERMGRP" 2085904 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-909 2080081 2081038 2081079 "PERMCAT" 2081525 NIL PERMCAT (NIL T) -9 NIL 2081830 NIL) (-908 2079734 2079775 2079899 "PERMAN" 2080034 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-907 2077222 2079399 2079521 "PENDTREE" 2079645 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-906 2075246 2076014 2076055 "PDRING" 2076712 NIL PDRING (NIL T) -9 NIL 2076998 NIL) (-905 2074349 2074567 2074929 "PDRING-" 2074934 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-904 2071564 2072342 2073010 "PDEPROB" 2073701 T PDEPROB (NIL) -8 NIL NIL NIL) (-903 2069109 2069613 2070168 "PDEPACK" 2071029 T PDEPACK (NIL) -7 NIL NIL NIL) (-902 2068021 2068211 2068462 "PDECOMP" 2068908 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-901 2065600 2066443 2066471 "PDECAT" 2067258 T PDECAT (NIL) -9 NIL 2067971 NIL) (-900 2065351 2065384 2065474 "PCOMP" 2065561 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-899 2063529 2064152 2064449 "PBWLB" 2065080 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-898 2056002 2057602 2058940 "PATTERN" 2062212 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-897 2055634 2055691 2055800 "PATTERN2" 2055939 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-896 2053391 2053779 2054236 "PATTERN1" 2055223 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-895 2050759 2051340 2051821 "PATRES" 2052956 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-894 2050323 2050390 2050522 "PATRES2" 2050686 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-893 2048206 2048611 2049018 "PATMATCH" 2049990 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-892 2047716 2047925 2047966 "PATMAB" 2048073 NIL PATMAB (NIL T) -9 NIL 2048156 NIL) (-891 2046234 2046570 2046828 "PATLRES" 2047521 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-890 2045780 2045903 2045944 "PATAB" 2045949 NIL PATAB (NIL T) -9 NIL 2046121 NIL) (-889 2043261 2043793 2044366 "PARTPERM" 2045227 T PARTPERM (NIL) -7 NIL NIL NIL) (-888 2042882 2042945 2043047 "PARSURF" 2043192 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-887 2042514 2042571 2042680 "PARSU2" 2042819 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-886 2042278 2042318 2042385 "PARSER" 2042467 T PARSER (NIL) -7 NIL NIL NIL) (-885 2041899 2041962 2042064 "PARSCURV" 2042209 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-884 2041531 2041588 2041697 "PARSC2" 2041836 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-883 2041170 2041228 2041325 "PARPCURV" 2041467 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-882 2040802 2040859 2040968 "PARPC2" 2041107 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-881 2039863 2040175 2040357 "PARAMAST" 2040640 T PARAMAST (NIL) -8 NIL NIL NIL) (-880 2039383 2039469 2039588 "PAN2EXPR" 2039764 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-879 2038160 2038504 2038732 "PALETTE" 2039175 T PALETTE (NIL) -8 NIL NIL NIL) (-878 2036553 2037165 2037525 "PAIR" 2037846 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-877 2030423 2035812 2036006 "PADICRC" 2036408 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-876 2023652 2029769 2029953 "PADICRAT" 2030271 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-875 2021967 2023589 2023634 "PADIC" 2023639 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-874 2019077 2020641 2020681 "PADICCT" 2021262 NIL PADICCT (NIL NIL) -9 NIL 2021544 NIL) (-873 2018034 2018234 2018502 "PADEPAC" 2018864 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-872 2017246 2017379 2017585 "PADE" 2017896 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-871 2015633 2016454 2016734 "OWP" 2017050 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-870 2015126 2015339 2015436 "OVERSET" 2015556 T OVERSET (NIL) -8 NIL NIL NIL) (-869 2014172 2014731 2014903 "OVAR" 2014994 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-868 2013436 2013557 2013718 "OUT" 2014031 T OUT (NIL) -7 NIL NIL NIL) (-867 2002308 2004545 2006745 "OUTFORM" 2011256 T OUTFORM (NIL) -8 NIL NIL NIL) (-866 2001644 2001905 2002032 "OUTBFILE" 2002201 T OUTBFILE (NIL) -8 NIL NIL NIL) (-865 2000951 2001116 2001144 "OUTBCON" 2001462 T OUTBCON (NIL) -9 NIL 2001628 NIL) (-864 2000552 2000664 2000821 "OUTBCON-" 2000826 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-863 1999932 2000281 2000370 "OSI" 2000483 T OSI (NIL) -8 NIL NIL NIL) (-862 1999462 1999800 1999828 "OSGROUP" 1999833 T OSGROUP (NIL) -9 NIL 1999855 NIL) (-861 1998207 1998434 1998719 "ORTHPOL" 1999209 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1995758 1998042 1998163 "OREUP" 1998168 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1993161 1995449 1995576 "ORESUP" 1995700 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1990689 1991189 1991750 "OREPCTO" 1992650 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1984375 1986576 1986617 "OREPCAT" 1988965 NIL OREPCAT (NIL T) -9 NIL 1990069 NIL) (-856 1981522 1982304 1983362 "OREPCAT-" 1983367 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1980673 1980971 1980999 "ORDSET" 1981308 T ORDSET (NIL) -9 NIL 1981472 NIL) (-854 1980104 1980252 1980476 "ORDSET-" 1980481 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1978669 1979460 1979488 "ORDRING" 1979690 T ORDRING (NIL) -9 NIL 1979815 NIL) (-852 1978314 1978408 1978552 "ORDRING-" 1978557 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1977694 1978157 1978185 "ORDMON" 1978190 T ORDMON (NIL) -9 NIL 1978211 NIL) (-850 1976856 1977003 1977198 "ORDFUNS" 1977543 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1976194 1976613 1976641 "ORDFIN" 1976706 T ORDFIN (NIL) -9 NIL 1976780 NIL) (-848 1972753 1974780 1975189 "ORDCOMP" 1975818 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-847 1972019 1972146 1972332 "ORDCOMP2" 1972613 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-846 1968600 1969510 1970324 "OPTPROB" 1971225 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1965402 1966041 1966745 "OPTPACK" 1967916 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1963089 1963855 1963883 "OPTCAT" 1964702 T OPTCAT (NIL) -9 NIL 1965352 NIL) (-843 1962473 1962766 1962871 "OPSIG" 1963004 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1962241 1962280 1962346 "OPQUERY" 1962427 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1959372 1960552 1961056 "OP" 1961770 NIL OP (NIL T) -8 NIL NIL NIL) (-840 1958746 1958972 1959013 "OPERCAT" 1959225 NIL OPERCAT (NIL T) -9 NIL 1959322 NIL) (-839 1958501 1958557 1958674 "OPERCAT-" 1958679 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-838 1955314 1957298 1957667 "ONECOMP" 1958165 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-837 1954619 1954734 1954908 "ONECOMP2" 1955186 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-836 1954038 1954144 1954274 "OMSERVER" 1954509 T OMSERVER (NIL) -7 NIL NIL NIL) (-835 1950900 1953478 1953518 "OMSAGG" 1953579 NIL OMSAGG (NIL T) -9 NIL 1953643 NIL) (-834 1949523 1949786 1950068 "OMPKG" 1950638 T OMPKG (NIL) -7 NIL NIL NIL) (-833 1948953 1949056 1949084 "OM" 1949383 T OM (NIL) -9 NIL NIL NIL) (-832 1947500 1948502 1948671 "OMLO" 1948834 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-831 1946460 1946607 1946827 "OMEXPR" 1947326 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-830 1945751 1946006 1946142 "OMERR" 1946344 T OMERR (NIL) -8 NIL NIL NIL) (-829 1944902 1945172 1945332 "OMERRK" 1945611 T OMERRK (NIL) -8 NIL NIL NIL) (-828 1944353 1944579 1944687 "OMENC" 1944814 T OMENC (NIL) -8 NIL NIL NIL) (-827 1938248 1939433 1940604 "OMDEV" 1943202 T OMDEV (NIL) -8 NIL NIL NIL) (-826 1937317 1937488 1937682 "OMCONN" 1938074 T OMCONN (NIL) -8 NIL NIL NIL) (-825 1935838 1936814 1936842 "OINTDOM" 1936847 T OINTDOM (NIL) -9 NIL 1936868 NIL) (-824 1933176 1934526 1934863 "OFMONOID" 1935533 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1932587 1933113 1933158 "ODVAR" 1933163 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1930010 1932332 1932487 "ODR" 1932492 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1922591 1929786 1929912 "ODPOL" 1929917 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1916413 1922463 1922568 "ODP" 1922573 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1915179 1915394 1915669 "ODETOOLS" 1916187 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1912146 1912804 1913520 "ODESYS" 1914512 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1907028 1907936 1908961 "ODERTRIC" 1911221 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1906454 1906536 1906730 "ODERED" 1906940 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1903342 1903890 1904567 "ODERAT" 1905877 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1900299 1900766 1901363 "ODEPRRIC" 1902871 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1898242 1898838 1899324 "ODEPROB" 1899833 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1894762 1895247 1895894 "ODEPRIM" 1897721 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1894011 1894113 1894373 "ODEPAL" 1894654 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1890173 1890964 1891828 "ODEPACK" 1893167 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1889234 1889341 1889563 "ODEINT" 1890062 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1883335 1884760 1886207 "ODEIFTBL" 1887807 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1878733 1879519 1880471 "ODEEF" 1882494 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1878082 1878171 1878394 "ODECONST" 1878638 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1876207 1876868 1876896 "ODECAT" 1877501 T ODECAT (NIL) -9 NIL 1878032 NIL) (-804 1873062 1875912 1876034 "OCT" 1876117 NIL OCT (NIL T) -8 NIL NIL NIL) (-803 1872700 1872743 1872870 "OCTCT2" 1873013 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-802 1867349 1869784 1869824 "OC" 1870921 NIL OC (NIL T) -9 NIL 1871779 NIL) (-801 1864576 1865324 1866314 "OC-" 1866408 NIL OC- (NIL T T) -8 NIL NIL NIL) (-800 1863928 1864396 1864424 "OCAMON" 1864429 T OCAMON (NIL) -9 NIL 1864450 NIL) (-799 1863459 1863800 1863828 "OASGP" 1863833 T OASGP (NIL) -9 NIL 1863853 NIL) (-798 1862720 1863209 1863237 "OAMONS" 1863277 T OAMONS (NIL) -9 NIL 1863320 NIL) (-797 1862134 1862567 1862595 "OAMON" 1862600 T OAMON (NIL) -9 NIL 1862620 NIL) (-796 1861392 1861910 1861938 "OAGROUP" 1861943 T OAGROUP (NIL) -9 NIL 1861963 NIL) (-795 1861082 1861132 1861220 "NUMTUBE" 1861336 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1854655 1856173 1857709 "NUMQUAD" 1859566 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1850411 1851399 1852424 "NUMODE" 1853650 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1847766 1848646 1848674 "NUMINT" 1849597 T NUMINT (NIL) -9 NIL 1850361 NIL) (-791 1846714 1846911 1847129 "NUMFMT" 1847568 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1833073 1836018 1838550 "NUMERIC" 1844221 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1827443 1832522 1832617 "NTSCAT" 1832622 NIL NTSCAT (NIL T T T T) -9 NIL 1832661 NIL) (-788 1826637 1826802 1826995 "NTPOLFN" 1827282 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1814714 1823462 1824274 "NSUP" 1825858 NIL NSUP (NIL T) -8 NIL NIL NIL) (-786 1814346 1814403 1814512 "NSUP2" 1814651 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-785 1804574 1814120 1814253 "NSMP" 1814258 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1803006 1803307 1803664 "NREP" 1804262 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1801597 1801849 1802207 "NPCOEF" 1802749 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1800663 1800778 1800994 "NORMRETR" 1801478 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1798704 1798994 1799403 "NORMPK" 1800371 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1798389 1798417 1798541 "NORMMA" 1798670 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1798189 1798346 1798375 "NONE" 1798380 T NONE (NIL) -8 NIL NIL NIL) (-778 1797978 1798007 1798076 "NONE1" 1798153 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-777 1797475 1797537 1797716 "NODE1" 1797910 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1795760 1796611 1796866 "NNI" 1797213 T NNI (NIL) -8 NIL NIL 1797448) (-775 1794180 1794493 1794857 "NLINSOL" 1795428 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1790421 1791416 1792315 "NIPROB" 1793301 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1789178 1789412 1789714 "NFINTBAS" 1790183 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1788352 1788828 1788869 "NETCLT" 1789041 NIL NETCLT (NIL T) -9 NIL 1789123 NIL) (-771 1787060 1787291 1787572 "NCODIV" 1788120 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1786822 1786859 1786934 "NCNTFRAC" 1787017 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1785002 1785366 1785786 "NCEP" 1786447 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1783853 1784626 1784654 "NASRING" 1784764 T NASRING (NIL) -9 NIL 1784844 NIL) (-767 1783648 1783692 1783786 "NASRING-" 1783791 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1782755 1783280 1783308 "NARNG" 1783425 T NARNG (NIL) -9 NIL 1783516 NIL) (-765 1782447 1782514 1782648 "NARNG-" 1782653 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1781326 1781533 1781768 "NAGSP" 1782232 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1772598 1774282 1775955 "NAGS" 1779673 T NAGS (NIL) -7 NIL NIL NIL) (-762 1771146 1771454 1771785 "NAGF07" 1772287 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1765684 1766975 1768282 "NAGF04" 1769859 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1758652 1760266 1761899 "NAGF02" 1764071 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1753876 1754976 1756093 "NAGF01" 1757555 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1747504 1749070 1750655 "NAGE04" 1752311 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1738673 1740794 1742924 "NAGE02" 1745394 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1734626 1735573 1736537 "NAGE01" 1737729 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1732421 1732955 1733513 "NAGD03" 1734088 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1724171 1726099 1728053 "NAGD02" 1730487 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1717982 1719407 1720847 "NAGD01" 1722751 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1714191 1715013 1715850 "NAGC06" 1717165 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1712656 1712988 1713344 "NAGC05" 1713855 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1712032 1712151 1712295 "NAGC02" 1712532 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1710991 1711574 1711614 "NAALG" 1711693 NIL NAALG (NIL T) -9 NIL 1711754 NIL) (-748 1710826 1710855 1710945 "NAALG-" 1710950 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1704776 1705884 1707071 "MULTSQFR" 1709722 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1704095 1704170 1704354 "MULTFACT" 1704688 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1696819 1700732 1700785 "MTSCAT" 1701855 NIL MTSCAT (NIL T T) -9 NIL 1702370 NIL) (-744 1696531 1696585 1696677 "MTHING" 1696759 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1696323 1696356 1696416 "MSYSCMD" 1696491 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1692405 1695078 1695398 "MSET" 1696036 NIL MSET (NIL T) -8 NIL NIL NIL) (-741 1689474 1691966 1692007 "MSETAGG" 1692012 NIL MSETAGG (NIL T) -9 NIL 1692046 NIL) (-740 1685315 1686853 1687598 "MRING" 1688774 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1684881 1684948 1685079 "MRF2" 1685242 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1684499 1684534 1684678 "MRATFAC" 1684840 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1682111 1682406 1682837 "MPRFF" 1684204 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1676408 1681965 1682062 "MPOLY" 1682067 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1675898 1675933 1676141 "MPCPF" 1676367 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1675412 1675455 1675639 "MPC3" 1675849 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1674607 1674688 1674909 "MPC2" 1675327 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1672908 1673245 1673635 "MONOTOOL" 1674267 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1672133 1672450 1672478 "MONOID" 1672697 T MONOID (NIL) -9 NIL 1672844 NIL) (-730 1671679 1671798 1671979 "MONOID-" 1671984 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1662154 1668105 1668164 "MONOGEN" 1668838 NIL MONOGEN (NIL T T) -9 NIL 1669294 NIL) (-728 1659372 1660107 1661107 "MONOGEN-" 1661226 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1658205 1658651 1658679 "MONADWU" 1659071 T MONADWU (NIL) -9 NIL 1659309 NIL) (-726 1657577 1657736 1657984 "MONADWU-" 1657989 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1656936 1657180 1657208 "MONAD" 1657415 T MONAD (NIL) -9 NIL 1657527 NIL) (-724 1656621 1656699 1656831 "MONAD-" 1656836 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1654910 1655534 1655813 "MOEBIUS" 1656374 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1654188 1654592 1654632 "MODULE" 1654637 NIL MODULE (NIL T) -9 NIL 1654676 NIL) (-721 1653756 1653852 1654042 "MODULE-" 1654047 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1651436 1652120 1652447 "MODRING" 1653580 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1648380 1649541 1650062 "MODOP" 1650965 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1646968 1647447 1647724 "MODMONOM" 1648243 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1637010 1645259 1645673 "MODMON" 1646605 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1634166 1635854 1636130 "MODFIELD" 1636885 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1633143 1633447 1633637 "MMLFORM" 1633996 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1632669 1632712 1632891 "MMAP" 1633094 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1630748 1631515 1631556 "MLO" 1631979 NIL MLO (NIL T) -9 NIL 1632221 NIL) (-712 1628114 1628630 1629232 "MLIFT" 1630229 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1627505 1627589 1627743 "MKUCFUNC" 1628025 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1627104 1627174 1627297 "MKRECORD" 1627428 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1626151 1626313 1626541 "MKFUNC" 1626915 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1625539 1625643 1625799 "MKFLCFN" 1626034 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1624816 1624918 1625103 "MKBCFUNC" 1625432 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1621523 1624370 1624506 "MINT" 1624700 T MINT (NIL) -8 NIL NIL NIL) (-705 1620335 1620578 1620855 "MHROWRED" 1621278 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1615715 1618870 1619275 "MFLOAT" 1619950 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1615072 1615148 1615319 "MFINFACT" 1615627 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1611387 1612235 1613119 "MESH" 1614208 T MESH (NIL) -7 NIL NIL NIL) (-701 1609777 1610089 1610442 "MDDFACT" 1611074 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1606572 1608936 1608977 "MDAGG" 1609232 NIL MDAGG (NIL T) -9 NIL 1609375 NIL) (-699 1596312 1605865 1606072 "MCMPLX" 1606385 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1595453 1595599 1595799 "MCDEN" 1596161 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1593343 1593613 1593993 "MCALCFN" 1595183 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1592268 1592508 1592741 "MAYBE" 1593149 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1589880 1590403 1590965 "MATSTOR" 1591739 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1585837 1589252 1589500 "MATRIX" 1589665 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1581601 1582310 1583046 "MATLIN" 1585194 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1571707 1574893 1574970 "MATCAT" 1579850 NIL MATCAT (NIL T T T) -9 NIL 1581267 NIL) (-691 1568063 1569084 1570440 "MATCAT-" 1570445 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-690 1566657 1566810 1567143 "MATCAT2" 1567898 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-689 1564769 1565093 1565477 "MAPPKG3" 1566332 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1563750 1563923 1564145 "MAPPKG2" 1564593 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1562249 1562533 1562860 "MAPPKG1" 1563456 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1561328 1561655 1561832 "MAPPAST" 1562092 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1560939 1560997 1561120 "MAPHACK3" 1561264 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1560531 1560592 1560706 "MAPHACK2" 1560871 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1559968 1560072 1560214 "MAPHACK1" 1560422 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1558047 1558668 1558972 "MAGMA" 1559696 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1557526 1557771 1557862 "MACROAST" 1557976 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1553944 1555765 1556226 "M3D" 1557098 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1548050 1552313 1552354 "LZSTAGG" 1553136 NIL LZSTAGG (NIL T) -9 NIL 1553431 NIL) (-678 1544007 1545181 1546638 "LZSTAGG-" 1546643 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1541094 1541898 1542385 "LWORD" 1543552 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1540670 1540898 1540973 "LSTAST" 1541039 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1533836 1540441 1540575 "LSQM" 1540580 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1533060 1533199 1533427 "LSPP" 1533691 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1530872 1531173 1531629 "LSMP" 1532749 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-672 1527651 1528325 1529055 "LSMP1" 1530174 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-671 1521528 1526818 1526859 "LSAGG" 1526921 NIL LSAGG (NIL T) -9 NIL 1526999 NIL) (-670 1518223 1519147 1520360 "LSAGG-" 1520365 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1515822 1517367 1517616 "LPOLY" 1518018 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1515404 1515489 1515612 "LPEFRAC" 1515731 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1513725 1514498 1514751 "LO" 1515236 NIL LO (NIL T T T) -8 NIL NIL NIL) (-666 1513377 1513489 1513517 "LOGIC" 1513628 T LOGIC (NIL) -9 NIL 1513709 NIL) (-665 1513239 1513262 1513333 "LOGIC-" 1513338 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-664 1512432 1512572 1512765 "LODOOPS" 1513095 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-663 1509855 1512348 1512414 "LODO" 1512419 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-662 1508393 1508628 1508981 "LODOF" 1509602 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-661 1504611 1507042 1507083 "LODOCAT" 1507521 NIL LODOCAT (NIL T) -9 NIL 1507732 NIL) (-660 1504344 1504402 1504529 "LODOCAT-" 1504534 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-659 1501664 1504185 1504303 "LODO2" 1504308 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-658 1499099 1501601 1501646 "LODO1" 1501651 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-657 1497980 1498145 1498450 "LODEEF" 1498922 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-656 1493219 1496110 1496151 "LNAGG" 1497098 NIL LNAGG (NIL T) -9 NIL 1497542 NIL) (-655 1492366 1492580 1492922 "LNAGG-" 1492927 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1488502 1489291 1489930 "LMOPS" 1491781 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1487905 1488293 1488334 "LMODULE" 1488339 NIL LMODULE (NIL T) -9 NIL 1488365 NIL) (-652 1485103 1487550 1487673 "LMDICT" 1487815 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1484509 1484730 1484771 "LLINSET" 1484962 NIL LLINSET (NIL T) -9 NIL 1485053 NIL) (-650 1484208 1484417 1484477 "LITERAL" 1484482 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1477371 1483142 1483446 "LIST" 1483937 NIL LIST (NIL T) -8 NIL NIL NIL) (-648 1476896 1476970 1477109 "LIST3" 1477291 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-647 1475903 1476081 1476309 "LIST2" 1476714 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1474037 1474349 1474748 "LIST2MAP" 1475550 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-645 1473633 1473870 1473911 "LINSET" 1473916 NIL LINSET (NIL T) -9 NIL 1473950 NIL) (-644 1472294 1472964 1473005 "LINEXP" 1473260 NIL LINEXP (NIL T) -9 NIL 1473409 NIL) (-643 1470941 1471201 1471498 "LINDEP" 1472046 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1467708 1468427 1469204 "LIMITRF" 1470196 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1466011 1466307 1466716 "LIMITPS" 1467403 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1460439 1465522 1465750 "LIE" 1465832 NIL LIE (NIL T T) -8 NIL NIL NIL) (-639 1459387 1459856 1459896 "LIECAT" 1460036 NIL LIECAT (NIL T) -9 NIL 1460187 NIL) (-638 1459228 1459255 1459343 "LIECAT-" 1459348 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-637 1451724 1458677 1458842 "LIB" 1459083 T LIB (NIL) -8 NIL NIL NIL) (-636 1447359 1448242 1449177 "LGROBP" 1450841 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1445357 1445631 1445981 "LF" 1447080 NIL LF (NIL T T) -7 NIL NIL NIL) (-634 1444197 1444889 1444917 "LFCAT" 1445124 T LFCAT (NIL) -9 NIL 1445263 NIL) (-633 1441099 1441729 1442417 "LEXTRIPK" 1443561 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1437843 1438669 1439172 "LEXP" 1440679 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1437319 1437564 1437656 "LETAST" 1437771 T LETAST (NIL) -8 NIL NIL NIL) (-630 1435717 1436030 1436431 "LEADCDET" 1437001 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1434907 1434981 1435210 "LAZM3PK" 1435638 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1429824 1432984 1433522 "LAUPOL" 1434419 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1429403 1429447 1429608 "LAPLACE" 1429774 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1427342 1428504 1428755 "LA" 1429236 NIL LA (NIL T T T) -8 NIL NIL NIL) (-625 1426336 1426920 1426961 "LALG" 1427023 NIL LALG (NIL T) -9 NIL 1427082 NIL) (-624 1426050 1426109 1426245 "LALG-" 1426250 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-623 1425885 1425909 1425950 "KVTFROM" 1426012 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1424808 1425252 1425437 "KTVLOGIC" 1425720 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1424643 1424667 1424708 "KRCFROM" 1424770 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1423547 1423734 1424033 "KOVACIC" 1424443 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1423382 1423406 1423447 "KONVERT" 1423509 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1423217 1423241 1423282 "KOERCE" 1423344 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1421047 1421810 1422187 "KERNEL" 1422873 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-616 1420543 1420624 1420756 "KERNEL2" 1420961 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-615 1414313 1419082 1419136 "KDAGG" 1419513 NIL KDAGG (NIL T T) -9 NIL 1419719 NIL) (-614 1413842 1413966 1414171 "KDAGG-" 1414176 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1406990 1413503 1413658 "KAFILE" 1413720 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1401418 1406501 1406729 "JORDAN" 1406811 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1400797 1401067 1401188 "JOINAST" 1401317 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1400643 1400702 1400757 "JAVACODE" 1400762 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1396895 1398848 1398902 "IXAGG" 1399831 NIL IXAGG (NIL T T) -9 NIL 1400290 NIL) (-608 1395814 1396120 1396539 "IXAGG-" 1396544 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1391344 1395736 1395795 "IVECTOR" 1395800 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1390110 1390347 1390613 "ITUPLE" 1391111 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1388612 1388789 1389084 "ITRIGMNP" 1389932 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1387357 1387561 1387844 "ITFUN3" 1388388 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1386989 1387046 1387155 "ITFUN2" 1387294 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1386148 1386469 1386643 "ITFORM" 1386835 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1384109 1385168 1385446 "ITAYLOR" 1385903 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1373054 1378246 1379409 "ISUPS" 1382979 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1372158 1372298 1372534 "ISUMP" 1372901 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1367533 1372103 1372144 "ISTRING" 1372149 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1367009 1367254 1367346 "ISAST" 1367461 T ISAST (NIL) -8 NIL NIL NIL) (-596 1366218 1366300 1366516 "IRURPK" 1366923 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1365154 1365355 1365595 "IRSN" 1365998 T IRSN (NIL) -7 NIL NIL NIL) (-594 1363225 1363580 1364009 "IRRF2F" 1364792 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1362972 1363010 1363086 "IRREDFFX" 1363181 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1361587 1361846 1362145 "IROOT" 1362705 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1358191 1359271 1359963 "IR" 1360927 NIL IR (NIL T) -8 NIL NIL NIL) (-590 1357396 1357684 1357835 "IRFORM" 1358060 T IRFORM (NIL) -8 NIL NIL NIL) (-589 1355009 1355504 1356070 "IR2" 1356874 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1354109 1354222 1354436 "IR2F" 1354892 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-587 1353900 1353934 1353994 "IPRNTPK" 1354069 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1350481 1353789 1353858 "IPF" 1353863 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1348808 1350406 1350463 "IPADIC" 1350468 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1348120 1348368 1348498 "IP4ADDR" 1348698 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1347494 1347749 1347881 "IOMODE" 1348008 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1346567 1347091 1347218 "IOBFILE" 1347387 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1346055 1346471 1346499 "IOBCON" 1346504 T IOBCON (NIL) -9 NIL 1346525 NIL) (-580 1345566 1345624 1345807 "INVLAPLA" 1345991 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1335214 1337568 1339954 "INTTR" 1343230 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1331549 1332291 1333156 "INTTOOLS" 1334399 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1331135 1331226 1331343 "INTSLPE" 1331452 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1329088 1331058 1331117 "INTRVL" 1331122 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1326690 1327202 1327777 "INTRF" 1328573 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1326101 1326198 1326340 "INTRET" 1326588 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1324098 1324487 1324957 "INTRAT" 1325709 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1321361 1321944 1322563 "INTPM" 1323583 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1318106 1318705 1319443 "INTPAF" 1320747 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1313285 1314247 1315298 "INTPACK" 1317075 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1310233 1313082 1313191 "INT" 1313196 T INT (NIL) -8 NIL NIL NIL) (-568 1309485 1309637 1309845 "INTHERTR" 1310075 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-567 1308924 1309004 1309192 "INTHERAL" 1309399 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-566 1306770 1307213 1307670 "INTHEORY" 1308487 T INTHEORY (NIL) -7 NIL NIL NIL) (-565 1298176 1299797 1301569 "INTG0" 1305122 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-564 1278749 1283539 1288349 "INTFTBL" 1293386 T INTFTBL (NIL) -8 NIL NIL NIL) (-563 1277998 1278136 1278309 "INTFACT" 1278608 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-562 1275425 1275871 1276428 "INTEF" 1277552 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-561 1273792 1274531 1274559 "INTDOM" 1274860 T INTDOM (NIL) -9 NIL 1275067 NIL) (-560 1273161 1273335 1273577 "INTDOM-" 1273582 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-559 1269549 1271477 1271531 "INTCAT" 1272330 NIL INTCAT (NIL T) -9 NIL 1272651 NIL) (-558 1269021 1269124 1269252 "INTBIT" 1269441 T INTBIT (NIL) -7 NIL NIL NIL) (-557 1267720 1267874 1268181 "INTALG" 1268866 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-556 1267203 1267293 1267450 "INTAF" 1267624 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-555 1260546 1267013 1267153 "INTABL" 1267158 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-554 1259887 1260353 1260418 "INT8" 1260452 T INT8 (NIL) -8 NIL NIL 1260497) (-553 1259227 1259693 1259758 "INT64" 1259792 T INT64 (NIL) -8 NIL NIL 1259837) (-552 1258567 1259033 1259098 "INT32" 1259132 T INT32 (NIL) -8 NIL NIL 1259177) (-551 1257907 1258373 1258438 "INT16" 1258472 T INT16 (NIL) -8 NIL NIL 1258517) (-550 1252817 1255530 1255558 "INS" 1256492 T INS (NIL) -9 NIL 1257157 NIL) (-549 1250057 1250828 1251802 "INS-" 1251875 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1248832 1249059 1249357 "INPSIGN" 1249810 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1247950 1248067 1248264 "INPRODPF" 1248712 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1246844 1246961 1247198 "INPRODFF" 1247830 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1245844 1245996 1246256 "INNMFACT" 1246680 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1245041 1245138 1245326 "INMODGCD" 1245743 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1243549 1243794 1244118 "INFSP" 1244786 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1242733 1242850 1243033 "INFPROD0" 1243429 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239588 1240798 1241313 "INFORM" 1242226 T INFORM (NIL) -8 NIL NIL NIL) (-540 1239198 1239258 1239356 "INFORM1" 1239523 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-539 1238721 1238810 1238924 "INFINITY" 1239104 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1237897 1238441 1238542 "INETCLTS" 1238640 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1236513 1236763 1237084 "INEP" 1237645 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1235762 1236410 1236475 "INDE" 1236480 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1235326 1235394 1235511 "INCRMAPS" 1235689 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1234144 1234595 1234801 "INBFILE" 1235140 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1229444 1230380 1231324 "INBFF" 1233232 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1228352 1228621 1228649 "INBCON" 1229162 T INBCON (NIL) -9 NIL 1229428 NIL) (-531 1227604 1227827 1228103 "INBCON-" 1228108 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1227083 1227328 1227419 "INAST" 1227533 T INAST (NIL) -8 NIL NIL NIL) (-529 1226510 1226762 1226868 "IMPTAST" 1226997 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1222956 1226354 1226458 "IMATRIX" 1226463 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1221668 1221791 1222106 "IMATQF" 1222812 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1219888 1220115 1220452 "IMATLIN" 1221424 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1214466 1219812 1219870 "ILIST" 1219875 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1212371 1214326 1214439 "IIARRAY2" 1214444 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1207769 1212282 1212346 "IFF" 1212351 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1207116 1207386 1207502 "IFAST" 1207673 T IFAST (NIL) -8 NIL NIL NIL) (-521 1202111 1206408 1206596 "IFARRAY" 1206973 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1201291 1202015 1202088 "IFAMON" 1202093 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1200875 1200940 1200994 "IEVALAB" 1201201 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1200550 1200618 1200778 "IEVALAB-" 1200783 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1200181 1200464 1200527 "IDPO" 1200532 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-516 1199431 1200070 1200145 "IDPOAMS" 1200150 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-515 1198738 1199320 1199395 "IDPOAM" 1199400 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-514 1197797 1198073 1198126 "IDPC" 1198539 NIL IDPC (NIL T T) -9 NIL 1198688 NIL) (-513 1197266 1197689 1197762 "IDPAM" 1197767 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1196642 1197158 1197231 "IDPAG" 1197236 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1196287 1196478 1196553 "IDENT" 1196587 T IDENT (NIL) -8 NIL NIL NIL) (-510 1192542 1193390 1194285 "IDECOMP" 1195444 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1185380 1186465 1187512 "IDEAL" 1191578 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1184544 1184656 1184855 "ICDEN" 1185264 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1183615 1184024 1184171 "ICARD" 1184417 T ICARD (NIL) -8 NIL NIL NIL) (-506 1181675 1181988 1182393 "IBPTOOLS" 1183292 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1177282 1181295 1181408 "IBITS" 1181594 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1174005 1174581 1175276 "IBATOOL" 1176699 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1171784 1172246 1172779 "IBACHIN" 1173540 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1169613 1171630 1171733 "IARRAY2" 1171738 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1165719 1169539 1169596 "IARRAY1" 1169601 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1159828 1164131 1164612 "IAN" 1165258 T IAN (NIL) -8 NIL NIL NIL) (-499 1159339 1159396 1159569 "IALGFACT" 1159765 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1158867 1158980 1159008 "HYPCAT" 1159215 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1158405 1158522 1158708 "HYPCAT-" 1158713 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1158000 1158200 1158283 "HOSTNAME" 1158342 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1157845 1157882 1157923 "HOMOTOP" 1157928 NIL HOMOTOP (NIL T) -9 NIL 1157961 NIL) (-494 1154477 1155855 1155896 "HOAGG" 1156877 NIL HOAGG (NIL T) -9 NIL 1157556 NIL) (-493 1153071 1153470 1153996 "HOAGG-" 1154001 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1147075 1152666 1152815 "HEXADEC" 1152942 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1145823 1146045 1146308 "HEUGCD" 1146852 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1144899 1145660 1145790 "HELLFDIV" 1145795 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1143078 1144676 1144764 "HEAP" 1144843 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1142341 1142630 1142764 "HEADAST" 1142964 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1136207 1142256 1142318 "HDP" 1142323 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1130195 1135842 1135994 "HDMP" 1136108 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1129519 1129659 1129823 "HB" 1130051 T HB (NIL) -7 NIL NIL NIL) (-484 1122905 1129365 1129469 "HASHTBL" 1129474 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1122381 1122626 1122718 "HASAST" 1122833 T HASAST (NIL) -8 NIL NIL NIL) (-482 1120159 1122003 1122185 "HACKPI" 1122219 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1115827 1120012 1120125 "GTSET" 1120130 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1109242 1115705 1115803 "GSTBL" 1115808 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1101520 1108273 1108538 "GSERIES" 1109033 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1100661 1101078 1101106 "GROUP" 1101309 T GROUP (NIL) -9 NIL 1101443 NIL) (-477 1100027 1100186 1100437 "GROUP-" 1100442 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1098394 1098715 1099102 "GROEBSOL" 1099704 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1097308 1097596 1097647 "GRMOD" 1098176 NIL GRMOD (NIL T T) -9 NIL 1098344 NIL) (-474 1097076 1097112 1097240 "GRMOD-" 1097245 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1092366 1093430 1094430 "GRIMAGE" 1096096 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1090832 1091093 1091417 "GRDEF" 1092062 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1090276 1090392 1090533 "GRAY" 1090711 T GRAY (NIL) -7 NIL NIL NIL) (-470 1089463 1089869 1089920 "GRALG" 1090073 NIL GRALG (NIL T T) -9 NIL 1090166 NIL) (-469 1089124 1089197 1089360 "GRALG-" 1089365 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1085901 1088709 1088887 "GPOLSET" 1089031 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1085255 1085312 1085570 "GOSPER" 1085838 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1080987 1081693 1082219 "GMODPOL" 1084954 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1079992 1080176 1080414 "GHENSEL" 1080799 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1074148 1074991 1076011 "GENUPS" 1079076 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1073845 1073896 1073985 "GENUFACT" 1074091 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1073257 1073334 1073499 "GENPGCD" 1073763 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1072731 1072766 1072979 "GENMFACT" 1073216 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1071297 1071554 1071861 "GENEEZ" 1072474 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1065443 1070908 1071070 "GDMP" 1071220 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1054785 1059214 1060320 "GCNAALG" 1064426 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1053112 1053974 1054002 "GCDDOM" 1054257 T GCDDOM (NIL) -9 NIL 1054414 NIL) (-456 1052582 1052709 1052924 "GCDDOM-" 1052929 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1051254 1051439 1051743 "GB" 1052361 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-454 1039870 1042200 1044592 "GBINTERN" 1048945 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-453 1037707 1037999 1038420 "GBF" 1039545 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-452 1036488 1036653 1036920 "GBEUCLID" 1037523 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-451 1035837 1035962 1036111 "GAUSSFAC" 1036359 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1034204 1034506 1034820 "GALUTIL" 1035556 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1032512 1032786 1033110 "GALPOLYU" 1033931 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1029877 1030167 1030574 "GALFACTU" 1032209 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1021682 1023182 1024790 "GALFACT" 1028309 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1019070 1019728 1019756 "FVFUN" 1020912 T FVFUN (NIL) -9 NIL 1021632 NIL) (-445 1018336 1018518 1018546 "FVC" 1018837 T FVC (NIL) -9 NIL 1019020 NIL) (-444 1017979 1018161 1018229 "FUNDESC" 1018288 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1017594 1017776 1017857 "FUNCTION" 1017931 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1015338 1015916 1016382 "FT" 1017148 T FT (NIL) -8 NIL NIL NIL) (-441 1014129 1014639 1014842 "FTEM" 1015155 T FTEM (NIL) -8 NIL NIL NIL) (-440 1012420 1012709 1013106 "FSUPFACT" 1013820 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1010817 1011106 1011438 "FST" 1012108 T FST (NIL) -8 NIL NIL NIL) (-438 1010016 1010122 1010310 "FSRED" 1010699 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1008715 1008971 1009318 "FSPRMELT" 1009731 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1006021 1006459 1006945 "FSPECF" 1008278 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 987659 995990 996031 "FS" 999915 NIL FS (NIL T) -9 NIL 1002204 NIL) (-434 976302 979295 983352 "FS-" 983652 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 975830 975884 976054 "FSINT" 976243 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-432 974122 974823 975126 "FSERIES" 975609 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-431 973164 973280 973504 "FSCINT" 974002 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-430 969372 972108 972149 "FSAGG" 972519 NIL FSAGG (NIL T) -9 NIL 972778 NIL) (-429 967134 967735 968531 "FSAGG-" 968626 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-428 966176 966319 966546 "FSAGG2" 966987 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-427 963858 964138 964685 "FS2UPS" 965894 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-426 963492 963535 963664 "FS2" 963809 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-425 962370 962541 962843 "FS2EXPXP" 963317 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-424 961796 961911 962063 "FRUTIL" 962250 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 953209 957291 958649 "FR" 960470 NIL FR (NIL T) -8 NIL NIL NIL) (-422 948178 950852 950892 "FRNAALG" 952288 NIL FRNAALG (NIL T) -9 NIL 952895 NIL) (-421 943851 944927 946202 "FRNAALG-" 946952 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-420 943489 943532 943659 "FRNAAF2" 943802 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-419 941869 942343 942638 "FRMOD" 943301 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-418 939620 940252 940569 "FRIDEAL" 941660 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 938815 938902 939191 "FRIDEAL2" 939527 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-416 937948 938362 938403 "FRETRCT" 938408 NIL FRETRCT (NIL T) -9 NIL 938584 NIL) (-415 937060 937291 937642 "FRETRCT-" 937647 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-414 934148 935358 935417 "FRAMALG" 936299 NIL FRAMALG (NIL T T) -9 NIL 936591 NIL) (-413 932282 932737 933367 "FRAMALG-" 933590 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-412 926203 931757 932033 "FRAC" 932038 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 925839 925896 926003 "FRAC2" 926140 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-410 925475 925532 925639 "FR2" 925776 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-409 919988 922881 922909 "FPS" 924028 T FPS (NIL) -9 NIL 924585 NIL) (-408 919437 919546 919710 "FPS-" 919856 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 916739 918408 918436 "FPC" 918661 T FPC (NIL) -9 NIL 918803 NIL) (-406 916532 916572 916669 "FPC-" 916674 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 915322 916020 916061 "FPATMAB" 916066 NIL FPATMAB (NIL T) -9 NIL 916218 NIL) (-404 912995 913498 913924 "FPARFRAC" 914959 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 908389 908887 909569 "FORTRAN" 912427 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 906105 906605 907144 "FORT" 907870 T FORT (NIL) -7 NIL NIL NIL) (-401 903781 904343 904371 "FORTFN" 905431 T FORTFN (NIL) -9 NIL 906055 NIL) (-400 903545 903595 903623 "FORTCAT" 903682 T FORTCAT (NIL) -9 NIL 903744 NIL) (-399 901651 902161 902551 "FORMULA" 903175 T FORMULA (NIL) -8 NIL NIL NIL) (-398 901439 901469 901538 "FORMULA1" 901615 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-397 900962 901014 901187 "FORDER" 901381 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 900058 900222 900415 "FOP" 900789 T FOP (NIL) -7 NIL NIL NIL) (-395 898639 899338 899512 "FNLA" 899940 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 897368 897783 897811 "FNCAT" 898271 T FNCAT (NIL) -9 NIL 898531 NIL) (-393 896907 897327 897355 "FNAME" 897360 T FNAME (NIL) -8 NIL NIL NIL) (-392 895470 896433 896461 "FMTC" 896466 T FMTC (NIL) -9 NIL 896502 NIL) (-391 894216 895406 895452 "FMONOID" 895457 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 891044 892212 892253 "FMONCAT" 893470 NIL FMONCAT (NIL T) -9 NIL 894075 NIL) (-389 890236 890786 890935 "FM" 890940 NIL FM (NIL T T) -8 NIL NIL NIL) (-388 887660 888306 888334 "FMFUN" 889478 T FMFUN (NIL) -9 NIL 890186 NIL) (-387 886929 887110 887138 "FMC" 887428 T FMC (NIL) -9 NIL 887610 NIL) (-386 884008 884868 884922 "FMCAT" 886117 NIL FMCAT (NIL T T) -9 NIL 886612 NIL) (-385 882874 883774 883874 "FM1" 883953 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-384 880648 881064 881558 "FLOATRP" 882425 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 874222 878377 878998 "FLOAT" 880047 T FLOAT (NIL) -8 NIL NIL NIL) (-382 871660 872160 872738 "FLOATCP" 873689 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-381 870400 871238 871279 "FLINEXP" 871284 NIL FLINEXP (NIL T) -9 NIL 871377 NIL) (-380 869554 869789 870117 "FLINEXP-" 870122 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 868630 868774 868998 "FLASORT" 869406 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 865746 866614 866666 "FLALG" 867893 NIL FLALG (NIL T T) -9 NIL 868360 NIL) (-377 859482 863232 863273 "FLAGG" 864535 NIL FLAGG (NIL T) -9 NIL 865187 NIL) (-376 858208 858547 859037 "FLAGG-" 859042 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-375 857250 857393 857620 "FLAGG2" 858061 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-374 854101 855109 855168 "FINRALG" 856296 NIL FINRALG (NIL T T) -9 NIL 856804 NIL) (-373 853261 853490 853829 "FINRALG-" 853834 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 852641 852880 852908 "FINITE" 853104 T FINITE (NIL) -9 NIL 853211 NIL) (-371 844998 847185 847225 "FINAALG" 850892 NIL FINAALG (NIL T) -9 NIL 852345 NIL) (-370 840330 841380 842524 "FINAALG-" 843903 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 839698 840085 840188 "FILE" 840260 NIL FILE (NIL T) -8 NIL NIL NIL) (-368 838356 838694 838748 "FILECAT" 839432 NIL FILECAT (NIL T T) -9 NIL 839648 NIL) (-367 836072 837600 837628 "FIELD" 837668 T FIELD (NIL) -9 NIL 837748 NIL) (-366 834692 835077 835588 "FIELD-" 835593 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 832542 833327 833674 "FGROUP" 834378 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 831632 831796 832016 "FGLMICPK" 832374 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 827464 831557 831614 "FFX" 831619 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 827065 827126 827261 "FFSLPE" 827397 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 823055 823837 824633 "FFPOLY" 826301 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-360 822559 822595 822804 "FFPOLY2" 823013 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-359 818403 822478 822541 "FFP" 822546 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 813801 818314 818378 "FF" 818383 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-357 808927 813144 813334 "FFNBX" 813655 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-356 803855 808062 808320 "FFNBP" 808781 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-355 798488 803139 803350 "FFNB" 803688 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-354 797320 797518 797833 "FFINTBAS" 798285 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-353 793389 795609 795637 "FFIELDC" 796257 T FFIELDC (NIL) -9 NIL 796633 NIL) (-352 792051 792422 792919 "FFIELDC-" 792924 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-351 791620 791666 791790 "FFHOM" 791993 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-350 789315 789802 790319 "FFF" 791135 NIL FFF (NIL T) -7 NIL NIL NIL) (-349 784933 789057 789158 "FFCGX" 789258 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-348 780555 784665 784772 "FFCGP" 784876 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-347 775738 780282 780390 "FFCG" 780491 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-346 757134 766215 766301 "FFCAT" 771466 NIL FFCAT (NIL T T T) -9 NIL 772917 NIL) (-345 752331 753379 754693 "FFCAT-" 755923 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 751742 751785 752020 "FFCAT2" 752282 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 741065 744714 745934 "FEXPR" 750594 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 740065 740500 740541 "FEVALAB" 740625 NIL FEVALAB (NIL T) -9 NIL 740886 NIL) (-341 739224 739434 739772 "FEVALAB-" 739777 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 737790 738607 738810 "FDIV" 739123 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-339 734810 735551 735666 "FDIVCAT" 737234 NIL FDIVCAT (NIL T T T T) -9 NIL 737671 NIL) (-338 734572 734599 734769 "FDIVCAT-" 734774 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-337 733792 733879 734156 "FDIV2" 734479 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-336 732766 733087 733289 "FCTRDATA" 733610 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 731452 731711 732000 "FCPAK1" 732497 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 730551 730952 731093 "FCOMP" 731343 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 714256 717701 721239 "FC" 727033 T FC (NIL) -8 NIL NIL NIL) (-332 706619 710647 710687 "FAXF" 712489 NIL FAXF (NIL T) -9 NIL 713181 NIL) (-331 703895 704553 705378 "FAXF-" 705843 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 698947 703271 703447 "FARRAY" 703752 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 693841 695908 695961 "FAMR" 696984 NIL FAMR (NIL T T) -9 NIL 697444 NIL) (-328 692731 693033 693468 "FAMR-" 693473 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 691900 692653 692706 "FAMONOID" 692711 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 689686 690396 690449 "FAMONC" 691390 NIL FAMONC (NIL T T) -9 NIL 691776 NIL) (-325 688350 689440 689577 "FAGROUP" 689582 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 686145 686464 686867 "FACUTIL" 688031 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 685244 685429 685651 "FACTFUNC" 685955 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 677666 684547 684746 "EXPUPXS" 685100 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 675149 675689 676275 "EXPRTUBE" 677100 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 671420 672012 672742 "EXPRODE" 674488 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 656905 670069 670498 "EXPR" 671024 NIL EXPR (NIL T) -8 NIL NIL NIL) (-318 651459 652046 652852 "EXPR2UPS" 656203 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-317 651091 651148 651257 "EXPR2" 651396 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-316 642481 650244 650534 "EXPEXPAN" 650928 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 642281 642438 642467 "EXIT" 642472 T EXIT (NIL) -8 NIL NIL NIL) (-314 641761 642005 642096 "EXITAST" 642210 T EXITAST (NIL) -8 NIL NIL NIL) (-313 641388 641450 641563 "EVALCYC" 641693 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 640929 641047 641088 "EVALAB" 641258 NIL EVALAB (NIL T) -9 NIL 641362 NIL) (-311 640410 640532 640753 "EVALAB-" 640758 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 637778 639080 639108 "EUCDOM" 639663 T EUCDOM (NIL) -9 NIL 640013 NIL) (-309 636183 636625 637215 "EUCDOM-" 637220 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 623721 626481 629231 "ESTOOLS" 633453 T ESTOOLS (NIL) -7 NIL NIL NIL) (-307 623353 623410 623519 "ESTOOLS2" 623658 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-306 623104 623146 623226 "ESTOOLS1" 623305 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-305 617141 618749 618777 "ES" 621545 T ES (NIL) -9 NIL 622955 NIL) (-304 612088 613375 615192 "ES-" 615356 NIL ES- (NIL T) -8 NIL NIL NIL) (-303 608462 609223 610003 "ESCONT" 611328 T ESCONT (NIL) -7 NIL NIL NIL) (-302 608207 608239 608321 "ESCONT1" 608424 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-301 607882 607932 608032 "ES2" 608151 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-300 607512 607570 607679 "ES1" 607818 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-299 606728 606857 607033 "ERROR" 607356 T ERROR (NIL) -7 NIL NIL NIL) (-298 600120 606587 606678 "EQTBL" 606683 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 592623 595434 596883 "EQ" 598704 NIL -2087 (NIL T) -8 NIL NIL NIL) (-296 592255 592312 592421 "EQ2" 592560 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-295 587545 588593 589686 "EP" 591194 NIL EP (NIL T) -7 NIL NIL NIL) (-294 586145 586436 586742 "ENV" 587259 T ENV (NIL) -8 NIL NIL NIL) (-293 585239 585793 585821 "ENTIRER" 585826 T ENTIRER (NIL) -9 NIL 585872 NIL) (-292 581706 583194 583564 "EMR" 585038 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 580850 581035 581089 "ELTAGG" 581469 NIL ELTAGG (NIL T T) -9 NIL 581680 NIL) (-290 580569 580631 580772 "ELTAGG-" 580777 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 580358 580387 580441 "ELTAB" 580525 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 579484 579630 579829 "ELFUTS" 580209 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 579226 579282 579310 "ELEMFUN" 579415 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 579096 579117 579185 "ELEMFUN-" 579190 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 573940 577196 577237 "ELAGG" 578177 NIL ELAGG (NIL T) -9 NIL 578640 NIL) (-284 572225 572659 573322 "ELAGG-" 573327 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 571537 571674 571830 "ELABOR" 572089 T ELABOR (NIL) -8 NIL NIL NIL) (-282 570198 570477 570771 "ELABEXPR" 571263 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 563062 564865 565692 "EFUPXS" 569474 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 556512 558313 559123 "EFULS" 562338 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 553997 554355 554827 "EFSTRUC" 556144 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 543788 545354 546902 "EF" 552512 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 542862 543273 543422 "EAB" 543659 T EAB (NIL) -8 NIL NIL NIL) (-276 542044 542821 542849 "E04UCFA" 542854 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 541226 542003 542031 "E04NAFA" 542036 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 540408 541185 541213 "E04MBFA" 541218 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 539590 540367 540395 "E04JAFA" 540400 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 538774 539549 539577 "E04GCFA" 539582 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 537958 538733 538761 "E04FDFA" 538766 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 537140 537917 537945 "E04DGFA" 537950 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 531313 532665 534029 "E04AGNT" 535796 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 529993 530499 530539 "DVARCAT" 531014 NIL DVARCAT (NIL T) -9 NIL 531213 NIL) (-267 529197 529409 529723 "DVARCAT-" 529728 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 522334 528996 529125 "DSMP" 529130 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 517115 518279 519347 "DROPT" 521286 T DROPT (NIL) -8 NIL NIL NIL) (-264 516780 516839 516937 "DROPT1" 517050 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-263 511895 513021 514158 "DROPT0" 515663 T DROPT0 (NIL) -7 NIL NIL NIL) (-262 510240 510565 510951 "DRAWPT" 511529 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 504827 505750 506829 "DRAW" 509214 NIL DRAW (NIL T) -7 NIL NIL NIL) (-260 504460 504513 504631 "DRAWHACK" 504768 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-259 503191 503460 503751 "DRAWCX" 504189 T DRAWCX (NIL) -7 NIL NIL NIL) (-258 502706 502775 502926 "DRAWCURV" 503117 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-257 493174 495136 497251 "DRAWCFUN" 500611 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-256 489938 491867 491908 "DQAGG" 492537 NIL DQAGG (NIL T) -9 NIL 492811 NIL) (-255 478062 484531 484614 "DPOLCAT" 486466 NIL DPOLCAT (NIL T T T T) -9 NIL 487011 NIL) (-254 472898 474247 476205 "DPOLCAT-" 476210 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 466020 472759 472857 "DPMO" 472862 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 459045 465800 465967 "DPMM" 465972 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 458523 458737 458835 "DOMTMPLT" 458967 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 457956 458325 458405 "DOMCTOR" 458463 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 457168 457436 457587 "DOMAIN" 457825 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 451156 456803 456955 "DMP" 457069 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 450756 450812 450956 "DLP" 451094 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 444578 450083 450273 "DLIST" 450598 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 441375 443431 443472 "DLAGG" 444022 NIL DLAGG (NIL T) -9 NIL 444252 NIL) (-244 440051 440715 440743 "DIVRING" 440835 T DIVRING (NIL) -9 NIL 440918 NIL) (-243 439288 439478 439778 "DIVRING-" 439783 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 437390 437747 438153 "DISPLAY" 438902 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 431278 437304 437367 "DIRPROD" 437372 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-240 430126 430329 430594 "DIRPROD2" 431071 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-239 418901 424907 424960 "DIRPCAT" 425370 NIL DIRPCAT (NIL NIL T) -9 NIL 426210 NIL) (-238 416227 416869 417750 "DIRPCAT-" 418087 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 415514 415674 415860 "DIOSP" 416061 T DIOSP (NIL) -7 NIL NIL NIL) (-236 412169 414426 414467 "DIOPS" 414901 NIL DIOPS (NIL T) -9 NIL 415130 NIL) (-235 411718 411832 412023 "DIOPS-" 412028 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 410541 411169 411197 "DIFRING" 411384 T DIFRING (NIL) -9 NIL 411494 NIL) (-233 410187 410264 410416 "DIFRING-" 410421 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 407923 409195 409236 "DIFEXT" 409599 NIL DIFEXT (NIL T) -9 NIL 409893 NIL) (-231 406208 406636 407302 "DIFEXT-" 407307 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 403483 405740 405781 "DIAGG" 405786 NIL DIAGG (NIL T) -9 NIL 405806 NIL) (-229 402867 403024 403276 "DIAGG-" 403281 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 398284 401826 402103 "DHMATRIX" 402636 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 393896 394805 395815 "DFSFUN" 397294 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 388975 392827 393139 "DFLOAT" 393604 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 387238 387519 387908 "DFINTTLS" 388683 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 384267 385259 385659 "DERHAM" 386904 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 382068 384042 384131 "DEQUEUE" 384211 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 381322 381455 381638 "DEGRED" 381930 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 377752 378497 379343 "DEFINTRF" 380550 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 375307 375776 376368 "DEFINTEF" 377271 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 374657 374927 375042 "DEFAST" 375212 T DEFAST (NIL) -8 NIL NIL NIL) (-218 368661 374252 374401 "DECIMAL" 374528 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 366173 366631 367137 "DDFACT" 368205 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 365769 365812 365963 "DBLRESP" 366124 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 363641 364002 364362 "DBASE" 365536 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 362883 363121 363267 "DATAARY" 363540 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 361989 362842 362870 "D03FAFA" 362875 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 361096 361948 361976 "D03EEFA" 361981 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 359046 359512 360001 "D03AGNT" 360627 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 358335 359005 359033 "D02EJFA" 359038 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 357624 358294 358322 "D02CJFA" 358327 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356913 357583 357611 "D02BHFA" 357616 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 356202 356872 356900 "D02BBFA" 356905 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 349399 350988 352594 "D02AGNT" 354616 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 347167 347690 348236 "D01WGTS" 348873 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 346234 347126 347154 "D01TRNS" 347159 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 345302 346193 346221 "D01GBFA" 346226 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 344370 345261 345289 "D01FCFA" 345294 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 343438 344329 344357 "D01ASFA" 344362 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 342506 343397 343425 "D01AQFA" 343430 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 341574 342465 342493 "D01APFA" 342498 T D01APFA (NIL) -8 NIL NIL NIL) (-198 340642 341533 341561 "D01ANFA" 341566 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 339710 340601 340629 "D01AMFA" 340634 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 338778 339669 339697 "D01ALFA" 339702 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 337846 338737 338765 "D01AKFA" 338770 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336914 337805 337833 "D01AJFA" 337838 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 330209 331762 333323 "D01AGNT" 335373 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 329546 329674 329826 "CYCLOTOM" 330077 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 326281 326994 327721 "CYCLES" 328839 T CYCLES (NIL) -7 NIL NIL NIL) (-190 325593 325727 325898 "CVMP" 326142 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 323434 323692 324061 "CTRIGMNP" 325321 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322870 323228 323301 "CTOR" 323381 T CTOR (NIL) -8 NIL NIL NIL) (-187 322379 322601 322702 "CTORKIND" 322789 T CTORKIND (NIL) -8 NIL NIL NIL) (-186 321670 321986 322014 "CTORCAT" 322196 T CTORCAT (NIL) -9 NIL 322309 NIL) (-185 321268 321379 321538 "CTORCAT-" 321543 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-184 320730 320942 321050 "CTORCALL" 321192 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-183 320104 320203 320356 "CSTTOOLS" 320627 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315903 316560 317318 "CRFP" 319416 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 315378 315624 315716 "CRCEAST" 315831 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 314425 314610 314838 "CRAPACK" 315182 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 313809 313910 314114 "CPMATCH" 314301 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-178 313534 313562 313668 "CPIMA" 313775 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-177 309882 310554 311273 "COORDSYS" 312869 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-176 309294 309415 309557 "CONTOUR" 309760 T CONTOUR (NIL) -8 NIL NIL NIL) (-175 305185 307297 307789 "CONTFRAC" 308834 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-174 305065 305086 305114 "CONDUIT" 305151 T CONDUIT (NIL) -9 NIL NIL NIL) (-173 304153 304707 304735 "COMRING" 304740 T COMRING (NIL) -9 NIL 304792 NIL) (-172 303207 303511 303695 "COMPPROP" 303989 T COMPPROP (NIL) -8 NIL NIL NIL) (-171 302868 302903 303031 "COMPLPAT" 303166 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-170 293159 302677 302786 "COMPLEX" 302791 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-169 292795 292852 292959 "COMPLEX2" 293096 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-168 292134 292255 292415 "COMPILER" 292655 T COMPILER (NIL) -8 NIL NIL NIL) (-167 291852 291887 291985 "COMPFACT" 292093 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275932 285926 285966 "COMPCAT" 286970 NIL COMPCAT (NIL T) -9 NIL 288318 NIL) (-165 265444 268371 271998 "COMPCAT-" 272354 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265173 265201 265304 "COMMUPC" 265410 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264967 265001 265060 "COMMONOP" 265134 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264523 264718 264805 "COMM" 264900 T COMM (NIL) -8 NIL NIL NIL) (-161 264099 264327 264402 "COMMAAST" 264468 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263348 263542 263570 "COMBOPC" 263908 T COMBOPC (NIL) -9 NIL 264083 NIL) (-159 262244 262454 262696 "COMBINAT" 263138 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258701 259275 259902 "COMBF" 261666 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257459 257817 258052 "COLOR" 258486 T COLOR (NIL) -8 NIL NIL NIL) (-156 256935 257180 257272 "COLONAST" 257387 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256575 256622 256747 "CMPLXRT" 256882 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256023 256275 256374 "CLLCTAST" 256496 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251522 252553 253633 "CLIP" 254963 T CLIP (NIL) -7 NIL NIL NIL) (-152 249868 250628 250867 "CLIF" 251349 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246043 248014 248055 "CLAGG" 248984 NIL CLAGG (NIL T) -9 NIL 249520 NIL) (-150 244465 244922 245505 "CLAGG-" 245510 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244009 244094 244234 "CINTSLPE" 244374 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241510 241981 242529 "CHVAR" 243537 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240684 241238 241266 "CHARZ" 241271 T CHARZ (NIL) -9 NIL 241286 NIL) (-146 240438 240478 240556 "CHARPOL" 240638 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239496 240083 240111 "CHARNZ" 240158 T CHARNZ (NIL) -9 NIL 240214 NIL) (-144 237402 238150 238503 "CHAR" 239163 T CHAR (NIL) -8 NIL NIL NIL) (-143 237128 237189 237217 "CFCAT" 237328 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236373 236484 236666 "CDEN" 237012 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232338 235526 235806 "CCLASS" 236113 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231589 231746 231923 "CATEGORY" 232181 T -10 (NIL) -8 NIL NIL NIL) (-139 231162 231508 231556 "CATCTOR" 231561 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230613 230865 230963 "CATAST" 231084 T CATAST (NIL) -8 NIL NIL NIL) (-137 230089 230334 230426 "CASEAST" 230541 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225098 226118 226871 "CARTEN" 229392 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224206 224354 224575 "CARTEN2" 224945 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222522 223356 223613 "CARD" 223969 T CARD (NIL) -8 NIL NIL NIL) (-133 222098 222326 222401 "CAPSLAST" 222467 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221602 221810 221838 "CACHSET" 221970 T CACHSET (NIL) -9 NIL 222048 NIL) (-131 221072 221394 221422 "CABMON" 221472 T CABMON (NIL) -9 NIL 221528 NIL) (-130 220545 220776 220886 "BYTEORD" 220982 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219527 220079 220221 "BYTE" 220384 T BYTE (NIL) -8 NIL NIL 220506) (-128 214877 219032 219204 "BYTEBUF" 219375 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212386 214569 214676 "BTREE" 214803 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209835 212034 212156 "BTOURN" 212296 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207205 209305 209346 "BTCAT" 209414 NIL BTCAT (NIL T) -9 NIL 209491 NIL) (-124 206872 206952 207101 "BTCAT-" 207106 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202137 206015 206043 "BTAGG" 206265 T BTAGG (NIL) -9 NIL 206426 NIL) (-122 201627 201752 201958 "BTAGG-" 201963 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198622 200905 201120 "BSTREE" 201444 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197760 197886 198070 "BRILL" 198478 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194412 196486 196527 "BRAGG" 197176 NIL BRAGG (NIL T) -9 NIL 197434 NIL) (-118 192941 193347 193902 "BRAGG-" 193907 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186170 192287 192471 "BPADICRT" 192789 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184485 186107 186152 "BPADIC" 186157 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184183 184213 184327 "BOUNDZRO" 184449 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179411 180609 181521 "BOP" 183291 T BOP (NIL) -8 NIL NIL NIL) (-113 177192 177596 178071 "BOP1" 178969 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176017 176766 176915 "BOOLEAN" 177063 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175296 175700 175754 "BMODULE" 175759 NIL BMODULE (NIL T T) -9 NIL 175824 NIL) (-110 171097 175094 175167 "BITS" 175243 T BITS (NIL) -8 NIL NIL NIL) (-109 170518 170637 170777 "BINDING" 170977 T BINDING (NIL) -8 NIL NIL NIL) (-108 164525 170115 170263 "BINARY" 170390 T BINARY (NIL) -8 NIL NIL NIL) (-107 162305 163780 163821 "BGAGG" 164081 NIL BGAGG (NIL T) -9 NIL 164218 NIL) (-106 162136 162168 162259 "BGAGG-" 162264 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161207 161520 161725 "BFUNCT" 161951 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159897 160075 160363 "BEZOUT" 161031 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156366 158749 159079 "BBTREE" 159600 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156100 156153 156181 "BASTYPE" 156300 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155952 155981 156054 "BASTYPE-" 156059 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155386 155462 155614 "BALFACT" 155863 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154242 154801 154987 "AUTOMOR" 155231 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153968 153973 153999 "ATTREG" 154004 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152220 152665 153017 "ATTRBUT" 153634 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151828 152048 152114 "ATTRAST" 152172 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151364 151477 151503 "ATRIG" 151704 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151173 151214 151301 "ATRIG-" 151306 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150818 151004 151030 "ASTCAT" 151035 T ASTCAT (NIL) -9 NIL 151065 NIL) (-92 150545 150604 150723 "ASTCAT-" 150728 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148694 150321 150409 "ASTACK" 150488 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147199 147496 147861 "ASSOCEQ" 148376 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146231 146858 146982 "ASP9" 147106 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145994 146179 146218 "ASP8" 146223 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144862 145599 145741 "ASP80" 145883 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143760 144497 144629 "ASP7" 144761 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142714 143437 143555 "ASP78" 143673 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141683 142394 142511 "ASP77" 142628 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140595 141321 141452 "ASP74" 141583 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139495 140230 140362 "ASP73" 140494 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138599 139321 139421 "ASP6" 139426 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137544 138276 138394 "ASP55" 138512 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136493 137218 137337 "ASP50" 137456 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135581 136194 136304 "ASP4" 136414 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134669 135282 135392 "ASP49" 135502 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133453 134208 134376 "ASP42" 134558 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132229 132986 133156 "ASP41" 133340 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131179 131906 132024 "ASP35" 132142 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130944 131127 131166 "ASP34" 131171 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130681 130748 130824 "ASP33" 130899 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129574 130316 130448 "ASP31" 130580 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129339 129522 129561 "ASP30" 129566 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129074 129143 129219 "ASP29" 129294 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128839 129022 129061 "ASP28" 129066 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128604 128787 128826 "ASP27" 128831 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127688 128302 128413 "ASP24" 128524 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126764 127490 127602 "ASP20" 127607 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125852 126465 126575 "ASP1" 126685 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124794 125526 125645 "ASP19" 125764 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124531 124598 124674 "ASP12" 124749 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123383 124130 124274 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T) ((-23) . T) ((-47 |#1| #0=(-569)) . T) ((-25) . T) ((-38 #1=(-412 (-569))) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-38 |#1|) |has| |#1| (-173)) ((-38 |#2|) |has| |#1| (-367)) ((-38 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-35) |has| |#1| (-38 (-412 (-569)))) ((-95) |has| |#1| (-38 (-412 (-569)))) ((-102) . T) ((-111 #1# #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-367)) ((-111 $ $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-131) . T) ((-145) -2776 (-12 (|has| |#1| (-367)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2776 (-12 (|has| |#1| (-367)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-621 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-621 (-569)) . T) ((-621 #2=(-1185)) -12 (|has| |#1| (-367)) (|has| |#2| (-1046 (-1185)))) ((-621 |#1|) |has| |#1| (-173)) ((-621 |#2|) . 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T) ((-173) -2776 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-619 (-226)) -12 (|has| |#1| (-367)) (|has| |#2| (-1030))) ((-619 (-383)) -12 (|has| |#1| (-367)) (|has| |#2| (-1030))) ((-619 (-541)) -12 (|has| |#1| (-367)) (|has| |#2| (-619 (-541)))) ((-619 (-898 (-383))) -12 (|has| |#1| (-367)) (|has| |#2| (-619 (-898 (-383))))) ((-619 (-898 (-569))) -12 (|has| |#1| (-367)) (|has| |#2| (-619 (-898 (-569))))) ((-232 |#2|) |has| |#1| (-367)) ((-234) -2776 (-12 (|has| |#1| (-367)) (|has| |#2| (-234))) (|has| |#1| (-15 * (|#1| (-569) |#1|)))) ((-244) |has| |#1| (-367)) ((-287) |has| |#1| (-38 (-412 (-569)))) ((-289 |#2| $) -12 (|has| |#1| (-367)) (|has| |#2| (-289 |#2| |#2|))) ((-289 $ $) |has| (-569) (-1120)) ((-293) -2776 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-310) |has| |#1| (-367)) ((-312 |#2|) -12 (|has| |#1| (-367)) (|has| |#2| (-312 |#2|))) ((-367) |has| |#1| (-367)) ((-342 |#2|) |has| |#1| (-367)) ((-381 |#2|) |has| |#1| (-367)) ((-405 |#2|) |has| |#1| (-367)) ((-457) |has| |#1| (-367)) ((-498) |has| |#1| (-38 (-412 (-569)))) ((-519 (-1185) |#2|) -12 (|has| |#1| (-367)) (|has| |#2| (-519 (-1185) |#2|))) ((-519 |#2| |#2|) -12 (|has| |#1| (-367)) (|has| |#2| (-312 |#2|))) ((-561) -2776 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-651 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-651 (-569)) . T) ((-651 |#1|) . T) ((-651 |#2|) |has| |#1| (-367)) ((-651 $) . T) ((-653 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-653 |#1|) . T) ((-653 |#2|) |has| |#1| (-367)) ((-653 $) . T) ((-645 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-645 |#1|) |has| |#1| (-173)) ((-645 |#2|) |has| |#1| (-367)) ((-645 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-644 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-644 (-569)))) ((-644 |#2|) |has| |#1| (-367)) ((-722 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-722 |#1|) |has| |#1| (-173)) ((-722 |#2|) |has| |#1| (-367)) ((-722 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367))) ((-731) . T) ((-796) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-797) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-799) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-800) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-825) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-853) -12 (|has| |#1| (-367)) (|has| |#2| (-825))) ((-855) -2776 (-12 (|has| |#1| (-367)) (|has| |#2| (-855))) (-12 (|has| |#1| (-367)) (|has| |#2| (-825)))) ((-906 (-1185)) -2776 (-12 (|has| |#1| (-367)) (|has| |#2| (-906 (-1185)))) (-12 (|has| |#1| (-15 * (|#1| (-569) |#1|))) (|has| |#1| (-906 (-1185))))) ((-892 (-383)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-383)))) ((-892 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-892 (-569)))) ((-890 |#2|) |has| |#1| (-367)) ((-915) -12 (|has| |#1| (-367)) (|has| |#2| (-915))) ((-981 |#1| #0# (-1090)) . T) ((-926) |has| |#1| (-367)) ((-1000 |#2|) |has| |#1| (-367)) ((-1010) |has| |#1| (-38 (-412 (-569)))) ((-1030) -12 (|has| |#1| (-367)) (|has| |#2| (-1030))) ((-1046 (-412 (-569))) -12 (|has| |#1| (-367)) (|has| |#2| (-1046 (-569)))) ((-1046 (-569)) -12 (|has| |#1| (-367)) (|has| |#2| (-1046 (-569)))) ((-1046 #2#) -12 (|has| |#1| (-367)) (|has| |#2| (-1046 (-1185)))) ((-1046 |#2|) . T) ((-1059 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-1059 |#1|) . T) ((-1059 |#2|) |has| |#1| (-367)) ((-1059 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1064 #1#) -2776 (|has| |#1| (-367)) (|has| |#1| (-38 (-412 (-569))))) ((-1064 |#1|) . T) ((-1064 |#2|) |has| |#1| (-367)) ((-1064 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1057) . T) ((-1066) . T) ((-1120) . T) ((-1108) . T) ((-1160) -12 (|has| |#1| (-367)) (|has| |#2| (-1160))) ((-1210) |has| |#1| (-38 (-412 (-569)))) ((-1213) |has| |#1| (-38 (-412 (-569)))) ((-1225) |has| |#1| (-367)) ((-1229) |has| |#1| (-367)) ((-1235 |#1|) . T) ((-1253 |#1| #0#) . 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T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #1#) |has| |#1| (-38 (-412 (-569)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #1#) |has| |#1| (-38 (-412 (-569)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) -2776 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-644 (-569)) |has| |#1| (-644 (-569))) ((-644 |#1|) . T) ((-722 #1#) |has| |#1| (-38 (-412 (-569)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) -2776 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367))) ((-731) . T) ((-906 #2#) . T) ((-906 (-1185)) |has| |#1| (-906 (-1185))) ((-892 (-383)) -12 (|has| (-1090) (-892 (-383))) (|has| |#1| (-892 (-383)))) ((-892 (-569)) -12 (|has| (-1090) (-892 (-569))) (|has| |#1| (-892 (-569)))) ((-955 |#1| #0# #2#) . T) ((-915) |has| |#1| (-915)) ((-926) |has| |#1| (-367)) ((-1046 (-412 (-569))) |has| |#1| (-1046 (-412 (-569)))) ((-1046 (-569)) |has| |#1| (-1046 (-569))) ((-1046 #2#) . T) ((-1046 |#1|) . T) ((-1059 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1059 |#1|) . T) ((-1059 $) -2776 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1064 #1#) |has| |#1| (-38 (-412 (-569)))) ((-1064 |#1|) . T) ((-1064 $) -2776 (|has| |#1| (-915)) (|has| |#1| (-561)) (|has| |#1| (-457)) (|has| |#1| (-367)) (|has| |#1| (-173))) ((-1057) . T) ((-1066) . T) ((-1120) . T) ((-1108) . T) ((-1160) |has| |#1| (-1160)) ((-1229) |has| |#1| (-915))) +((-1712 (((-649 (-1090)) $) 34)) (-1883 (($ $) 31)) (-3923 (($ |#2| |#3|) NIL) (($ $ (-1090) |#3|) 28) (($ $ (-649 (-1090)) (-649 |#3|)) 27)) (-1849 (($ $) 14)) (-1857 ((|#2| $) 12)) (-4339 ((|#3| $) 10))) +(((-1252 |#1| |#2| |#3|) (-10 -8 (-15 -1712 ((-649 (-1090)) |#1|)) (-15 -3923 (|#1| |#1| (-649 (-1090)) (-649 |#3|))) (-15 -3923 (|#1| |#1| (-1090) |#3|)) (-15 -1883 (|#1| |#1|)) (-15 -3923 (|#1| |#2| |#3|)) (-15 -4339 (|#3| |#1|)) (-15 -1849 (|#1| |#1|)) (-15 -1857 (|#2| |#1|))) (-1253 |#2| |#3|) (-1057) (-797)) (T -1252)) +NIL +(-10 -8 (-15 -1712 ((-649 (-1090)) |#1|)) (-15 -3923 (|#1| |#1| (-649 (-1090)) (-649 |#3|))) (-15 -3923 (|#1| |#1| (-1090) |#3|)) (-15 -1883 (|#1| |#1|)) (-15 -3923 (|#1| |#2| |#3|)) (-15 -4339 (|#3| |#1|)) (-15 -1849 (|#1| |#1|)) (-15 -1857 (|#2| |#1|))) +((-2417 (((-112) $ $) 7)) (-4143 (((-112) $) 17)) (-1712 (((-649 (-1090)) $) 86)) (-2672 (((-1185) $) 115)) (-2194 (((-2 (|:| -2736 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-412 (-569))) |has| |#1| (-38 (-412 (-569)))) ((-38 |#1|) |has| |#1| (-173)) ((-38 $) |has| |#1| (-561)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-412 (-569)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2776 (|has| |#1| (-561)) (|has| |#1| (-173))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-621 #0#) |has| |#1| (-38 (-412 (-569)))) ((-621 (-569)) . T) ((-621 |#1|) |has| |#1| (-173)) ((-621 $) |has| |#1| (-561)) ((-618 (-867)) . T) ((-173) -2776 (|has| |#1| (-561)) (|has| |#1| (-173))) ((-234) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-289 $ $) |has| |#2| (-1120)) ((-293) |has| |#1| (-561)) ((-561) |has| |#1| (-561)) ((-651 #0#) |has| |#1| (-38 (-412 (-569)))) ((-651 (-569)) . T) ((-651 |#1|) . T) ((-651 $) . T) ((-653 #0#) |has| |#1| (-38 (-412 (-569)))) ((-653 |#1|) . T) ((-653 $) . T) ((-645 #0#) |has| |#1| (-38 (-412 (-569)))) ((-645 |#1|) |has| |#1| (-173)) ((-645 $) |has| |#1| (-561)) ((-722 #0#) |has| |#1| (-38 (-412 (-569)))) ((-722 |#1|) |has| |#1| (-173)) ((-722 $) |has| |#1| (-561)) ((-731) . T) ((-906 (-1185)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-906 (-1185)))) ((-981 |#1| |#2| (-1090)) . T) ((-1059 #0#) |has| |#1| (-38 (-412 (-569)))) ((-1059 |#1|) . T) ((-1059 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-173))) ((-1064 #0#) |has| |#1| (-38 (-412 (-569)))) ((-1064 |#1|) . T) ((-1064 $) -2776 (|has| |#1| (-561)) (|has| |#1| (-173))) ((-1057) . T) ((-1066) . T) ((-1120) . T) ((-1108) . 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"WHILEAST" 3179007 T WHILEAST (NIL) -8 NIL NIL NIL) (-1285 3178129 3178374 3178468 "WHEREAST" 3178585 T WHEREAST (NIL) -8 NIL NIL NIL) (-1284 3177015 3177213 3177508 "WFFINTBS" 3177926 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1283 3174919 3175346 3175808 "WEIER" 3176587 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1282 3173965 3174415 3174457 "VSPACE" 3174593 NIL VSPACE (NIL T) -9 NIL 3174667 NIL) (-1281 3173803 3173830 3173921 "VSPACE-" 3173926 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1280 3173612 3173654 3173722 "VOID" 3173757 T VOID (NIL) -8 NIL NIL NIL) (-1279 3171748 3172107 3172513 "VIEW" 3173228 T VIEW (NIL) -7 NIL NIL NIL) (-1278 3168172 3168811 3169548 "VIEWDEF" 3171033 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1277 3157476 3159720 3161893 "VIEW3D" 3166021 T VIEW3D (NIL) -8 NIL NIL NIL) (-1276 3149727 3151387 3152966 "VIEW2D" 3155919 T VIEW2D (NIL) -8 NIL NIL NIL) (-1275 3145080 3149497 3149589 "VECTOR" 3149670 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1274 3143657 3143916 3144234 "VECTOR2" 3144810 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1273 3137131 3141438 3141481 "VECTCAT" 3142476 NIL VECTCAT (NIL T) -9 NIL 3143063 NIL) (-1272 3136145 3136399 3136789 "VECTCAT-" 3136794 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1271 3135599 3135796 3135916 "VARIABLE" 3136060 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1270 3135532 3135537 3135567 "UTYPE" 3135572 T UTYPE (NIL) -9 NIL NIL NIL) (-1269 3134362 3134516 3134778 "UTSODETL" 3135358 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1268 3131802 3132262 3132786 "UTSODE" 3133903 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1267 3123639 3129428 3129917 "UTS" 3131371 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1266 3114513 3119880 3119923 "UTSCAT" 3121035 NIL UTSCAT (NIL T) -9 NIL 3121793 NIL) (-1265 3111860 3112583 3113572 "UTSCAT-" 3113577 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1264 3111487 3111530 3111663 "UTS2" 3111811 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1263 3105713 3108325 3108368 "URAGG" 3110438 NIL URAGG (NIL T) -9 NIL 3111161 NIL) (-1262 3102652 3103515 3104638 "URAGG-" 3104643 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1261 3098361 3101287 3101752 "UPXSSING" 3102316 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1260 3090427 3097608 3097881 "UPXS" 3098146 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1259 3083500 3090331 3090403 "UPXSCONS" 3090408 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1258 3073245 3080038 3080100 "UPXSCCA" 3080674 NIL UPXSCCA (NIL T T) -9 NIL 3080907 NIL) (-1257 3072883 3072968 3073142 "UPXSCCA-" 3073147 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1256 3062480 3069046 3069089 "UPXSCAT" 3069737 NIL UPXSCAT (NIL T) -9 NIL 3070346 NIL) (-1255 3061910 3061989 3062168 "UPXS2" 3062395 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1254 3060564 3060817 3061168 "UPSQFREE" 3061653 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1253 3053985 3057042 3057097 "UPSCAT" 3058258 NIL UPSCAT (NIL T T) -9 NIL 3059032 NIL) (-1252 3053189 3053396 3053723 "UPSCAT-" 3053728 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1251 3038844 3046612 3046655 "UPOLYC" 3048756 NIL UPOLYC (NIL T) -9 NIL 3049977 NIL) (-1250 3030172 3032598 3035745 "UPOLYC-" 3035750 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1249 3029799 3029842 3029975 "UPOLYC2" 3030123 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1248 3021610 3029482 3029611 "UP" 3029718 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1247 3020949 3021056 3021220 "UPMP" 3021499 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1246 3020502 3020583 3020722 "UPDIVP" 3020862 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1245 3019070 3019319 3019635 "UPDECOMP" 3020251 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1244 3018301 3018413 3018599 "UPCDEN" 3018954 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1243 3017820 3017889 3018038 "UP2" 3018226 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1242 3016287 3017024 3017301 "UNISEG" 3017578 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1241 3015502 3015629 3015834 "UNISEG2" 3016130 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1240 3014562 3014742 3014968 "UNIFACT" 3015318 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1239 2998494 3013739 3013990 "ULS" 3014369 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1238 2986492 2998398 2998470 "ULSCONS" 2998475 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1237 2968509 2980494 2980556 "ULSCCAT" 2981194 NIL ULSCCAT (NIL T T) -9 NIL 2981483 NIL) (-1236 2967559 2967804 2968192 "ULSCCAT-" 2968197 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 2956933 2963413 2963456 "ULSCAT" 2964319 NIL ULSCAT (NIL T) -9 NIL 2965050 NIL) (-1234 2956363 2956442 2956621 "ULS2" 2956848 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1233 2955490 2956000 2956107 "UINT8" 2956218 T UINT8 (NIL) -8 NIL NIL 2956303) (-1232 2954616 2955126 2955233 "UINT64" 2955344 T UINT64 (NIL) -8 NIL NIL 2955429) (-1231 2953742 2954252 2954359 "UINT32" 2954470 T UINT32 (NIL) -8 NIL NIL 2954555) (-1230 2952868 2953378 2953485 "UINT16" 2953596 T UINT16 (NIL) -8 NIL NIL 2953681) (-1229 2951171 2952128 2952158 "UFD" 2952370 T UFD (NIL) -9 NIL 2952484 NIL) (-1228 2950965 2951011 2951106 "UFD-" 2951111 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1227 2950047 2950230 2950446 "UDVO" 2950771 T UDVO (NIL) -7 NIL NIL NIL) (-1226 2947863 2948272 2948743 "UDPO" 2949611 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1225 2947796 2947801 2947831 "TYPE" 2947836 T TYPE (NIL) -9 NIL NIL NIL) (-1224 2947556 2947751 2947782 "TYPEAST" 2947787 T TYPEAST (NIL) -8 NIL NIL NIL) (-1223 2946527 2946729 2946969 "TWOFACT" 2947350 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1222 2945550 2945936 2946171 "TUPLE" 2946327 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1221 2943241 2943760 2944299 "TUBETOOL" 2945033 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1220 2942090 2942295 2942536 "TUBE" 2943034 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1219 2936819 2941062 2941345 "TS" 2941842 NIL TS (NIL T) -8 NIL NIL NIL) (-1218 2925459 2929578 2929675 "TSETCAT" 2934944 NIL TSETCAT (NIL T T T T) -9 NIL 2936475 NIL) (-1217 2920191 2921791 2923682 "TSETCAT-" 2923687 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1216 2914830 2915677 2916606 "TRMANIP" 2919327 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1215 2914271 2914334 2914497 "TRIMAT" 2914762 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1214 2912137 2912374 2912731 "TRIGMNIP" 2914020 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1213 2911657 2911770 2911800 "TRIGCAT" 2912013 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1212 2911326 2911405 2911546 "TRIGCAT-" 2911551 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1211 2908171 2910184 2910465 "TREE" 2911080 NIL TREE (NIL T) -8 NIL NIL NIL) (-1210 2907445 2907973 2908003 "TRANFUN" 2908038 T TRANFUN (NIL) -9 NIL 2908104 NIL) (-1209 2906724 2906915 2907195 "TRANFUN-" 2907200 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1208 2906528 2906560 2906621 "TOPSP" 2906685 T TOPSP (NIL) -7 NIL NIL NIL) (-1207 2905876 2905991 2906145 "TOOLSIGN" 2906409 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1206 2904510 2905053 2905292 "TEXTFILE" 2905659 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1205 2902422 2902963 2903392 "TEX" 2904103 T TEX (NIL) -8 NIL NIL NIL) (-1204 2902203 2902234 2902306 "TEX1" 2902385 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1203 2901851 2901914 2902004 "TEMUTL" 2902135 T TEMUTL (NIL) -7 NIL NIL NIL) (-1202 2900005 2900285 2900610 "TBCMPPK" 2901574 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1201 2891782 2898165 2898221 "TBAGG" 2898621 NIL TBAGG (NIL T T) -9 NIL 2898832 NIL) (-1200 2886852 2888340 2890094 "TBAGG-" 2890099 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1199 2886236 2886343 2886488 "TANEXP" 2886741 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1198 2879626 2886093 2886186 "TABLE" 2886191 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1197 2879038 2879137 2879275 "TABLEAU" 2879523 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1196 2873646 2874866 2876114 "TABLBUMP" 2877824 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1195 2872868 2873015 2873196 "SYSTEM" 2873487 T SYSTEM (NIL) -8 NIL NIL NIL) (-1194 2869327 2870026 2870809 "SYSSOLP" 2872119 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1193 2869125 2869282 2869313 "SYSPTR" 2869318 T SYSPTR (NIL) -8 NIL NIL NIL) (-1192 2868169 2868674 2868793 "SYSNNI" 2868979 NIL SYSNNI (NIL NIL) -8 NIL NIL 2869064) (-1191 2867476 2867935 2868014 "SYSINT" 2868074 NIL SYSINT (NIL NIL) -8 NIL NIL 2868119) (-1190 2863808 2864754 2865464 "SYNTAX" 2866788 T SYNTAX (NIL) -8 NIL NIL NIL) (-1189 2860966 2861568 2862200 "SYMTAB" 2863198 T SYMTAB (NIL) -8 NIL NIL NIL) (-1188 2856215 2857117 2858100 "SYMS" 2860005 T SYMS (NIL) -8 NIL NIL NIL) (-1187 2853450 2855673 2855903 "SYMPOLY" 2856020 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1186 2852967 2853042 2853165 "SYMFUNC" 2853362 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1185 2848987 2850279 2851092 "SYMBOL" 2852176 T SYMBOL (NIL) -8 NIL NIL NIL) (-1184 2842526 2844215 2845935 "SWITCH" 2847289 T SWITCH (NIL) -8 NIL NIL NIL) (-1183 2835760 2841347 2841650 "SUTS" 2842281 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1182 2827826 2835007 2835280 "SUPXS" 2835545 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1181 2819585 2827444 2827570 "SUP" 2827735 NIL SUP (NIL T) -8 NIL NIL NIL) (-1180 2818744 2818871 2819088 "SUPFRACF" 2819453 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1179 2818365 2818424 2818537 "SUP2" 2818679 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1178 2816813 2817087 2817443 "SUMRF" 2818064 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1177 2816148 2816214 2816406 "SUMFS" 2816734 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1176 2800115 2815325 2815576 "SULS" 2815955 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1175 2799717 2799937 2800007 "SUCHTAST" 2800067 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1174 2799012 2799242 2799382 "SUCH" 2799625 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1173 2792878 2793918 2794877 "SUBSPACE" 2798100 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1172 2792308 2792398 2792562 "SUBRESP" 2792766 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1171 2785674 2786973 2788284 "STTF" 2791044 NIL STTF (NIL T) -7 NIL NIL NIL) (-1170 2779847 2780967 2782114 "STTFNC" 2784574 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1169 2771158 2773029 2774823 "STTAYLOR" 2778088 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1168 2764288 2771022 2771105 "STRTBL" 2771110 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1167 2759652 2764243 2764274 "STRING" 2764279 T STRING (NIL) -8 NIL NIL NIL) (-1166 2754513 2759025 2759055 "STRICAT" 2759114 T STRICAT (NIL) -9 NIL 2759176 NIL) (-1165 2747266 2752132 2752743 "STREAM" 2753937 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1164 2746776 2746853 2746997 "STREAM3" 2747183 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1163 2745758 2745941 2746176 "STREAM2" 2746589 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1162 2745446 2745498 2745591 "STREAM1" 2745700 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1161 2744462 2744643 2744874 "STINPROD" 2745262 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1160 2744014 2744224 2744254 "STEP" 2744334 T STEP (NIL) -9 NIL 2744412 NIL) (-1159 2743201 2743503 2743651 "STEPAST" 2743888 T STEPAST (NIL) -8 NIL NIL NIL) (-1158 2736633 2743100 2743177 "STBL" 2743182 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1157 2731759 2735854 2735897 "STAGG" 2736050 NIL STAGG (NIL T) -9 NIL 2736139 NIL) (-1156 2729461 2730063 2730935 "STAGG-" 2730940 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1155 2727608 2729231 2729323 "STACK" 2729404 NIL STACK (NIL T) -8 NIL NIL NIL) (-1154 2720303 2725749 2726205 "SREGSET" 2727238 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1153 2712728 2714097 2715610 "SRDCMPK" 2718909 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1152 2705645 2710168 2710198 "SRAGG" 2711501 T SRAGG (NIL) -9 NIL 2712109 NIL) (-1151 2704662 2704917 2705296 "SRAGG-" 2705301 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1150 2699122 2703609 2704030 "SQMATRIX" 2704288 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1149 2692807 2695840 2696567 "SPLTREE" 2698467 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1148 2688770 2689463 2690109 "SPLNODE" 2692233 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1147 2687817 2688050 2688080 "SPFCAT" 2688524 T SPFCAT (NIL) -9 NIL NIL NIL) (-1146 2686554 2686764 2687028 "SPECOUT" 2687575 T SPECOUT (NIL) -7 NIL NIL NIL) (-1145 2677664 2679536 2679566 "SPADXPT" 2684242 T SPADXPT (NIL) -9 NIL 2686406 NIL) (-1144 2677425 2677465 2677534 "SPADPRSR" 2677617 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1143 2675474 2677380 2677411 "SPADAST" 2677416 T SPADAST (NIL) -8 NIL NIL NIL) (-1142 2667419 2669192 2669235 "SPACEC" 2673608 NIL SPACEC (NIL T) -9 NIL 2675424 NIL) (-1141 2665549 2667351 2667400 "SPACE3" 2667405 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1140 2664301 2664472 2664763 "SORTPAK" 2665354 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1139 2662393 2662696 2663108 "SOLVETRA" 2663965 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1138 2661443 2661665 2661926 "SOLVESER" 2662166 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1137 2656747 2657635 2658630 "SOLVERAD" 2660495 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1136 2652562 2653171 2653900 "SOLVEFOR" 2656114 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1135 2646832 2651911 2652008 "SNTSCAT" 2652013 NIL SNTSCAT (NIL T T T T) -9 NIL 2652083 NIL) (-1134 2640938 2645155 2645546 "SMTS" 2646522 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1133 2635623 2640826 2640903 "SMP" 2640908 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1132 2633782 2634083 2634481 "SMITH" 2635320 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1131 2626495 2630691 2630794 "SMATCAT" 2632145 NIL SMATCAT (NIL NIL T T T) -9 NIL 2632695 NIL) (-1130 2623435 2624258 2625436 "SMATCAT-" 2625441 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1129 2621101 2622671 2622714 "SKAGG" 2622975 NIL SKAGG (NIL T) -9 NIL 2623110 NIL) (-1128 2617412 2620517 2620712 "SINT" 2620899 T SINT (NIL) -8 NIL NIL 2621072) (-1127 2617184 2617222 2617288 "SIMPAN" 2617368 T SIMPAN (NIL) -7 NIL NIL NIL) (-1126 2616463 2616719 2616859 "SIG" 2617066 T SIG (NIL) -8 NIL NIL NIL) (-1125 2615301 2615522 2615797 "SIGNRF" 2616222 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1124 2614134 2614285 2614569 "SIGNEF" 2615130 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1123 2613440 2613717 2613841 "SIGAST" 2614032 T SIGAST (NIL) -8 NIL NIL NIL) (-1122 2611130 2611584 2612090 "SHP" 2612981 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1121 2604982 2611031 2611107 "SHDP" 2611112 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1120 2604555 2604747 2604777 "SGROUP" 2604870 T SGROUP (NIL) -9 NIL 2604932 NIL) (-1119 2604413 2604439 2604512 "SGROUP-" 2604517 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1118 2601248 2601946 2602669 "SGCF" 2603712 T SGCF (NIL) -7 NIL NIL NIL) (-1117 2595616 2600695 2600792 "SFRTCAT" 2600797 NIL SFRTCAT (NIL T T T T) -9 NIL 2600836 NIL) (-1116 2589037 2590055 2591191 "SFRGCD" 2594599 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1115 2582163 2583236 2584422 "SFQCMPK" 2587970 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1114 2581783 2581872 2581983 "SFORT" 2582104 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1113 2580901 2581623 2581744 "SEXOF" 2581749 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1112 2580008 2580782 2580850 "SEX" 2580855 T SEX (NIL) -8 NIL NIL NIL) (-1111 2575521 2576236 2576331 "SEXCAT" 2579268 NIL SEXCAT (NIL T T T T T) -9 NIL 2579846 NIL) (-1110 2572674 2575455 2575503 "SET" 2575508 NIL SET (NIL T) -8 NIL NIL NIL) (-1109 2570898 2571387 2571692 "SETMN" 2572415 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1108 2570394 2570546 2570576 "SETCAT" 2570752 T SETCAT (NIL) -9 NIL 2570862 NIL) (-1107 2570086 2570164 2570294 "SETCAT-" 2570299 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1106 2566447 2568547 2568590 "SETAGG" 2569460 NIL SETAGG (NIL T) -9 NIL 2569800 NIL) (-1105 2565905 2566021 2566258 "SETAGG-" 2566263 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1104 2565348 2565601 2565702 "SEQAST" 2565826 T SEQAST (NIL) -8 NIL NIL NIL) (-1103 2564547 2564841 2564902 "SEGXCAT" 2565188 NIL SEGXCAT (NIL T T) -9 NIL 2565308 NIL) (-1102 2563553 2564213 2564395 "SEG" 2564400 NIL SEG (NIL T) -8 NIL NIL NIL) (-1101 2562532 2562746 2562789 "SEGCAT" 2563311 NIL SEGCAT (NIL T) -9 NIL 2563532 NIL) (-1100 2561464 2561895 2562103 "SEGBIND" 2562359 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1099 2561085 2561144 2561257 "SEGBIND2" 2561399 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1098 2560658 2560886 2560963 "SEGAST" 2561030 T SEGAST (NIL) -8 NIL NIL NIL) (-1097 2559877 2560003 2560207 "SEG2" 2560502 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1096 2559287 2559812 2559859 "SDVAR" 2559864 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1095 2551814 2559057 2559187 "SDPOL" 2559192 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1094 2550407 2550673 2550992 "SCPKG" 2551529 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1093 2549571 2549743 2549935 "SCOPE" 2550237 T SCOPE (NIL) -8 NIL NIL NIL) (-1092 2548791 2548925 2549104 "SCACHE" 2549426 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1091 2548437 2548623 2548653 "SASTCAT" 2548658 T SASTCAT (NIL) -9 NIL 2548671 NIL) (-1090 2547924 2548272 2548348 "SAOS" 2548383 T SAOS (NIL) -8 NIL NIL NIL) (-1089 2547489 2547524 2547697 "SAERFFC" 2547883 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1088 2541428 2547386 2547466 "SAE" 2547471 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1087 2541021 2541056 2541215 "SAEFACT" 2541387 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1086 2539342 2539656 2540057 "RURPK" 2540687 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1085 2537979 2538285 2538590 "RULESET" 2539176 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1084 2535202 2535732 2536190 "RULE" 2537660 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1083 2534814 2534996 2535079 "RULECOLD" 2535154 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1082 2534604 2534632 2534703 "RTVALUE" 2534765 T RTVALUE (NIL) -8 NIL NIL NIL) (-1081 2534075 2534321 2534415 "RSTRCAST" 2534532 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1080 2528923 2529718 2530638 "RSETGCD" 2533274 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1079 2518153 2523232 2523329 "RSETCAT" 2527448 NIL RSETCAT (NIL T T T T) -9 NIL 2528545 NIL) (-1078 2516080 2516619 2517443 "RSETCAT-" 2517448 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1077 2508466 2509842 2511362 "RSDCMPK" 2514679 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1076 2506445 2506912 2506986 "RRCC" 2508072 NIL RRCC (NIL T T) -9 NIL 2508416 NIL) (-1075 2505796 2505970 2506249 "RRCC-" 2506254 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1074 2505239 2505492 2505593 "RPTAST" 2505717 T RPTAST (NIL) -8 NIL NIL NIL) (-1073 2479085 2488444 2488511 "RPOLCAT" 2499177 NIL RPOLCAT (NIL T T T) -9 NIL 2502337 NIL) (-1072 2470583 2472923 2476045 "RPOLCAT-" 2476050 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1071 2461514 2468794 2469276 "ROUTINE" 2470123 T ROUTINE (NIL) -8 NIL NIL NIL) (-1070 2458312 2461140 2461280 "ROMAN" 2461396 T ROMAN (NIL) -8 NIL NIL NIL) (-1069 2456556 2457172 2457432 "ROIRC" 2458117 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1068 2452788 2455072 2455102 "RNS" 2455406 T RNS (NIL) -9 NIL 2455680 NIL) (-1067 2451297 2451680 2452214 "RNS-" 2452289 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1066 2450700 2451108 2451138 "RNG" 2451143 T RNG (NIL) -9 NIL 2451164 NIL) (-1065 2449703 2450065 2450267 "RNGBIND" 2450551 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1064 2449102 2449490 2449533 "RMODULE" 2449538 NIL RMODULE (NIL T) -9 NIL 2449565 NIL) (-1063 2447938 2448032 2448368 "RMCAT2" 2449003 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1062 2444788 2447284 2447581 "RMATRIX" 2447700 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1061 2437615 2439875 2439990 "RMATCAT" 2443349 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2444331 NIL) (-1060 2436990 2437137 2437444 "RMATCAT-" 2437449 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1059 2436391 2436612 2436655 "RLINSET" 2436849 NIL RLINSET (NIL T) -9 NIL 2436940 NIL) (-1058 2435958 2436033 2436161 "RINTERP" 2436310 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1057 2435016 2435570 2435600 "RING" 2435656 T RING (NIL) -9 NIL 2435748 NIL) (-1056 2434808 2434852 2434949 "RING-" 2434954 NIL RING- (NIL T) -8 NIL NIL NIL) (-1055 2433649 2433886 2434144 "RIDIST" 2434572 T RIDIST (NIL) -7 NIL NIL NIL) (-1054 2424938 2433117 2433323 "RGCHAIN" 2433497 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1053 2424288 2424694 2424735 "RGBCSPC" 2424793 NIL RGBCSPC (NIL T) -9 NIL 2424845 NIL) (-1052 2423446 2423827 2423868 "RGBCMDL" 2424100 NIL RGBCMDL (NIL T) -9 NIL 2424214 NIL) (-1051 2420440 2421054 2421724 "RF" 2422810 NIL RF (NIL T) -7 NIL NIL NIL) (-1050 2420086 2420149 2420252 "RFFACTOR" 2420371 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1049 2419811 2419846 2419943 "RFFACT" 2420045 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1048 2417928 2418292 2418674 "RFDIST" 2419451 T RFDIST (NIL) -7 NIL NIL NIL) (-1047 2417381 2417473 2417636 "RETSOL" 2417830 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1046 2417017 2417097 2417140 "RETRACT" 2417273 NIL RETRACT (NIL T) -9 NIL 2417360 NIL) (-1045 2416866 2416891 2416978 "RETRACT-" 2416983 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1044 2416468 2416688 2416758 "RETAST" 2416818 T RETAST (NIL) -8 NIL NIL NIL) (-1043 2409206 2416121 2416248 "RESULT" 2416363 T RESULT (NIL) -8 NIL NIL NIL) (-1042 2407797 2408475 2408674 "RESRING" 2409109 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1041 2407433 2407482 2407580 "RESLATC" 2407734 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1040 2407138 2407173 2407280 "REPSQ" 2407392 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1039 2404560 2405140 2405742 "REP" 2406558 T REP (NIL) -7 NIL NIL NIL) (-1038 2404257 2404292 2404403 "REPDB" 2404519 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1037 2398157 2399546 2400769 "REP2" 2403069 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1036 2394534 2395215 2396023 "REP1" 2397384 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1035 2387230 2392675 2393131 "REGSET" 2394164 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1034 2385995 2386378 2386628 "REF" 2387015 NIL REF (NIL T) -8 NIL NIL NIL) (-1033 2385372 2385475 2385642 "REDORDER" 2385879 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1032 2381340 2384585 2384812 "RECLOS" 2385200 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1031 2380392 2380573 2380788 "REALSOLV" 2381147 T REALSOLV (NIL) -7 NIL NIL NIL) (-1030 2380238 2380279 2380309 "REAL" 2380314 T REAL (NIL) -9 NIL 2380349 NIL) (-1029 2376721 2377523 2378407 "REAL0Q" 2379403 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1028 2372322 2373310 2374371 "REAL0" 2375702 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1027 2371793 2372039 2372133 "RDUCEAST" 2372250 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1026 2371198 2371270 2371477 "RDIV" 2371715 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1025 2370266 2370440 2370653 "RDIST" 2371020 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1024 2368863 2369150 2369522 "RDETRS" 2369974 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1023 2366675 2367129 2367667 "RDETR" 2368405 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1022 2365300 2365578 2365975 "RDEEFS" 2366391 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1021 2363809 2364115 2364540 "RDEEF" 2364988 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1020 2357870 2360790 2360820 "RCFIELD" 2362115 T RCFIELD (NIL) -9 NIL 2362846 NIL) (-1019 2355934 2356438 2357134 "RCFIELD-" 2357209 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1018 2352203 2354035 2354078 "RCAGG" 2355162 NIL RCAGG (NIL T) -9 NIL 2355627 NIL) (-1017 2351831 2351925 2352088 "RCAGG-" 2352093 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1016 2351166 2351278 2351443 "RATRET" 2351715 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1015 2350719 2350786 2350907 "RATFACT" 2351094 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1014 2350027 2350147 2350299 "RANDSRC" 2350589 T RANDSRC (NIL) -7 NIL NIL NIL) (-1013 2349761 2349805 2349878 "RADUTIL" 2349976 T RADUTIL (NIL) -7 NIL NIL NIL) (-1012 2342875 2348592 2348903 "RADIX" 2349484 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1011 2334494 2342717 2342847 "RADFF" 2342852 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1010 2334141 2334216 2334246 "RADCAT" 2334406 T RADCAT (NIL) -9 NIL NIL NIL) (-1009 2333923 2333971 2334071 "RADCAT-" 2334076 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1008 2332021 2333693 2333785 "QUEUE" 2333866 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1007 2328558 2331954 2332002 "QUAT" 2332007 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1006 2328189 2328232 2328363 "QUATCT2" 2328509 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1005 2321638 2324983 2325025 "QUATCAT" 2325816 NIL QUATCAT (NIL T) -9 NIL 2326582 NIL) (-1004 2317777 2318814 2320204 "QUATCAT-" 2320300 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1003 2315242 2316853 2316896 "QUAGG" 2317277 NIL QUAGG (NIL T) -9 NIL 2317452 NIL) (-1002 2314844 2315064 2315134 "QQUTAST" 2315194 T QQUTAST (NIL) -8 NIL NIL NIL) (-1001 2313737 2314237 2314411 "QFORM" 2314716 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1000 2304730 2309969 2310011 "QFCAT" 2310679 NIL QFCAT (NIL T) -9 NIL 2311680 NIL) (-999 2300300 2301501 2303093 "QFCAT-" 2303188 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-998 2299934 2299977 2300106 "QFCAT2" 2300251 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2299394 2299504 2299634 "QEQUAT" 2299824 T QEQUAT (NIL) -8 NIL NIL NIL) (-996 2292540 2293613 2294797 "QCMPACK" 2298327 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-995 2290089 2290537 2290965 "QALGSET" 2292195 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-994 2289334 2289508 2289740 "QALGSET2" 2289909 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-993 2288024 2288248 2288565 "PWFFINTB" 2289107 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-992 2286206 2286374 2286728 "PUSHVAR" 2287838 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-991 2282124 2283178 2283219 "PTRANFN" 2285103 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-990 2280526 2280817 2281139 "PTPACK" 2281835 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-989 2280158 2280215 2280324 "PTFUNC2" 2280463 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-988 2274635 2279030 2279071 "PTCAT" 2279367 NIL PTCAT (NIL T) -9 NIL 2279520 NIL) (-987 2274293 2274328 2274452 "PSQFR" 2274594 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-986 2272888 2273186 2273520 "PSEUDLIN" 2273991 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-985 2259651 2262022 2264346 "PSETPK" 2270648 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-984 2252669 2255409 2255505 "PSETCAT" 2258526 NIL PSETCAT (NIL T T T T) -9 NIL 2259340 NIL) (-983 2250505 2251139 2251960 "PSETCAT-" 2251965 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-982 2249854 2250019 2250047 "PSCURVE" 2250315 T PSCURVE (NIL) -9 NIL 2250482 NIL) (-981 2245852 2247368 2247433 "PSCAT" 2248277 NIL PSCAT (NIL T T T) -9 NIL 2248517 NIL) (-980 2244915 2245131 2245531 "PSCAT-" 2245536 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-979 2243620 2244280 2244485 "PRTITION" 2244730 T PRTITION (NIL) -8 NIL NIL NIL) (-978 2243095 2243341 2243433 "PRTDAST" 2243548 T PRTDAST (NIL) -8 NIL NIL NIL) (-977 2232185 2234399 2236587 "PRS" 2240957 NIL PRS (NIL T T) -7 NIL NIL NIL) (-976 2229996 2231535 2231575 "PRQAGG" 2231758 NIL PRQAGG (NIL T) -9 NIL 2231860 NIL) (-975 2229200 2229505 2229533 "PROPLOG" 2229780 T PROPLOG (NIL) -9 NIL 2229946 NIL) (-974 2228804 2228861 2228984 "PROPFUN2" 2229123 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-973 2228311 2228393 2228527 "PROPFUN1" 2228703 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-972 2226492 2227058 2227355 "PROPFRML" 2228047 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-971 2225961 2226068 2226196 "PROPERTY" 2226384 T PROPERTY (NIL) -8 NIL NIL NIL) (-970 2220019 2224127 2224947 "PRODUCT" 2225187 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-969 2217297 2219477 2219711 "PR" 2219830 NIL PR (NIL T T) -8 NIL NIL NIL) (-968 2217093 2217125 2217184 "PRINT" 2217258 T PRINT (NIL) -7 NIL NIL NIL) (-967 2216433 2216550 2216702 "PRIMES" 2216973 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-966 2214498 2214899 2215365 "PRIMELT" 2216012 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-965 2214227 2214276 2214304 "PRIMCAT" 2214428 T PRIMCAT (NIL) -9 NIL NIL NIL) (-964 2210342 2214165 2214210 "PRIMARR" 2214215 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-963 2209349 2209527 2209755 "PRIMARR2" 2210160 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-962 2208992 2209048 2209159 "PREASSOC" 2209287 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-961 2208467 2208600 2208628 "PPCURVE" 2208833 T PPCURVE (NIL) -9 NIL 2208969 NIL) (-960 2208062 2208262 2208345 "PORTNUM" 2208404 T PORTNUM (NIL) -8 NIL NIL NIL) (-959 2205421 2205820 2206412 "POLYROOT" 2207643 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-958 2199603 2205025 2205185 "POLY" 2205294 NIL POLY (NIL T) -8 NIL NIL NIL) (-957 2198986 2199044 2199278 "POLYLIFT" 2199539 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-956 2195261 2195710 2196339 "POLYCATQ" 2198531 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-955 2181973 2187101 2187166 "POLYCAT" 2190680 NIL POLYCAT (NIL T T T) -9 NIL 2192558 NIL) (-954 2175422 2177284 2179668 "POLYCAT-" 2179673 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-953 2175009 2175077 2175197 "POLY2UP" 2175348 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-952 2174641 2174698 2174807 "POLY2" 2174946 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-951 2173326 2173565 2173841 "POLUTIL" 2174415 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-950 2171681 2171958 2172289 "POLTOPOL" 2173048 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-949 2167146 2171617 2171663 "POINT" 2171668 NIL POINT (NIL T) -8 NIL NIL NIL) (-948 2165333 2165690 2166065 "PNTHEORY" 2166791 T PNTHEORY (NIL) -7 NIL NIL NIL) (-947 2163791 2164088 2164487 "PMTOOLS" 2165031 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-946 2163384 2163462 2163579 "PMSYM" 2163707 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-945 2162892 2162961 2163136 "PMQFCAT" 2163309 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-944 2162247 2162357 2162513 "PMPRED" 2162769 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-943 2161640 2161726 2161888 "PMPREDFS" 2162148 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-942 2160304 2160512 2160890 "PMPLCAT" 2161402 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-941 2159836 2159915 2160067 "PMLSAGG" 2160219 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-940 2159309 2159385 2159567 "PMKERNEL" 2159754 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-939 2158926 2159001 2159114 "PMINS" 2159228 NIL PMINS (NIL T) -7 NIL NIL NIL) (-938 2158368 2158437 2158646 "PMFS" 2158851 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-937 2157596 2157714 2157919 "PMDOWN" 2158245 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-936 2156763 2156921 2157102 "PMASS" 2157435 T PMASS (NIL) -7 NIL NIL NIL) (-935 2156036 2156146 2156309 "PMASSFS" 2156650 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-934 2155691 2155759 2155853 "PLOTTOOL" 2155962 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-933 2150298 2151502 2152650 "PLOT" 2154563 T PLOT (NIL) -8 NIL NIL NIL) (-932 2146102 2147146 2148067 "PLOT3D" 2149397 T PLOT3D (NIL) -8 NIL NIL NIL) (-931 2145014 2145191 2145426 "PLOT1" 2145906 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-930 2120403 2125080 2129931 "PLEQN" 2140280 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-929 2119721 2119843 2120023 "PINTERP" 2120268 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-928 2119414 2119461 2119564 "PINTERPA" 2119668 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-927 2118635 2119183 2119270 "PI" 2119310 T PI (NIL) -8 NIL NIL 2119377) (-926 2116932 2117907 2117935 "PID" 2118117 T PID (NIL) -9 NIL 2118251 NIL) (-925 2116683 2116720 2116795 "PICOERCE" 2116889 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-924 2116003 2116142 2116318 "PGROEB" 2116539 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-923 2111590 2112404 2113309 "PGE" 2115118 T PGE (NIL) -7 NIL NIL NIL) (-922 2109713 2109960 2110326 "PGCD" 2111307 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-921 2109051 2109154 2109315 "PFRPAC" 2109597 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-920 2105691 2107599 2107952 "PFR" 2108730 NIL PFR (NIL T) -8 NIL NIL NIL) (-919 2104080 2104324 2104649 "PFOTOOLS" 2105438 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-918 2102613 2102852 2103203 "PFOQ" 2103837 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-917 2101114 2101326 2101682 "PFO" 2102397 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-916 2097667 2101003 2101072 "PF" 2101077 NIL PF (NIL NIL) -8 NIL NIL NIL) (-915 2095001 2096272 2096300 "PFECAT" 2096885 T PFECAT (NIL) -9 NIL 2097269 NIL) (-914 2094446 2094600 2094814 "PFECAT-" 2094819 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-913 2093049 2093301 2093602 "PFBRU" 2094195 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-912 2090915 2091267 2091699 "PFBR" 2092700 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-911 2086797 2088291 2088967 "PERM" 2090272 NIL PERM (NIL T) -8 NIL NIL NIL) (-910 2082031 2083004 2083874 "PERMGRP" 2085960 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-909 2080137 2081094 2081135 "PERMCAT" 2081581 NIL 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1998486 1998771 "ORTHPOL" 1999261 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-860 1995810 1998094 1998215 "OREUP" 1998220 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-859 1993213 1995501 1995628 "ORESUP" 1995752 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-858 1990741 1991241 1991802 "OREPCTO" 1992702 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-857 1984427 1986628 1986669 "OREPCAT" 1989017 NIL OREPCAT (NIL T) -9 NIL 1990121 NIL) (-856 1981574 1982356 1983414 "OREPCAT-" 1983419 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-855 1980725 1981023 1981051 "ORDSET" 1981360 T ORDSET (NIL) -9 NIL 1981524 NIL) (-854 1980156 1980304 1980528 "ORDSET-" 1980533 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-853 1978721 1979512 1979540 "ORDRING" 1979742 T ORDRING (NIL) -9 NIL 1979867 NIL) (-852 1978366 1978460 1978604 "ORDRING-" 1978609 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-851 1977746 1978209 1978237 "ORDMON" 1978242 T ORDMON (NIL) -9 NIL 1978263 NIL) (-850 1976908 1977055 1977250 "ORDFUNS" 1977595 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-849 1976246 1976665 1976693 "ORDFIN" 1976758 T ORDFIN (NIL) -9 NIL 1976832 NIL) (-848 1972805 1974832 1975241 "ORDCOMP" 1975870 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-847 1972071 1972198 1972384 "ORDCOMP2" 1972665 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-846 1968652 1969562 1970376 "OPTPROB" 1971277 T OPTPROB (NIL) -8 NIL NIL NIL) (-845 1965454 1966093 1966797 "OPTPACK" 1967968 T OPTPACK (NIL) -7 NIL NIL NIL) (-844 1963141 1963907 1963935 "OPTCAT" 1964754 T OPTCAT (NIL) -9 NIL 1965404 NIL) (-843 1962525 1962818 1962923 "OPSIG" 1963056 T OPSIG (NIL) -8 NIL NIL NIL) (-842 1962293 1962332 1962398 "OPQUERY" 1962479 T OPQUERY (NIL) -7 NIL NIL NIL) (-841 1959424 1960604 1961108 "OP" 1961822 NIL OP (NIL T) -8 NIL NIL NIL) (-840 1958798 1959024 1959065 "OPERCAT" 1959277 NIL OPERCAT (NIL T) -9 NIL 1959374 NIL) (-839 1958553 1958609 1958726 "OPERCAT-" 1958731 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-838 1955366 1957350 1957719 "ONECOMP" 1958217 NIL ONECOMP (NIL T) -8 NIL NIL 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T OINTDOM (NIL) -9 NIL 1936920 NIL) (-824 1933228 1934578 1934915 "OFMONOID" 1935585 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-823 1932639 1933165 1933210 "ODVAR" 1933215 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-822 1930062 1932384 1932539 "ODR" 1932544 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-821 1922643 1929838 1929964 "ODPOL" 1929969 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-820 1916465 1922515 1922620 "ODP" 1922625 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-819 1915231 1915446 1915721 "ODETOOLS" 1916239 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-818 1912198 1912856 1913572 "ODESYS" 1914564 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-817 1907080 1907988 1909013 "ODERTRIC" 1911273 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-816 1906506 1906588 1906782 "ODERED" 1906992 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-815 1903394 1903942 1904619 "ODERAT" 1905929 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-814 1900351 1900818 1901415 "ODEPRRIC" 1902923 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-813 1898294 1898890 1899376 "ODEPROB" 1899885 T ODEPROB (NIL) -8 NIL NIL NIL) (-812 1894814 1895299 1895946 "ODEPRIM" 1897773 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-811 1894063 1894165 1894425 "ODEPAL" 1894706 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-810 1890225 1891016 1891880 "ODEPACK" 1893219 T ODEPACK (NIL) -7 NIL NIL NIL) (-809 1889286 1889393 1889615 "ODEINT" 1890114 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-808 1883387 1884812 1886259 "ODEIFTBL" 1887859 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-807 1878785 1879571 1880523 "ODEEF" 1882546 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-806 1878134 1878223 1878446 "ODECONST" 1878690 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-805 1876259 1876920 1876948 "ODECAT" 1877553 T ODECAT (NIL) -9 NIL 1878084 NIL) (-804 1873114 1875964 1876086 "OCT" 1876169 NIL OCT (NIL T) -8 NIL NIL NIL) (-803 1872752 1872795 1872922 "OCTCT2" 1873065 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-802 1867401 1869836 1869876 "OC" 1870973 NIL OC (NIL T) -9 NIL 1871831 NIL) (-801 1864628 1865376 1866366 "OC-" 1866460 NIL OC- (NIL T T) -8 NIL NIL NIL) (-800 1863980 1864448 1864476 "OCAMON" 1864481 T OCAMON (NIL) -9 NIL 1864502 NIL) (-799 1863511 1863852 1863880 "OASGP" 1863885 T OASGP (NIL) -9 NIL 1863905 NIL) (-798 1862772 1863261 1863289 "OAMONS" 1863329 T OAMONS (NIL) -9 NIL 1863372 NIL) (-797 1862186 1862619 1862647 "OAMON" 1862652 T OAMON (NIL) -9 NIL 1862672 NIL) (-796 1861444 1861962 1861990 "OAGROUP" 1861995 T OAGROUP (NIL) -9 NIL 1862015 NIL) (-795 1861134 1861184 1861272 "NUMTUBE" 1861388 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-794 1854707 1856225 1857761 "NUMQUAD" 1859618 T NUMQUAD (NIL) -7 NIL NIL NIL) (-793 1850463 1851451 1852476 "NUMODE" 1853702 T NUMODE (NIL) -7 NIL NIL NIL) (-792 1847818 1848698 1848726 "NUMINT" 1849649 T NUMINT (NIL) -9 NIL 1850413 NIL) (-791 1846766 1846963 1847181 "NUMFMT" 1847620 T NUMFMT (NIL) -7 NIL NIL NIL) (-790 1833125 1836070 1838602 "NUMERIC" 1844273 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-789 1827495 1832574 1832669 "NTSCAT" 1832674 NIL NTSCAT (NIL T T T T) -9 NIL 1832713 NIL) (-788 1826689 1826854 1827047 "NTPOLFN" 1827334 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-787 1814766 1823514 1824326 "NSUP" 1825910 NIL NSUP (NIL T) -8 NIL NIL NIL) (-786 1814398 1814455 1814564 "NSUP2" 1814703 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-785 1804624 1814172 1814305 "NSMP" 1814310 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-784 1803056 1803357 1803714 "NREP" 1804312 NIL NREP (NIL T) -7 NIL NIL NIL) (-783 1801647 1801899 1802257 "NPCOEF" 1802799 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-782 1800713 1800828 1801044 "NORMRETR" 1801528 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-781 1798754 1799044 1799453 "NORMPK" 1800421 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-780 1798439 1798467 1798591 "NORMMA" 1798720 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-779 1798239 1798396 1798425 "NONE" 1798430 T NONE (NIL) -8 NIL NIL NIL) (-778 1798028 1798057 1798126 "NONE1" 1798203 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-777 1797525 1797587 1797766 "NODE1" 1797960 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-776 1795810 1796661 1796916 "NNI" 1797263 T NNI (NIL) -8 NIL NIL 1797498) (-775 1794230 1794543 1794907 "NLINSOL" 1795478 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-774 1790471 1791466 1792365 "NIPROB" 1793351 T NIPROB (NIL) -8 NIL NIL NIL) (-773 1789228 1789462 1789764 "NFINTBAS" 1790233 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-772 1788402 1788878 1788919 "NETCLT" 1789091 NIL NETCLT (NIL T) -9 NIL 1789173 NIL) (-771 1787110 1787341 1787622 "NCODIV" 1788170 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-770 1786872 1786909 1786984 "NCNTFRAC" 1787067 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-769 1785052 1785416 1785836 "NCEP" 1786497 NIL NCEP (NIL T) -7 NIL NIL NIL) (-768 1783903 1784676 1784704 "NASRING" 1784814 T NASRING (NIL) -9 NIL 1784894 NIL) (-767 1783698 1783742 1783836 "NASRING-" 1783841 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-766 1782805 1783330 1783358 "NARNG" 1783475 T NARNG (NIL) -9 NIL 1783566 NIL) (-765 1782497 1782564 1782698 "NARNG-" 1782703 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-764 1781376 1781583 1781818 "NAGSP" 1782282 T NAGSP (NIL) -7 NIL NIL NIL) (-763 1772648 1774332 1776005 "NAGS" 1779723 T NAGS (NIL) -7 NIL NIL NIL) (-762 1771196 1771504 1771835 "NAGF07" 1772337 T NAGF07 (NIL) -7 NIL NIL NIL) (-761 1765734 1767025 1768332 "NAGF04" 1769909 T NAGF04 (NIL) -7 NIL NIL NIL) (-760 1758702 1760316 1761949 "NAGF02" 1764121 T NAGF02 (NIL) -7 NIL NIL NIL) (-759 1753926 1755026 1756143 "NAGF01" 1757605 T NAGF01 (NIL) -7 NIL NIL NIL) (-758 1747554 1749120 1750705 "NAGE04" 1752361 T NAGE04 (NIL) -7 NIL NIL NIL) (-757 1738723 1740844 1742974 "NAGE02" 1745444 T NAGE02 (NIL) -7 NIL NIL NIL) (-756 1734676 1735623 1736587 "NAGE01" 1737779 T NAGE01 (NIL) -7 NIL NIL NIL) (-755 1732471 1733005 1733563 "NAGD03" 1734138 T NAGD03 (NIL) -7 NIL NIL NIL) (-754 1724221 1726149 1728103 "NAGD02" 1730537 T NAGD02 (NIL) -7 NIL NIL NIL) (-753 1718032 1719457 1720897 "NAGD01" 1722801 T NAGD01 (NIL) -7 NIL NIL NIL) (-752 1714241 1715063 1715900 "NAGC06" 1717215 T NAGC06 (NIL) -7 NIL NIL NIL) (-751 1712706 1713038 1713394 "NAGC05" 1713905 T NAGC05 (NIL) -7 NIL NIL NIL) (-750 1712082 1712201 1712345 "NAGC02" 1712582 T NAGC02 (NIL) -7 NIL NIL NIL) (-749 1711041 1711624 1711664 "NAALG" 1711743 NIL NAALG (NIL T) -9 NIL 1711804 NIL) (-748 1710876 1710905 1710995 "NAALG-" 1711000 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-747 1704826 1705934 1707121 "MULTSQFR" 1709772 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-746 1704145 1704220 1704404 "MULTFACT" 1704738 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-745 1696869 1700782 1700835 "MTSCAT" 1701905 NIL MTSCAT (NIL T T) -9 NIL 1702420 NIL) (-744 1696581 1696635 1696727 "MTHING" 1696809 NIL MTHING (NIL T) -7 NIL NIL NIL) (-743 1696373 1696406 1696466 "MSYSCMD" 1696541 T MSYSCMD (NIL) -7 NIL NIL NIL) (-742 1692455 1695128 1695448 "MSET" 1696086 NIL MSET (NIL T) -8 NIL NIL NIL) (-741 1689524 1692016 1692057 "MSETAGG" 1692062 NIL MSETAGG (NIL T) -9 NIL 1692096 NIL) (-740 1685365 1686903 1687648 "MRING" 1688824 NIL MRING (NIL T T) -8 NIL NIL NIL) (-739 1684931 1684998 1685129 "MRF2" 1685292 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-738 1684549 1684584 1684728 "MRATFAC" 1684890 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-737 1682161 1682456 1682887 "MPRFF" 1684254 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-736 1676458 1682015 1682112 "MPOLY" 1682117 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-735 1675948 1675983 1676191 "MPCPF" 1676417 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-734 1675462 1675505 1675689 "MPC3" 1675899 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-733 1674657 1674738 1674959 "MPC2" 1675377 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-732 1672958 1673295 1673685 "MONOTOOL" 1674317 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-731 1672183 1672500 1672528 "MONOID" 1672747 T MONOID (NIL) -9 NIL 1672894 NIL) (-730 1671729 1671848 1672029 "MONOID-" 1672034 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-729 1662204 1668155 1668214 "MONOGEN" 1668888 NIL MONOGEN (NIL T T) -9 NIL 1669344 NIL) (-728 1659422 1660157 1661157 "MONOGEN-" 1661276 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-727 1658255 1658701 1658729 "MONADWU" 1659121 T MONADWU (NIL) -9 NIL 1659359 NIL) (-726 1657627 1657786 1658034 "MONADWU-" 1658039 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-725 1656986 1657230 1657258 "MONAD" 1657465 T MONAD (NIL) -9 NIL 1657577 NIL) (-724 1656671 1656749 1656881 "MONAD-" 1656886 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-723 1654960 1655584 1655863 "MOEBIUS" 1656424 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-722 1654238 1654642 1654682 "MODULE" 1654687 NIL MODULE (NIL T) -9 NIL 1654726 NIL) (-721 1653806 1653902 1654092 "MODULE-" 1654097 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-720 1651486 1652170 1652497 "MODRING" 1653630 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-719 1648430 1649591 1650112 "MODOP" 1651015 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-718 1647018 1647497 1647774 "MODMONOM" 1648293 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-717 1637060 1645309 1645723 "MODMON" 1646655 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-716 1634216 1635904 1636180 "MODFIELD" 1636935 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-715 1633193 1633497 1633687 "MMLFORM" 1634046 T MMLFORM (NIL) -8 NIL NIL NIL) (-714 1632719 1632762 1632941 "MMAP" 1633144 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-713 1630798 1631565 1631606 "MLO" 1632029 NIL MLO (NIL T) -9 NIL 1632271 NIL) (-712 1628164 1628680 1629282 "MLIFT" 1630279 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-711 1627555 1627639 1627793 "MKUCFUNC" 1628075 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-710 1627154 1627224 1627347 "MKRECORD" 1627478 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-709 1626201 1626363 1626591 "MKFUNC" 1626965 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-708 1625589 1625693 1625849 "MKFLCFN" 1626084 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-707 1624866 1624968 1625153 "MKBCFUNC" 1625482 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-706 1621573 1624420 1624556 "MINT" 1624750 T MINT (NIL) -8 NIL NIL NIL) (-705 1620385 1620628 1620905 "MHROWRED" 1621328 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-704 1615765 1618920 1619325 "MFLOAT" 1620000 T MFLOAT (NIL) -8 NIL NIL NIL) (-703 1615122 1615198 1615369 "MFINFACT" 1615677 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-702 1611437 1612285 1613169 "MESH" 1614258 T MESH (NIL) -7 NIL NIL NIL) (-701 1609827 1610139 1610492 "MDDFACT" 1611124 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-700 1606622 1608986 1609027 "MDAGG" 1609282 NIL MDAGG (NIL T) -9 NIL 1609425 NIL) (-699 1596362 1605915 1606122 "MCMPLX" 1606435 T MCMPLX (NIL) -8 NIL NIL NIL) (-698 1595499 1595645 1595846 "MCDEN" 1596211 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-697 1593389 1593659 1594039 "MCALCFN" 1595229 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-696 1592314 1592554 1592787 "MAYBE" 1593195 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-695 1589926 1590449 1591011 "MATSTOR" 1591785 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-694 1585883 1589298 1589546 "MATRIX" 1589711 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-693 1581647 1582356 1583092 "MATLIN" 1585240 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-692 1571753 1574939 1575016 "MATCAT" 1579896 NIL MATCAT (NIL T T T) -9 NIL 1581313 NIL) (-691 1568109 1569130 1570486 "MATCAT-" 1570491 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-690 1566703 1566856 1567189 "MATCAT2" 1567944 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-689 1564815 1565139 1565523 "MAPPKG3" 1566378 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-688 1563796 1563969 1564191 "MAPPKG2" 1564639 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-687 1562295 1562579 1562906 "MAPPKG1" 1563502 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-686 1561374 1561701 1561878 "MAPPAST" 1562138 T MAPPAST (NIL) -8 NIL NIL NIL) (-685 1560985 1561043 1561166 "MAPHACK3" 1561310 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-684 1560577 1560638 1560752 "MAPHACK2" 1560917 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-683 1560014 1560118 1560260 "MAPHACK1" 1560468 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-682 1558093 1558714 1559018 "MAGMA" 1559742 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-681 1557572 1557817 1557908 "MACROAST" 1558022 T MACROAST (NIL) -8 NIL NIL NIL) (-680 1553990 1555811 1556272 "M3D" 1557144 NIL M3D (NIL T) -8 NIL NIL NIL) (-679 1548096 1552359 1552400 "LZSTAGG" 1553182 NIL LZSTAGG (NIL T) -9 NIL 1553477 NIL) (-678 1544053 1545227 1546684 "LZSTAGG-" 1546689 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-677 1541140 1541944 1542431 "LWORD" 1543598 NIL LWORD (NIL T) -8 NIL NIL NIL) (-676 1540716 1540944 1541019 "LSTAST" 1541085 T LSTAST (NIL) -8 NIL NIL NIL) (-675 1533882 1540487 1540621 "LSQM" 1540626 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-674 1533106 1533245 1533473 "LSPP" 1533737 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-673 1530918 1531219 1531675 "LSMP" 1532795 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-672 1527697 1528371 1529101 "LSMP1" 1530220 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-671 1521574 1526864 1526905 "LSAGG" 1526967 NIL LSAGG (NIL T) -9 NIL 1527045 NIL) (-670 1518269 1519193 1520406 "LSAGG-" 1520411 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-669 1515868 1517413 1517662 "LPOLY" 1518064 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-668 1515450 1515535 1515658 "LPEFRAC" 1515777 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-667 1513771 1514544 1514797 "LO" 1515282 NIL LO (NIL T T T) -8 NIL NIL NIL) (-666 1513423 1513535 1513563 "LOGIC" 1513674 T LOGIC (NIL) -9 NIL 1513755 NIL) (-665 1513285 1513308 1513379 "LOGIC-" 1513384 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-664 1512478 1512618 1512811 "LODOOPS" 1513141 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-663 1509901 1512394 1512460 "LODO" 1512465 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-662 1508439 1508674 1509027 "LODOF" 1509648 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-661 1504657 1507088 1507129 "LODOCAT" 1507567 NIL LODOCAT (NIL T) -9 NIL 1507778 NIL) (-660 1504390 1504448 1504575 "LODOCAT-" 1504580 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-659 1501710 1504231 1504349 "LODO2" 1504354 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-658 1499145 1501647 1501692 "LODO1" 1501697 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-657 1498026 1498191 1498496 "LODEEF" 1498968 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-656 1493265 1496156 1496197 "LNAGG" 1497144 NIL LNAGG (NIL T) -9 NIL 1497588 NIL) (-655 1492412 1492626 1492968 "LNAGG-" 1492973 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-654 1488548 1489337 1489976 "LMOPS" 1491827 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-653 1487951 1488339 1488380 "LMODULE" 1488385 NIL LMODULE (NIL T) -9 NIL 1488411 NIL) (-652 1485149 1487596 1487719 "LMDICT" 1487861 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-651 1484555 1484776 1484817 "LLINSET" 1485008 NIL LLINSET (NIL T) -9 NIL 1485099 NIL) (-650 1484254 1484463 1484523 "LITERAL" 1484528 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-649 1477417 1483188 1483492 "LIST" 1483983 NIL LIST (NIL T) -8 NIL NIL NIL) (-648 1476942 1477016 1477155 "LIST3" 1477337 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-647 1475949 1476127 1476355 "LIST2" 1476760 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-646 1474083 1474395 1474794 "LIST2MAP" 1475596 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-645 1473679 1473916 1473957 "LINSET" 1473962 NIL LINSET (NIL T) -9 NIL 1473996 NIL) (-644 1472340 1473010 1473051 "LINEXP" 1473306 NIL LINEXP (NIL T) -9 NIL 1473455 NIL) (-643 1470987 1471247 1471544 "LINDEP" 1472092 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-642 1467754 1468473 1469250 "LIMITRF" 1470242 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-641 1466057 1466353 1466762 "LIMITPS" 1467449 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-640 1460485 1465568 1465796 "LIE" 1465878 NIL LIE (NIL T T) -8 NIL NIL NIL) (-639 1459433 1459902 1459942 "LIECAT" 1460082 NIL LIECAT (NIL T) -9 NIL 1460233 NIL) (-638 1459274 1459301 1459389 "LIECAT-" 1459394 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-637 1451770 1458723 1458888 "LIB" 1459129 T LIB (NIL) -8 NIL NIL NIL) (-636 1447405 1448288 1449223 "LGROBP" 1450887 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-635 1445403 1445677 1446027 "LF" 1447126 NIL LF (NIL T T) -7 NIL NIL NIL) (-634 1444243 1444935 1444963 "LFCAT" 1445170 T LFCAT (NIL) -9 NIL 1445309 NIL) (-633 1441145 1441775 1442463 "LEXTRIPK" 1443607 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-632 1437889 1438715 1439218 "LEXP" 1440725 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-631 1437365 1437610 1437702 "LETAST" 1437817 T LETAST (NIL) -8 NIL NIL NIL) (-630 1435763 1436076 1436477 "LEADCDET" 1437047 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-629 1434953 1435027 1435256 "LAZM3PK" 1435684 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-628 1429870 1433030 1433568 "LAUPOL" 1434465 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-627 1429449 1429493 1429654 "LAPLACE" 1429820 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-626 1427388 1428550 1428801 "LA" 1429282 NIL LA (NIL T T T) -8 NIL NIL NIL) (-625 1426382 1426966 1427007 "LALG" 1427069 NIL LALG (NIL T) -9 NIL 1427128 NIL) (-624 1426096 1426155 1426291 "LALG-" 1426296 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-623 1425931 1425955 1425996 "KVTFROM" 1426058 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-622 1424854 1425298 1425483 "KTVLOGIC" 1425766 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-621 1424689 1424713 1424754 "KRCFROM" 1424816 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-620 1423593 1423780 1424079 "KOVACIC" 1424489 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-619 1423428 1423452 1423493 "KONVERT" 1423555 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-618 1423263 1423287 1423328 "KOERCE" 1423390 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-617 1421093 1421856 1422233 "KERNEL" 1422919 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-616 1420589 1420670 1420802 "KERNEL2" 1421007 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-615 1414359 1419128 1419182 "KDAGG" 1419559 NIL KDAGG (NIL T T) -9 NIL 1419765 NIL) (-614 1413888 1414012 1414217 "KDAGG-" 1414222 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-613 1407036 1413549 1413704 "KAFILE" 1413766 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-612 1401464 1406547 1406775 "JORDAN" 1406857 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-611 1400843 1401113 1401234 "JOINAST" 1401363 T JOINAST (NIL) -8 NIL NIL NIL) (-610 1400689 1400748 1400803 "JAVACODE" 1400808 T JAVACODE (NIL) -8 NIL NIL NIL) (-609 1396941 1398894 1398948 "IXAGG" 1399877 NIL IXAGG (NIL T T) -9 NIL 1400336 NIL) (-608 1395860 1396166 1396585 "IXAGG-" 1396590 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-607 1391390 1395782 1395841 "IVECTOR" 1395846 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-606 1390156 1390393 1390659 "ITUPLE" 1391157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-605 1388658 1388835 1389130 "ITRIGMNP" 1389978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-604 1387403 1387607 1387890 "ITFUN3" 1388434 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-603 1387035 1387092 1387201 "ITFUN2" 1387340 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-602 1386194 1386515 1386689 "ITFORM" 1386881 T ITFORM (NIL) -8 NIL NIL NIL) (-601 1384155 1385214 1385492 "ITAYLOR" 1385949 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-600 1373100 1378292 1379455 "ISUPS" 1383025 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-599 1372204 1372344 1372580 "ISUMP" 1372947 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-598 1367579 1372149 1372190 "ISTRING" 1372195 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-597 1367055 1367300 1367392 "ISAST" 1367507 T ISAST (NIL) -8 NIL NIL NIL) (-596 1366264 1366346 1366562 "IRURPK" 1366969 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-595 1365200 1365401 1365641 "IRSN" 1366044 T IRSN (NIL) -7 NIL NIL NIL) (-594 1363271 1363626 1364055 "IRRF2F" 1364838 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-593 1363018 1363056 1363132 "IRREDFFX" 1363227 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-592 1361633 1361892 1362191 "IROOT" 1362751 NIL IROOT (NIL T) -7 NIL NIL NIL) (-591 1358237 1359317 1360009 "IR" 1360973 NIL IR (NIL T) -8 NIL NIL NIL) (-590 1357442 1357730 1357881 "IRFORM" 1358106 T IRFORM (NIL) -8 NIL NIL NIL) (-589 1355055 1355550 1356116 "IR2" 1356920 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-588 1354155 1354268 1354482 "IR2F" 1354938 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-587 1353946 1353980 1354040 "IPRNTPK" 1354115 T IPRNTPK (NIL) -7 NIL NIL NIL) (-586 1350527 1353835 1353904 "IPF" 1353909 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-585 1348854 1350452 1350509 "IPADIC" 1350514 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-584 1348166 1348414 1348544 "IP4ADDR" 1348744 T IP4ADDR (NIL) -8 NIL NIL NIL) (-583 1347540 1347795 1347927 "IOMODE" 1348054 T IOMODE (NIL) -8 NIL NIL NIL) (-582 1346613 1347137 1347264 "IOBFILE" 1347433 T IOBFILE (NIL) -8 NIL NIL NIL) (-581 1346101 1346517 1346545 "IOBCON" 1346550 T IOBCON (NIL) -9 NIL 1346571 NIL) (-580 1345612 1345670 1345853 "INVLAPLA" 1346037 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-579 1335260 1337614 1340000 "INTTR" 1343276 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-578 1331595 1332337 1333202 "INTTOOLS" 1334445 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-577 1331181 1331272 1331389 "INTSLPE" 1331498 T INTSLPE (NIL) -7 NIL NIL NIL) (-576 1329134 1331104 1331163 "INTRVL" 1331168 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-575 1326736 1327248 1327823 "INTRF" 1328619 NIL INTRF (NIL T) -7 NIL NIL NIL) (-574 1326147 1326244 1326386 "INTRET" 1326634 NIL INTRET (NIL T) -7 NIL NIL NIL) (-573 1324144 1324533 1325003 "INTRAT" 1325755 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-572 1321407 1321990 1322609 "INTPM" 1323629 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-571 1318152 1318751 1319489 "INTPAF" 1320793 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-570 1313331 1314293 1315344 "INTPACK" 1317121 T INTPACK (NIL) -7 NIL NIL NIL) (-569 1310279 1313128 1313237 "INT" 1313242 T INT (NIL) -8 NIL NIL NIL) (-568 1309531 1309683 1309891 "INTHERTR" 1310121 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-567 1308970 1309050 1309238 "INTHERAL" 1309445 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-566 1306816 1307259 1307716 "INTHEORY" 1308533 T INTHEORY (NIL) -7 NIL NIL NIL) (-565 1298222 1299843 1301615 "INTG0" 1305168 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-564 1278795 1283585 1288395 "INTFTBL" 1293432 T INTFTBL (NIL) -8 NIL NIL NIL) (-563 1278044 1278182 1278355 "INTFACT" 1278654 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-562 1275471 1275917 1276474 "INTEF" 1277598 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-561 1273838 1274577 1274605 "INTDOM" 1274906 T INTDOM (NIL) -9 NIL 1275113 NIL) (-560 1273207 1273381 1273623 "INTDOM-" 1273628 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-559 1269595 1271523 1271577 "INTCAT" 1272376 NIL INTCAT (NIL T) -9 NIL 1272697 NIL) (-558 1269067 1269170 1269298 "INTBIT" 1269487 T INTBIT (NIL) -7 NIL NIL NIL) (-557 1267766 1267920 1268227 "INTALG" 1268912 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-556 1267249 1267339 1267496 "INTAF" 1267670 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-555 1260592 1267059 1267199 "INTABL" 1267204 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-554 1259933 1260399 1260464 "INT8" 1260498 T INT8 (NIL) -8 NIL NIL 1260543) (-553 1259273 1259739 1259804 "INT64" 1259838 T INT64 (NIL) -8 NIL NIL 1259883) (-552 1258613 1259079 1259144 "INT32" 1259178 T INT32 (NIL) -8 NIL NIL 1259223) (-551 1257953 1258419 1258484 "INT16" 1258518 T INT16 (NIL) -8 NIL NIL 1258563) (-550 1252863 1255576 1255604 "INS" 1256538 T INS (NIL) -9 NIL 1257203 NIL) (-549 1250103 1250874 1251848 "INS-" 1251921 NIL INS- (NIL T) -8 NIL NIL NIL) (-548 1248878 1249105 1249403 "INPSIGN" 1249856 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-547 1247996 1248113 1248310 "INPRODPF" 1248758 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-546 1246890 1247007 1247244 "INPRODFF" 1247876 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-545 1245890 1246042 1246302 "INNMFACT" 1246726 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-544 1245087 1245184 1245372 "INMODGCD" 1245789 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-543 1243595 1243840 1244164 "INFSP" 1244832 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-542 1242779 1242896 1243079 "INFPROD0" 1243475 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-541 1239634 1240844 1241359 "INFORM" 1242272 T INFORM (NIL) -8 NIL NIL NIL) (-540 1239244 1239304 1239402 "INFORM1" 1239569 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-539 1238767 1238856 1238970 "INFINITY" 1239150 T INFINITY (NIL) -7 NIL NIL NIL) (-538 1237943 1238487 1238588 "INETCLTS" 1238686 T INETCLTS (NIL) -8 NIL NIL NIL) (-537 1236559 1236809 1237130 "INEP" 1237691 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-536 1235808 1236456 1236521 "INDE" 1236526 NIL INDE (NIL T) -8 NIL NIL NIL) (-535 1235372 1235440 1235557 "INCRMAPS" 1235735 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-534 1234190 1234641 1234847 "INBFILE" 1235186 T INBFILE (NIL) -8 NIL NIL NIL) (-533 1229490 1230426 1231370 "INBFF" 1233278 NIL INBFF (NIL T) -7 NIL NIL NIL) (-532 1228398 1228667 1228695 "INBCON" 1229208 T INBCON (NIL) -9 NIL 1229474 NIL) (-531 1227650 1227873 1228149 "INBCON-" 1228154 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-530 1227129 1227374 1227465 "INAST" 1227579 T INAST (NIL) -8 NIL NIL NIL) (-529 1226556 1226808 1226914 "IMPTAST" 1227043 T IMPTAST (NIL) -8 NIL NIL NIL) (-528 1223002 1226400 1226504 "IMATRIX" 1226509 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-527 1221710 1221833 1222149 "IMATQF" 1222858 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-526 1219930 1220157 1220494 "IMATLIN" 1221466 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-525 1214508 1219854 1219912 "ILIST" 1219917 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-524 1212413 1214368 1214481 "IIARRAY2" 1214486 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-523 1207811 1212324 1212388 "IFF" 1212393 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-522 1207158 1207428 1207544 "IFAST" 1207715 T IFAST (NIL) -8 NIL NIL NIL) (-521 1202153 1206450 1206638 "IFARRAY" 1207015 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-520 1201333 1202057 1202130 "IFAMON" 1202135 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-519 1200917 1200982 1201036 "IEVALAB" 1201243 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-518 1200592 1200660 1200820 "IEVALAB-" 1200825 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-517 1200223 1200506 1200569 "IDPO" 1200574 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-516 1199473 1200112 1200187 "IDPOAMS" 1200192 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-515 1198780 1199362 1199437 "IDPOAM" 1199442 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-514 1197839 1198115 1198168 "IDPC" 1198581 NIL IDPC (NIL T T) -9 NIL 1198730 NIL) (-513 1197308 1197731 1197804 "IDPAM" 1197809 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-512 1196684 1197200 1197273 "IDPAG" 1197278 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-511 1196329 1196520 1196595 "IDENT" 1196629 T IDENT (NIL) -8 NIL NIL NIL) (-510 1192584 1193432 1194327 "IDECOMP" 1195486 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-509 1185422 1186507 1187554 "IDEAL" 1191620 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-508 1184582 1184694 1184894 "ICDEN" 1185306 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-507 1183653 1184062 1184209 "ICARD" 1184455 T ICARD (NIL) -8 NIL NIL NIL) (-506 1181713 1182026 1182431 "IBPTOOLS" 1183330 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-505 1177320 1181333 1181446 "IBITS" 1181632 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-504 1174043 1174619 1175314 "IBATOOL" 1176737 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-503 1171822 1172284 1172817 "IBACHIN" 1173578 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-502 1169651 1171668 1171771 "IARRAY2" 1171776 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-501 1165757 1169577 1169634 "IARRAY1" 1169639 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-500 1159866 1164169 1164650 "IAN" 1165296 T IAN (NIL) -8 NIL NIL NIL) (-499 1159377 1159434 1159607 "IALGFACT" 1159803 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-498 1158905 1159018 1159046 "HYPCAT" 1159253 T HYPCAT (NIL) -9 NIL NIL NIL) (-497 1158443 1158560 1158746 "HYPCAT-" 1158751 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-496 1158038 1158238 1158321 "HOSTNAME" 1158380 T HOSTNAME (NIL) -8 NIL NIL NIL) (-495 1157883 1157920 1157961 "HOMOTOP" 1157966 NIL HOMOTOP (NIL T) -9 NIL 1157999 NIL) (-494 1154515 1155893 1155934 "HOAGG" 1156915 NIL HOAGG (NIL T) -9 NIL 1157594 NIL) (-493 1153109 1153508 1154034 "HOAGG-" 1154039 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-492 1147111 1152702 1152852 "HEXADEC" 1152979 T HEXADEC (NIL) -8 NIL NIL NIL) (-491 1145859 1146081 1146344 "HEUGCD" 1146888 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-490 1144935 1145696 1145826 "HELLFDIV" 1145831 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-489 1143114 1144712 1144800 "HEAP" 1144879 NIL HEAP (NIL T) -8 NIL NIL NIL) (-488 1142377 1142666 1142800 "HEADAST" 1143000 T HEADAST (NIL) -8 NIL NIL NIL) (-487 1136243 1142292 1142354 "HDP" 1142359 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-486 1130231 1135878 1136030 "HDMP" 1136144 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-485 1129555 1129695 1129859 "HB" 1130087 T HB (NIL) -7 NIL NIL NIL) (-484 1122941 1129401 1129505 "HASHTBL" 1129510 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-483 1122417 1122662 1122754 "HASAST" 1122869 T HASAST (NIL) -8 NIL NIL NIL) (-482 1120195 1122039 1122221 "HACKPI" 1122255 T HACKPI (NIL) -8 NIL NIL NIL) (-481 1115863 1120048 1120161 "GTSET" 1120166 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-480 1109278 1115741 1115839 "GSTBL" 1115844 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-479 1101556 1108309 1108574 "GSERIES" 1109069 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-478 1100697 1101114 1101142 "GROUP" 1101345 T GROUP (NIL) -9 NIL 1101479 NIL) (-477 1100063 1100222 1100473 "GROUP-" 1100478 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-476 1098430 1098751 1099138 "GROEBSOL" 1099740 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-475 1097344 1097632 1097683 "GRMOD" 1098212 NIL GRMOD (NIL T T) -9 NIL 1098380 NIL) (-474 1097112 1097148 1097276 "GRMOD-" 1097281 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-473 1092402 1093466 1094466 "GRIMAGE" 1096132 T GRIMAGE (NIL) -8 NIL NIL NIL) (-472 1090868 1091129 1091453 "GRDEF" 1092098 T GRDEF (NIL) -7 NIL NIL NIL) (-471 1090312 1090428 1090569 "GRAY" 1090747 T GRAY (NIL) -7 NIL NIL NIL) (-470 1089499 1089905 1089956 "GRALG" 1090109 NIL GRALG (NIL T T) -9 NIL 1090202 NIL) (-469 1089160 1089233 1089396 "GRALG-" 1089401 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-468 1085937 1088745 1088923 "GPOLSET" 1089067 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-467 1085291 1085348 1085606 "GOSPER" 1085874 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-466 1081023 1081729 1082255 "GMODPOL" 1084990 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-465 1080028 1080212 1080450 "GHENSEL" 1080835 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-464 1074184 1075027 1076047 "GENUPS" 1079112 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-463 1073881 1073932 1074021 "GENUFACT" 1074127 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-462 1073293 1073370 1073535 "GENPGCD" 1073799 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-461 1072767 1072802 1073015 "GENMFACT" 1073252 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-460 1071333 1071590 1071897 "GENEEZ" 1072510 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-459 1065479 1070944 1071106 "GDMP" 1071256 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-458 1054821 1059250 1060356 "GCNAALG" 1064462 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-457 1053148 1054010 1054038 "GCDDOM" 1054293 T GCDDOM (NIL) -9 NIL 1054450 NIL) (-456 1052618 1052745 1052960 "GCDDOM-" 1052965 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-455 1051290 1051475 1051779 "GB" 1052397 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-454 1039906 1042236 1044628 "GBINTERN" 1048981 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-453 1037743 1038035 1038456 "GBF" 1039581 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-452 1036524 1036689 1036956 "GBEUCLID" 1037559 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-451 1035873 1035998 1036147 "GAUSSFAC" 1036395 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-450 1034240 1034542 1034856 "GALUTIL" 1035592 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-449 1032548 1032822 1033146 "GALPOLYU" 1033967 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-448 1029913 1030203 1030610 "GALFACTU" 1032245 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-447 1021718 1023218 1024826 "GALFACT" 1028345 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-446 1019106 1019764 1019792 "FVFUN" 1020948 T FVFUN (NIL) -9 NIL 1021668 NIL) (-445 1018372 1018554 1018582 "FVC" 1018873 T FVC (NIL) -9 NIL 1019056 NIL) (-444 1018015 1018197 1018265 "FUNDESC" 1018324 T FUNDESC (NIL) -8 NIL NIL NIL) (-443 1017630 1017812 1017893 "FUNCTION" 1017967 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-442 1015374 1015952 1016418 "FT" 1017184 T FT (NIL) -8 NIL NIL NIL) (-441 1014165 1014675 1014878 "FTEM" 1015191 T FTEM (NIL) -8 NIL NIL NIL) (-440 1012456 1012745 1013142 "FSUPFACT" 1013856 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-439 1010853 1011142 1011474 "FST" 1012144 T FST (NIL) -8 NIL NIL NIL) (-438 1010052 1010158 1010346 "FSRED" 1010735 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-437 1008751 1009007 1009354 "FSPRMELT" 1009767 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-436 1006057 1006495 1006981 "FSPECF" 1008314 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-435 987695 996026 996067 "FS" 999951 NIL FS (NIL T) -9 NIL 1002240 NIL) (-434 976338 979331 983388 "FS-" 983688 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 975866 975920 976090 "FSINT" 976279 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-432 974158 974859 975162 "FSERIES" 975645 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-431 973200 973316 973540 "FSCINT" 974038 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-430 969408 972144 972185 "FSAGG" 972555 NIL FSAGG (NIL T) -9 NIL 972814 NIL) (-429 967170 967771 968567 "FSAGG-" 968662 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-428 966212 966355 966582 "FSAGG2" 967023 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-427 963894 964174 964721 "FS2UPS" 965930 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-426 963528 963571 963700 "FS2" 963845 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-425 962406 962577 962879 "FS2EXPXP" 963353 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-424 961832 961947 962099 "FRUTIL" 962286 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-423 953245 957327 958685 "FR" 960506 NIL FR (NIL T) -8 NIL NIL NIL) (-422 948214 950888 950928 "FRNAALG" 952324 NIL FRNAALG (NIL T) -9 NIL 952931 NIL) (-421 943887 944963 946238 "FRNAALG-" 946988 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-420 943525 943568 943695 "FRNAAF2" 943838 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-419 941900 942374 942670 "FRMOD" 943337 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-418 939643 940275 940593 "FRIDEAL" 941691 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-417 938834 938921 939212 "FRIDEAL2" 939550 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-416 937967 938381 938422 "FRETRCT" 938427 NIL FRETRCT (NIL T) -9 NIL 938603 NIL) (-415 937079 937310 937661 "FRETRCT-" 937666 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-414 934167 935377 935436 "FRAMALG" 936318 NIL FRAMALG (NIL T T) -9 NIL 936610 NIL) (-413 932301 932756 933386 "FRAMALG-" 933609 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-412 926220 931774 932051 "FRAC" 932056 NIL FRAC (NIL T) -8 NIL NIL NIL) (-411 925856 925913 926020 "FRAC2" 926157 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-410 925492 925549 925656 "FR2" 925793 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-409 920005 922898 922926 "FPS" 924045 T FPS (NIL) -9 NIL 924602 NIL) (-408 919454 919563 919727 "FPS-" 919873 NIL FPS- (NIL T) -8 NIL NIL NIL) (-407 916756 918425 918453 "FPC" 918678 T FPC (NIL) -9 NIL 918820 NIL) (-406 916549 916589 916686 "FPC-" 916691 NIL FPC- (NIL T) -8 NIL NIL NIL) (-405 915339 916037 916078 "FPATMAB" 916083 NIL FPATMAB (NIL T) -9 NIL 916235 NIL) (-404 913012 913515 913941 "FPARFRAC" 914976 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-403 908406 908904 909586 "FORTRAN" 912444 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-402 906122 906622 907161 "FORT" 907887 T FORT (NIL) -7 NIL NIL NIL) (-401 903798 904360 904388 "FORTFN" 905448 T FORTFN (NIL) -9 NIL 906072 NIL) (-400 903562 903612 903640 "FORTCAT" 903699 T FORTCAT (NIL) -9 NIL 903761 NIL) (-399 901668 902178 902568 "FORMULA" 903192 T FORMULA (NIL) -8 NIL NIL NIL) (-398 901456 901486 901555 "FORMULA1" 901632 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-397 900979 901031 901204 "FORDER" 901398 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-396 900075 900239 900432 "FOP" 900806 T FOP (NIL) -7 NIL NIL NIL) (-395 898656 899355 899529 "FNLA" 899957 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-394 897385 897800 897828 "FNCAT" 898288 T FNCAT (NIL) -9 NIL 898548 NIL) (-393 896924 897344 897372 "FNAME" 897377 T FNAME (NIL) -8 NIL NIL NIL) (-392 895487 896450 896478 "FMTC" 896483 T FMTC (NIL) -9 NIL 896519 NIL) (-391 894233 895423 895469 "FMONOID" 895474 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-390 891061 892229 892270 "FMONCAT" 893487 NIL FMONCAT (NIL T) -9 NIL 894092 NIL) (-389 890253 890803 890952 "FM" 890957 NIL FM (NIL T T) -8 NIL NIL NIL) (-388 887677 888323 888351 "FMFUN" 889495 T FMFUN (NIL) -9 NIL 890203 NIL) (-387 886946 887127 887155 "FMC" 887445 T FMC (NIL) -9 NIL 887627 NIL) (-386 884025 884885 884939 "FMCAT" 886134 NIL FMCAT (NIL T T) -9 NIL 886629 NIL) (-385 882891 883791 883891 "FM1" 883970 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-384 880665 881081 881575 "FLOATRP" 882442 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-383 874239 878394 879015 "FLOAT" 880064 T FLOAT (NIL) -8 NIL NIL NIL) (-382 871677 872177 872755 "FLOATCP" 873706 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-381 870417 871255 871296 "FLINEXP" 871301 NIL FLINEXP (NIL T) -9 NIL 871394 NIL) (-380 869571 869806 870134 "FLINEXP-" 870139 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-379 868647 868791 869015 "FLASORT" 869423 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-378 865763 866631 866683 "FLALG" 867910 NIL FLALG (NIL T T) -9 NIL 868377 NIL) (-377 859499 863249 863290 "FLAGG" 864552 NIL FLAGG (NIL T) -9 NIL 865204 NIL) (-376 858225 858564 859054 "FLAGG-" 859059 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-375 857267 857410 857637 "FLAGG2" 858078 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-374 854118 855126 855185 "FINRALG" 856313 NIL FINRALG (NIL T T) -9 NIL 856821 NIL) (-373 853278 853507 853846 "FINRALG-" 853851 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-372 852658 852897 852925 "FINITE" 853121 T FINITE (NIL) -9 NIL 853228 NIL) (-371 845015 847202 847242 "FINAALG" 850909 NIL FINAALG (NIL T) -9 NIL 852362 NIL) (-370 840347 841397 842541 "FINAALG-" 843920 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-369 839715 840102 840205 "FILE" 840277 NIL FILE (NIL T) -8 NIL NIL NIL) (-368 838373 838711 838765 "FILECAT" 839449 NIL FILECAT (NIL T T) -9 NIL 839665 NIL) (-367 836089 837617 837645 "FIELD" 837685 T FIELD (NIL) -9 NIL 837765 NIL) (-366 834709 835094 835605 "FIELD-" 835610 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-365 832559 833344 833691 "FGROUP" 834395 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-364 831649 831813 832033 "FGLMICPK" 832391 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-363 827481 831574 831631 "FFX" 831636 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-362 827082 827143 827278 "FFSLPE" 827414 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-361 823072 823854 824650 "FFPOLY" 826318 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-360 822576 822612 822821 "FFPOLY2" 823030 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-359 818420 822495 822558 "FFP" 822563 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-358 813818 818331 818395 "FF" 818400 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-357 808944 813161 813351 "FFNBX" 813672 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-356 803872 808079 808337 "FFNBP" 808798 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-355 798505 803156 803367 "FFNB" 803705 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-354 797337 797535 797850 "FFINTBAS" 798302 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-353 793406 795626 795654 "FFIELDC" 796274 T FFIELDC (NIL) -9 NIL 796650 NIL) (-352 792068 792439 792936 "FFIELDC-" 792941 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-351 791637 791683 791807 "FFHOM" 792010 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-350 789332 789819 790336 "FFF" 791152 NIL FFF (NIL T) -7 NIL NIL NIL) (-349 784950 789074 789175 "FFCGX" 789275 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-348 780572 784682 784789 "FFCGP" 784893 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-347 775755 780299 780407 "FFCG" 780508 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-346 757151 766232 766318 "FFCAT" 771483 NIL FFCAT (NIL T T T) -9 NIL 772934 NIL) (-345 752348 753396 754710 "FFCAT-" 755940 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-344 751759 751802 752037 "FFCAT2" 752299 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-343 741082 744731 745951 "FEXPR" 750611 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-342 740082 740517 740558 "FEVALAB" 740642 NIL FEVALAB (NIL T) -9 NIL 740903 NIL) (-341 739241 739451 739789 "FEVALAB-" 739794 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-340 737807 738624 738827 "FDIV" 739140 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-339 734827 735568 735683 "FDIVCAT" 737251 NIL FDIVCAT (NIL T T T T) -9 NIL 737688 NIL) (-338 734589 734616 734786 "FDIVCAT-" 734791 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-337 733809 733896 734173 "FDIV2" 734496 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-336 732783 733104 733306 "FCTRDATA" 733627 T FCTRDATA (NIL) -8 NIL NIL NIL) (-335 731469 731728 732017 "FCPAK1" 732514 T FCPAK1 (NIL) -7 NIL NIL NIL) (-334 730568 730969 731110 "FCOMP" 731360 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-333 714273 717718 721256 "FC" 727050 T FC (NIL) -8 NIL NIL NIL) (-332 706636 710664 710704 "FAXF" 712506 NIL FAXF (NIL T) -9 NIL 713198 NIL) (-331 703912 704570 705395 "FAXF-" 705860 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-330 698964 703288 703464 "FARRAY" 703769 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-329 693858 695925 695978 "FAMR" 697001 NIL FAMR (NIL T T) -9 NIL 697461 NIL) (-328 692748 693050 693485 "FAMR-" 693490 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-327 691917 692670 692723 "FAMONOID" 692728 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-326 689703 690413 690466 "FAMONC" 691407 NIL FAMONC (NIL T T) -9 NIL 691793 NIL) (-325 688367 689457 689594 "FAGROUP" 689599 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-324 686162 686481 686884 "FACUTIL" 688048 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-323 685261 685446 685668 "FACTFUNC" 685972 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-322 677683 684564 684763 "EXPUPXS" 685117 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-321 675166 675706 676292 "EXPRTUBE" 677117 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-320 671437 672029 672759 "EXPRODE" 674505 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-319 656922 670086 670515 "EXPR" 671041 NIL EXPR (NIL T) -8 NIL NIL NIL) (-318 651476 652063 652869 "EXPR2UPS" 656220 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-317 651108 651165 651274 "EXPR2" 651413 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-316 642496 650259 650550 "EXPEXPAN" 650944 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-315 642296 642453 642482 "EXIT" 642487 T EXIT (NIL) -8 NIL NIL NIL) (-314 641776 642020 642111 "EXITAST" 642225 T EXITAST (NIL) -8 NIL NIL NIL) (-313 641403 641465 641578 "EVALCYC" 641708 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-312 640944 641062 641103 "EVALAB" 641273 NIL EVALAB (NIL T) -9 NIL 641377 NIL) (-311 640425 640547 640768 "EVALAB-" 640773 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-310 637793 639095 639123 "EUCDOM" 639678 T EUCDOM (NIL) -9 NIL 640028 NIL) (-309 636198 636640 637230 "EUCDOM-" 637235 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-308 623736 626496 629246 "ESTOOLS" 633468 T ESTOOLS (NIL) -7 NIL NIL NIL) (-307 623368 623425 623534 "ESTOOLS2" 623673 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-306 623119 623161 623241 "ESTOOLS1" 623320 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-305 617156 618764 618792 "ES" 621560 T ES (NIL) -9 NIL 622970 NIL) (-304 612103 613390 615207 "ES-" 615371 NIL ES- (NIL T) -8 NIL NIL NIL) (-303 608477 609238 610018 "ESCONT" 611343 T ESCONT (NIL) -7 NIL NIL NIL) (-302 608222 608254 608336 "ESCONT1" 608439 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-301 607897 607947 608047 "ES2" 608166 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-300 607527 607585 607694 "ES1" 607833 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-299 606743 606872 607048 "ERROR" 607371 T ERROR (NIL) -7 NIL NIL NIL) (-298 600135 606602 606693 "EQTBL" 606698 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-297 592638 595449 596898 "EQ" 598719 NIL -2091 (NIL T) -8 NIL NIL NIL) (-296 592270 592327 592436 "EQ2" 592575 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-295 587560 588608 589701 "EP" 591209 NIL EP (NIL T) -7 NIL NIL NIL) (-294 586160 586451 586757 "ENV" 587274 T ENV (NIL) -8 NIL NIL NIL) (-293 585254 585808 585836 "ENTIRER" 585841 T ENTIRER (NIL) -9 NIL 585887 NIL) (-292 581721 583209 583579 "EMR" 585053 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-291 580865 581050 581104 "ELTAGG" 581484 NIL ELTAGG (NIL T T) -9 NIL 581695 NIL) (-290 580584 580646 580787 "ELTAGG-" 580792 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-289 580373 580402 580456 "ELTAB" 580540 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-288 579499 579645 579844 "ELFUTS" 580224 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-287 579241 579297 579325 "ELEMFUN" 579430 T ELEMFUN (NIL) -9 NIL NIL NIL) (-286 579111 579132 579200 "ELEMFUN-" 579205 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-285 573955 577211 577252 "ELAGG" 578192 NIL ELAGG (NIL T) -9 NIL 578655 NIL) (-284 572240 572674 573337 "ELAGG-" 573342 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-283 571552 571689 571845 "ELABOR" 572104 T ELABOR (NIL) -8 NIL NIL NIL) (-282 570213 570492 570786 "ELABEXPR" 571278 T ELABEXPR (NIL) -8 NIL NIL NIL) (-281 563077 564880 565707 "EFUPXS" 569489 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-280 556527 558328 559138 "EFULS" 562353 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-279 554012 554370 554842 "EFSTRUC" 556159 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-278 543803 545369 546917 "EF" 552527 NIL EF (NIL T T) -7 NIL NIL NIL) (-277 542877 543288 543437 "EAB" 543674 T EAB (NIL) -8 NIL NIL NIL) (-276 542059 542836 542864 "E04UCFA" 542869 T E04UCFA (NIL) -8 NIL NIL NIL) (-275 541241 542018 542046 "E04NAFA" 542051 T E04NAFA (NIL) -8 NIL NIL NIL) (-274 540423 541200 541228 "E04MBFA" 541233 T E04MBFA (NIL) -8 NIL NIL NIL) (-273 539605 540382 540410 "E04JAFA" 540415 T E04JAFA (NIL) -8 NIL NIL NIL) (-272 538789 539564 539592 "E04GCFA" 539597 T E04GCFA (NIL) -8 NIL NIL NIL) (-271 537973 538748 538776 "E04FDFA" 538781 T E04FDFA (NIL) -8 NIL NIL NIL) (-270 537155 537932 537960 "E04DGFA" 537965 T E04DGFA (NIL) -8 NIL NIL NIL) (-269 531328 532680 534044 "E04AGNT" 535811 T E04AGNT (NIL) -7 NIL NIL NIL) (-268 530008 530514 530554 "DVARCAT" 531029 NIL DVARCAT (NIL T) -9 NIL 531228 NIL) (-267 529212 529424 529738 "DVARCAT-" 529743 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-266 522349 529011 529140 "DSMP" 529145 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-265 517130 518294 519362 "DROPT" 521301 T DROPT (NIL) -8 NIL NIL NIL) (-264 516795 516854 516952 "DROPT1" 517065 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-263 511910 513036 514173 "DROPT0" 515678 T DROPT0 (NIL) -7 NIL NIL NIL) (-262 510255 510580 510966 "DRAWPT" 511544 T DRAWPT (NIL) -7 NIL NIL NIL) (-261 504842 505765 506844 "DRAW" 509229 NIL DRAW (NIL T) -7 NIL NIL NIL) (-260 504475 504528 504646 "DRAWHACK" 504783 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-259 503206 503475 503766 "DRAWCX" 504204 T DRAWCX (NIL) -7 NIL NIL NIL) (-258 502721 502790 502941 "DRAWCURV" 503132 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-257 493189 495151 497266 "DRAWCFUN" 500626 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-256 489953 491882 491923 "DQAGG" 492552 NIL DQAGG (NIL T) -9 NIL 492826 NIL) (-255 478077 484546 484629 "DPOLCAT" 486481 NIL DPOLCAT (NIL T T T T) -9 NIL 487026 NIL) (-254 472913 474262 476220 "DPOLCAT-" 476225 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-253 466035 472774 472872 "DPMO" 472877 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-252 459060 465815 465982 "DPMM" 465987 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-251 458538 458752 458850 "DOMTMPLT" 458982 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-250 457971 458340 458420 "DOMCTOR" 458478 T DOMCTOR (NIL) -8 NIL NIL NIL) (-249 457183 457451 457602 "DOMAIN" 457840 T DOMAIN (NIL) -8 NIL NIL NIL) (-248 451171 456818 456970 "DMP" 457084 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-247 450771 450827 450971 "DLP" 451109 NIL DLP (NIL T) -7 NIL NIL NIL) (-246 444593 450098 450288 "DLIST" 450613 NIL DLIST (NIL T) -8 NIL NIL NIL) (-245 441390 443446 443487 "DLAGG" 444037 NIL DLAGG (NIL T) -9 NIL 444267 NIL) (-244 440066 440730 440758 "DIVRING" 440850 T DIVRING (NIL) -9 NIL 440933 NIL) (-243 439303 439493 439793 "DIVRING-" 439798 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-242 437405 437762 438168 "DISPLAY" 438917 T DISPLAY (NIL) -7 NIL NIL NIL) (-241 431293 437319 437382 "DIRPROD" 437387 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-240 430141 430344 430609 "DIRPROD2" 431086 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-239 418916 424922 424975 "DIRPCAT" 425385 NIL DIRPCAT (NIL NIL T) -9 NIL 426225 NIL) (-238 416242 416884 417765 "DIRPCAT-" 418102 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-237 415529 415689 415875 "DIOSP" 416076 T DIOSP (NIL) -7 NIL NIL NIL) (-236 412184 414441 414482 "DIOPS" 414916 NIL DIOPS (NIL T) -9 NIL 415145 NIL) (-235 411733 411847 412038 "DIOPS-" 412043 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-234 410556 411184 411212 "DIFRING" 411399 T DIFRING (NIL) -9 NIL 411509 NIL) (-233 410202 410279 410431 "DIFRING-" 410436 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-232 407938 409210 409251 "DIFEXT" 409614 NIL DIFEXT (NIL T) -9 NIL 409908 NIL) (-231 406223 406651 407317 "DIFEXT-" 407322 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-230 403498 405755 405796 "DIAGG" 405801 NIL DIAGG (NIL T) -9 NIL 405821 NIL) (-229 402882 403039 403291 "DIAGG-" 403296 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-228 398299 401841 402118 "DHMATRIX" 402651 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-227 393911 394820 395830 "DFSFUN" 397309 T DFSFUN (NIL) -7 NIL NIL NIL) (-226 388990 392842 393154 "DFLOAT" 393619 T DFLOAT (NIL) -8 NIL NIL NIL) (-225 387253 387534 387923 "DFINTTLS" 388698 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-224 384282 385274 385674 "DERHAM" 386919 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-223 382083 384057 384146 "DEQUEUE" 384226 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-222 381337 381470 381653 "DEGRED" 381945 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-221 377767 378512 379358 "DEFINTRF" 380565 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-220 375322 375791 376383 "DEFINTEF" 377286 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-219 374672 374942 375057 "DEFAST" 375227 T DEFAST (NIL) -8 NIL NIL NIL) (-218 368674 374265 374415 "DECIMAL" 374542 T DECIMAL (NIL) -8 NIL NIL NIL) (-217 366186 366644 367150 "DDFACT" 368218 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-216 365782 365825 365976 "DBLRESP" 366137 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-215 363654 364015 364375 "DBASE" 365549 NIL DBASE (NIL T) -8 NIL NIL NIL) (-214 362896 363134 363280 "DATAARY" 363553 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-213 362002 362855 362883 "D03FAFA" 362888 T D03FAFA (NIL) -8 NIL NIL NIL) (-212 361109 361961 361989 "D03EEFA" 361994 T D03EEFA (NIL) -8 NIL NIL NIL) (-211 359059 359525 360014 "D03AGNT" 360640 T D03AGNT (NIL) -7 NIL NIL NIL) (-210 358348 359018 359046 "D02EJFA" 359051 T D02EJFA (NIL) -8 NIL NIL NIL) (-209 357637 358307 358335 "D02CJFA" 358340 T D02CJFA (NIL) -8 NIL NIL NIL) (-208 356926 357596 357624 "D02BHFA" 357629 T D02BHFA (NIL) -8 NIL NIL NIL) (-207 356215 356885 356913 "D02BBFA" 356918 T D02BBFA (NIL) -8 NIL NIL NIL) (-206 349412 351001 352607 "D02AGNT" 354629 T D02AGNT (NIL) -7 NIL NIL NIL) (-205 347180 347703 348249 "D01WGTS" 348886 T D01WGTS (NIL) -7 NIL NIL NIL) (-204 346247 347139 347167 "D01TRNS" 347172 T D01TRNS (NIL) -8 NIL NIL NIL) (-203 345315 346206 346234 "D01GBFA" 346239 T D01GBFA (NIL) -8 NIL NIL NIL) (-202 344383 345274 345302 "D01FCFA" 345307 T D01FCFA (NIL) -8 NIL NIL NIL) (-201 343451 344342 344370 "D01ASFA" 344375 T D01ASFA (NIL) -8 NIL NIL NIL) (-200 342519 343410 343438 "D01AQFA" 343443 T D01AQFA (NIL) -8 NIL NIL NIL) (-199 341587 342478 342506 "D01APFA" 342511 T D01APFA (NIL) -8 NIL NIL NIL) (-198 340655 341546 341574 "D01ANFA" 341579 T D01ANFA (NIL) -8 NIL NIL NIL) (-197 339723 340614 340642 "D01AMFA" 340647 T D01AMFA (NIL) -8 NIL NIL NIL) (-196 338791 339682 339710 "D01ALFA" 339715 T D01ALFA (NIL) -8 NIL NIL NIL) (-195 337859 338750 338778 "D01AKFA" 338783 T D01AKFA (NIL) -8 NIL NIL NIL) (-194 336927 337818 337846 "D01AJFA" 337851 T D01AJFA (NIL) -8 NIL NIL NIL) (-193 330222 331775 333336 "D01AGNT" 335386 T D01AGNT (NIL) -7 NIL NIL NIL) (-192 329559 329687 329839 "CYCLOTOM" 330090 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-191 326294 327007 327734 "CYCLES" 328852 T CYCLES (NIL) -7 NIL NIL NIL) (-190 325606 325740 325911 "CVMP" 326155 NIL CVMP (NIL T) -7 NIL NIL NIL) (-189 323447 323705 324074 "CTRIGMNP" 325334 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-188 322883 323241 323314 "CTOR" 323394 T CTOR (NIL) -8 NIL NIL NIL) (-187 322392 322614 322715 "CTORKIND" 322802 T CTORKIND (NIL) -8 NIL NIL NIL) (-186 321683 321999 322027 "CTORCAT" 322209 T CTORCAT (NIL) -9 NIL 322322 NIL) (-185 321281 321392 321551 "CTORCAT-" 321556 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-184 320743 320955 321063 "CTORCALL" 321205 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-183 320117 320216 320369 "CSTTOOLS" 320640 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-182 315916 316573 317331 "CRFP" 319429 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-181 315391 315637 315729 "CRCEAST" 315844 T CRCEAST (NIL) -8 NIL NIL NIL) (-180 314438 314623 314851 "CRAPACK" 315195 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-179 313822 313923 314127 "CPMATCH" 314314 NIL CPMATCH (NIL T T T) 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ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 8e2b47b0..5f5756b0 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,297 +1,279 @@ -(733187 . 3479296390) -(((*1 *1 *1 *2 *3) - (-12 (-5 *3 (-649 *6)) (-4 *6 (-855)) (-4 *4 (-367)) (-4 *5 (-798)) - (-5 *1 (-509 *4 *5 *6 *2)) (-4 *2 (-955 *4 *5 *6)))) - ((*1 *1 *1 *2) - (-12 (-4 *3 (-367)) (-4 *4 (-798)) (-4 *5 (-855)) - (-5 *1 (-509 *3 *4 *5 *2)) (-4 *2 (-955 *3 *4 *5))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4445)) (-4 *1 (-119 *2)) (-4 *2 (-1223))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-989 *2)) (-4 *2 (-1208))))) +(733544 . 3479376212) +(((*1 *1) (-4 *1 (-23))) ((*1 *1) (-4 *1 (-34))) + ((*1 *1) (-5 *1 (-129))) + ((*1 *1) + (-12 (-5 *1 (-136 *2 *3 *4)) (-14 *2 (-569)) (-14 *3 (-776)) + (-4 *4 (-173)))) + ((*1 *1) (-5 *1 (-551))) ((*1 *1) (-5 *1 (-552))) + ((*1 *1) (-5 *1 (-553))) ((*1 *1) (-5 *1 (-554))) + ((*1 *1) (-4 *1 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(-1055)))) + ((*1 *2 *1) (-12 (-4 *1 (-618 *2)) (-4 *2 (-1225)))) + ((*1 *1 *2) (-12 (-4 *1 (-621 *2)) (-4 *2 (-1225)))) + ((*1 *1 *2) (-12 (-4 *1 (-625 *2)) (-4 *2 (-1057)))) ((*1 *2 *1) - (-12 (-5 *2 (-1293 *3 *4)) (-5 *1 (-632 *3 *4 *5)) (-4 *3 (-855)) + (-12 (-5 *2 (-1295 *3 *4)) (-5 *1 (-632 *3 *4 *5)) (-4 *3 (-855)) (-4 *4 (-13 (-173) (-722 (-412 (-569))))) (-14 *5 (-927)))) ((*1 *2 *1) - (-12 (-5 *2 (-1288 *3 *4)) (-5 *1 (-632 *3 *4 *5)) (-4 *3 (-855)) + (-12 (-5 *2 (-1290 *3 *4)) (-5 *1 (-632 *3 *4 *5)) (-4 *3 (-855)) (-4 *4 (-13 (-173) (-722 (-412 (-569))))) (-14 *5 (-927)))) ((*1 *1 *2) (-12 (-4 *3 (-173)) (-5 *1 (-640 *3 *2)) (-4 *2 (-749 *3)))) @@ -3843,15 +3706,15 @@ ((*1 *2 *1) (-12 (-5 *2 (-824 *3)) (-5 *1 (-677 *3)) (-4 *3 (-855)))) ((*1 *2 *1) (-12 (-5 *2 (-964 (-964 (-964 *3)))) (-5 *1 (-680 *3)) - (-4 *3 (-1106)))) + (-4 *3 (-1108)))) ((*1 *1 *2) - (-12 (-5 *2 (-964 (-964 (-964 *3)))) (-4 *3 (-1106)) + (-12 (-5 *2 (-964 (-964 (-964 *3)))) (-4 *3 (-1108)) (-5 *1 (-680 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"failed") *3 *3)) @@ -3872,68 +3735,68 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-649 (-2 (|:| -1433 *3) (|:| -3345 *4)))) - (-4 *3 (-1055)) (-4 *4 (-731)) (-5 *1 (-740 *3 *4)))) + (-12 (-5 *2 (-649 (-2 (|:| -1435 *3) (|:| -3348 *4)))) + (-4 *3 (-1057)) (-4 *4 (-731)) (-5 *1 (-740 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-569)) (-4 *1 (-768)))) ((*1 *1 *2) (-12 (-5 *2 (-3 (|:| |nia| - (-2 (|:| |var| (-1183)) (|:| |fn| (-319 (-226))) - (|:| -2080 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) + (-2 (|:| |var| (-1185)) (|:| |fn| (-319 (-226))) + (|:| -3743 (-1102 (-848 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (|:| |mdnia| (-2 (|:| |fn| (-319 (-226))) - (|:| -2080 (-649 (-1100 (-848 (-226))))) + (|:| -3743 (-649 (-1102 (-848 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))))) (-5 *1 (-774)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-319 (-226))) - (|:| -2080 (-649 (-1100 (-848 (-226))))) (|:| |abserr| (-226)) + (|:| -3743 (-649 (-1102 (-848 (-226))))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *1 (-774)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |var| (-1183)) (|:| |fn| (-319 (-226))) - (|:| -2080 (-1100 (-848 (-226)))) (|:| |abserr| (-226)) + (-2 (|:| |var| (-1185)) (|:| |fn| (-319 (-226))) + (|:| -3743 (-1102 (-848 (-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *1 (-774)))) - ((*1 *2 *3) (-12 (-5 *2 (-779)) (-5 *1 (-778 *3)) (-4 *3 (-1223)))) + ((*1 *2 *3) (-12 (-5 *2 (-779)) (-5 *1 (-778 *3)) (-4 *3 (-1225)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |xinit| (-226)) (|:| |xend| (-226)) - (|:| |fn| (-1273 (-319 (-226)))) (|:| |yinit| (-649 (-226))) + (|:| |fn| (-1275 (-319 (-226)))) (|:| |yinit| (-649 (-226))) (|:| |intvals| (-649 (-226))) (|:| |g| (-319 (-226))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *1 (-813)))) - ((*1 *1 *2) (-12 (-5 *2 (-1183)) (-5 *1 (-829)))) + ((*1 *1 *2) (-12 (-5 *2 (-1185)) (-5 *1 (-829)))) ((*1 *1 *2) (-12 (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-319 (-226))) (|:| -2305 (-649 (-226))) + (-2 (|:| |fn| (-319 (-226))) (|:| -2307 (-649 (-226))) (|:| |lb| (-649 (-848 (-226)))) (|:| |cf| (-649 (-319 (-226)))) (|:| |ub| (-649 (-848 (-226)))))) (|:| |lsa| (-2 (|:| |lfn| (-649 (-319 (-226)))) - (|:| -2305 (-649 (-226))))))) + (|:| -2307 (-649 (-226))))))) (-5 *1 (-846)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-649 (-319 (-226)))) (|:| -2305 (-649 (-226))))) + (-2 (|:| |lfn| (-649 (-319 (-226)))) (|:| -2307 (-649 (-226))))) (-5 *1 (-846)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-319 (-226))) (|:| -2305 (-649 (-226))) + (-2 (|:| |fn| (-319 (-226))) (|:| -2307 (-649 (-226))) (|:| |lb| (-649 (-848 (-226)))) (|:| |cf| (-649 (-319 (-226)))) (|:| |ub| (-649 (-848 (-226)))))) (-5 *1 (-846)))) @@ -3955,446 +3818,492 @@ (-2 (|:| |start| (-226)) (|:| |finish| (-226)) (|:| |grid| (-776)) (|:| |boundaryType| (-569)) (|:| |dStart| (-694 (-226))) (|:| |dFinish| (-694 (-226)))))) - (|:| |f| (-649 (-649 (-319 (-226))))) 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(-226)))) (|:| |abserr| (-226)) (|:| |relerr| (-226)))) (-5 *2 (-2 @@ -15381,10 +15480,10 @@ (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| - (-3 (|:| |str| (-1163 (-226))) + (-3 (|:| |str| (-1165 (-226))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -2080 + (|:| -3743 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -15392,756 +15491,816 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-564))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1273 (-649 (-2 (|:| -2185 *4) (|:| -2150 (-1126)))))) - (-4 *4 (-353)) (-5 *2 (-776)) (-5 *1 (-350 *4)))) - ((*1 *2) - (-12 (-5 *2 (-776)) (-5 *1 (-355 *3 *4)) (-14 *3 (-927)) - (-14 *4 (-927)))) - ((*1 *2) - (-12 (-5 *2 (-776)) (-5 *1 (-356 *3 *4)) (-4 *3 (-353)) - (-14 *4 - (-3 (-1179 *3) - (-1273 (-649 (-2 (|:| -2185 *3) (|:| -2150 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28908) + (-4300 . 28138) (-4301 . 27772) (-4302 . 27554) (-4303 . 27455) + (-4304 . 27404) (-4305 . 27227) (-4306 . 27097) (-4307 . 26939) + (-4308 . 26652) (-4309 . 26579) (-4310 . 26470) (-4311 . 26397) + (-4312 . 26187) (-4313 . 26125) (-4314 . 25979) (-4315 . 25908) + (-4316 . 25825) (-4317 . 25732) (-4318 . 25538) (-4319 . 25479) + (-4320 . 25378) (-4321 . 25196) (-4322 . 25139) (-4323 . 24987) + (-4324 . 24829) (-4325 . 24494) (-4326 . 24441) (-4327 . 24389) + (-4328 . 24233) (-4329 . 24098) (-4330 . 23999) (-4331 . 23712) + (-4332 . 23549) (-4333 . 23497) (-4334 . 23411) (-4335 . 22771) + (-4336 . 22671) (-4337 . 22637) (-4338 . 22585) (-4339 . 20471) + (-4340 . 20400) (-4341 . 20279) (-4342 . 20172) (-4343 . 20051) + (-4344 . 19977) (-4345 . 19878) (-4346 . 19797) (-4347 . 19598) + (-4348 . 19371) (-4349 . 19321) (-4350 . 19034) (-4351 . 18913) + (-4352 . 18733) (-4353 . 18422) (-4354 . 18247) (-4355 . 18216) + (-4356 . 18159) (-4357 . 18091) (-4358 . 17784) (-4359 . 17718) + 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(-4423 . 810) + (-4424 . 719) (-4425 . 659) (-4426 . 564) (-4427 . 30))
\ No newline at end of file |