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 | 7 | ||||
| -rw-r--r-- | src/algebra/op.spad.pamphlet | 27 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1284 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1216 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1311 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8942 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30284 |
10 files changed, 21561 insertions, 21532 deletions
@@ -1,6 +1,6 @@ #! /bin/sh # Guess values for system-dependent variables and create Makefiles. -# Generated by GNU Autoconf 2.60 for OpenAxiom 1.3.0-2009-05-04. +# Generated by GNU Autoconf 2.60 for OpenAxiom 1.3.0-2009-05-06. # # Report bugs to <open-axiom-bugs@lists.sf.net>. # @@ -713,8 +713,8 @@ SHELL=${CONFIG_SHELL-/bin/sh} # Identity of this package. PACKAGE_NAME='OpenAxiom' PACKAGE_TARNAME='openaxiom' -PACKAGE_VERSION='1.3.0-2009-05-04' -PACKAGE_STRING='OpenAxiom 1.3.0-2009-05-04' +PACKAGE_VERSION='1.3.0-2009-05-06' +PACKAGE_STRING='OpenAxiom 1.3.0-2009-05-06' PACKAGE_BUGREPORT='open-axiom-bugs@lists.sf.net' ac_unique_file="src/Makefile.pamphlet" @@ -1406,7 +1406,7 @@ if test "$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 1.3.0-2009-05-04 to adapt to many kinds of systems. +\`configure' configures OpenAxiom 1.3.0-2009-05-06 to adapt to many kinds of systems. Usage: $0 [OPTION]... [VAR=VALUE]... @@ -1476,7 +1476,7 @@ fi if test -n "$ac_init_help"; then case $ac_init_help in - short | recursive ) echo "Configuration of OpenAxiom 1.3.0-2009-05-04:";; + short | recursive ) echo "Configuration of OpenAxiom 1.3.0-2009-05-06:";; esac cat <<\_ACEOF @@ -1580,7 +1580,7 @@ fi test -n "$ac_init_help" && exit $ac_status if $ac_init_version; then cat <<\_ACEOF -OpenAxiom configure 1.3.0-2009-05-04 +OpenAxiom configure 1.3.0-2009-05-06 generated by GNU Autoconf 2.60 Copyright (C) 1992, 1993, 1994, 1995, 1996, 1998, 1999, 2000, 2001, @@ -1594,7 +1594,7 @@ 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 1.3.0-2009-05-04, which was +It was created by OpenAxiom $as_me 1.3.0-2009-05-06, which was generated by GNU Autoconf 2.60. Invocation command line was $ $0 $@ @@ -26808,7 +26808,7 @@ 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 1.3.0-2009-05-04, which was +This file was extended by OpenAxiom $as_me 1.3.0-2009-05-06, which was generated by GNU Autoconf 2.60. Invocation command line was CONFIG_FILES = $CONFIG_FILES @@ -26857,7 +26857,7 @@ Report bugs to <bug-autoconf@gnu.org>." _ACEOF cat >>$CONFIG_STATUS <<_ACEOF ac_cs_version="\\ -OpenAxiom config.status 1.3.0-2009-05-04 +OpenAxiom config.status 1.3.0-2009-05-06 configured by $0, generated by GNU Autoconf 2.60, with options \\"`echo "$ac_configure_args" | sed 's/^ //; s/[\\""\`\$]/\\\\&/g'`\\" diff --git a/configure.ac b/configure.ac index 2e095780..8c1b631b 100644 --- a/configure.ac +++ b/configure.ac @@ -1,6 +1,6 @@ sinclude(config/open-axiom.m4) sinclude(config/aclocal.m4) -AC_INIT([OpenAxiom], [1.3.0-2009-05-04], +AC_INIT([OpenAxiom], [1.3.0-2009-05-06], [open-axiom-bugs@lists.sf.net]) AC_CONFIG_AUX_DIR(config) diff --git a/configure.ac.pamphlet b/configure.ac.pamphlet index e6579895..464b12d6 100644 --- a/configure.ac.pamphlet +++ b/configure.ac.pamphlet @@ -1131,7 +1131,7 @@ information: <<Autoconf init>>= sinclude(config/open-axiom.m4) sinclude(config/aclocal.m4) -AC_INIT([OpenAxiom], [1.3.0-2009-05-04], +AC_INIT([OpenAxiom], [1.3.0-2009-05-06], [open-axiom-bugs@lists.sf.net]) @ diff --git a/src/ChangeLog b/src/ChangeLog index a0a2950a..5dd46aed 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,12 @@ 2009-05-05 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/op.spad.pamphlet (property$BasicOperator): Overload with + a version that takes an identifier. + (deleteProperty$BasicOpetrator): Likewise. + (setProperty$BasicOperator): Likewise. + +2009-05-05 Gabriel Dos Reis <gdr@cs.tamu.edu> + Fix SF/2785271 * interp/sys-constants.boot ($Primitives): Remove. * interp/br-con.boot (conOpPage1): Replace $Primitives by diff --git a/src/algebra/op.spad.pamphlet b/src/algebra/op.spad.pamphlet index 525835b9..10f34a74 100644 --- a/src/algebra/op.spad.pamphlet +++ b/src/algebra/op.spad.pamphlet @@ -96,13 +96,24 @@ BasicOperator(): Exports == Implementation where deleteProperty_!: ($, String) -> $ ++ deleteProperty!(op, s) unattaches property s from op. ++ Argument op is modified "in place", i.e. no copy is made. + deleteProperty!: ($, Identifier) -> $ + ++ \spad{deleteProperty!(op, p)} unattaches property \spad{p} from + ++ \spad{op}. Argument \spad}op} is modified "in place", + ++ i.e. no copy is made. property : ($, String) -> Union(None, "failed") ++ property(op, s) returns the value of property s if ++ it is attached to op, and "failed" otherwise. + property : (%, Identifier) -> Maybe None + ++ \spad{property(op, p)} returns the value of property \spad{p} if + ++ it is attached to \spad{op}, otherwise \spad{nothing}. setProperty : ($, String, None) -> $ ++ setProperty(op, s, v) attaches property s to op, ++ and sets its value to v. ++ Argument op is modified "in place", 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", i.e. no copy is made. setProperties : ($, P) -> $ ++ setProperties(op, l) sets the property list of op to l. ++ Argument op is modified "in place", i.e. no copy is made. @@ -119,7 +130,11 @@ BasicOperator(): Exports == Implementation where setProperties(op, l) == (op.props := l; op) operator s == oper(s, -1::SingleInteger, table()) operator(s, n) == oper(s, n::Integer::SingleInteger, table()) - property(op, name) == search(name, op.props) + property(op: %, name: String) == search(name, op.props) + property(op: %, p: Identifier) == + case search(STRING(p)$Lisp, op.props) is + val@None => just val + otherwise => nothing assert(op, s) == setProperty(op, s, NIL$Lisp) has?(op, name) == key?(name, op.props) oper(se, n, prop) == [se, n, prop] @@ -130,8 +145,14 @@ BasicOperator(): Exports == Implementation where equality(op, func) == setProperty(op, EQUAL?, func pretend None) comparison(op, func) == setProperty(op, LESS?, func pretend None) display(op:$, f:O -> O) == display(op, f first #1) - deleteProperty_!(op, name) == (remove_!(name, properties op); op) - setProperty(op, name, valu) == (op.props.name := valu; op) + deleteProperty_!(op: %, name: String) == (remove_!(name, properties op); op) + deleteProperty!(op: %, p: Identifier) == + remove!(STRING(p)$Foreign(Builtin), properties op) + op + setProperty(op: %, name: String, valu: None) == (op.props.name := valu; op) + setProperty(op: %, p: Identifier, valu: None) == + op.props.(STRING(p)$Foreign(Builtin)@String) := valu + op coerce(op:$):OutputForm == name(op)::OutputForm input(op:$, f:List SEX -> SEX) == setProperty(op, SEXPR, f pretend None) display(op:$, f:List O -> O) == setProperty(op, DISPLAY, f pretend None) diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index f71153ac..a767c6a0 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2283354 . 3449600530) +(2283967 . 3450528888) (-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."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4408 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4404 . T) (-4409 . T) (-4403 . T)) +((-4409 . T) (-4407 . T) (-4406 . T) ((-4414 "*") . T) (-4405 . T) (-4410 . T) (-4404 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3378) +(-32 R -3438) ((|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 -1035) (QUOTE (-564))))) (-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 -4411))) +((|HasAttribute| |#1| (QUOTE -4412))) (-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}."))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . 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 -3378 UP UPUP -4022) +(-40 -3438 UP UPUP -3756) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4002 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4002 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4002 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -3378) +((-4405 |has| (-407 |#2|) (-363)) (-4410 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4012 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4012 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4012 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4012 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -3438) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-307)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4408 |has| |#1| (-556)) (-4406 . T) (-4405 . T)) +((-4409 |has| |#1| (-556)) (-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-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."))) -((-4411 . T) (-4412 . T)) -((-4002 (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|))))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|))))))) +((-4412 . T) (-4413 . T)) +((-4012 (-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|))))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) (-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|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4408 . T)) +((-4409 . 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 -3378) +(-54 |Base| R -3438) ((|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"))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . 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}"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-61 -4363) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-61 -4337) ((|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 -4363) +(-62 -4337) ((|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 -4363) +(-63 -4337) ((|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 -4363) +(-64 -4337) ((|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 -4363) +(-65 -4337) ((|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 -4363) +(-66 -4337) ((|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 -4363) +(-67 -4337) ((|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 -4363) +(-68 -4337) ((|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 -4363) +(-69 -4337) ((|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 -4363) +(-70 -4337) ((|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 -4363) +(-71 -4337) ((|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 -4363) +(-72 -4337) ((|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 -4363) +(-73 -4337) ((|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 -4363) +(-74 -4337) ((|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 -4363) +(-77 -4337) ((|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 -4363) +(-78 -4337) ((|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 -4363) +(-79 -4337) ((|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 -4363) +(-80 -4337) ((|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 -4363) +(-81 -4337) ((|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 -4363) +(-82 -4337) ((|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 -4363) +(-83 -4337) ((|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 -4363) +(-84 -4337) ((|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 -4363) +(-85 -4337) ((|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 -4363) +(-86 -4337) ((|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 -4363) +(-87 -4337) ((|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 -4363) +(-88 -4337) ((|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 -4363) +(-89 -4337) ((|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 (-363)))) (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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\"."))) -((-4411 . T)) +((-4412 . 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."))) -((-4411 . T) ((-4413 "*") . T) (-4412 . T) (-4408 . T) (-4406 . T) (-4405 . T) (-4404 . T) (-4409 . T) (-4403 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4399 . T) (-4407 . T) (-4410 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4398 . T)) +((-4412 . T) ((-4414 "*") . T) (-4413 . T) (-4409 . T) (-4407 . T) (-4406 . T) (-4405 . T) (-4410 . T) (-4404 . T) (-4403 . T) (-4402 . T) (-4401 . T) (-4400 . T) (-4408 . T) (-4411 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4399 . 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}."))) -((-4408 . T)) +((-4409 . T)) NIL (-100 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -342,15 +342,15 @@ NIL NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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 (-4413 "*")))) +((|HasAttribute| |#1| (QUOTE (-4414 "*")))) (-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"))) -((-4411 . T)) +((-4412 . 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."))) -((-4412 . T)) +((-4413 . 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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4012 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-859))))) (-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}"))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -385,25 +385,25 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-847)))) (-114) -((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) +((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3378 UP) +(-115 -3438 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}."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . 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}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4002 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4012 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4412))) +((|HasAttribute| |#1| (QUOTE -4413))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4002 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4012 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4413 "*") . T)) +(((-4414 "*") . T)) NIL -(-135 |minix| -2592 S T$) +(-135 |minix| -2880 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2592 R) +(-136 |minix| -2880 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) -((-4411 . T) (-4401 . T) (-4412 . T)) -((-4002 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4412 . T) (-4402 . T) (-4413 . T)) +((-4012 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -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."))) -((-4408 . T)) +((-4409 . 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."))) -((-4408 . T)) +((-4409 . T)) NIL -(-148 -3378 UP UPUP) +(-148 -3438 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 -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4411))) +((|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasAttribute| |#1| (QUOTE -4412))) (-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."))) -((-4406 . T) (-4405 . T) (-4408 . T)) +((-4407 . T) (-4406 . T) (-4409 . 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 -3378) +(-158 R -3438) ((|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 (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-999))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-847)))) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-999))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasAttribute| |#2| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-847)))) (-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})"))) -((-4404 -4002 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2305 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 -4012 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4408 |has| |#1| (-6 -4408)) (-4411 |has| |#1| (-6 -4411)) (-2453 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . 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."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4404 -4002 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2305 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| 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(QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4411)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -618,7 +618,7 @@ NIL NIL (-172) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-173) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -626,7 +626,7 @@ NIL NIL (-174 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4413 "*") . T) (-4404 . T) (-4409 . T) (-4403 . T) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") . T) (-4405 . T) (-4410 . T) (-4404 . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-175) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `nothing.")) (|push| (($ (|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}."))) @@ -677,10 +677,10 @@ NIL NIL NIL (-187) -((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) +((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3378) +(-188 R -3438) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-215 -3378 UP UPUP R) +(-215 -3438 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 -(-216 -3378 FP) +(-216 -3438 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 (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4012 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3378) +(-219 R -3438) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -818,19 +818,19 @@ NIL NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) -((-4408 . T)) +((-4409 . T)) NIL -(-224 R -3378) +(-224 R -3438) ((|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 (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2441 . T) (-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -838,15 +838,15 @@ NIL NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4414 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-229 S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) -((-4412 . T)) +((-4413 . T)) NIL (-230 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}."))) @@ -854,7 +854,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (-231 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4408 . T)) +((-4409 . T)) NIL (-232 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -862,36 +862,36 @@ NIL NIL (-233) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4408 . T)) +((-4409 . T)) NIL (-234 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4411))) +((|HasAttribute| |#1| (QUOTE -4412))) (-235 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}."))) -((-4412 . T)) +((-4413 . T)) NIL (-236) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -2592 R) +(-237 S -2880 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 (-363))) (|HasCategory| |#3| (QUOTE (-790))) (|HasCategory| |#3| (QUOTE (-845))) (|HasAttribute| |#3| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -2592 R) +((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-790))) (|HasCategory| |#3| (QUOTE (-845))) (|HasAttribute| |#3| (QUOTE -4409)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (QUOTE (-1094)))) +(-238 -2880 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"))) -((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . T)) +((-4406 |has| |#2| (-1046)) (-4407 |has| |#2| (-1046)) (-4409 |has| |#2| (-6 -4409)) ((-4414 "*") |has| |#2| (-172)) (-4412 . T)) NIL -(-239 -2592 A B) +(-239 -2880 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 -(-240 -2592 R) +(-240 -2880 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."))) -((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . 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(|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4012 (|HasCategory| |#2| (QUOTE (-1046))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-241) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -902,7 +902,7 @@ NIL NIL (-243) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4404 . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-244 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) @@ -910,16 +910,16 @@ NIL NIL (-245 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}"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4414 "*") |has| |#2| (-172)) (-4405 |has| |#2| (-556)) (-4410 |has| |#2| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-906))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-248) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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T)) -((-4002 (-12 (|HasCategory| |#4| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-233))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-723))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-790))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-845))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1046))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 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 (-233)))) (-253 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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL (-254 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-255) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -986,8 +986,8 @@ NIL NIL (-264 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 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 @@ -1032,11 +1032,11 @@ 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 -(-276 R -3378) +(-276 R -3438) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-277 R -3378) +(-277 R -3438) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1058,7 +1058,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094)))) (-282 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4412 . T)) +((-4413 . T)) NIL (-283 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1079,18 +1079,18 @@ NIL (-287 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4412))) +((|HasAttribute| |#1| (QUOTE -4413))) (-288 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-289 S R |Mod| -3753 -4012 |exactQuo|) +(-289 S R |Mod| -3126 -3678 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-290) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4404 . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-291) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|List| (|Property|)) (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `nothing.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-296) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-297 -3378 S) +(-297 -3438 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 -(-298 E -3378) +(-298 E -3438) ((|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 @@ -1158,7 +1158,7 @@ NIL NIL (-307) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-308 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1168,7 +1168,7 @@ 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 -(-310 -3378) +(-310 -3438) ((|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 @@ -1182,8 +1182,8 @@ NIL NIL (-313 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . 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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 @@ -1194,9 +1194,9 @@ NIL NIL (-316 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."))) -((-4408 -4002 (-4266 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-4002 (-4266 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1046)) (|has| |#1| (-473)))) (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 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(-4012 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1046)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4012 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4012 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4012 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4012 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) +(-317 R -3438) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1206,8 +1206,8 @@ NIL NIL (-319 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1218,7 +1218,7 @@ NIL NIL (-322 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-789)))) (-323 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1234,19 +1234,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) (-326 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-327 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -3378) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -3438) ((|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 (-368)))) -(-329 -3378) +(-329 -3438) ((|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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-330) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10."))) @@ -1264,15 +1264,15 @@ 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 -(-334 S -3378 UP UPUP R) +(-334 S -3438 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 -(-335 -3378 UP UPUP R) +(-335 -3438 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 -(-336 -3378 UP UPUP R) +(-336 -3438 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 @@ -1286,32 +1286,32 @@ NIL NIL (-339 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-379)))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) (-340 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-341 S -3378 UP UPUP) +(-341 S -3438 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -3378 UP UPUP) +(-342 -3438 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 |has| (-407 |#2|) (-363)) (-4410 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1326,33 +1326,33 @@ NIL NIL (-349) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL -(-350 R UP -3378) +(-350 R UP -3438) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-351 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -3378 GF) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -3438 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 @@ -1360,21 +1360,21 @@ 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 -(-358 -3378 FP FPP) +(-358 -3438 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-361 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4408 . T)) +((-4409 . T)) NIL (-362 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1382,7 +1382,7 @@ NIL NIL (-363) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-364 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1398,7 +1398,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-556)))) (-367 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4408 |has| |#1| (-556)) (-4406 . T) (-4405 . T)) +((-4409 |has| |#1| (-556)) (-4407 . T) (-4406 . T)) NIL (-368) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1410,7 +1410,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-363)))) (-370 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL (-371 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1419,14 +1419,14 @@ NIL (-372 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4413)) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094)))) (-373 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4411 . T)) +((-4412 . T)) NIL (-374 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4406 . T) (-4405 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4407 . T) (-4406 . T)) NIL (-375 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1438,7 +1438,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-377 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4408 . T)) +((-4409 . T)) NIL (-378 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4394 . T) (-4402 . T) (-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4395 . T) (-4403 . T) (-2441 . T) (-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1454,11 +1454,11 @@ NIL NIL (-381 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-382 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-383) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) @@ -1470,7 +1470,7 @@ NIL NIL (-385 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (QUOTE (-172)))) (-386 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1478,7 +1478,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-847)))) (-387) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-388) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1490,13 +1490,13 @@ NIL NIL (-390 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-391) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-392 -3378 UP UPUP R) +(-392 -3438 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 @@ -1520,11 +1520,11 @@ 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 -(-398 -4363 |returnType| -4229 |symbols|) +(-398 -4337 |returnType| -2841 |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 -(-399 -3378 UP) +(-399 -3438 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1538,15 +1538,15 @@ NIL NIL (-402) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-403 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#1| (QUOTE -4402))) +((|HasAttribute| |#1| (QUOTE -4395)) (|HasAttribute| |#1| (QUOTE -4403))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2441 . T) (-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1558,15 +1558,15 @@ NIL NIL (-407 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4398 -12 (|has| |#1| (-6 -4409)) (|has| |#1| (-452)) (|has| |#1| (-6 -4398))) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4002 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4398)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((-4399 -12 (|has| |#1| (-6 -4410)) (|has| |#1| (-452)) (|has| |#1| (-6 -4399))) (-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4012 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4410)) (|HasAttribute| |#1| (QUOTE -4399)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-409 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL (-410 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -3378 UP A) +(-413 R -3438 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4408 . T)) +((-4409 . T)) NIL -(-414 R -3378 UP A |ibasis|) +(-414 R -3438 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1035) (|devaluate| |#2|)))) @@ -1598,12 +1598,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-417 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4408 |has| |#1| (-556)) (-4406 . T) (-4405 . T)) +((-4409 |has| |#1| (-556)) (-4407 . T) (-4406 . T)) NIL (-418 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1630,17 +1630,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-368)))) (-425 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4411 . T) (-4401 . T) (-4412 . T)) +((-4412 . T) (-4402 . T) (-4413 . T)) NIL -(-426 R -3378) +(-426 R -3438) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-427 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4398 -12 (|has| |#1| (-6 -4398)) (|has| |#2| (-6 -4398))) (-4405 . T) (-4406 . T) (-4408 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4398)) (|HasAttribute| |#2| (QUOTE -4398)))) -(-428 R -3378) +((-4399 -12 (|has| |#1| (-6 -4399)) (|has| |#2| (-6 -4399))) (-4406 . T) (-4407 . T) (-4409 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4399)) (|HasAttribute| |#2| (QUOTE -4399)))) +(-428 R -3438) ((|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 @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4408 -4002 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-556)) (-4403 |has| |#1| (-556))) +((-4409 -4012 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) ((-4414 "*") |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-556)) (-4404 |has| |#1| (-556))) NIL -(-431 R -3378) +(-431 R -3438) ((|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 -(-432 R -3378) +(-432 R -3438) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-433 R -3378) +(-433 R -3438) ((|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 @@ -1668,7 +1668,7 @@ 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 -(-435 R -3378 UP) +(-435 R -3438 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 -1035) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ 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 -(-443 R UP -3378) +(-443 R UP -3438) ((|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 @@ -1738,16 +1738,16 @@ NIL NIL (-452) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-453 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4408 |has| (-407 (-949 |#1|)) (-556)) (-4406 . T) (-4405 . T)) +((-4409 |has| (-407 (-949 |#1|)) (-556)) (-4407 . T) (-4406 . T)) ((|HasCategory| (-407 (-949 |#1|)) (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-407 (-949 |#1|)) (QUOTE (-556)))) (-454 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4414 "*") |has| |#2| (-172)) (-4405 |has| |#2| (-556)) (-4410 |has| |#2| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-906))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1774,7 +1774,7 @@ NIL NIL (-461 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-462 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1782,7 +1782,7 @@ NIL NIL (-463 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-859))))) (-464 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1812,7 +1812,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -3378 R) +(-471 |lv| -3438 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1822,23 +1822,23 @@ NIL NIL (-473) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4408 . T)) +((-4409 . T)) NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094)))) +((-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094)))) (-476 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-859))))) (-477) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-478) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1846,29 +1846,29 @@ NIL NIL (-479 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-480) ((|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 (-481 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4012 (|HasCategory| |#2| (QUOTE (-1046))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL NIL (-484 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}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-485 -3378 UP UPUP R) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-485 -3438 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 @@ -1878,12 +1878,12 @@ NIL NIL (-487) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4012 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4411)) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) +((|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4413)) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-489 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,33 +1904,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -3378 UP |AlExt| |AlPol|) +(-494 -3438 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-495) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-498 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-499 R UP -3378) +(-499 R UP -3438) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-500 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -309) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-112) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-112) (QUOTE (-1094))) (|HasCategory| (-112) (LIST (QUOTE -611) (QUOTE (-859))))) (-501 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1944,7 +1944,7 @@ 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{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -3378 |Expon| |VarSet| |DPoly|) +(-504 -3438 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1953,7 +1953,7 @@ NIL NIL NIL (-506) -((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")) (|new| (($) "returns a new identifier,{} different from any other identifier in the running system"))) +((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) NIL NIL (-507 A S) @@ -1994,36 +1994,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-789)))) (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4002 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((-4012 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-520 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4412))) +((|HasAttribute| |#3| (QUOTE -4413))) (-522 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4412))) +((|HasAttribute| |#7| (QUOTE -4413))) (-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4414 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2056,7 +2056,7 @@ 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 -(-532 K -3378 |Par|) +(-532 K -3438 |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 @@ -2080,7 +2080,7 @@ 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 -(-538 K -3378 |Par|) +(-538 K -3438 |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 @@ -2110,7 +2110,7 @@ NIL NIL (-545) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4409 . T) (-4410 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4410 . T) (-4411 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-546) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2130,13 +2130,13 @@ NIL NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) -(-551 R -3378) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +(-551 R -3438) ((|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 -(-552 R0 -3378 UP UPUP R) +(-552 R0 -3438 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 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."))) -((-2299 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2441 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-555 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."))) @@ -2154,9 +2154,9 @@ NIL NIL (-556) ((|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."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL -(-557 R -3378) +(-557 R -3438) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2168,7 +2168,7 @@ 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 -(-560 R -3378 L) +(-560 R -3438 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -652) (|devaluate| |#2|)))) @@ -2176,31 +2176,31 @@ 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 -(-562 -3378 UP UPUP R) +(-562 -3438 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 -(-563 -3378 UP) +(-563 -3438 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 (-564) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4393 . T) (-4399 . T) (-4403 . T) (-4398 . T) (-4409 . T) (-4410 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4394 . T) (-4400 . T) (-4404 . T) (-4399 . T) (-4410 . T) (-4411 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-565) ((|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 -(-566 R -3378 L) +(-566 R -3438 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -652) (|devaluate| |#2|)))) -(-567 R -3378) +(-567 R -3438) ((|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 -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -3378 UP) +(-568 -3438 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2208,27 +2208,27 @@ 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 -(-570 -3378) +(-570 -3438) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-571 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."))) -((-2299 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2441 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-572) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-573 R -3378) +(-573 R -3438) ((|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 -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -3378 UP) +(-574 -3438 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-575 R -3378) +(-575 R -3438) ((|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 @@ -2250,27 +2250,27 @@ NIL NIL (-580 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-581 |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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) (-582) ((|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 -(-583 R -3378) +(-583 R -3438) ((|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 -(-584 E -3378) +(-584 E -3438) ((|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 -(-585 -3378) +(-585 -3438) ((|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}."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-586 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"))) @@ -2298,19 +2298,19 @@ NIL NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4002 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4012 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 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 (-594 |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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4406 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4408 . T)) +((-4407 |has| |#1| (-556)) (-4406 |has| |#1| (-556)) ((-4414 "*") |has| |#1| (-556)) (-4405 |has| |#1| (-556)) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-556)))) (-596 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) @@ -2320,7 +2320,7 @@ 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 -(-598 R -3378 FG) +(-598 R -3438 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2330,12 +2330,12 @@ NIL NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 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 -4412)) (|HasCategory| |#2| (QUOTE (-847))) (|HasAttribute| |#1| (QUOTE -4411)) (|HasCategory| |#3| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4413)) (|HasCategory| |#2| (QUOTE (-847))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#3| (QUOTE (-1094)))) (-602 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,19 +2350,19 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4408 -4002 (-4266 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4002 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4409 -4012 (-4264 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4407 . T) (-4406 . T)) +((-4012 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-607 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 (-608 |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}."))) -((-4412 . T)) +((-4413 . T)) NIL (-609 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"))) @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -3378 UP) +(-613 -3438 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2402,19 +2402,19 @@ NIL NIL (-618 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."))) -((-4408 . T)) +((-4409 . T)) NIL (-619 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}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-845)))) -(-620 R -3378) +(-620 R -3438) ((|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 (-621 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"))) -((-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4404 . T) (-4408 . T)) +((-4407 . T) (-4406 . T) ((-4414 "*") . T) (-4405 . T) (-4409 . T)) ((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (-622 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."))) @@ -2430,7 +2430,7 @@ NIL NIL (-625 |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}}."))) -((-4408 . T)) +((-4409 . T)) NIL (-626 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}}."))) @@ -2440,30 +2440,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-628 R -3378) +(-628 R -3438) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-629 |lv| -3378) +(-629 |lv| -3438) ((|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 (-630) ((|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."))) -((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094)))) +((-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2575) (QUOTE (-52))))))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (QUOTE (-1094)))) (-631 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-632 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4406 . T) (-4405 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4407 . T) (-4406 . T)) NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4408 -4002 (-4266 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4002 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4409 -4012 (-4264 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4407 . T) (-4406 . T)) +((-4012 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 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 @@ -2475,10 +2475,10 @@ NIL (-636 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 -((-4254 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-4253 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 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}."))) -((-4408 . T)) +((-4409 . T)) NIL (-638 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2494,16 +2494,16 @@ NIL NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2515,22 +2515,22 @@ NIL (-646 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 -4412))) +((|HasAttribute| |#1| (QUOTE -4413))) (-647 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 -(-648 R -3378 L) +(-648 R -3438 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 (-649 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}}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-650 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-651 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2538,15 +2538,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-652 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}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL -(-653 -3378 UP) +(-653 -3438 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)))) -(-654 A -3691) +(-654 A -3750) ((|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}}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) (-655 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."))) @@ -2562,7 +2562,7 @@ NIL NIL (-658 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}."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) ((|HasCategory| |#1| (QUOTE (-788)))) (-659 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2570,7 +2570,7 @@ NIL NIL (-660 |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) (-4406 . T) (-4405 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4407 . T) (-4406 . T)) ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-172)))) (-661 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}."))) @@ -2578,13 +2578,13 @@ NIL NIL (-662 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}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL -(-663 -3378) +(-663 -3438) ((|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 -(-664 -3378 |Row| |Col| M) +(-664 -3438 |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 @@ -2594,8 +2594,8 @@ NIL NIL (-666 |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."))) -((-4408 . T) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4002 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4409 . T) (-4412 . T) (-4406 . T) (-4407 . T)) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4414 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4012 (|HasAttribute| |#2| (QUOTE (-4414 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|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 @@ -2615,7 +2615,7 @@ NIL (-671 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 -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|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 @@ -2659,10 +2659,10 @@ NIL (-682 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) +((|HasAttribute| |#2| (QUOTE (-4414 "*"))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556)))) (-683 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-684 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."))) @@ -2670,8 +2670,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556)))) (-685 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."))) -((-4411 . T) (-4412 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4412 . T) (-4413 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4414 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 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 @@ -2680,7 +2680,7 @@ 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 -(-688 S -3378 FLAF FLAS) +(-688 S -3438 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 @@ -2690,11 +2690,11 @@ NIL NIL (-690) ((|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"))) -((-4404 . T) (-4409 |has| (-695) (-363)) (-4403 |has| (-695) (-363)) (-2305 . T) (-4410 |has| (-695) (-6 -4410)) (-4407 |has| (-695) (-6 -4407)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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T) (-4410 |has| (-695) (-363)) (-4404 |has| (-695) (-363)) (-2453 . T) (-4411 |has| (-695) (-6 -4411)) (-4408 |has| (-695) (-6 -4408)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-4012 (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-4012 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4012 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1019))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-999))) (|HasCategory| (-695) (QUOTE (-1194)))) (-4012 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (-4012 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906))) (-4012 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363)))) (-4012 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-847))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4411)) (|HasAttribute| (-695) (QUOTE -4408)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-145)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 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}."))) -((-4412 . T)) +((-4413 . T)) NIL (-692 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}."))) @@ -2704,13 +2704,13 @@ 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 -(-694 OV E -3378 PG) +(-694 OV E -3438 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 (-695) ((|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}"))) -((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2441 . T) (-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-696 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."))) @@ -2718,7 +2718,7 @@ NIL NIL (-697) ((|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}"))) -((-4410 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4411 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-698 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"))) @@ -2740,7 +2740,7 @@ 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 -(-703 S -3190 I) +(-703 S -2238 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 @@ -2750,7 +2750,7 @@ NIL NIL (-705 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)}.}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL (-706 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}."))) @@ -2760,25 +2760,25 @@ 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 -(-708 R |Mod| -3753 -4012 |exactQuo|) +(-708 R |Mod| -3126 -3678 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-709 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-710 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-711 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) +((-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-712 R |Mod| -3753 -4012 |exactQuo|) +(-712 R |Mod| -3126 -3678 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4408 . T)) +((-4409 . T)) NIL (-713 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2786,11 +2786,11 @@ NIL NIL (-714 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL -(-715 -3378) +(-715 -3438) ((|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]]}."))) -((-4408 . T)) +((-4409 . T)) NIL (-716 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."))) @@ -2814,7 +2814,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-349))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-368)))) (-721 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."))) -((-4404 |has| |#1| (-363)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 |has| |#1| (-363)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-722 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."))) @@ -2824,7 +2824,7 @@ 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 -(-724 -3378 UP) +(-724 -3438 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 @@ -2842,8 +2842,8 @@ NIL NIL (-728 |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."))) -(((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4414 "*") |has| |#2| (-172)) (-4405 |has| |#2| (-556)) (-4410 |has| |#2| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-906))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-729 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2858,15 +2858,15 @@ NIL NIL (-732 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) +((-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) (-4409 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-847)))) (-733 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4401 . T) (-4412 . T)) +((-4402 . T) (-4413 . T)) NIL (-734 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}."))) -((-4411 . T) (-4401 . T) (-4412 . T)) +((-4412 . T) (-4402 . T) (-4413 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-735) ((|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."))) @@ -2878,7 +2878,7 @@ NIL NIL (-737 |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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL (-738 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"))) @@ -2894,7 +2894,7 @@ NIL NIL (-741 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}."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-742) ((|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}."))) @@ -2976,11 +2976,11 @@ 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 -(-762 -3378) +(-762 -3438) ((|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 -(-763 P -3378) +(-763 P -3438) ((|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 @@ -2988,7 +2988,7 @@ NIL NIL NIL NIL -(-765 UP -3378) +(-765 UP -3438) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3002,9 +3002,9 @@ NIL NIL (-768) ((|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."))) -(((-4413 "*") . T)) +(((-4414 "*") . T)) NIL -(-769 R -3378) +(-769 R -3438) ((|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 @@ -3024,7 +3024,7 @@ 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 -(-774 -3378 |ExtF| |SUEx| |ExtP| |n|) +(-774 -3438 |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 @@ -3038,23 +3038,23 @@ NIL NIL (-777 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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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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 (-779 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 -407) (QUOTE (-564)))))) (-781 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.}"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-782 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}."))) @@ -3106,25 +3106,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-368)))) (-794 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL -(-795 -4002 R OS S) +(-795 -4012 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-796 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4002 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) +((-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-4012 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (-797) ((|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 -(-798 R -3378 L) +(-798 R -3438 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-799 R -3378) +(-799 R -3438) ((|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 @@ -3132,7 +3132,7 @@ 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 -(-801 R -3378) +(-801 R -3438) ((|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 @@ -3140,11 +3140,11 @@ 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 -(-803 -3378 UP UPUP R) +(-803 -3438 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 -(-804 -3378 UP L LQ) +(-804 -3438 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 @@ -3152,41 +3152,41 @@ 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 -(-806 -3378 UP L LQ) +(-806 -3438 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-807 -3378 UP) +(-807 -3438 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 -(-808 -3378 L UP A LO) +(-808 -3438 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 -(-809 -3378 UP) +(-809 -3438 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-810 -3378 LO) +(-810 -3438 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 -(-811 -3378 LODO) +(-811 -3438 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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T)) +((|HasCategory| |#1| (QUOTE (-906))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-814 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4413 "*") |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4409 |has| |#2| (-363)) (-4403 |has| |#2| (-363)) (-4408 . T) (-4406 . T) (-4405 . T)) +(((-4414 "*") |has| |#2| (-363)) (-4405 |has| |#2| (-363)) (-4410 |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4409 . T) (-4407 . T) (-4406 . T)) ((|HasCategory| |#2| (QUOTE (-363)))) (-815 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}))."))) @@ -3198,7 +3198,7 @@ NIL NIL (-817) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-818) ((|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}"))) @@ -3226,7 +3226,7 @@ NIL NIL (-824 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}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-233)))) (-825) ((|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."))) @@ -3238,7 +3238,7 @@ NIL NIL (-827 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4411 . T) (-4401 . T) (-4412 . T)) +((-4412 . T) (-4402 . T) (-4413 . T)) NIL (-828) ((|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."))) @@ -3250,8 +3250,8 @@ NIL NIL (-830 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."))) -((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4002 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4409 |has| |#1| (-845))) +((|HasCategory| |#1| (QUOTE (-845))) (-4012 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4012 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-831 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3262,7 +3262,7 @@ NIL NIL (-833 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) +((-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) (-834) ((|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)."))) @@ -3290,13 +3290,13 @@ NIL NIL (-840 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4002 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4409 |has| |#1| (-845))) +((|HasCategory| |#1| (QUOTE (-845))) (-4012 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4012 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-841) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-842 -2592 S) +(-842 -2880 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3310,7 +3310,7 @@ NIL NIL (-845) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4408 . T)) +((-4409 . T)) NIL (-846 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3326,19 +3326,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172)))) (-849 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL (-850 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 (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-851 R |sigma| -2689) +(-851 R |sigma| -3225) ((|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."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-852 |x| R |sigma| -2689) +(-852 |x| R |sigma| -3225) ((|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}."))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) (-853 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..)}."))) @@ -3382,7 +3382,7 @@ NIL NIL (-863 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) +((-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-864 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3394,24 +3394,24 @@ NIL NIL (-866 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-867 |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)."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-868 |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)."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4002 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4012 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) (-869 |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)}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4002 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4012 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-870 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 (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-871) ((|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 @@ -3467,7 +3467,7 @@ NIL (-884 |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 (-4254 (|HasCategory| |#2| (QUOTE (-1046)))) (-4254 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4254 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) +((-12 (-4253 (|HasCategory| |#2| (QUOTE (-1046)))) (-4253 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4253 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-885 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 @@ -3476,7 +3476,7 @@ 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 -(-887 R -3190) +(-887 R -2238) ((|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 @@ -3500,7 +3500,7 @@ 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 -(-893 UP -3378) +(-893 UP -3438) ((|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 @@ -3518,19 +3518,19 @@ NIL NIL (-897 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}."))) -((-4408 . T)) +((-4409 . T)) NIL (-898 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 (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-899 |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 (-900 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."))) -((-4408 . T)) +((-4409 . T)) NIL (-901 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3538,8 +3538,8 @@ NIL NIL (-902 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4408 . T)) -((-4002 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) +((-4409 . T)) +((-4012 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (-903 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3554,13 +3554,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-145)))) (-906) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-907 |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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-908 R0 -3378 UP UPUP R) +(-908 R0 -3438 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 @@ -3574,7 +3574,7 @@ NIL NIL (-911 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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-912 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."))) @@ -3588,7 +3588,7 @@ 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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-915 -3378) +(-915 -3438) ((|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 @@ -3598,17 +3598,17 @@ NIL NIL (-917) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-918) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4413 "*") . T)) +(((-4414 "*") . T)) NIL -(-919 -3378 P) +(-919 -3438 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-920 |xx| -3378) +(-920 |xx| -3438) ((|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 @@ -3632,7 +3632,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-926 R -3378) +(-926 R -3438) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3644,7 +3644,7 @@ 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 -(-929 S R -3378) +(-929 S R -3438) ((|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 @@ -3664,11 +3664,11 @@ 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 -883) (|devaluate| |#1|)))) -(-934 R -3378 -3190) +(-934 R -3438 -2238) ((|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 -(-935 -3190) +(-935 -2238) ((|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 @@ -3690,8 +3690,8 @@ NIL NIL (-940 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-941 |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 @@ -3711,12 +3711,12 @@ NIL (-945 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 (-906))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-847)))) +((|HasCategory| |#2| (QUOTE (-906))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#4| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#4| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#4| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-847)))) (-946 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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL -(-947 E V R P -3378) +(-947 E V R P -3438) ((|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 @@ -3726,9 +3726,9 @@ NIL NIL (-949 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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-950 E V R P -3378) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-950 E V R P -3438) ((|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 (-452)))) @@ -3750,13 +3750,13 @@ NIL NIL (-955 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"))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-956) ((|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 -(-957 -3378) +(-957 -3438) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3770,12 +3770,12 @@ NIL NIL (-960 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}"))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4409))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4410))) (-961 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"))) -((-4408 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4002 (-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 (-790))) (|HasCategory| |#2| (QUOTE 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(|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) +((-4409 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4012 (-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 (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-4012 (-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 (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-962) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3790,7 +3790,7 @@ NIL NIL (-965 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-966 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}}"))) @@ -3810,7 +3810,7 @@ NIL NIL (-970 |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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-971) ((|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}."))) @@ -3822,7 +3822,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-556)))) (-973 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."))) -((-4411 . T)) +((-4412 . T)) NIL (-974 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."))) @@ -3838,7 +3838,7 @@ NIL NIL (-977 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}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-978 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3856,7 +3856,7 @@ NIL ((|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 -(-982 K R UP -3378) +(-982 K R UP -3438) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3886,7 +3886,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145)))) (-989 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}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-990 |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}."))) @@ -3898,7 +3898,7 @@ NIL NIL (-992 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."))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-993 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}."))) @@ -3906,7 +3906,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-290)))) (-994 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}."))) -((-4404 |has| |#1| (-290)) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 |has| |#1| (-290)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-995 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}."))) @@ -3914,12 +3914,12 @@ NIL NIL (-996 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.}"))) -((-4404 |has| |#1| (-290)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) +((-4405 |has| |#1| (-290)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) (-997 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}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-998 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3928,14 +3928,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1000 -3378 UP UPUP |radicnd| |n|) +(-1000 -3438 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4002 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4002 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4002 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((-4405 |has| (-407 |#2|) (-363)) (-4410 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4012 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4012 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4012 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4012 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1001 |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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4012 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1002) ((|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 @@ -3955,7 +3955,7 @@ NIL (-1006 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 -4412)) (|HasCategory| |#2| (QUOTE (-1094)))) +((|HasAttribute| |#1| (QUOTE -4413)) (|HasCategory| |#2| (QUOTE (-1094)))) (-1007 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 @@ -3966,21 +3966,21 @@ NIL NIL (-1009) ((|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}}"))) -((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) +((-4405 . T) (-4410 . T) (-4404 . T) (-4407 . T) (-4406 . T) ((-4414 "*") . T) (-4409 . T)) NIL -(-1010 R -3378) +(-1010 R -3438) ((|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 -(-1011 R -3378) +(-1011 R -3438) ((|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 -(-1012 -3378 UP) +(-1012 -3438 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 -(-1013 -3378 UP) +(-1013 -3438 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 @@ -4014,9 +4014,9 @@ NIL NIL (-1021 |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"))) -((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) -((-4002 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) -(-1022 -3378 L) +((-4405 . T) (-4410 . T) (-4404 . T) (-4407 . T) (-4406 . T) ((-4414 "*") . T) (-4409 . T)) +((-4012 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) +(-1022 -3438 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4026,12 +4026,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1094)))) (-1024 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."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-859))))) (-1025 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4413 "*")))) +((|HasAttribute| |#1| (QUOTE (-4414 "*")))) (-1026 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 @@ -4052,14 +4052,14 @@ NIL ((|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 -(-1031 -3378 |Expon| |VarSet| |FPol| |LFPol|) +(-1031 -3438 |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"))) -(((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1032) ((|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.}"))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2575) (QUOTE (-52))))))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1033) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4102,7 +4102,7 @@ NIL NIL (-1043 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}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| (-777 |#1| (-861 |#2|)) (QUOTE (-1094))) (|HasCategory| (-777 |#1| (-861 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -777) (|devaluate| |#1|) (LIST (QUOTE -861) (|devaluate| |#2|)))))) (|HasCategory| (-777 |#1| (-861 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-777 |#1| (-861 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| (-861 |#2|) (QUOTE (-368))) (|HasCategory| (-777 |#1| (-861 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-1044) ((|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"))) @@ -4114,9 +4114,9 @@ NIL NIL (-1046) ((|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."))) -((-4408 . T)) +((-4409 . T)) NIL -(-1047 |xx| -3378) +(-1047 |xx| -3438) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4126,12 +4126,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-307))) (|HasCategory| |#4| (QUOTE (-363))) (|HasCategory| |#4| (QUOTE (-556))) (|HasCategory| |#4| (QUOTE (-172)))) (-1049 |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"))) -((-4411 . T) (-4406 . T) (-4405 . T)) +((-4412 . T) (-4407 . T) (-4406 . T)) NIL (-1050 |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}."))) -((-4411 . T) (-4406 . T) (-4405 . T)) -((-4002 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4407 . T) (-4406 . T)) +((-4012 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859))))) (-1051 |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 @@ -4150,7 +4150,7 @@ NIL NIL (-1055) ((|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."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1056 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4158,19 +4158,19 @@ NIL NIL (-1057) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4399 . T) (-4403 . T) (-4398 . T) (-4409 . T) (-4410 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4400 . T) (-4404 . T) (-4399 . T) (-4410 . T) (-4411 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1058) ((|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}"))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2575) (QUOTE (-52))))))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1059 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -989) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-1170))))) (-1060 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL (-1061) ((|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'."))) @@ -4194,7 +4194,7 @@ NIL NIL (-1066 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1067 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."))) @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -3378) +(-1070 |Base| R -3438) ((|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 -(-1071 |Base| R -3378) +(-1071 |Base| R -3438) ((|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 @@ -4226,8 +4226,8 @@ NIL NIL (-1074 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."))) -((-4404 |has| |#1| (-363)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4405 |has| |#1| (-363)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 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 @@ -4254,8 +4254,8 @@ NIL NIL (-1081 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"))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1082 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 @@ -4298,7 +4298,7 @@ NIL NIL (-1092 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}."))) -((-4401 . T)) +((-4402 . T)) NIL (-1093 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4314,8 +4314,8 @@ NIL NIL (-1096 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)}}"))) -((-4411 . T) (-4401 . T) (-4412 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4412 . T) (-4402 . T) (-4413 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4342,7 +4342,7 @@ NIL NIL (-1103 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.}"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1104) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4358,8 +4358,8 @@ NIL NIL (-1107 |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}."))) -((-4405 |has| |#3| (-1046)) (-4406 |has| |#3| (-1046)) (-4408 |has| |#3| (-6 -4408)) ((-4413 "*") |has| |#3| (-172)) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-790))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-845))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|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 @@ -4368,7 +4368,7 @@ NIL ((|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 -(-1110 R -3378) +(-1110 R -3438) ((|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 @@ -4386,19 +4386,19 @@ NIL NIL (-1114) ((|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."))) -((-4399 . T) (-4403 . T) (-4398 . T) (-4409 . T) (-4410 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4400 . T) (-4404 . T) (-4399 . T) (-4410 . T) (-4411 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1115 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4411 . T) (-4412 . T)) +((-4412 . T) (-4413 . T)) NIL (-1116 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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 (-363))) (|HasAttribute| |#3| (QUOTE (-4413 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) +((|HasCategory| |#3| (QUOTE (-363))) (|HasAttribute| |#3| (QUOTE (-4414 "*"))) (|HasCategory| |#3| (QUOTE (-172)))) (-1117 |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."))) -((-4411 . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4412 . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1118 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}."))) @@ -4406,17 +4406,17 @@ NIL NIL (-1119 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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-906))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1120 |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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 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}"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL -(-1122 UP -3378) +(-1122 UP -3438) ((|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 @@ -4470,19 +4470,19 @@ NIL NIL (-1135 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4002 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4012 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4408 . T) (-4400 |has| |#2| (-6 (-4413 "*"))) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-4002 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((-4409 . T) (-4401 |has| |#2| (-6 (-4414 "*"))) (-4412 . T) (-4406 . T) (-4407 . T)) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4414 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-4012 (|HasAttribute| |#2| (QUOTE (-4414 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1138) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1139 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.}"))) @@ -4490,12 +4490,12 @@ NIL NIL (-1140 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."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-859))))) (-1141 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}."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1142 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 @@ -4506,8 +4506,8 @@ NIL NIL (-1144 |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."))) -((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094)))) +((-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094)))) (-1145) ((|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 @@ -4530,20 +4530,20 @@ NIL NIL (-1150 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."))) -((-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4413 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1152) NIL -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#1|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-1154 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1168 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1169) ((|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 @@ -4618,8 +4618,8 @@ NIL NIL (-1172 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4409))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-6 -4410)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4012 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4410))) (-1173) ((|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 @@ -4658,8 +4658,8 @@ NIL NIL (-1182 |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}"))) -((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-4412 . T) (-4413 . T)) +((-12 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1350) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2575) (|devaluate| |#2|)))))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4012 (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4670,7 +4670,7 @@ NIL NIL (-1185 |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})}."))) -((-4412 . T)) +((-4413 . T)) NIL (-1186 |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."))) @@ -4710,8 +4710,8 @@ NIL NIL (-1195 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4412 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-4413 . T) (-4412 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -3378) +(-1198 R -3438) ((|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 @@ -4728,7 +4728,7 @@ NIL ((|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 -(-1200 R -3378) +(-1200 R -3438) ((|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 -612) (LIST (QUOTE -889) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -883) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -883) (|devaluate| |#1|))))) @@ -4738,12 +4738,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-368)))) (-1202 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |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 @@ -4756,7 +4756,7 @@ NIL ((|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 (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-1207 -3378) +(-1207 -3438) ((|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 @@ -4782,7 +4782,7 @@ NIL NIL (-1213) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1214) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4806,7 +4806,7 @@ NIL NIL (-1219 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1220 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)}."))) @@ -4814,16 +4814,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-363)))) (-1221 |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)}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1222 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . 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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 @@ -4858,8 +4858,8 @@ NIL NIL (-1232 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. 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T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +(((-4414 "*") |has| |#2| (-172)) (-4405 |has| |#2| (-556)) (-4408 |has| |#2| (-363)) (-4410 |has| |#2| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4012 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4012 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4012 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1233 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4870,15 +4870,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1145)))) (-1235 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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4408 |has| |#1| (-363)) (-4410 |has| |#1| (-6 -4410)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL (-1236 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 -897) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1765) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3714) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1238 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) @@ -4890,7 +4890,7 @@ NIL NIL (-1240 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1241 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)}."))) @@ -4898,24 +4898,24 @@ NIL NIL (-1242 |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)}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1243 |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)}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |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}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4410 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4012 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 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))}."))) -(((-4413 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4404 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-4002 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +(((-4414 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4405 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-4012 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4412))) +((|HasAttribute| |#1| (QUOTE -4413))) (-1247 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,20 +4927,20 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3591) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4039) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |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."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1251 |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|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +(((-4414 "*") |has| |#1| (-172)) (-4405 |has| |#1| (-556)) (-4406 . T) (-4407 . T) (-4409 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4012 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3714) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4012 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -4039) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4292) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1252 |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 -(-1253 -3378 UP L UTS) +(-1253 -3438 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 (-556)))) @@ -4958,7 +4958,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-999))) (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1257 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) NIL (-1258 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4966,8 +4966,8 @@ NIL NIL (-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4412 . T) (-4411 . T)) -((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4413 . T) (-4412 . T)) +((-4012 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4012 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4012 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -4994,13 +4994,13 @@ NIL NIL (-1266 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4406 . T) (-4405 . T)) +((-4407 . T) (-4406 . T)) NIL (-1267 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 -(-1268 K R UP -3378) +(-1268 K R UP -3438) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5014,56 +5014,56 @@ NIL NIL (-1271 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)"))) -((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) +((-4407 |has| |#1| (-172)) (-4406 |has| |#1| (-172)) (-4409 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363)))) (-1272 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}}."))) -((-4412 . T) (-4411 . T)) +((-4413 . T) (-4412 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#4| (LIST (QUOTE -309) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#4| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#4| (LIST (QUOTE -611) (QUOTE (-859))))) (-1273 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})"))) -((-4405 . T) (-4406 . T) (-4408 . T)) +((-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1274 |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."))) -((-4408 . T) (-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4404))) +((-4409 . T) (-4405 |has| |#2| (-6 -4405)) (-4407 . T) (-4406 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4405))) (-1275 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 (-1276 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) +((-4405 |has| |#2| (-6 -4405)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL -(-1277 S -3378) +(-1277 S -3438) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -3378) +(-1278 -3438) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 . T) (-4410 . T) (-4405 . T) ((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL (-1279 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -714) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4404))) +((-4405 |has| |#2| (-6 -4405)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -714) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasAttribute| |#2| (QUOTE -4405))) (-1280 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) +((-4405 |has| |#2| (-6 -4405)) (-4407 . T) (-4406 . T) (-4409 . T)) NIL (-1281 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4404 |has| |#1| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4404))) +((-4405 |has| |#1| (-6 -4405)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasAttribute| |#1| (QUOTE -4405))) (-1282 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4408 . T) (-4409 |has| |#1| (-6 -4409)) (-4404 |has| |#1| (-6 -4404)) (-4406 . T) (-4405 . T)) -((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4408)) (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4404))) +((-4409 . T) (-4410 |has| |#1| (-6 -4410)) (-4405 |has| |#1| (-6 -4405)) (-4407 . T) (-4406 . T)) +((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4410)) (|HasAttribute| |#1| (QUOTE -4405))) (-1283 |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."))) -((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4404))) +((-4405 |has| |#2| (-6 -4405)) (-4407 . T) (-4406 . T) (-4409 . T)) +((|HasCategory| |#2| (QUOTE (-172))) (|HasAttribute| |#2| (QUOTE -4405))) (-1284 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 @@ -5078,7 +5078,7 @@ NIL NIL (-1287 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +(((-4414 "*") . T) (-4406 . T) (-4407 . T) (-4409 . T)) NIL NIL NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2283334 2283339 2283344 2283349) (-2 NIL 2283314 2283319 2283324 2283329) (-1 NIL 2283294 2283299 2283304 2283309) (0 NIL 2283274 2283279 2283284 2283289) (-1287 "ZMOD.spad" 2283083 2283096 2283212 2283269) (-1286 "ZLINDEP.spad" 2282127 2282138 2283073 2283078) (-1285 "ZDSOLVE.spad" 2271976 2271998 2282117 2282122) (-1284 "YSTREAM.spad" 2271469 2271480 2271966 2271971) (-1283 "XRPOLY.spad" 2270689 2270709 2271325 2271394) (-1282 "XPR.spad" 2268480 2268493 2270407 2270506) (-1281 "XPOLY.spad" 2268035 2268046 2268336 2268405) (-1280 "XPOLYC.spad" 2267352 2267368 2267961 2268030) (-1279 "XPBWPOLY.spad" 2265789 2265809 2267132 2267201) (-1278 "XF.spad" 2264250 2264265 2265691 2265784) (-1277 "XF.spad" 2262691 2262708 2264134 2264139) (-1276 "XFALG.spad" 2259715 2259731 2262617 2262686) (-1275 "XEXPPKG.spad" 2258966 2258992 2259705 2259710) (-1274 "XDPOLY.spad" 2258580 2258596 2258822 2258891) (-1273 "XALG.spad" 2258240 2258251 2258536 2258575) (-1272 "WUTSET.spad" 2254079 2254096 2257886 2257913) (-1271 "WP.spad" 2253278 2253322 2253937 2254004) (-1270 "WHILEAST.spad" 2253076 2253085 2253268 2253273) (-1269 "WHEREAST.spad" 2252747 2252756 2253066 2253071) (-1268 "WFFINTBS.spad" 2250310 2250332 2252737 2252742) (-1267 "WEIER.spad" 2248524 2248535 2250300 2250305) (-1266 "VSPACE.spad" 2248197 2248208 2248492 2248519) (-1265 "VSPACE.spad" 2247890 2247903 2248187 2248192) (-1264 "VOID.spad" 2247567 2247576 2247880 2247885) (-1263 "VIEW.spad" 2245189 2245198 2247557 2247562) (-1262 "VIEWDEF.spad" 2240386 2240395 2245179 2245184) (-1261 "VIEW3D.spad" 2224221 2224230 2240376 2240381) (-1260 "VIEW2D.spad" 2211958 2211967 2224211 2224216) (-1259 "VECTOR.spad" 2210633 2210644 2210884 2210911) (-1258 "VECTOR2.spad" 2209260 2209273 2210623 2210628) (-1257 "VECTCAT.spad" 2207160 2207171 2209228 2209255) (-1256 "VECTCAT.spad" 2204868 2204881 2206938 2206943) (-1255 "VARIABLE.spad" 2204648 2204663 2204858 2204863) (-1254 "UTYPE.spad" 2204292 2204301 2204638 2204643) (-1253 "UTSODETL.spad" 2203585 2203609 2204248 2204253) (-1252 "UTSODE.spad" 2201773 2201793 2203575 2203580) (-1251 "UTS.spad" 2196562 2196590 2200240 2200337) (-1250 "UTSCAT.spad" 2194013 2194029 2196460 2196557) (-1249 "UTSCAT.spad" 2191108 2191126 2193557 2193562) (-1248 "UTS2.spad" 2190701 2190736 2191098 2191103) (-1247 "URAGG.spad" 2185333 2185344 2190691 2190696) (-1246 "URAGG.spad" 2179929 2179942 2185289 2185294) (-1245 "UPXSSING.spad" 2177572 2177598 2179010 2179143) (-1244 "UPXS.spad" 2174720 2174748 2175704 2175853) (-1243 "UPXSCONS.spad" 2172477 2172497 2172852 2173001) (-1242 "UPXSCCA.spad" 2171042 2171062 2172323 2172472) (-1241 "UPXSCCA.spad" 2169749 2169771 2171032 2171037) (-1240 "UPXSCAT.spad" 2168330 2168346 2169595 2169744) (-1239 "UPXS2.spad" 2167871 2167924 2168320 2168325) (-1238 "UPSQFREE.spad" 2166283 2166297 2167861 2167866) (-1237 "UPSCAT.spad" 2163876 2163900 2166181 2166278) (-1236 "UPSCAT.spad" 2161175 2161201 2163482 2163487) (-1235 "UPOLYC.spad" 2156153 2156164 2161017 2161170) (-1234 "UPOLYC.spad" 2151023 2151036 2155889 2155894) (-1233 "UPOLYC2.spad" 2150492 2150511 2151013 2151018) (-1232 "UP.spad" 2147649 2147664 2148042 2148195) (-1231 "UPMP.spad" 2146539 2146552 2147639 2147644) (-1230 "UPDIVP.spad" 2146102 2146116 2146529 2146534) (-1229 "UPDECOMP.spad" 2144339 2144353 2146092 2146097) (-1228 "UPCDEN.spad" 2143546 2143562 2144329 2144334) (-1227 "UP2.spad" 2142908 2142929 2143536 2143541) (-1226 "UNISEG.spad" 2142261 2142272 2142827 2142832) (-1225 "UNISEG2.spad" 2141754 2141767 2142217 2142222) (-1224 "UNIFACT.spad" 2140855 2140867 2141744 2141749) (-1223 "ULS.spad" 2131407 2131435 2132500 2132929) (-1222 "ULSCONS.spad" 2123801 2123821 2124173 2124322) (-1221 "ULSCCAT.spad" 2121530 2121550 2123647 2123796) (-1220 "ULSCCAT.spad" 2119367 2119389 2121486 2121491) (-1219 "ULSCAT.spad" 2117583 2117599 2119213 2119362) (-1218 "ULS2.spad" 2117095 2117148 2117573 2117578) (-1217 "UINT8.spad" 2116972 2116981 2117085 2117090) (-1216 "UINT64.spad" 2116848 2116857 2116962 2116967) (-1215 "UINT32.spad" 2116724 2116733 2116838 2116843) (-1214 "UINT16.spad" 2116600 2116609 2116714 2116719) (-1213 "UFD.spad" 2115665 2115674 2116526 2116595) (-1212 "UFD.spad" 2114792 2114803 2115655 2115660) (-1211 "UDVO.spad" 2113639 2113648 2114782 2114787) (-1210 "UDPO.spad" 2111066 2111077 2113595 2113600) (-1209 "TYPE.spad" 2110998 2111007 2111056 2111061) (-1208 "TYPEAST.spad" 2110917 2110926 2110988 2110993) (-1207 "TWOFACT.spad" 2109567 2109582 2110907 2110912) (-1206 "TUPLE.spad" 2109051 2109062 2109466 2109471) (-1205 "TUBETOOL.spad" 2105888 2105897 2109041 2109046) (-1204 "TUBE.spad" 2104529 2104546 2105878 2105883) (-1203 "TS.spad" 2103118 2103134 2104094 2104191) (-1202 "TSETCAT.spad" 2090245 2090262 2103086 2103113) (-1201 "TSETCAT.spad" 2077358 2077377 2090201 2090206) (-1200 "TRMANIP.spad" 2071724 2071741 2077064 2077069) (-1199 "TRIMAT.spad" 2070683 2070708 2071714 2071719) (-1198 "TRIGMNIP.spad" 2069200 2069217 2070673 2070678) (-1197 "TRIGCAT.spad" 2068712 2068721 2069190 2069195) (-1196 "TRIGCAT.spad" 2068222 2068233 2068702 2068707) (-1195 "TREE.spad" 2066793 2066804 2067829 2067856) (-1194 "TRANFUN.spad" 2066624 2066633 2066783 2066788) (-1193 "TRANFUN.spad" 2066453 2066464 2066614 2066619) (-1192 "TOPSP.spad" 2066127 2066136 2066443 2066448) (-1191 "TOOLSIGN.spad" 2065790 2065801 2066117 2066122) (-1190 "TEXTFILE.spad" 2064347 2064356 2065780 2065785) (-1189 "TEX.spad" 2061479 2061488 2064337 2064342) (-1188 "TEX1.spad" 2061035 2061046 2061469 2061474) (-1187 "TEMUTL.spad" 2060590 2060599 2061025 2061030) (-1186 "TBCMPPK.spad" 2058683 2058706 2060580 2060585) (-1185 "TBAGG.spad" 2057719 2057742 2058663 2058678) (-1184 "TBAGG.spad" 2056763 2056788 2057709 2057714) (-1183 "TANEXP.spad" 2056139 2056150 2056753 2056758) (-1182 "TABLE.spad" 2054550 2054573 2054820 2054847) (-1181 "TABLEAU.spad" 2054031 2054042 2054540 2054545) (-1180 "TABLBUMP.spad" 2050814 2050825 2054021 2054026) (-1179 "SYSTEM.spad" 2050042 2050051 2050804 2050809) (-1178 "SYSSOLP.spad" 2047515 2047526 2050032 2050037) (-1177 "SYSNNI.spad" 2046695 2046706 2047505 2047510) (-1176 "SYSINT.spad" 2046099 2046110 2046685 2046690) (-1175 "SYNTAX.spad" 2042293 2042302 2046089 2046094) (-1174 "SYMTAB.spad" 2040349 2040358 2042283 2042288) (-1173 "SYMS.spad" 2036334 2036343 2040339 2040344) (-1172 "SYMPOLY.spad" 2035341 2035352 2035423 2035550) (-1171 "SYMFUNC.spad" 2034816 2034827 2035331 2035336) (-1170 "SYMBOL.spad" 2032243 2032252 2034806 2034811) (-1169 "SWITCH.spad" 2029000 2029009 2032233 2032238) (-1168 "SUTS.spad" 2025899 2025927 2027467 2027564) (-1167 "SUPXS.spad" 2023034 2023062 2024031 2024180) (-1166 "SUP.spad" 2019803 2019814 2020584 2020737) (-1165 "SUPFRACF.spad" 2018908 2018926 2019793 2019798) (-1164 "SUP2.spad" 2018298 2018311 2018898 2018903) (-1163 "SUMRF.spad" 2017264 2017275 2018288 2018293) (-1162 "SUMFS.spad" 2016897 2016914 2017254 2017259) (-1161 "SULS.spad" 2007436 2007464 2008542 2008971) (-1160 "SUCHTAST.spad" 2007205 2007214 2007426 2007431) (-1159 "SUCH.spad" 2006885 2006900 2007195 2007200) (-1158 "SUBSPACE.spad" 1998892 1998907 2006875 2006880) (-1157 "SUBRESP.spad" 1998052 1998066 1998848 1998853) (-1156 "STTF.spad" 1994151 1994167 1998042 1998047) (-1155 "STTFNC.spad" 1990619 1990635 1994141 1994146) (-1154 "STTAYLOR.spad" 1983017 1983028 1990500 1990505) (-1153 "STRTBL.spad" 1981522 1981539 1981671 1981698) (-1152 "STRING.spad" 1980931 1980940 1980945 1980972) (-1151 "STRICAT.spad" 1980719 1980728 1980899 1980926) (-1150 "STREAM.spad" 1977577 1977588 1980244 1980259) (-1149 "STREAM3.spad" 1977122 1977137 1977567 1977572) (-1148 "STREAM2.spad" 1976190 1976203 1977112 1977117) (-1147 "STREAM1.spad" 1975894 1975905 1976180 1976185) (-1146 "STINPROD.spad" 1974800 1974816 1975884 1975889) (-1145 "STEP.spad" 1974001 1974010 1974790 1974795) (-1144 "STBL.spad" 1972527 1972555 1972694 1972709) (-1143 "STAGG.spad" 1971602 1971613 1972517 1972522) (-1142 "STAGG.spad" 1970675 1970688 1971592 1971597) (-1141 "STACK.spad" 1970026 1970037 1970282 1970309) (-1140 "SREGSET.spad" 1967730 1967747 1969672 1969699) (-1139 "SRDCMPK.spad" 1966275 1966295 1967720 1967725) (-1138 "SRAGG.spad" 1961372 1961381 1966243 1966270) (-1137 "SRAGG.spad" 1956489 1956500 1961362 1961367) (-1136 "SQMATRIX.spad" 1954105 1954123 1955021 1955108) (-1135 "SPLTREE.spad" 1948657 1948670 1953541 1953568) (-1134 "SPLNODE.spad" 1945245 1945258 1948647 1948652) (-1133 "SPFCAT.spad" 1944022 1944031 1945235 1945240) (-1132 "SPECOUT.spad" 1942572 1942581 1944012 1944017) (-1131 "SPADXPT.spad" 1934711 1934720 1942562 1942567) (-1130 "spad-parser.spad" 1934176 1934185 1934701 1934706) (-1129 "SPADAST.spad" 1933877 1933886 1934166 1934171) (-1128 "SPACEC.spad" 1917890 1917901 1933867 1933872) (-1127 "SPACE3.spad" 1917666 1917677 1917880 1917885) (-1126 "SORTPAK.spad" 1917211 1917224 1917622 1917627) (-1125 "SOLVETRA.spad" 1914968 1914979 1917201 1917206) (-1124 "SOLVESER.spad" 1913488 1913499 1914958 1914963) (-1123 "SOLVERAD.spad" 1909498 1909509 1913478 1913483) (-1122 "SOLVEFOR.spad" 1907918 1907936 1909488 1909493) (-1121 "SNTSCAT.spad" 1907518 1907535 1907886 1907913) (-1120 "SMTS.spad" 1905778 1905804 1907083 1907180) (-1119 "SMP.spad" 1903217 1903237 1903607 1903734) (-1118 "SMITH.spad" 1902060 1902085 1903207 1903212) (-1117 "SMATCAT.spad" 1900170 1900200 1902004 1902055) (-1116 "SMATCAT.spad" 1898212 1898244 1900048 1900053) (-1115 "SKAGG.spad" 1897173 1897184 1898180 1898207) (-1114 "SINT.spad" 1895999 1896008 1897039 1897168) (-1113 "SIMPAN.spad" 1895727 1895736 1895989 1895994) (-1112 "SIG.spad" 1895055 1895064 1895717 1895722) (-1111 "SIGNRF.spad" 1894163 1894174 1895045 1895050) (-1110 "SIGNEF.spad" 1893432 1893449 1894153 1894158) (-1109 "SIGAST.spad" 1892813 1892822 1893422 1893427) (-1108 "SHP.spad" 1890731 1890746 1892769 1892774) (-1107 "SHDP.spad" 1880442 1880469 1880951 1881082) (-1106 "SGROUP.spad" 1880050 1880059 1880432 1880437) (-1105 "SGROUP.spad" 1879656 1879667 1880040 1880045) (-1104 "SGCF.spad" 1872537 1872546 1879646 1879651) (-1103 "SFRTCAT.spad" 1871465 1871482 1872505 1872532) (-1102 "SFRGCD.spad" 1870528 1870548 1871455 1871460) (-1101 "SFQCMPK.spad" 1865165 1865185 1870518 1870523) (-1100 "SFORT.spad" 1864600 1864614 1865155 1865160) (-1099 "SEXOF.spad" 1864443 1864483 1864590 1864595) (-1098 "SEX.spad" 1864335 1864344 1864433 1864438) (-1097 "SEXCAT.spad" 1861886 1861926 1864325 1864330) (-1096 "SET.spad" 1860186 1860197 1861307 1861346) (-1095 "SETMN.spad" 1858620 1858637 1860176 1860181) (-1094 "SETCAT.spad" 1858105 1858114 1858610 1858615) (-1093 "SETCAT.spad" 1857588 1857599 1858095 1858100) (-1092 "SETAGG.spad" 1854109 1854120 1857568 1857583) (-1091 "SETAGG.spad" 1850638 1850651 1854099 1854104) (-1090 "SEQAST.spad" 1850341 1850350 1850628 1850633) (-1089 "SEGXCAT.spad" 1849463 1849476 1850331 1850336) (-1088 "SEG.spad" 1849276 1849287 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(-845 "ORDRING.spad" 1396871 1396879 1397461 1397476) (-844 "ORDRING.spad" 1396269 1396279 1396861 1396866) (-843 "ORDMON.spad" 1396124 1396132 1396259 1396264) (-842 "ORDFUNS.spad" 1395250 1395266 1396114 1396119) (-841 "ORDFIN.spad" 1395070 1395078 1395240 1395245) (-840 "ORDCOMP.spad" 1393535 1393545 1394617 1394646) (-839 "ORDCOMP2.spad" 1392820 1392832 1393525 1393530) (-838 "OPTPROB.spad" 1391458 1391466 1392810 1392815) (-837 "OPTPACK.spad" 1383843 1383851 1391448 1391453) (-836 "OPTCAT.spad" 1381518 1381526 1383833 1383838) (-835 "OPSIG.spad" 1381170 1381178 1381508 1381513) (-834 "OPQUERY.spad" 1380719 1380727 1381160 1381165) (-833 "OP.spad" 1380461 1380471 1380541 1380608) (-832 "OPERCAT.spad" 1380049 1380059 1380451 1380456) (-831 "OPERCAT.spad" 1379635 1379647 1380039 1380044) (-830 "ONECOMP.spad" 1378380 1378390 1379182 1379211) (-829 "ONECOMP2.spad" 1377798 1377810 1378370 1378375) (-828 "OMSERVER.spad" 1376800 1376808 1377788 1377793) (-827 "OMSAGG.spad" 1376588 1376598 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1298018 1298139 1298144) (-788 "OAGROUP.spad" 1297872 1297880 1298000 1298005) (-787 "NUMTUBE.spad" 1297459 1297475 1297862 1297867) (-786 "NUMQUAD.spad" 1285321 1285329 1297449 1297454) (-785 "NUMODE.spad" 1276457 1276465 1285311 1285316) (-784 "NUMINT.spad" 1274015 1274023 1276447 1276452) (-783 "NUMFMT.spad" 1272855 1272863 1274005 1274010) (-782 "NUMERIC.spad" 1264927 1264937 1272660 1272665) (-781 "NTSCAT.spad" 1263429 1263445 1264895 1264922) (-780 "NTPOLFN.spad" 1262974 1262984 1263346 1263351) (-779 "NSUP.spad" 1255984 1255994 1260524 1260677) (-778 "NSUP2.spad" 1255376 1255388 1255974 1255979) (-777 "NSMP.spad" 1251571 1251590 1251879 1252006) (-776 "NREP.spad" 1249943 1249957 1251561 1251566) (-775 "NPCOEF.spad" 1249189 1249209 1249933 1249938) (-774 "NORMRETR.spad" 1248787 1248826 1249179 1249184) (-773 "NORMPK.spad" 1246689 1246708 1248777 1248782) (-772 "NORMMA.spad" 1246377 1246403 1246679 1246684) (-771 "NONE.spad" 1246118 1246126 1246367 1246372) (-770 "NONE1.spad" 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1151512) (-732 "MRING.spad" 1148333 1148345 1151070 1151137) (-731 "MRF2.spad" 1147901 1147915 1148323 1148328) (-730 "MRATFAC.spad" 1147447 1147464 1147891 1147896) (-729 "MPRFF.spad" 1145477 1145496 1147437 1147442) (-728 "MPOLY.spad" 1142912 1142927 1143271 1143398) (-727 "MPCPF.spad" 1142176 1142195 1142902 1142907) (-726 "MPC3.spad" 1141991 1142031 1142166 1142171) (-725 "MPC2.spad" 1141633 1141666 1141981 1141986) (-724 "MONOTOOL.spad" 1139968 1139985 1141623 1141628) (-723 "MONOID.spad" 1139287 1139295 1139958 1139963) (-722 "MONOID.spad" 1138604 1138614 1139277 1139282) (-721 "MONOGEN.spad" 1137350 1137363 1138464 1138599) (-720 "MONOGEN.spad" 1136118 1136133 1137234 1137239) (-719 "MONADWU.spad" 1134132 1134140 1136108 1136113) (-718 "MONADWU.spad" 1132144 1132154 1134122 1134127) (-717 "MONAD.spad" 1131288 1131296 1132134 1132139) (-716 "MONAD.spad" 1130430 1130440 1131278 1131283) (-715 "MOEBIUS.spad" 1129116 1129130 1130410 1130425) (-714 "MODULE.spad" 1128986 1128996 1129084 1129111) (-713 "MODULE.spad" 1128876 1128888 1128976 1128981) (-712 "MODRING.spad" 1128207 1128246 1128856 1128871) (-711 "MODOP.spad" 1126866 1126878 1128029 1128096) (-710 "MODMONOM.spad" 1126595 1126613 1126856 1126861) (-709 "MODMON.spad" 1123354 1123370 1124073 1124226) (-708 "MODFIELD.spad" 1122712 1122751 1123256 1123349) (-707 "MMLFORM.spad" 1121572 1121580 1122702 1122707) (-706 "MMAP.spad" 1121312 1121346 1121562 1121567) (-705 "MLO.spad" 1119739 1119749 1121268 1121307) (-704 "MLIFT.spad" 1118311 1118328 1119729 1119734) (-703 "MKUCFUNC.spad" 1117844 1117862 1118301 1118306) (-702 "MKRECORD.spad" 1117446 1117459 1117834 1117839) (-701 "MKFUNC.spad" 1116827 1116837 1117436 1117441) (-700 "MKFLCFN.spad" 1115783 1115793 1116817 1116822) (-699 "MKCHSET.spad" 1115648 1115658 1115773 1115778) (-698 "MKBCFUNC.spad" 1115133 1115151 1115638 1115643) (-697 "MINT.spad" 1114572 1114580 1115035 1115128) (-696 "MHROWRED.spad" 1113073 1113083 1114562 1114567) (-695 "MFLOAT.spad" 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"MAPHACK3.spad" 1069557 1069571 1069739 1069744) (-675 "MAPHACK2.spad" 1069322 1069334 1069547 1069552) (-674 "MAPHACK1.spad" 1068952 1068962 1069312 1069317) (-673 "MAGMA.spad" 1066742 1066759 1068942 1068947) (-672 "MACROAST.spad" 1066321 1066329 1066732 1066737) (-671 "M3D.spad" 1064017 1064027 1065699 1065704) (-670 "LZSTAGG.spad" 1061245 1061255 1064007 1064012) (-669 "LZSTAGG.spad" 1058471 1058483 1061235 1061240) (-668 "LWORD.spad" 1055176 1055193 1058461 1058466) (-667 "LSTAST.spad" 1054960 1054968 1055166 1055171) (-666 "LSQM.spad" 1053186 1053200 1053584 1053635) (-665 "LSPP.spad" 1052719 1052736 1053176 1053181) (-664 "LSMP.spad" 1051559 1051587 1052709 1052714) (-663 "LSMP1.spad" 1049363 1049377 1051549 1051554) (-662 "LSAGG.spad" 1049032 1049042 1049331 1049358) (-661 "LSAGG.spad" 1048721 1048733 1049022 1049027) (-660 "LPOLY.spad" 1047675 1047694 1048577 1048646) (-659 "LPEFRAC.spad" 1046932 1046942 1047665 1047670) (-658 "LO.spad" 1046333 1046347 1046866 1046893) (-657 "LOGIC.spad" 1045935 1045943 1046323 1046328) (-656 "LOGIC.spad" 1045535 1045545 1045925 1045930) (-655 "LODOOPS.spad" 1044453 1044465 1045525 1045530) (-654 "LODO.spad" 1043837 1043853 1044133 1044172) (-653 "LODOF.spad" 1042881 1042898 1043794 1043799) (-652 "LODOCAT.spad" 1041539 1041549 1042837 1042876) (-651 "LODOCAT.spad" 1040195 1040207 1041495 1041500) (-650 "LODO2.spad" 1039468 1039480 1039875 1039914) (-649 "LODO1.spad" 1038868 1038878 1039148 1039187) (-648 "LODEEF.spad" 1037640 1037658 1038858 1038863) (-647 "LNAGG.spad" 1033442 1033452 1037630 1037635) (-646 "LNAGG.spad" 1029208 1029220 1033398 1033403) (-645 "LMOPS.spad" 1025944 1025961 1029198 1029203) (-644 "LMODULE.spad" 1025586 1025596 1025934 1025939) (-643 "LMDICT.spad" 1024869 1024879 1025137 1025164) (-642 "LITERAL.spad" 1024775 1024786 1024859 1024864) (-641 "LIST.spad" 1022493 1022503 1023922 1023949) (-640 "LIST3.spad" 1021784 1021798 1022483 1022488) (-639 "LIST2.spad" 1020424 1020436 1021774 1021779) (-638 "LIST2MAP.spad" 1017301 1017313 1020414 1020419) (-637 "LINEXP.spad" 1016733 1016743 1017281 1017296) (-636 "LINDEP.spad" 1015510 1015522 1016645 1016650) (-635 "LIMITRF.spad" 1013424 1013434 1015500 1015505) (-634 "LIMITPS.spad" 1012307 1012320 1013414 1013419) (-633 "LIE.spad" 1010321 1010333 1011597 1011742) (-632 "LIECAT.spad" 1009797 1009807 1010247 1010316) (-631 "LIECAT.spad" 1009301 1009313 1009753 1009758) (-630 "LIB.spad" 1007349 1007357 1007960 1007975) (-629 "LGROBP.spad" 1004702 1004721 1007339 1007344) (-628 "LF.spad" 1003621 1003637 1004692 1004697) (-627 "LFCAT.spad" 1002640 1002648 1003611 1003616) (-626 "LEXTRIPK.spad" 998143 998158 1002630 1002635) (-625 "LEXP.spad" 996146 996173 998123 998138) (-624 "LETAST.spad" 995845 995853 996136 996141) (-623 "LEADCDET.spad" 994229 994246 995835 995840) (-622 "LAZM3PK.spad" 992933 992955 994219 994224) (-621 "LAUPOL.spad" 991622 991635 992526 992595) (-620 "LAPLACE.spad" 991195 991211 991612 991617) (-619 "LA.spad" 990635 990649 991117 991156) (-618 "LALG.spad" 990411 990421 990615 990630) (-617 "LALG.spad" 990195 990207 990401 990406) (-616 "KVTFROM.spad" 989930 989940 990185 990190) (-615 "KTVLOGIC.spad" 989353 989361 989920 989925) (-614 "KRCFROM.spad" 989091 989101 989343 989348) (-613 "KOVACIC.spad" 987804 987821 989081 989086) (-612 "KONVERT.spad" 987526 987536 987794 987799) (-611 "KOERCE.spad" 987263 987273 987516 987521) (-610 "KERNEL.spad" 985798 985808 987047 987052) (-609 "KERNEL2.spad" 985501 985513 985788 985793) (-608 "KDAGG.spad" 984604 984626 985481 985496) (-607 "KDAGG.spad" 983715 983739 984594 984599) (-606 "KAFILE.spad" 982678 982694 982913 982940) (-605 "JORDAN.spad" 980505 980517 981968 982113) (-604 "JOINAST.spad" 980199 980207 980495 980500) (-603 "JAVACODE.spad" 980065 980073 980189 980194) (-602 "IXAGG.spad" 978188 978212 980055 980060) (-601 "IXAGG.spad" 976166 976192 978035 978040) (-600 "IVECTOR.spad" 974937 974952 975092 975119) (-599 "ITUPLE.spad" 974082 974092 974927 974932) (-598 "ITRIGMNP.spad" 972893 972912 974072 974077) (-597 "ITFUN3.spad" 972387 972401 972883 972888) (-596 "ITFUN2.spad" 972117 972129 972377 972382) (-595 "ITAYLOR.spad" 969909 969924 971953 972078) (-594 "ISUPS.spad" 962320 962335 968883 968980) (-593 "ISUMP.spad" 961817 961833 962310 962315) (-592 "ISTRING.spad" 960820 960833 960986 961013) (-591 "ISAST.spad" 960539 960547 960810 960815) (-590 "IRURPK.spad" 959252 959271 960529 960534) (-589 "IRSN.spad" 957212 957220 959242 959247) (-588 "IRRF2F.spad" 955687 955697 957168 957173) (-587 "IRREDFFX.spad" 955288 955299 955677 955682) (-586 "IROOT.spad" 953619 953629 955278 955283) (-585 "IR.spad" 951408 951422 953474 953501) (-584 "IR2.spad" 950428 950444 951398 951403) (-583 "IR2F.spad" 949628 949644 950418 950423) (-582 "IPRNTPK.spad" 949388 949396 949618 949623) (-581 "IPF.spad" 948953 948965 949193 949286) (-580 "IPADIC.spad" 948714 948740 948879 948948) (-579 "IP4ADDR.spad" 948271 948279 948704 948709) (-578 "IOMODE.spad" 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900771 901692 901697) (-557 "INTEF.spad" 899076 899092 900751 900756) (-556 "INTDOM.spad" 897691 897699 899002 899071) (-555 "INTDOM.spad" 896368 896378 897681 897686) (-554 "INTCAT.spad" 894621 894631 896282 896363) (-553 "INTBIT.spad" 894124 894132 894611 894616) (-552 "INTALG.spad" 893306 893333 894114 894119) (-551 "INTAF.spad" 892798 892814 893296 893301) (-550 "INTABL.spad" 891316 891347 891479 891506) (-549 "INT8.spad" 891196 891204 891306 891311) (-548 "INT64.spad" 891075 891083 891186 891191) (-547 "INT32.spad" 890954 890962 891065 891070) (-546 "INT16.spad" 890833 890841 890944 890949) (-545 "INS.spad" 888300 888308 890735 890828) (-544 "INS.spad" 885853 885863 888290 888295) (-543 "INPSIGN.spad" 885287 885300 885843 885848) (-542 "INPRODPF.spad" 884353 884372 885277 885282) (-541 "INPRODFF.spad" 883411 883435 884343 884348) (-540 "INNMFACT.spad" 882382 882399 883401 883406) (-539 "INMODGCD.spad" 881866 881896 882372 882377) (-538 "INFSP.spad" 880151 880173 881856 881861) (-537 "INFPROD0.spad" 879201 879220 880141 880146) (-536 "INFORM.spad" 876362 876370 879191 879196) (-535 "INFORM1.spad" 875987 875997 876352 876357) (-534 "INFINITY.spad" 875539 875547 875977 875982) (-533 "INETCLTS.spad" 875516 875524 875529 875534) (-532 "INEP.spad" 874048 874070 875506 875511) (-531 "INDE.spad" 873777 873794 874038 874043) (-530 "INCRMAPS.spad" 873198 873208 873767 873772) (-529 "INBFILE.spad" 872270 872278 873188 873193) (-528 "INBFF.spad" 868040 868051 872260 872265) (-527 "INBCON.spad" 866328 866336 868030 868035) (-526 "INBCON.spad" 864614 864624 866318 866323) (-525 "INAST.spad" 864275 864283 864604 864609) (-524 "IMPTAST.spad" 863983 863991 864265 864270) (-523 "IMATRIX.spad" 862928 862954 863440 863467) (-522 "IMATQF.spad" 862022 862066 862884 862889) (-521 "IMATLIN.spad" 860627 860651 861978 861983) (-520 "ILIST.spad" 859283 859298 859810 859837) (-519 "IIARRAY2.spad" 858671 858709 858890 858917) (-518 "IFF.spad" 858081 858097 858352 858445) (-517 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(-394 "FORMULA.spad" 645230 645238 647756 647761) (-393 "FORMULA1.spad" 644709 644719 645220 645225) (-392 "FORDER.spad" 644400 644424 644699 644704) (-391 "FOP.spad" 643601 643609 644390 644395) (-390 "FNLA.spad" 643025 643047 643569 643596) (-389 "FNCAT.spad" 641612 641620 643015 643020) (-388 "FNAME.spad" 641504 641512 641602 641607) (-387 "FMTC.spad" 641302 641310 641430 641499) (-386 "FMONOID.spad" 638357 638367 641258 641263) (-385 "FM.spad" 638052 638064 638291 638318) (-384 "FMFUN.spad" 635082 635090 638042 638047) (-383 "FMC.spad" 634134 634142 635072 635077) (-382 "FMCAT.spad" 631788 631806 634102 634129) (-381 "FM1.spad" 631145 631157 631722 631749) (-380 "FLOATRP.spad" 628866 628880 631135 631140) (-379 "FLOAT.spad" 622154 622162 628732 628861) (-378 "FLOATCP.spad" 619571 619585 622144 622149) (-377 "FLINEXP.spad" 619283 619293 619551 619566) (-376 "FLINEXP.spad" 618949 618961 619219 619224) (-375 "FLASORT.spad" 618269 618281 618939 618944) (-374 "FLALG.spad" 615915 615934 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"CYCLES.spad" 221786 221794 224944 224949) (-189 "CVMP.spad" 221203 221213 221776 221781) (-188 "CTRIGMNP.spad" 219693 219709 221193 221198) (-187 "CTOR.spad" 219388 219396 219683 219688) (-186 "CTORKIND.spad" 218991 218999 219378 219383) (-185 "CTORCAT.spad" 218240 218248 218981 218986) (-184 "CTORCAT.spad" 217487 217497 218230 218235) (-183 "CTORCALL.spad" 217067 217075 217477 217482) (-182 "CSTTOOLS.spad" 216310 216323 217057 217062) (-181 "CRFP.spad" 210014 210027 216300 216305) (-180 "CRCEAST.spad" 209734 209742 210004 210009) (-179 "CRAPACK.spad" 208777 208787 209724 209729) (-178 "CPMATCH.spad" 208277 208292 208702 208707) (-177 "CPIMA.spad" 207982 208001 208267 208272) (-176 "COORDSYS.spad" 202875 202885 207972 207977) (-175 "CONTOUR.spad" 202286 202294 202865 202870) (-174 "CONTFRAC.spad" 197898 197908 202188 202281) (-173 "CONDUIT.spad" 197656 197664 197888 197893) (-172 "COMRING.spad" 197330 197338 197594 197651) (-171 "COMPPROP.spad" 196844 196852 197320 197325) (-170 "COMPLPAT.spad" 196611 196626 196834 196839) (-169 "COMPLEX.spad" 190635 190645 190879 191140) (-168 "COMPLEX2.spad" 190348 190360 190625 190630) (-167 "COMPFACT.spad" 189950 189964 190338 190343) (-166 "COMPCAT.spad" 188018 188028 189684 189945) (-165 "COMPCAT.spad" 185779 185791 187447 187452) (-164 "COMMUPC.spad" 185525 185543 185769 185774) (-163 "COMMONOP.spad" 185058 185066 185515 185520) (-162 "COMM.spad" 184867 184875 185048 185053) (-161 "COMMAAST.spad" 184630 184638 184857 184862) (-160 "COMBOPC.spad" 183535 183543 184620 184625) (-159 "COMBINAT.spad" 182280 182290 183525 183530) (-158 "COMBF.spad" 179648 179664 182270 182275) (-157 "COLOR.spad" 178485 178493 179638 179643) (-156 "COLONAST.spad" 178151 178159 178475 178480) (-155 "CMPLXRT.spad" 177860 177877 178141 178146) (-154 "CLLCTAST.spad" 177522 177530 177850 177855) (-153 "CLIP.spad" 173614 173622 177512 177517) (-152 "CLIF.spad" 172253 172269 173570 173609) (-151 "CLAGG.spad" 168738 168748 172243 172248) (-150 "CLAGG.spad" 165094 165106 168601 168606) (-149 "CINTSLPE.spad" 164419 164432 165084 165089) (-148 "CHVAR.spad" 162497 162519 164409 164414) (-147 "CHARZ.spad" 162412 162420 162477 162492) (-146 "CHARPOL.spad" 161920 161930 162402 162407) (-145 "CHARNZ.spad" 161673 161681 161900 161915) (-144 "CHAR.spad" 159541 159549 161663 161668) (-143 "CFCAT.spad" 158857 158865 159531 159536) (-142 "CDEN.spad" 158015 158029 158847 158852) (-141 "CCLASS.spad" 156164 156172 157426 157465) (-140 "CATEGORY.spad" 155254 155262 156154 156159) (-139 "CATCTOR.spad" 155145 155153 155244 155249) (-138 "CATAST.spad" 154763 154771 155135 155140) (-137 "CASEAST.spad" 154477 154485 154753 154758) (-136 "CARTEN.spad" 149580 149604 154467 154472) (-135 "CARTEN2.spad" 148966 148993 149570 149575) (-134 "CARD.spad" 146255 146263 148940 148961) (-133 "CAPSLAST.spad" 146029 146037 146245 146250) (-132 "CACHSET.spad" 145651 145659 146019 146024) (-131 "CABMON.spad" 145204 145212 145641 145646) (-130 "BYTEORD.spad" 144879 144887 145194 145199) (-129 "BYTE.spad" 144304 144312 144869 144874) (-128 "BYTEBUF.spad" 142161 142169 143473 143500) (-127 "BTREE.spad" 141230 141240 141768 141795) (-126 "BTOURN.spad" 140233 140243 140837 140864) (-125 "BTCAT.spad" 139621 139631 140201 140228) (-124 "BTCAT.spad" 139029 139041 139611 139616) (-123 "BTAGG.spad" 138151 138159 138997 139024) (-122 "BTAGG.spad" 137293 137303 138141 138146) (-121 "BSTREE.spad" 136028 136038 136900 136927) (-120 "BRILL.spad" 134223 134234 136018 136023) (-119 "BRAGG.spad" 133147 133157 134213 134218) (-118 "BRAGG.spad" 132035 132047 133103 133108) (-117 "BPADICRT.spad" 130016 130028 130271 130364) (-116 "BPADIC.spad" 129680 129692 129942 130011) (-115 "BOUNDZRO.spad" 129336 129353 129670 129675) (-114 "BOP.spad" 124800 124808 129326 129331) (-113 "BOP1.spad" 122186 122196 124756 124761) (-112 "BOOLEAN.spad" 121510 121518 122176 122181) (-111 "BMODULE.spad" 121222 121234 121478 121505) (-110 "BITS.spad" 120641 120649 120858 120885) (-109 "BINDING.spad" 120060 120068 120631 120636) (-108 "BINARY.spad" 118171 118179 118527 118620) (-107 "BGAGG.spad" 117368 117378 118151 118166) (-106 "BGAGG.spad" 116573 116585 117358 117363) (-105 "BFUNCT.spad" 116137 116145 116553 116568) (-104 "BEZOUT.spad" 115271 115298 116087 116092) (-103 "BBTREE.spad" 112090 112100 114878 114905) (-102 "BASTYPE.spad" 111762 111770 112080 112085) (-101 "BASTYPE.spad" 111432 111442 111752 111757) (-100 "BALFACT.spad" 110871 110884 111422 111427) (-99 "AUTOMOR.spad" 110318 110327 110851 110866) (-98 "ATTREG.spad" 107037 107044 110070 110313) (-97 "ATTRBUT.spad" 103060 103067 107017 107032) (-96 "ATTRAST.spad" 102777 102784 103050 103055) (-95 "ATRIG.spad" 102247 102254 102767 102772) (-94 "ATRIG.spad" 101715 101724 102237 102242) (-93 "ASTCAT.spad" 101619 101626 101705 101710) (-92 "ASTCAT.spad" 101521 101530 101609 101614) (-91 "ASTACK.spad" 100854 100863 101128 101155) (-90 "ASSOCEQ.spad" 99654 99665 100810 100815) (-89 "ASP9.spad" 98735 98748 99644 99649) (-88 "ASP8.spad" 97778 97791 98725 98730) (-87 "ASP80.spad" 97100 97113 97768 97773) (-86 "ASP7.spad" 96260 96273 97090 97095) (-85 "ASP78.spad" 95711 95724 96250 96255) (-84 "ASP77.spad" 95080 95093 95701 95706) (-83 "ASP74.spad" 94172 94185 95070 95075) (-82 "ASP73.spad" 93443 93456 94162 94167) (-81 "ASP6.spad" 92310 92323 93433 93438) (-80 "ASP55.spad" 90819 90832 92300 92305) (-79 "ASP50.spad" 88636 88649 90809 90814) (-78 "ASP4.spad" 87931 87944 88626 88631) (-77 "ASP49.spad" 86930 86943 87921 87926) (-76 "ASP42.spad" 85337 85376 86920 86925) (-75 "ASP41.spad" 83916 83955 85327 85332) (-74 "ASP35.spad" 82904 82917 83906 83911) (-73 "ASP34.spad" 82205 82218 82894 82899) (-72 "ASP33.spad" 81765 81778 82195 82200) (-71 "ASP31.spad" 80905 80918 81755 81760) (-70 "ASP30.spad" 79797 79810 80895 80900) (-69 "ASP29.spad" 79263 79276 79787 79792) (-68 "ASP28.spad" 70536 70549 79253 79258) (-67 "ASP27.spad" 69433 69446 70526 70531) (-66 "ASP24.spad" 68520 68533 69423 69428) (-65 "ASP20.spad" 67984 67997 68510 68515) (-64 "ASP1.spad" 67365 67378 67974 67979) (-63 "ASP19.spad" 62051 62064 67355 67360) (-62 "ASP12.spad" 61465 61478 62041 62046) (-61 "ASP10.spad" 60736 60749 61455 61460) (-60 "ARRAY2.spad" 60096 60105 60343 60370) (-59 "ARRAY1.spad" 58931 58940 59279 59306) (-58 "ARRAY12.spad" 57600 57611 58921 58926) (-57 "ARR2CAT.spad" 53262 53283 57568 57595) (-56 "ARR2CAT.spad" 48944 48967 53252 53257) (-55 "ARITY.spad" 48512 48519 48934 48939) (-54 "APPRULE.spad" 47756 47778 48502 48507) (-53 "APPLYORE.spad" 47371 47384 47746 47751) (-52 "ANY.spad" 45713 45720 47361 47366) (-51 "ANY1.spad" 44784 44793 45703 45708) (-50 "ANTISYM.spad" 43223 43239 44764 44779) (-49 "ANON.spad" 42916 42923 43213 43218) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2283947 2283952 2283957 2283962) (-2 NIL 2283927 2283932 2283937 2283942) (-1 NIL 2283907 2283912 2283917 2283922) (0 NIL 2283887 2283892 2283897 2283902) (-1287 "ZMOD.spad" 2283696 2283709 2283825 2283882) (-1286 "ZLINDEP.spad" 2282740 2282751 2283686 2283691) (-1285 "ZDSOLVE.spad" 2272589 2272611 2282730 2282735) (-1284 "YSTREAM.spad" 2272082 2272093 2272579 2272584) (-1283 "XRPOLY.spad" 2271302 2271322 2271938 2272007) (-1282 "XPR.spad" 2269093 2269106 2271020 2271119) (-1281 "XPOLY.spad" 2268648 2268659 2268949 2269018) (-1280 "XPOLYC.spad" 2267965 2267981 2268574 2268643) (-1279 "XPBWPOLY.spad" 2266402 2266422 2267745 2267814) (-1278 "XF.spad" 2264863 2264878 2266304 2266397) (-1277 "XF.spad" 2263304 2263321 2264747 2264752) (-1276 "XFALG.spad" 2260328 2260344 2263230 2263299) (-1275 "XEXPPKG.spad" 2259579 2259605 2260318 2260323) (-1274 "XDPOLY.spad" 2259193 2259209 2259435 2259504) (-1273 "XALG.spad" 2258853 2258864 2259149 2259188) (-1272 "WUTSET.spad" 2254692 2254709 2258499 2258526) (-1271 "WP.spad" 2253891 2253935 2254550 2254617) (-1270 "WHILEAST.spad" 2253689 2253698 2253881 2253886) (-1269 "WHEREAST.spad" 2253360 2253369 2253679 2253684) (-1268 "WFFINTBS.spad" 2250923 2250945 2253350 2253355) (-1267 "WEIER.spad" 2249137 2249148 2250913 2250918) (-1266 "VSPACE.spad" 2248810 2248821 2249105 2249132) (-1265 "VSPACE.spad" 2248503 2248516 2248800 2248805) (-1264 "VOID.spad" 2248180 2248189 2248493 2248498) (-1263 "VIEW.spad" 2245802 2245811 2248170 2248175) (-1262 "VIEWDEF.spad" 2240999 2241008 2245792 2245797) (-1261 "VIEW3D.spad" 2224834 2224843 2240989 2240994) (-1260 "VIEW2D.spad" 2212571 2212580 2224824 2224829) (-1259 "VECTOR.spad" 2211246 2211257 2211497 2211524) (-1258 "VECTOR2.spad" 2209873 2209886 2211236 2211241) (-1257 "VECTCAT.spad" 2207773 2207784 2209841 2209868) (-1256 "VECTCAT.spad" 2205481 2205494 2207551 2207556) (-1255 "VARIABLE.spad" 2205261 2205276 2205471 2205476) (-1254 "UTYPE.spad" 2204905 2204914 2205251 2205256) (-1253 "UTSODETL.spad" 2204198 2204222 2204861 2204866) (-1252 "UTSODE.spad" 2202386 2202406 2204188 2204193) (-1251 "UTS.spad" 2197175 2197203 2200853 2200950) (-1250 "UTSCAT.spad" 2194626 2194642 2197073 2197170) (-1249 "UTSCAT.spad" 2191721 2191739 2194170 2194175) (-1248 "UTS2.spad" 2191314 2191349 2191711 2191716) (-1247 "URAGG.spad" 2185946 2185957 2191304 2191309) (-1246 "URAGG.spad" 2180542 2180555 2185902 2185907) (-1245 "UPXSSING.spad" 2178185 2178211 2179623 2179756) (-1244 "UPXS.spad" 2175333 2175361 2176317 2176466) (-1243 "UPXSCONS.spad" 2173090 2173110 2173465 2173614) (-1242 "UPXSCCA.spad" 2171655 2171675 2172936 2173085) (-1241 "UPXSCCA.spad" 2170362 2170384 2171645 2171650) (-1240 "UPXSCAT.spad" 2168943 2168959 2170208 2170357) (-1239 "UPXS2.spad" 2168484 2168537 2168933 2168938) (-1238 "UPSQFREE.spad" 2166896 2166910 2168474 2168479) (-1237 "UPSCAT.spad" 2164489 2164513 2166794 2166891) (-1236 "UPSCAT.spad" 2161788 2161814 2164095 2164100) (-1235 "UPOLYC.spad" 2156766 2156777 2161630 2161783) (-1234 "UPOLYC.spad" 2151636 2151649 2156502 2156507) (-1233 "UPOLYC2.spad" 2151105 2151124 2151626 2151631) (-1232 "UP.spad" 2148262 2148277 2148655 2148808) (-1231 "UPMP.spad" 2147152 2147165 2148252 2148257) (-1230 "UPDIVP.spad" 2146715 2146729 2147142 2147147) (-1229 "UPDECOMP.spad" 2144952 2144966 2146705 2146710) (-1228 "UPCDEN.spad" 2144159 2144175 2144942 2144947) (-1227 "UP2.spad" 2143521 2143542 2144149 2144154) (-1226 "UNISEG.spad" 2142874 2142885 2143440 2143445) (-1225 "UNISEG2.spad" 2142367 2142380 2142830 2142835) (-1224 "UNIFACT.spad" 2141468 2141480 2142357 2142362) (-1223 "ULS.spad" 2132020 2132048 2133113 2133542) (-1222 "ULSCONS.spad" 2124414 2124434 2124786 2124935) (-1221 "ULSCCAT.spad" 2122143 2122163 2124260 2124409) (-1220 "ULSCCAT.spad" 2119980 2120002 2122099 2122104) (-1219 "ULSCAT.spad" 2118196 2118212 2119826 2119975) (-1218 "ULS2.spad" 2117708 2117761 2118186 2118191) (-1217 "UINT8.spad" 2117585 2117594 2117698 2117703) (-1216 "UINT64.spad" 2117461 2117470 2117575 2117580) (-1215 "UINT32.spad" 2117337 2117346 2117451 2117456) (-1214 "UINT16.spad" 2117213 2117222 2117327 2117332) (-1213 "UFD.spad" 2116278 2116287 2117139 2117208) (-1212 "UFD.spad" 2115405 2115416 2116268 2116273) (-1211 "UDVO.spad" 2114252 2114261 2115395 2115400) (-1210 "UDPO.spad" 2111679 2111690 2114208 2114213) (-1209 "TYPE.spad" 2111611 2111620 2111669 2111674) (-1208 "TYPEAST.spad" 2111530 2111539 2111601 2111606) (-1207 "TWOFACT.spad" 2110180 2110195 2111520 2111525) (-1206 "TUPLE.spad" 2109664 2109675 2110079 2110084) (-1205 "TUBETOOL.spad" 2106501 2106510 2109654 2109659) (-1204 "TUBE.spad" 2105142 2105159 2106491 2106496) (-1203 "TS.spad" 2103731 2103747 2104707 2104804) (-1202 "TSETCAT.spad" 2090858 2090875 2103699 2103726) (-1201 "TSETCAT.spad" 2077971 2077990 2090814 2090819) (-1200 "TRMANIP.spad" 2072337 2072354 2077677 2077682) (-1199 "TRIMAT.spad" 2071296 2071321 2072327 2072332) (-1198 "TRIGMNIP.spad" 2069813 2069830 2071286 2071291) (-1197 "TRIGCAT.spad" 2069325 2069334 2069803 2069808) (-1196 "TRIGCAT.spad" 2068835 2068846 2069315 2069320) (-1195 "TREE.spad" 2067406 2067417 2068442 2068469) (-1194 "TRANFUN.spad" 2067237 2067246 2067396 2067401) (-1193 "TRANFUN.spad" 2067066 2067077 2067227 2067232) (-1192 "TOPSP.spad" 2066740 2066749 2067056 2067061) (-1191 "TOOLSIGN.spad" 2066403 2066414 2066730 2066735) (-1190 "TEXTFILE.spad" 2064960 2064969 2066393 2066398) (-1189 "TEX.spad" 2062092 2062101 2064950 2064955) (-1188 "TEX1.spad" 2061648 2061659 2062082 2062087) (-1187 "TEMUTL.spad" 2061203 2061212 2061638 2061643) (-1186 "TBCMPPK.spad" 2059296 2059319 2061193 2061198) (-1185 "TBAGG.spad" 2058332 2058355 2059276 2059291) (-1184 "TBAGG.spad" 2057376 2057401 2058322 2058327) (-1183 "TANEXP.spad" 2056752 2056763 2057366 2057371) (-1182 "TABLE.spad" 2055163 2055186 2055433 2055460) (-1181 "TABLEAU.spad" 2054644 2054655 2055153 2055158) (-1180 "TABLBUMP.spad" 2051427 2051438 2054634 2054639) (-1179 "SYSTEM.spad" 2050655 2050664 2051417 2051422) (-1178 "SYSSOLP.spad" 2048128 2048139 2050645 2050650) (-1177 "SYSNNI.spad" 2047308 2047319 2048118 2048123) (-1176 "SYSINT.spad" 2046712 2046723 2047298 2047303) (-1175 "SYNTAX.spad" 2042906 2042915 2046702 2046707) (-1174 "SYMTAB.spad" 2040962 2040971 2042896 2042901) (-1173 "SYMS.spad" 2036947 2036956 2040952 2040957) (-1172 "SYMPOLY.spad" 2035954 2035965 2036036 2036163) (-1171 "SYMFUNC.spad" 2035429 2035440 2035944 2035949) (-1170 "SYMBOL.spad" 2032856 2032865 2035419 2035424) (-1169 "SWITCH.spad" 2029613 2029622 2032846 2032851) (-1168 "SUTS.spad" 2026512 2026540 2028080 2028177) (-1167 "SUPXS.spad" 2023647 2023675 2024644 2024793) (-1166 "SUP.spad" 2020416 2020427 2021197 2021350) (-1165 "SUPFRACF.spad" 2019521 2019539 2020406 2020411) (-1164 "SUP2.spad" 2018911 2018924 2019511 2019516) (-1163 "SUMRF.spad" 2017877 2017888 2018901 2018906) (-1162 "SUMFS.spad" 2017510 2017527 2017867 2017872) (-1161 "SULS.spad" 2008049 2008077 2009155 2009584) (-1160 "SUCHTAST.spad" 2007818 2007827 2008039 2008044) (-1159 "SUCH.spad" 2007498 2007513 2007808 2007813) (-1158 "SUBSPACE.spad" 1999505 1999520 2007488 2007493) (-1157 "SUBRESP.spad" 1998665 1998679 1999461 1999466) (-1156 "STTF.spad" 1994764 1994780 1998655 1998660) (-1155 "STTFNC.spad" 1991232 1991248 1994754 1994759) (-1154 "STTAYLOR.spad" 1983630 1983641 1991113 1991118) (-1153 "STRTBL.spad" 1982135 1982152 1982284 1982311) (-1152 "STRING.spad" 1981544 1981553 1981558 1981585) (-1151 "STRICAT.spad" 1981332 1981341 1981512 1981539) (-1150 "STREAM.spad" 1978190 1978201 1980857 1980872) (-1149 "STREAM3.spad" 1977735 1977750 1978180 1978185) (-1148 "STREAM2.spad" 1976803 1976816 1977725 1977730) (-1147 "STREAM1.spad" 1976507 1976518 1976793 1976798) (-1146 "STINPROD.spad" 1975413 1975429 1976497 1976502) (-1145 "STEP.spad" 1974614 1974623 1975403 1975408) (-1144 "STBL.spad" 1973140 1973168 1973307 1973322) (-1143 "STAGG.spad" 1972215 1972226 1973130 1973135) (-1142 "STAGG.spad" 1971288 1971301 1972205 1972210) (-1141 "STACK.spad" 1970639 1970650 1970895 1970922) (-1140 "SREGSET.spad" 1968343 1968360 1970285 1970312) (-1139 "SRDCMPK.spad" 1966888 1966908 1968333 1968338) (-1138 "SRAGG.spad" 1961985 1961994 1966856 1966883) (-1137 "SRAGG.spad" 1957102 1957113 1961975 1961980) (-1136 "SQMATRIX.spad" 1954718 1954736 1955634 1955721) (-1135 "SPLTREE.spad" 1949270 1949283 1954154 1954181) (-1134 "SPLNODE.spad" 1945858 1945871 1949260 1949265) (-1133 "SPFCAT.spad" 1944635 1944644 1945848 1945853) (-1132 "SPECOUT.spad" 1943185 1943194 1944625 1944630) (-1131 "SPADXPT.spad" 1935324 1935333 1943175 1943180) (-1130 "spad-parser.spad" 1934789 1934798 1935314 1935319) (-1129 "SPADAST.spad" 1934490 1934499 1934779 1934784) (-1128 "SPACEC.spad" 1918503 1918514 1934480 1934485) (-1127 "SPACE3.spad" 1918279 1918290 1918493 1918498) (-1126 "SORTPAK.spad" 1917824 1917837 1918235 1918240) (-1125 "SOLVETRA.spad" 1915581 1915592 1917814 1917819) (-1124 "SOLVESER.spad" 1914101 1914112 1915571 1915576) (-1123 "SOLVERAD.spad" 1910111 1910122 1914091 1914096) (-1122 "SOLVEFOR.spad" 1908531 1908549 1910101 1910106) (-1121 "SNTSCAT.spad" 1908131 1908148 1908499 1908526) (-1120 "SMTS.spad" 1906391 1906417 1907696 1907793) (-1119 "SMP.spad" 1903830 1903850 1904220 1904347) (-1118 "SMITH.spad" 1902673 1902698 1903820 1903825) (-1117 "SMATCAT.spad" 1900783 1900813 1902617 1902668) (-1116 "SMATCAT.spad" 1898825 1898857 1900661 1900666) (-1115 "SKAGG.spad" 1897786 1897797 1898793 1898820) (-1114 "SINT.spad" 1896612 1896621 1897652 1897781) (-1113 "SIMPAN.spad" 1896340 1896349 1896602 1896607) (-1112 "SIG.spad" 1895668 1895677 1896330 1896335) (-1111 "SIGNRF.spad" 1894776 1894787 1895658 1895663) (-1110 "SIGNEF.spad" 1894045 1894062 1894766 1894771) (-1109 "SIGAST.spad" 1893426 1893435 1894035 1894040) (-1108 "SHP.spad" 1891344 1891359 1893382 1893387) (-1107 "SHDP.spad" 1881055 1881082 1881564 1881695) (-1106 "SGROUP.spad" 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1298757) (-788 "OAGROUP.spad" 1298485 1298493 1298613 1298618) (-787 "NUMTUBE.spad" 1298072 1298088 1298475 1298480) (-786 "NUMQUAD.spad" 1285934 1285942 1298062 1298067) (-785 "NUMODE.spad" 1277070 1277078 1285924 1285929) (-784 "NUMINT.spad" 1274628 1274636 1277060 1277065) (-783 "NUMFMT.spad" 1273468 1273476 1274618 1274623) (-782 "NUMERIC.spad" 1265540 1265550 1273273 1273278) (-781 "NTSCAT.spad" 1264042 1264058 1265508 1265535) (-780 "NTPOLFN.spad" 1263587 1263597 1263959 1263964) (-779 "NSUP.spad" 1256597 1256607 1261137 1261290) (-778 "NSUP2.spad" 1255989 1256001 1256587 1256592) (-777 "NSMP.spad" 1252184 1252203 1252492 1252619) (-776 "NREP.spad" 1250556 1250570 1252174 1252179) (-775 "NPCOEF.spad" 1249802 1249822 1250546 1250551) (-774 "NORMRETR.spad" 1249400 1249439 1249792 1249797) (-773 "NORMPK.spad" 1247302 1247321 1249390 1249395) (-772 "NORMMA.spad" 1246990 1247016 1247292 1247297) (-771 "NONE.spad" 1246731 1246739 1246980 1246985) (-770 "NONE1.spad" 1246407 1246417 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1070184 1070352 1070357) (-675 "MAPHACK2.spad" 1069935 1069947 1070160 1070165) (-674 "MAPHACK1.spad" 1069565 1069575 1069925 1069930) (-673 "MAGMA.spad" 1067355 1067372 1069555 1069560) (-672 "MACROAST.spad" 1066934 1066942 1067345 1067350) (-671 "M3D.spad" 1064630 1064640 1066312 1066317) (-670 "LZSTAGG.spad" 1061858 1061868 1064620 1064625) (-669 "LZSTAGG.spad" 1059084 1059096 1061848 1061853) (-668 "LWORD.spad" 1055789 1055806 1059074 1059079) (-667 "LSTAST.spad" 1055573 1055581 1055779 1055784) (-666 "LSQM.spad" 1053799 1053813 1054197 1054248) (-665 "LSPP.spad" 1053332 1053349 1053789 1053794) (-664 "LSMP.spad" 1052172 1052200 1053322 1053327) (-663 "LSMP1.spad" 1049976 1049990 1052162 1052167) (-662 "LSAGG.spad" 1049645 1049655 1049944 1049971) (-661 "LSAGG.spad" 1049334 1049346 1049635 1049640) (-660 "LPOLY.spad" 1048288 1048307 1049190 1049259) (-659 "LPEFRAC.spad" 1047545 1047555 1048278 1048283) (-658 "LO.spad" 1046946 1046960 1047479 1047506) (-657 "LOGIC.spad" 1046548 1046556 1046936 1046941) (-656 "LOGIC.spad" 1046148 1046158 1046538 1046543) (-655 "LODOOPS.spad" 1045066 1045078 1046138 1046143) (-654 "LODO.spad" 1044450 1044466 1044746 1044785) (-653 "LODOF.spad" 1043494 1043511 1044407 1044412) (-652 "LODOCAT.spad" 1042152 1042162 1043450 1043489) (-651 "LODOCAT.spad" 1040808 1040820 1042108 1042113) (-650 "LODO2.spad" 1040081 1040093 1040488 1040527) (-649 "LODO1.spad" 1039481 1039491 1039761 1039800) (-648 "LODEEF.spad" 1038253 1038271 1039471 1039476) (-647 "LNAGG.spad" 1034055 1034065 1038243 1038248) (-646 "LNAGG.spad" 1029821 1029833 1034011 1034016) (-645 "LMOPS.spad" 1026557 1026574 1029811 1029816) (-644 "LMODULE.spad" 1026199 1026209 1026547 1026552) (-643 "LMDICT.spad" 1025482 1025492 1025750 1025777) (-642 "LITERAL.spad" 1025388 1025399 1025472 1025477) (-641 "LIST.spad" 1023106 1023116 1024535 1024562) (-640 "LIST3.spad" 1022397 1022411 1023096 1023101) (-639 "LIST2.spad" 1021037 1021049 1022387 1022392) (-638 "LIST2MAP.spad" 1017914 1017926 1021027 1021032) (-637 "LINEXP.spad" 1017346 1017356 1017894 1017909) (-636 "LINDEP.spad" 1016123 1016135 1017258 1017263) (-635 "LIMITRF.spad" 1014037 1014047 1016113 1016118) (-634 "LIMITPS.spad" 1012920 1012933 1014027 1014032) (-633 "LIE.spad" 1010934 1010946 1012210 1012355) (-632 "LIECAT.spad" 1010410 1010420 1010860 1010929) (-631 "LIECAT.spad" 1009914 1009926 1010366 1010371) (-630 "LIB.spad" 1007962 1007970 1008573 1008588) (-629 "LGROBP.spad" 1005315 1005334 1007952 1007957) (-628 "LF.spad" 1004234 1004250 1005305 1005310) (-627 "LFCAT.spad" 1003253 1003261 1004224 1004229) (-626 "LEXTRIPK.spad" 998756 998771 1003243 1003248) (-625 "LEXP.spad" 996759 996786 998736 998751) (-624 "LETAST.spad" 996458 996466 996749 996754) (-623 "LEADCDET.spad" 994842 994859 996448 996453) (-622 "LAZM3PK.spad" 993546 993568 994832 994837) (-621 "LAUPOL.spad" 992235 992248 993139 993208) (-620 "LAPLACE.spad" 991808 991824 992225 992230) (-619 "LA.spad" 991248 991262 991730 991769) (-618 "LALG.spad" 991024 991034 991228 991243) (-617 "LALG.spad" 990808 990820 991014 991019) (-616 "KVTFROM.spad" 990543 990553 990798 990803) (-615 "KTVLOGIC.spad" 989966 989974 990533 990538) (-614 "KRCFROM.spad" 989704 989714 989956 989961) (-613 "KOVACIC.spad" 988417 988434 989694 989699) (-612 "KONVERT.spad" 988139 988149 988407 988412) (-611 "KOERCE.spad" 987876 987886 988129 988134) (-610 "KERNEL.spad" 986411 986421 987660 987665) (-609 "KERNEL2.spad" 986114 986126 986401 986406) (-608 "KDAGG.spad" 985217 985239 986094 986109) (-607 "KDAGG.spad" 984328 984352 985207 985212) (-606 "KAFILE.spad" 983291 983307 983526 983553) (-605 "JORDAN.spad" 981118 981130 982581 982726) (-604 "JOINAST.spad" 980812 980820 981108 981113) (-603 "JAVACODE.spad" 980678 980686 980802 980807) (-602 "IXAGG.spad" 978801 978825 980668 980673) (-601 "IXAGG.spad" 976779 976805 978648 978653) (-600 "IVECTOR.spad" 975550 975565 975705 975732) (-599 "ITUPLE.spad" 974695 974705 975540 975545) (-598 "ITRIGMNP.spad" 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(-577 "IOBFILE.spad" 947866 947874 948495 948500) (-576 "IOBCON.spad" 947731 947739 947856 947861) (-575 "INVLAPLA.spad" 947376 947392 947721 947726) (-574 "INTTR.spad" 940622 940639 947366 947371) (-573 "INTTOOLS.spad" 938333 938349 940196 940201) (-572 "INTSLPE.spad" 937639 937647 938323 938328) (-571 "INTRVL.spad" 937205 937215 937553 937634) (-570 "INTRF.spad" 935569 935583 937195 937200) (-569 "INTRET.spad" 935001 935011 935559 935564) (-568 "INTRAT.spad" 933676 933693 934991 934996) (-567 "INTPM.spad" 932039 932055 933319 933324) (-566 "INTPAF.spad" 929807 929825 931971 931976) (-565 "INTPACK.spad" 920117 920125 929797 929802) (-564 "INT.spad" 919478 919486 919971 920112) (-563 "INTHERTR.spad" 918744 918761 919468 919473) (-562 "INTHERAL.spad" 918410 918434 918734 918739) (-561 "INTHEORY.spad" 914823 914831 918400 918405) (-560 "INTG0.spad" 908286 908304 914755 914760) (-559 "INTFTBL.spad" 902315 902323 908276 908281) (-558 "INTFACT.spad" 901374 901384 902305 902310) (-557 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771064) (-455 "GENEEZ.spad" 768460 768473 770511 770516) (-454 "GDMP.spad" 765478 765495 766254 766381) (-453 "GCNAALG.spad" 759373 759400 765272 765339) (-452 "GCDDOM.spad" 758545 758553 759299 759368) (-451 "GCDDOM.spad" 757779 757789 758535 758540) (-450 "GB.spad" 755297 755335 757735 757740) (-449 "GBINTERN.spad" 751317 751355 755287 755292) (-448 "GBF.spad" 747074 747112 751307 751312) (-447 "GBEUCLID.spad" 744948 744986 747064 747069) (-446 "GAUSSFAC.spad" 744245 744253 744938 744943) (-445 "GALUTIL.spad" 742567 742577 744201 744206) (-444 "GALPOLYU.spad" 741013 741026 742557 742562) (-443 "GALFACTU.spad" 739178 739197 741003 741008) (-442 "GALFACT.spad" 729311 729322 739168 739173) (-441 "FVFUN.spad" 726334 726342 729301 729306) (-440 "FVC.spad" 725386 725394 726324 726329) (-439 "FUNDESC.spad" 725064 725072 725376 725381) (-438 "FUNCTION.spad" 724913 724925 725054 725059) (-437 "FT.spad" 723206 723214 724903 724908) (-436 "FTEM.spad" 722369 722377 723196 723201) (-435 "FSUPFACT.spad" 721269 721288 722305 722310) (-434 "FST.spad" 719355 719363 721259 721264) (-433 "FSRED.spad" 718833 718849 719345 719350) (-432 "FSPRMELT.spad" 717657 717673 718790 718795) (-431 "FSPECF.spad" 715734 715750 717647 717652) (-430 "FS.spad" 709796 709806 715509 715729) (-429 "FS.spad" 703636 703648 709351 709356) (-428 "FSINT.spad" 703294 703310 703626 703631) (-427 "FSERIES.spad" 702481 702493 703114 703213) (-426 "FSCINT.spad" 701794 701810 702471 702476) (-425 "FSAGG.spad" 700911 700921 701750 701789) (-424 "FSAGG.spad" 699990 700002 700831 700836) (-423 "FSAGG2.spad" 698689 698705 699980 699985) (-422 "FS2UPS.spad" 693172 693206 698679 698684) (-421 "FS2.spad" 692817 692833 693162 693167) (-420 "FS2EXPXP.spad" 691940 691963 692807 692812) (-419 "FRUTIL.spad" 690882 690892 691930 691935) (-418 "FR.spad" 684576 684586 689906 689975) (-417 "FRNAALG.spad" 679663 679673 684518 684571) (-416 "FRNAALG.spad" 674762 674774 679619 679624) (-415 "FRNAAF2.spad" 674216 674234 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"FORMULA.spad" 645823 645831 648349 648354) (-393 "FORMULA1.spad" 645302 645312 645813 645818) (-392 "FORDER.spad" 644993 645017 645292 645297) (-391 "FOP.spad" 644194 644202 644983 644988) (-390 "FNLA.spad" 643618 643640 644162 644189) (-389 "FNCAT.spad" 642205 642213 643608 643613) (-388 "FNAME.spad" 642097 642105 642195 642200) (-387 "FMTC.spad" 641895 641903 642023 642092) (-386 "FMONOID.spad" 638950 638960 641851 641856) (-385 "FM.spad" 638645 638657 638884 638911) (-384 "FMFUN.spad" 635675 635683 638635 638640) (-383 "FMC.spad" 634727 634735 635665 635670) (-382 "FMCAT.spad" 632381 632399 634695 634722) (-381 "FM1.spad" 631738 631750 632315 632342) (-380 "FLOATRP.spad" 629459 629473 631728 631733) (-379 "FLOAT.spad" 622747 622755 629325 629454) (-378 "FLOATCP.spad" 620164 620178 622737 622742) (-377 "FLINEXP.spad" 619876 619886 620144 620159) (-376 "FLINEXP.spad" 619542 619554 619812 619817) (-375 "FLASORT.spad" 618862 618874 619532 619537) (-374 "FLALG.spad" 616508 616527 618788 618857) (-373 "FLAGG.spad" 613526 613536 616488 616503) (-372 "FLAGG.spad" 610445 610457 613409 613414) (-371 "FLAGG2.spad" 609126 609142 610435 610440) (-370 "FINRALG.spad" 607155 607168 609082 609121) (-369 "FINRALG.spad" 605110 605125 607039 607044) (-368 "FINITE.spad" 604262 604270 605100 605105) (-367 "FINAALG.spad" 593243 593253 604204 604257) (-366 "FINAALG.spad" 582236 582248 593199 593204) (-365 "FILE.spad" 581819 581829 582226 582231) (-364 "FILECAT.spad" 580337 580354 581809 581814) (-363 "FIELD.spad" 579743 579751 580239 580332) (-362 "FIELD.spad" 579235 579245 579733 579738) (-361 "FGROUP.spad" 577844 577854 579215 579230) (-360 "FGLMICPK.spad" 576631 576646 577834 577839) (-359 "FFX.spad" 576006 576021 576347 576440) (-358 "FFSLPE.spad" 575495 575516 575996 576001) (-357 "FFPOLY.spad" 566747 566758 575485 575490) (-356 "FFPOLY2.spad" 565807 565824 566737 566742) (-355 "FFP.spad" 565204 565224 565523 565616) (-354 "FF.spad" 564652 564668 564885 564978) (-353 "FFNBX.spad" 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(-332 "FCPAK1.spad" 516018 516026 517455 517460) (-331 "FCOMP.spad" 515397 515407 516008 516013) (-330 "FC.spad" 505312 505320 515387 515392) (-329 "FAXF.spad" 498247 498261 505214 505307) (-328 "FAXF.spad" 491234 491250 498203 498208) (-327 "FARRAY.spad" 489380 489390 490417 490444) (-326 "FAMR.spad" 487500 487512 489278 489375) (-325 "FAMR.spad" 485604 485618 487384 487389) (-324 "FAMONOID.spad" 485254 485264 485558 485563) (-323 "FAMONC.spad" 483476 483488 485244 485249) (-322 "FAGROUP.spad" 483082 483092 483372 483399) (-321 "FACUTIL.spad" 481278 481295 483072 483077) (-320 "FACTFUNC.spad" 480454 480464 481268 481273) (-319 "EXPUPXS.spad" 477287 477310 478586 478735) (-318 "EXPRTUBE.spad" 474515 474523 477277 477282) (-317 "EXPRODE.spad" 471387 471403 474505 474510) (-316 "EXPR.spad" 466662 466672 467376 467783) (-315 "EXPR2UPS.spad" 462754 462767 466652 466657) (-314 "EXPR2.spad" 462457 462469 462744 462749) (-313 "EXPEXPAN.spad" 459395 459420 460029 460122) (-312 "EXIT.spad" 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"ENV.spad" 409614 409622 410928 410933) (-290 "ENTIRER.spad" 409282 409290 409558 409609) (-289 "EMR.spad" 408483 408524 409208 409277) (-288 "ELTAGG.spad" 406723 406742 408473 408478) (-287 "ELTAGG.spad" 404927 404948 406679 406684) (-286 "ELTAB.spad" 404374 404392 404917 404922) (-285 "ELFUTS.spad" 403753 403772 404364 404369) (-284 "ELEMFUN.spad" 403442 403450 403743 403748) (-283 "ELEMFUN.spad" 403129 403139 403432 403437) (-282 "ELAGG.spad" 401072 401082 403109 403124) (-281 "ELAGG.spad" 398952 398964 400991 400996) (-280 "ELABEXPR.spad" 397875 397883 398942 398947) (-279 "EFUPXS.spad" 394651 394681 397831 397836) (-278 "EFULS.spad" 391487 391510 394607 394612) (-277 "EFSTRUC.spad" 389442 389458 391477 391482) (-276 "EF.spad" 384208 384224 389432 389437) (-275 "EAB.spad" 382484 382492 384198 384203) (-274 "E04UCFA.spad" 382020 382028 382474 382479) (-273 "E04NAFA.spad" 381597 381605 382010 382015) (-272 "E04MBFA.spad" 381177 381185 381587 381592) (-271 "E04JAFA.spad" 380713 380721 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(-250 "DPMM.spad" 304012 304030 304137 304438) (-249 "DOMCTOR.spad" 303904 303912 304002 304007) (-248 "DOMAIN.spad" 303035 303043 303894 303899) (-247 "DMP.spad" 300257 300272 300829 300956) (-246 "DLP.spad" 299605 299615 300247 300252) (-245 "DLIST.spad" 298184 298194 298788 298815) (-244 "DLAGG.spad" 296595 296605 298174 298179) (-243 "DIVRING.spad" 296137 296145 296539 296590) (-242 "DIVRING.spad" 295723 295733 296127 296132) (-241 "DISPLAY.spad" 293903 293911 295713 295718) (-240 "DIRPROD.spad" 283483 283499 284123 284254) (-239 "DIRPROD2.spad" 282291 282309 283473 283478) (-238 "DIRPCAT.spad" 281233 281249 282155 282286) (-237 "DIRPCAT.spad" 279904 279922 280828 280833) (-236 "DIOSP.spad" 278729 278737 279894 279899) (-235 "DIOPS.spad" 277713 277723 278709 278724) (-234 "DIOPS.spad" 276671 276683 277669 277674) (-233 "DIFRING.spad" 275963 275971 276651 276666) (-232 "DIFRING.spad" 275263 275273 275953 275958) (-231 "DIFEXT.spad" 274422 274432 275243 275258) (-230 "DIFEXT.spad" 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -474,10 +474,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -488,7 +488,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-388) (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4012 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4012 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-859)) . T)) ((((-1175)) . T)) (|has| |#1| (-817)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-847)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-906)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-859)) . T)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-556))) ((((-859)) . T)) ((((-859)) . T)) ((((-859)) . T)) (((|#1| (-1259 |#1|) (-1259 |#1|)) . T)) ((((-564) (-144)) . T)) ((($) . T)) -(-4002 (|has| |#4| (-172)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4002 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4012 (|has| |#4| (-172)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4012 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-1175)) . T) (((-859)) . T)) ((((-1175)) . T)) ((((-859)) . T)) @@ -878,14 +878,14 @@ (((|#1| (-968)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) -(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4012 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4012 (|has| |#2| (-790)) (|has| |#2| (-845))) (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4002 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) (((|#1|) . T)) (|has| |#2| (-790)) -(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4012 (|has| |#2| (-790)) (|has| |#2| (-845))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#2| (-845)) @@ -901,8 +901,8 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 (-564))) . T) (($) . T)) -((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-564)) . T)) -((($) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +((($) |has| |#1| (-556)) ((|#1|) . T) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-564)) . T)) +((($) . T) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) (|has| |#1| (-825)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) (|has| |#1| (-1094)) @@ -913,30 +913,30 @@ (((|#3|) |has| |#3| (-1094))) (|has| |#3| (-368)) (((|#1|) . T) (((-859)) . T)) -((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +((((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) (((|#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) (((|#1| |#2|) . T)) (((|#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556)))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-363)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((((-407 (-564))) . T) (((-564)) . T)) -((($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($) -4002 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($ $) -4012 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($) -4012 (|has| |#1| (-172)) (|has| |#1| (-556))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046)))) +((($) -4012 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((|#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046)))) ((((-144)) . T)) ((((-144)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-564)) . T)) (((|#1| |#2| |#3|) . T)) -(-4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +(-4012 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -944,14 +944,14 @@ ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -962,7 +962,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-845)) -(((|#2| (-240 (-2589 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-240 (-2779 |#1|) (-768)) (-861 |#1|)) . T)) (|has| |#3| (-845)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -977,20 +977,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4002 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1046))) -(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) -(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) +(((|#2|) . T) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +(-4012 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4012 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1014,11 +1014,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -((((-564)) -4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1046))) ((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094)))) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +((((-564)) -4012 (|has| |#2| (-172)) (|has| |#2| (-845)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1046))) ((|#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094)))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1026,8 +1026,8 @@ ((((-859)) . T)) ((((-859)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) |has| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (-309 (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))))) ((((-859)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1038,10 +1038,10 @@ ((($ $) . T) ((#0=(-861 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1129,11 +1129,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-897 (-1170)))) -(-4002 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-4012 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-859)) . T)) ((((-859)) . T)) @@ -1141,8 +1141,8 @@ ((((-907 |#1|)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1151,16 +1151,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-867 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . 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T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1171,8 +1171,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -4012 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -1187,14 +1187,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) -((($) . T) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . T) (((-407 (-564))) -4012 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))))) +(((#0=(-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) #0#) |has| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (-309 (-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))))) (|has| |#2| (-847)) ((($) . T)) (((|#2|) |has| |#2| (-1094))) -((((-859)) -4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +((((-859)) -4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) (|has| |#1| (-847)) (|has| |#1| (-847)) ((((-1152) (-52)) . T)) @@ -1203,10 +1203,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-859)) . T)) ((((-907 |#1|)) . T)) (|has| |#1| (-363)) @@ -1233,21 +1233,21 @@ ((((-859)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#1| |#2|) . 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T)) +((((-859)) -4012 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-859))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) -(((|#2| |#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($ $) |has| |#2| (-172))) +(-4012 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(((|#2| |#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-859)) . T)) ((((-859)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T) ((|#2|) . T)) ((((-859)) . T)) ((((-859)) . T)) ((((-1152) (-1170) (-564) (-225) (-859)) . T)) @@ -1322,8 +1322,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +(((|#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-890 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) @@ -1335,11 +1335,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1376,7 +1376,7 @@ ((((-996 |#1|)) . T) ((|#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1384,9 +1384,9 @@ (|has| |#1| (-847)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1399,7 +1399,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) #0#) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) #0#) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1434,19 +1434,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) #0#) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) #0#) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-847)) (((|#2| (-768) (-1076)) . T)) (((|#1| |#2|) . T)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-788)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4002 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-4002 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-4012 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-4012 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1460,10 +1460,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) -(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4012 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1477,8 +1477,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2351 (-1152)) (|:| -1327 #0#))) . T)) +((((-859)) -4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1350 (-1152)) (|:| -2575 #0#))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1486,7 +1486,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-4002 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4012 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) (|has| |#1| (-363)) ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1497,8 +1497,8 @@ (|has| |#1| (-845)) ((((-859)) . T)) (((|#2|) . T)) -((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1507,7 +1507,7 @@ ((((-859)) . T)) ((((-859)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2589 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-482 (-2779 |#1|) (-768)) (-861 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1527,16 +1527,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +((((-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-907 |#1|)) . T)) -(((|#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +(((|#1|) -4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4012 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) (|has| |#1| (-847)) (|has| |#1| (-847)) @@ -1555,11 +1555,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-847)) (|has| |#1| (-847)) -(((|#3|) -4002 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-4002 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) +(((|#3|) -4012 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-4012 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1568,7 +1568,7 @@ (|has| |#1| (-817)) (|has| |#1| (-817)) (((|#1|) . T)) -(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-845)) (|has| |#1| (-845)) (|has| |#1| (-845)) @@ -1577,13 +1577,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-1170)) |has| |#1| (-897 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((#0=(-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))))) +(((#0=(-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) #0#) |has| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (-309 (-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-859)) . T) (((-1175)) . T)) @@ -1602,11 +1602,11 @@ (((|#1| (-768) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4002 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4012 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1629,32 +1629,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1771,18 +1771,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-859)) . T)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) (((|#3|) . T)) -(-4002 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4012 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-859)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-859)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4002 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4012 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-768)) . T)) -((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-883 (-564))) (((-379)) |has| |#1| (-883 (-379)))) @@ -1790,7 +1790,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-859)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1798,7 +1798,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4012 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-817)) @@ -1808,8 +1808,8 @@ (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| (-564) (-1076)) . T)) -(-4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +(-4012 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (|has| |#1| (-847)) @@ -1822,33 +1822,33 @@ (|has| |#1| (-1094)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +((((-564)) -4012 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) -((((-685 (-339 (-1776) (-1776 (QUOTE X) (QUOTE HESS)) (-695)))) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-1046))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1924,7 +1924,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -4002 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -4012 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1945,25 +1945,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-845)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1035 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-859)) -4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-859)) -4012 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))) . T)) ((((-859)) . T)) ((((-564) |#1|) . T)) ((((-859)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-949 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-847)) @@ -1974,14 +1974,14 @@ (((|#3|) |has| |#3| (-1046))) ((((-1170)) |has| |#2| (-897 (-1170)))) ((((-859)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2002,11 +2002,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-847)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) |has| (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)) (-309 (-2 (|:| -1350 |#1|) (|:| -2575 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2024,11 +2024,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-889 (-564))) |has| |#1| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#1| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#1| (-1019))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-859)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -4012 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2039,11 +2039,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-859)) . T)) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-906))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-906))) (((|#1|) . T)) (|has| |#1| (-847)) (|has| |#1| (-847)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-768)) . T)) @@ -2054,13 +2054,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564)))) (($) . T)) ((((-564)) . T)) (|has| |#1| (-363)) -(-4002 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4002 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4012 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4012 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2075,23 +2075,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4012 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) ((((-859)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-949 |#1|)) . T) (((-859)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4002 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -4012 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))) . T)) ((((-949 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-897 (-1170)))) -(((|#1|) . T) (($) -4002 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -4012 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-859)) . T)) (((|#1|) . T)) @@ -2099,8 +2099,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-867 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4002 (|has| |#4| (-790)) (|has| |#4| (-845))) -(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4012 (|has| |#4| (-790)) (|has| |#4| (-845))) +(-4012 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) ((((-859)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2116,17 +2116,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1035 (-407 (-564)))) (((-564)) |has| #0# (-1035 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-768)) . T)) (|has| |#1| (-847)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4012 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4012 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))))) +((((-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))) |has| (-2 (|:| -1350 (-1152)) (|:| -2575 (-52))) (-309 (-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-845)) (|has| |#1| (-38 (-407 (-564)))) @@ -2150,29 +2150,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-859)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) +(((|#2|) . T) (((-564)) . T) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) (((|#1| |#2|) . T)) ((((-144)) . T)) ((((-777 |#1| (-861 |#2|))) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (|has| |#1| (-1194)) ((((-859)) . T)) (((|#1|) . T)) -(-4002 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) +(-4012 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) (((|#2|) . T)) -((($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-907 |#1|)) . T)) ((($) . T)) ((((-407 (-949 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-859)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) |has| (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|)) (-309 (-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-847)) @@ -2181,16 +2181,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-4002 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4002 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4012 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4012 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-845)) (((|#1| |#2|) . T)) @@ -2214,9 +2214,9 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -4012 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2238,13 +2238,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . 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T)) -(((|#2|) |has| |#2| (-6 (-4413 "*")))) +(((|#2|) |has| |#2| (-6 (-4414 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#3|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-564)) -4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4002 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-564)) -4012 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4012 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1035 (-407 (-564)))) (((-564)) |has| |#2| (-1035 (-564))) ((|#2|) . T) (((-861 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) @@ -2273,12 +2273,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) ((((-859)) . T)) -(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2298,14 +2298,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-4002 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-768)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-906)) -(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4012 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-859)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-907 |#1|)) . T)) @@ -2314,14 +2314,14 @@ ((((-859)) . T)) ((($) . T)) ((($) . T)) -(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-4002 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4012 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-859)) . T)) @@ -2354,27 +2354,27 @@ (((|#1|) |has| |#1| (-172))) ((((-859)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -4002 (|has| |#2| (-6 (-4413 "*"))) (|has| |#2| (-172)))) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(((|#2|) -4012 (|has| |#2| (-6 (-4414 "*"))) (|has| |#2| (-172)))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#2| (-847)) (|has| |#2| (-906)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) ((((-859)) . T)) ((((-536)) . T) (((-564)) . T) (((-889 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-4002 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-4012 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-845)) @@ -2390,7 +2390,7 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-187)) . T) (((-859)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2403,7 +2403,7 @@ ((((-859)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) (|has| |#1| (-847)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2415,16 +2415,16 @@ (((|#2|) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-4002 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4002 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4012 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4012 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-1170) (-52)) . T)) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (|has| |#1| (-906)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-906)) @@ -2441,12 +2441,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-817)) (((#0=(-907 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-845)) -((((-1195 |#1|)) . T) (((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1046)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046)))) @@ -2457,11 +2457,11 @@ (((|#2|) . T)) ((((-859)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2351 (-1170)) (|:| -1327 #0#))) . T)) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -1350 (-1170)) (|:| -2575 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-859)) . T)) @@ -2469,15 +2469,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-859)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -4002 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -4002 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4012 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4012 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2500,7 +2500,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2538,7 +2538,7 @@ (|has| |#2| (-1019)) ((($) . T)) (|has| |#1| (-906)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2546,9 +2546,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-907 |#1|)) . T)) -((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-4002 (|has| |#1| (-368)) (|has| |#1| (-847))) +(-4012 (|has| |#1| (-368)) (|has| |#1| (-847))) (((|#1|) . T)) ((((-768)) . T)) ((((-859)) . T)) @@ -2559,16 +2559,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-768) |#1|) . T)) -(((|#2| (-240 (-2589 |#1|) (-768))) . T)) +(((|#2| (-240 (-2779 |#1|) (-768))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-1152)) . T) (((-859)) . T)) -(((#0=(-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))))) +(((#0=(-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) #0#) |has| (-2 (|:| -1350 (-1170)) (|:| -2575 (-52))) (-309 (-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-906)) (|has| |#2| (-363)) -(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) (((|#1|) . T)) @@ -2585,11 +2585,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-825))) ((((-859)) . T)) -((((-1170)) -4002 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) +((((-1170)) -4012 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-897 (-1170))))) (|has| |#1| (-363)) @@ -2600,7 +2600,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2625,9 +2625,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-883 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-883 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2636,22 +2636,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#2|) . T)) (((|#2|) . T)) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2659,7 +2659,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4002 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) ((($) . T)) @@ -2686,7 +2686,7 @@ ((((-859)) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2708,7 +2708,7 @@ ((((-564)) . T)) ((((-859)) . T)) ((((-564)) . T)) -(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4012 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2720,9 +2720,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -(-4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +(-4012 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-1145)) ((((-564) |#1|) . T)) (((|#1|) . T)) @@ -2742,8 +2742,8 @@ (((|#1|) . T)) (|has| |#1| (-556)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2752,7 +2752,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-777 |#1| (-861 |#2|))) |has| (-777 |#1| (-861 |#2|)) (-309 (-777 |#1| (-861 |#2|))))) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2764,13 +2764,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) ((((-859)) . T)) -(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4012 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) ((((-1114)) . T) (((-859)) . T)) ((((-536)) . T) (((-859)) . T)) @@ -2781,12 +2781,12 @@ ((((-564)) . T)) (((|#3|) . T)) ((((-859)) . T)) -(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) -((((-564)) . T) (((-407 (-564))) -4002 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1035 (-407 (-564))))) ((|#2|) . T) (($) -4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((-861 |#1|)) . T)) -((((-1119 |#1| |#2|)) . T) ((|#2|) . T) (($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-564)) . T)) -((((-1166 |#1|)) . T) (((-564)) . T) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) +(-4012 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) -4012 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2794,13 +2794,13 @@ ((((-581 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) ((($) . T) (((-407 (-564))) . T)) ((($) . T) (((-407 (-564))) . T)) -(((|#2|) |has| |#2| (-6 (-4413 "*")))) +(((|#2|) |has| |#2| (-6 (-4414 "*")))) (((|#1|) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (((|#1|) . T)) ((((-859)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -4002 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -4012 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2808,21 +2808,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-906)) (|has| |#1| (-906)) -((($) -4002 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4012 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-859)) . T)) (((|#1|) . T)) -((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -1350 (-1152)) (|:| -2575 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2837,10 +2837,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . 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T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3289,13 +3289,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4012 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-768)) . T)) @@ -3310,16 +3310,16 @@ ((((-889 (-379))) . T) (((-889 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-859)) . 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T)) -(-4002 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4012 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046)))) -(-4002 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) +(-4012 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3345,7 +3345,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-4002 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4012 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3357,7 +3357,7 @@ (((|#1|) . T)) (((|#1|) . 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T)) -((((-859)) -4002 (-12 (|has| |#1| (-611 (-859))) (|has| |#2| (-611 (-859)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-859)) -4012 (-12 (|has| |#1| (-611 (-859))) (|has| |#2| (-611 (-859)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3387,19 +3387,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-4002 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4002 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4012 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4012 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-859)) . T) (((-1175)) . 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T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) -((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) +((((-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1019)) -(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) ((((-859)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-889 (-564))) |has| |#2| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#2| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#2| (-1019))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3434,15 +3434,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-859)) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-564) |#1|) . 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T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-859)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3466,13 +3466,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) -(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4012 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4012 (|has| |#1| (-847)) (|has| |#1| (-1094))) ((((-859)) . T)) ((((-859)) . T)) ((((-859)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) +((((-2 (|:| -1350 (-1170)) (|:| -2575 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3486,8 +3486,8 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) -(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4012 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4012 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((($) . T)) (((|#2| (-531 (-861 |#1|))) . T)) ((((-1175)) . T)) @@ -3502,13 +3502,13 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4012 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-768)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -1350 |#1|) (|:| -2575 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3517,14 +3517,14 @@ ((((-564)) . T) (($) . 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. -349) NIL) ((-519 . -611) 148849) ((-379 . -792) T) ((-223 . -1094) T) ((-379 . -789) T) ((-225 . -791) T) ((-225 . -788) T) ((-59 . -612) 148810) ((-59 . -611) 148722) ((-225 . -723) T) ((-516 . -612) 148683) ((-516 . -611) 148595) ((-497 . -611) 148527) ((-496 . -612) 148488) ((-496 . -611) 148400) ((-1074 . -363) 148351) ((-40 . -411) 148328) ((-77 . -1209) T) ((-868 . -906) NIL) ((-359 . -329) 148312) ((-359 . -363) T) ((-353 . -329) 148296) ((-353 . -363) T) ((-345 . -329) 148280) ((-345 . -363) T) ((-316 . -284) 148259) ((-108 . -363) T) ((-70 . -1209) T) ((-1223 . -338) 148211) ((-868 . -644) 148156) ((-1223 . -377) 148108) ((-961 . -131) 147963) ((-812 . -131) 147833) ((-955 . -647) 147817) ((-1081 . -172) 147728) ((-955 . -373) 147712) ((-1057 . -791) T) ((-1057 . -788) T) ((-869 . -614) 147610) ((-779 . -172) 147501) ((-777 . -172) 147412) ((-813 . -47) 147374) ((-1057 . -723) T) ((-327 . -489) 147358) ((-949 . -723) T) ((-454 . -172) 147269) ((-245 . -286) 147246) ((-1272 . -309) 147184) ((-1251 . -897) 147097) ((-481 . -723) T) ((-1244 . -897) 147003) ((-1243 . -1052) 146838) ((-1223 . -897) 146671) ((-1222 . -1052) 146479) ((-1203 . -290) 146458) ((-1179 . -1209) T) ((-1177 . -368) T) ((-1176 . -368) T) ((-1140 . -151) 146442) ((-1114 . -102) T) ((-1112 . -1094) T) ((-1074 . -23) T) ((-1069 . -102) T) ((-924 . -952) T) ((-734 . -309) 146380) ((-75 . -1209) T) ((-30 . -952) T) ((-169 . -906) 146333) ((-660 . -382) 146305) ((-112 . -841) T) ((-1 . -611) 146287) ((-1074 . -1106) T) ((-128 . -647) 146269) ((-50 . -618) 146253) ((-1000 . -409) 146225) ((-594 . -897) 146138) ((-438 . -102) T) ((-141 . -309) NIL) ((-128 . -373) 146120) ((-869 . -1046) T) ((-830 . -847) 146099) ((-81 . -1209) T) ((-708 . -290) T) ((-40 . -1053) T) ((-581 . -172) T) ((-518 . -172) T) ((-511 . -611) 146081) ((-169 . -644) 145991) ((-507 . -611) 145973) ((-351 . -147) 145955) ((-351 . -145) T) ((-359 . -1106) T) ((-353 . -1106) T) ((-345 . -1106) T) ((-1001 . -307) T) ((-911 . 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142458) ((-454 . -290) 142389) ((-1032 . -309) 142240) ((-677 . -490) 142221) ((-571 . -723) T) ((-672 . -490) 142202) ((-677 . -611) 142152) ((-672 . -611) 142118) ((-658 . -611) 142100) ((-478 . -490) 142081) ((-478 . -611) 142047) ((-245 . -612) 142008) ((-245 . -490) 141985) ((-138 . -490) 141966) ((-137 . -490) 141947) ((-133 . -490) 141928) ((-245 . -611) 141820) ((-213 . -102) T) ((-138 . -611) 141786) ((-137 . -611) 141752) ((-133 . -611) 141718) ((-1141 . -34) T) ((-940 . -1209) T) ((-343 . -714) 141663) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141644) ((-474 . -1046) T) ((-633 . -417) 141609) ((-605 . -417) 141574) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141553) ((-474 . -233) 141505) ((-474 . -243) 141484) ((-1223 . -307) 141463) ((-1223 . -1019) NIL) ((-1074 . -131) T) ((-869 . -792) 141442) ((-144 . -102) T) ((-40 . -1094) T) ((-869 . -789) 141421) ((-641 . -1007) 141405) ((-580 . -1053) T) ((-564 . -1053) T) ((-495 . -1053) T) 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137523) ((-955 . -34) T) ((-355 . -233) 137502) ((-355 . -243) T) ((-352 . -233) 137481) ((-352 . -243) T) ((-344 . -233) 137460) ((-344 . -243) T) ((-247 . -326) 137417) ((-264 . -326) 137389) ((-264 . -233) 137368) ((-1150 . -151) 137352) ((-251 . -897) 137284) ((-250 . -897) 137216) ((-1076 . -847) T) ((-414 . -1106) T) ((-1050 . -23) T) ((-907 . -1046) T) ((-322 . -644) 137198) ((-1021 . -845) T) ((-1203 . -999) 137164) ((-1167 . -917) 137143) ((-1161 . -917) 137122) ((-1161 . -817) NIL) ((-907 . -243) T) ((-814 . -363) 137101) ((-385 . -23) T) ((-127 . -1094) 137079) ((-121 . -1094) 137057) ((-907 . -233) T) ((-128 . -34) T) ((-379 . -644) 137022) ((-867 . -714) 137009) ((-1043 . -151) 136974) ((-40 . -172) T) ((-690 . -411) 136956) ((-709 . -309) 136943) ((-833 . -644) 136903) ((-824 . -644) 136877) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136856) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136833) ((-313 . -231) 136794) ((-1166 . -883) NIL) ((-55 . -1094) T) ((-1119 . -883) 136653) ((-129 . -847) T) ((-1166 . -1035) 136533) ((-1119 . -1035) 136416) ((-183 . -611) 136398) ((-851 . -1035) 136294) ((-779 . -286) 136221) ((-814 . -1106) T) ((-1031 . -723) T) ((-600 . -647) 136205) ((-1043 . -973) 136134) ((-996 . -102) T) ((-814 . -23) T) ((-709 . -1145) 136112) ((-690 . -1053) T) ((-600 . -373) 136096) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -723) T) ((-707 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136078) ((-1166 . -377) 136062) ((-1119 . -377) 136046) ((-1021 . -411) 136008) ((-141 . -229) 135990) ((-379 . -791) T) ((-379 . -788) T) ((-867 . -172) T) ((-379 . -723) T) ((-708 . -611) 135972) ((-709 . -38) 135801) ((-1259 . -1257) 135785) ((-351 . -402) T) ((-1259 . -1094) 135735) ((-580 . -714) 135722) ((-564 . -714) 135709) ((-495 . -714) 135674) ((-316 . -627) 135653) ((-833 . -723) T) ((-824 . -723) T) 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133609) ((-454 . -612) 133470) ((-1032 . -229) 133416) ((-869 . -906) 133395) ((-126 . -34) T) ((-814 . -131) T) ((-645 . -611) 133377) ((-578 . -102) T) ((-355 . -1278) 133361) ((-352 . -1278) 133345) ((-344 . -1278) 133329) ((-127 . -514) 133262) ((-121 . -514) 133195) ((-511 . -789) T) ((-511 . -792) T) ((-510 . -791) T) ((-103 . -309) 133133) ((-222 . -102) 133111) ((-690 . -1094) T) ((-695 . -172) T) ((-869 . -644) 133063) ((-65 . -384) T) ((-275 . -611) 133045) ((-65 . -395) T) ((-949 . -377) 133029) ((-867 . -290) T) ((-50 . -611) 133011) ((-996 . -38) 132959) ((-581 . -611) 132941) ((-481 . -377) 132925) ((-581 . -612) 132907) ((-518 . -611) 132889) ((-907 . -1278) 132876) ((-868 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132842) ((-487 . -363) T) ((-355 . -368) 132821) ((-352 . -368) 132800) ((-344 . -368) 132779) ((-711 . -723) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132763) ((-868 . -881) 132740) ((-868 . -883) NIL) ((-961 . -847) 132639) ((-812 . -847) 132590) ((-1216 . -102) T) ((-650 . -652) 132574) ((-1195 . -34) T) ((-171 . -611) 132556) ((-1107 . -21) 132466) ((-1107 . -25) 132317) ((-868 . -1035) 132294) ((-949 . -897) 132275) ((-1232 . -47) 132252) ((-907 . -368) T) ((-59 . -647) 132236) ((-516 . -647) 132220) ((-481 . -897) 132197) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132181) ((-59 . -373) 132165) ((-621 . -172) T) ((-516 . -373) 132149) ((-496 . -373) 132133) ((-824 . -705) 132117) ((-1166 . -307) 132096) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132034) ((-169 . -1209) T) ((-633 . -741) 132018) ((-605 . -741) 132002) ((-1271 . -131) T) ((-1244 . -917) 131981) ((-1223 . -917) 131960) ((-1223 . -817) NIL) ((-690 . -714) 131910) ((-1222 . -906) 131863) ((-1021 . -1094) T) ((-868 . -377) 131840) ((-868 . -338) 131817) ((-902 . -1106) T) ((-169 . -881) 131801) ((-169 . -883) 131726) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1035) 131622) ((-319 . -847) T) ((-1259 . -514) 131555) ((-1243 . -644) 131452) ((-1222 . -644) 131322) ((-869 . -791) 131301) ((-869 . -788) 131280) ((-869 . -723) T) ((-487 . -23) T) ((-223 . -611) 131262) ((-174 . -452) T) ((-222 . -309) 131200) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131179) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1035) 131163) ((-495 . -290) T) ((-136 . -470) 131118) ((-48 . -1094) T) ((-709 . -231) 131102) ((-868 . -897) NIL) ((-1232 . -883) NIL) ((-886 . -102) T) ((-882 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131086) ((-169 . -338) 131070) ((-1232 . -1035) 130950) ((-852 . -1035) 130846) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130754) ((-658 . -789) 130733) ((-658 . -792) 130712) ((-571 . -1035) 130694) ((-294 . -1266) 130664) ((-863 . -102) T) ((-960 . -556) 130643) ((-1203 . -1052) 130526) ((-482 . -637) 130432) ((-901 . -1094) T) ((-1021 . -714) 130369) ((-708 . -1052) 130334) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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((-708 . -1046) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1021 . -172) T) ((-708 . -243) T) ((-1057 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 129049) ((-394 . -611) 129031) ((-474 . -723) T) ((-1114 . -845) T) ((-889 . -1035) 128999) ((-108 . -847) T) ((-654 . -1052) 128983) ((-487 . -131) T) ((-1245 . -1053) T) ((-217 . -131) T) ((-1150 . -102) 128961) ((-99 . -1094) T) ((-245 . -662) 128945) ((-245 . -647) 128929) ((-654 . -111) 128908) ((-585 . -614) 128892) ((-316 . -411) 128876) ((-245 . -373) 128860) ((-1153 . -235) 128807) ((-996 . -231) 128791) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128773) ((-1081 . -1052) 128616) ((-264 . -906) 128595) ((-247 . -906) 128574) ((-779 . -1052) 128397) ((-777 . -1052) 128240) ((-606 . -1209) T) ((-1158 . -611) 128222) ((-1081 . -111) 128051) ((-1043 . -102) T) ((-475 . -1209) T) ((-461 . -1052) 128022) ((-454 . -1052) 127865) 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-1053) T) ((-128 . -1209) T) ((-779 . -614) 125834) ((-777 . -614) 125600) ((-654 . -1046) T) ((-1287 . -1094) T) ((-454 . -614) 125385) ((-169 . -307) 125316) ((-418 . -23) T) ((-40 . -611) 125298) ((-40 . -612) 125282) ((-108 . -989) 125264) ((-116 . -866) 125248) ((-645 . -614) 125232) ((-48 . -514) 125198) ((-1195 . -1007) 125182) ((-1175 . -611) 125149) ((-1182 . -34) T) ((-951 . -611) 125115) ((-918 . -611) 125097) ((-1107 . -847) 125048) ((-768 . -611) 125030) ((-668 . -611) 125012) ((-1150 . -309) 124950) ((-479 . -34) T) ((-1086 . -1209) T) ((-477 . -452) T) ((-1135 . -34) T) ((-1081 . -1046) T) ((-50 . -614) 124919) ((-779 . -1046) T) ((-777 . -1046) T) ((-643 . -235) 124903) ((-630 . -235) 124849) ((-581 . -614) 124799) ((-518 . -614) 124729) ((-1232 . -307) 124708) ((-1081 . -326) 124669) ((-454 . -1046) T) ((-1172 . -21) T) ((-1081 . -233) 124648) ((-779 . -326) 124625) ((-779 . -233) T) ((-777 . -326) 124597) ((-728 . -1213) 124576) ((-327 . -647) 124560) ((-1172 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124539) ((-327 . -373) 124523) ((-497 . -34) T) ((-496 . -34) T) ((-1000 . -1145) NIL) ((-728 . -556) 124454) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -723) T) ((-352 . -723) T) ((-344 . -723) T) ((-264 . -723) T) ((-247 . -723) T) ((-1043 . -309) 124362) ((-898 . -1094) 124340) ((-50 . -1046) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 124319) ((-1167 . -1213) 124298) ((-581 . -1046) T) ((-518 . -1046) T) ((-1161 . -1213) 124277) ((-361 . -1035) 124261) ((-322 . -1035) 124245) ((-1021 . -290) T) ((-379 . -883) 124227) ((-1167 . -556) 124178) ((-1161 . -556) 124129) ((-1000 . -38) 124074) ((-796 . -1106) T) ((-907 . -723) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 124053) ((-354 . -290) T) ((-643 . -691) 124037) ((-379 . -1035) 123997) ((-1114 . -1053) T) ((-103 . -125) 123981) ((-796 . -23) T) ((-1281 . -1276) 123957) ((-1259 . -286) 123934) ((-407 . -309) 123899) ((-1279 . -1276) 123878) ((-1245 . -1094) T) ((-867 . -611) 123860) ((-833 . -1035) 123829) ((-203 . -784) T) ((-202 . -784) T) ((-201 . -784) T) ((-200 . -784) T) ((-199 . -784) T) ((-198 . -784) T) ((-197 . -784) T) ((-196 . -784) T) ((-195 . -784) T) ((-194 . -784) T) ((-547 . -611) 123811) ((-495 . -999) T) ((-274 . -836) T) ((-273 . -836) T) ((-272 . -836) T) ((-271 . -836) T) ((-48 . -290) T) ((-270 . -836) T) ((-269 . -836) T) ((-268 . -836) T) ((-193 . -784) T) ((-610 . -847) T) ((-650 . -411) 123795) ((-223 . -614) 123757) ((-110 . -847) T) ((-649 . -21) T) ((-649 . -25) T) ((-1282 . -38) 123727) ((-117 . -286) 123678) ((-1259 . -19) 123662) ((-1259 . -602) 123639) ((-1272 . -1094) T) ((-1071 . -1094) T) ((-984 . -1094) T) ((-960 . -131) T) ((-734 . -1094) T) ((-732 . -131) T) ((-712 . -131) T) ((-511 . -790) T) ((-407 . -1145) 123617) ((-453 . -131) T) ((-511 . -791) T) ((-223 . -1046) T) ((-294 . -102) 123399) ((-141 . -1094) T) ((-695 . -999) T) ((-91 . -1209) T) 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121769) ((-898 . -514) 121702) ((-343 . -1046) T) ((-117 . -612) NIL) ((-117 . -611) 121684) ((-869 . -1209) T) ((-666 . -417) 121668) ((-666 . -1117) 121613) ((-500 . -151) 121595) ((-343 . -233) T) ((-343 . -243) T) ((-40 . -1052) 121540) ((-869 . -881) 121524) ((-869 . -883) 121449) ((-709 . -1053) T) ((-690 . -999) NIL) ((-3 . |UnionCategory|) T) ((-1243 . -47) 121419) ((-1222 . -47) 121396) ((-1135 . -1007) 121367) ((-225 . -917) T) ((-40 . -111) 121296) ((-869 . -1035) 121160) ((-1114 . -714) 121147) ((-1099 . -611) 121129) ((-1074 . -147) 121108) ((-1074 . -145) 121059) ((-1001 . -363) T) ((-319 . -1197) 121025) ((-379 . -307) T) ((-319 . -1194) 120991) ((-316 . -172) 120970) ((-313 . -172) T) ((-1000 . -231) 120947) ((-911 . -363) T) ((-581 . -1278) 120934) ((-518 . -1278) 120911) ((-359 . -147) 120890) ((-359 . -145) 120841) ((-353 . -147) 120820) ((-353 . -145) 120771) ((-606 . -1185) 120747) ((-345 . -147) 120726) ((-345 . -145) 120677) ((-319 . -35) 120643) ((-475 . -1185) 120622) ((0 . |EnumerationCategory|) T) ((-319 . -95) 120588) ((-379 . -1019) T) ((-108 . -147) T) ((-108 . -145) NIL) ((-45 . -235) 120538) ((-650 . -1094) T) ((-606 . -107) 120485) ((-485 . -131) T) ((-475 . -107) 120435) ((-240 . -1106) 120345) ((-869 . -377) 120329) ((-869 . -338) 120313) ((-240 . -23) 120183) ((-40 . -614) 120113) ((-1057 . -917) T) ((-1057 . -817) T) ((-581 . -368) T) ((-518 . -368) T) ((-351 . -1145) T) ((-327 . -34) T) ((-44 . -417) 120097) ((-1175 . -614) 120033) ((-870 . -1209) T) ((-390 . -741) 120017) ((-1272 . -514) 119950) ((-728 . -131) T) ((-668 . -614) 119934) ((-1251 . -556) 119913) ((-1244 . -1213) 119892) ((-1244 . -556) 119843) ((-1223 . -1213) 119822) ((-311 . -1077) T) ((-1223 . -556) 119773) ((-734 . -514) 119706) ((-1222 . -1209) 119685) ((-1222 . -883) 119558) ((-890 . -1094) T) ((-144 . -841) T) ((-1222 . -881) 119528) ((-687 . -611) 119510) ((-1168 . -131) T) ((-523 . -309) 119448) ((-1167 . -131) T) ((-141 . -514) NIL) ((-1161 . -131) T) 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((-1203 . -644) 118430) ((-960 . -21) T) ((-960 . -25) T) ((-732 . -21) T) ((-732 . -25) T) ((-712 . -21) T) ((-712 . -25) T) ((-708 . -644) 118395) ((-453 . -21) T) ((-453 . -25) T) ((-339 . -102) T) ((-174 . -102) T) ((-996 . -1053) T) ((-867 . -1046) T) ((-771 . -102) T) ((-1244 . -363) 118374) ((-1243 . -897) 118280) ((-1223 . -363) 118259) ((-1222 . -897) 118110) ((-1021 . -611) 118092) ((-407 . -825) 118045) ((-1168 . -493) 118011) ((-169 . -917) 117942) ((-1167 . -493) 117908) ((-1161 . -493) 117874) ((-709 . -1094) T) ((-1120 . -493) 117840) ((-580 . -1052) 117827) ((-564 . -1052) 117814) ((-495 . -1052) 117779) ((-316 . -290) 117758) ((-313 . -290) T) ((-354 . -611) 117740) ((-418 . -25) T) ((-418 . -21) T) ((-99 . -286) 117719) ((-580 . -111) 117704) ((-564 . -111) 117689) ((-495 . -111) 117645) ((-1170 . -883) 117612) ((-898 . -489) 117596) ((-48 . -611) 117578) ((-48 . -612) 117523) ((-240 . -131) 117393) ((-1232 . -917) 117372) ((-813 . -1213) 117351) ((-388 . -490) 117332) ((-1032 . -514) 117176) ((-388 . -611) 117142) ((-813 . -556) 117073) ((-585 . -644) 117048) ((-264 . -47) 117020) ((-247 . -47) 116977) ((-531 . -509) 116954) ((-580 . -614) 116926) ((-564 . -614) 116898) ((-495 . -614) 116831) ((-997 . -1209) T) ((-695 . -1052) 116796) ((-1251 . -23) T) ((-1251 . -1106) T) ((-1244 . -1106) T) ((-1223 . -1106) T) ((-1000 . -370) 116768) ((-112 . -368) T) ((-474 . -897) 116674) ((-1244 . -23) T) ((-901 . -611) 116656) ((-55 . -614) 116638) ((-91 . -107) 116622) ((-1203 . -723) T) ((-902 . -847) 116573) ((-697 . -1145) T) ((-695 . -111) 116529) ((-1223 . -23) T) ((-595 . -1106) T) ((-594 . -1106) T) ((-709 . -714) 116358) ((-708 . -723) T) ((-1114 . -290) T) ((-1001 . -131) T) ((-487 . -847) T) ((-968 . -131) T) ((-911 . -131) T) ((-796 . -25) T) ((-217 . -847) T) ((-796 . -21) T) ((-580 . -1046) T) ((-564 . -1046) T) ((-495 . -1046) T) ((-595 . -23) T) ((-343 . -1278) 116335) ((-319 . -452) 116314) ((-339 . -309) 116301) ((-594 . -23) T) ((-427 . -131) T) ((-654 . -644) 116275) ((-245 . -1007) 116259) ((-869 . -307) T) ((-1283 . -1273) 116243) ((-768 . -789) T) ((-768 . -792) T) ((-697 . -38) 116230) ((-564 . -233) T) ((-495 . -243) T) ((-495 . -233) T) ((-1144 . -235) 116180) ((-1081 . -906) 116159) ((-116 . -38) 116146) ((-209 . -797) T) ((-208 . -797) T) ((-207 . -797) T) ((-206 . -797) T) ((-869 . -1019) 116124) ((-1272 . -489) 116108) ((-779 . -906) 116087) ((-777 . -906) 116066) ((-1182 . -1209) T) ((-454 . -906) 116045) ((-734 . -489) 116029) ((-1081 . -644) 115954) ((-695 . -614) 115889) ((-779 . -644) 115814) ((-621 . -1052) 115801) ((-479 . -1209) T) ((-343 . -368) T) ((-141 . -489) 115783) ((-777 . -644) 115708) ((-1135 . -1209) T) ((-549 . -847) T) ((-461 . -644) 115679) ((-264 . -883) 115538) ((-247 . -883) NIL) ((-117 . -1052) 115483) ((-454 . -644) 115408) ((-660 . -1035) 115385) ((-621 . -111) 115370) ((-355 . -1035) 115354) ((-352 . -1035) 115338) ((-344 . -1035) 115322) ((-264 . -1035) 115166) ((-247 . 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. -243) T) ((-48 . -233) T) ((-650 . -286) 110051) ((-550 . -235) 110001) ((-139 . -611) 109968) ((-136 . -611) 109950) ((-114 . -611) 109932) ((-477 . -38) 109897) ((-1283 . -1280) 109876) ((-1274 . -131) T) ((-1282 . -1053) T) ((-1076 . -102) T) ((-88 . -1209) T) ((-500 . -309) NIL) ((-997 . -107) 109860) ((-886 . -1094) T) ((-882 . -1094) T) ((-1259 . -647) 109844) ((-1259 . -373) 109828) ((-327 . -1209) T) ((-592 . -847) T) ((-1136 . -1094) T) ((-1136 . -1049) 109768) ((-103 . -514) 109701) ((-924 . -611) 109683) ((-343 . -723) T) ((-30 . -611) 109665) ((-863 . -1094) T) ((-840 . -1053) 109644) ((-40 . -644) 109589) ((-225 . -1213) T) ((-407 . -1053) T) ((-1152 . -151) 109571) ((-996 . -290) 109522) ((-615 . -1094) T) ((-225 . -556) T) ((-319 . -1240) 109506) ((-319 . -1237) 109476) ((-1182 . -1185) 109455) ((-1069 . -611) 109437) ((-643 . -151) 109421) ((-630 . -151) 109367) ((-1182 . -107) 109317) ((-479 . -1185) 109296) ((-487 . -147) T) ((-487 . -145) NIL) ((-1114 . -612) 109211) ((-438 . -611) 109193) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 109175) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 109127) ((-479 . -107) 109077) ((-990 . -23) T) ((-1283 . -38) 109047) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1057 . -1213) T) ((-311 . -102) T) ((-851 . -1106) T) ((-949 . -1213) 109026) ((-481 . -1213) 109005) ((-728 . -847) 108984) ((-1057 . -556) T) ((-949 . -556) 108915) ((-1166 . -23) T) ((-1119 . -23) T) ((-851 . -23) T) ((-481 . -556) 108846) ((-1136 . -714) 108778) ((-1140 . -514) 108711) ((-1032 . -612) NIL) ((-1032 . -611) 108693) ((-96 . -1077) T) ((-863 . -714) 108663) ((-1203 . -47) 108632) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-1000 . -1094) T) ((-62 . -611) 108614) ((-1161 . -847) NIL) ((-1021 . -789) T) ((-1021 . -792) T) ((-1287 . -1052) 108601) ((-1287 . -111) 108586) ((-867 . -644) 108573) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) 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-883) NIL) ((-868 . -1106) T) ((-117 . -906) NIL) ((-1281 . -1280) 105427) ((-1279 . -1280) 105406) ((-779 . -883) NIL) ((-777 . -883) 105265) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105243) ((-1100 . -395) T) ((-621 . -644) 105230) ((-454 . -883) NIL) ((-671 . -102) 105208) ((-1081 . -1035) 105035) ((-868 . -23) T) ((-779 . -1035) 104894) ((-777 . -1035) 104751) ((-117 . -644) 104696) ((-454 . -1035) 104572) ((-316 . -614) 104136) ((-313 . -614) 104019) ((-645 . -1035) 104003) ((-625 . -102) T) ((-222 . -489) 103987) ((-1259 . -34) T) ((-136 . -614) 103971) ((-633 . -714) 103955) ((-605 . -714) 103939) ((-666 . -38) 103899) ((-319 . -102) T) ((-85 . -611) 103881) ((-50 . -1035) 103865) ((-1114 . -1052) 103852) ((-1081 . -377) 103836) ((-779 . -377) 103820) ((-695 . -723) T) ((-695 . -791) T) ((-695 . -788) T) ((-581 . -1035) 103807) ((-518 . -1035) 103784) ((-60 . -57) 103746) ((-324 . -131) T) ((-316 . -1046) 103636) ((-313 . -1046) T) ((-169 . -1106) T) ((-777 . -377) 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101734) ((-1021 . -644) 101671) ((-523 . -1094) 101649) ((-359 . -102) T) ((-353 . -102) T) ((-345 . -102) T) ((-108 . -102) T) ((-504 . -1094) T) ((-354 . -644) 101594) ((-1166 . -637) 101542) ((-1119 . -637) 101490) ((-385 . -509) 101469) ((-830 . -845) 101448) ((-379 . -1213) T) ((-690 . -723) T) ((-339 . -1053) T) ((-1223 . -989) 101400) ((-174 . -1053) T) ((-103 . -611) 101332) ((-1168 . -145) 101311) ((-1168 . -147) 101290) ((-379 . -556) T) ((-1167 . -147) 101269) ((-1167 . -145) 101248) ((-1161 . -145) 101155) ((-407 . -290) T) ((-1161 . -147) 101062) ((-1120 . -147) 101041) ((-1120 . -145) 101020) ((-319 . -38) 100861) ((-169 . -131) T) ((-313 . -792) NIL) ((-313 . -789) NIL) ((-650 . -1046) T) ((-48 . -644) 100826) ((-890 . -614) 100803) ((-1160 . -102) T) ((-991 . -102) T) ((-990 . -21) T) ((-127 . -1007) 100787) ((-121 . -1007) 100771) ((-990 . -25) T) ((-898 . -119) 100755) ((-1152 . -102) T) ((-813 . -847) 100734) ((-1232 . -131) T) ((-1166 . -25) T) ((-1166 . -21) T) 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((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99759) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99549) ((-830 . -411) 99533) ((-1114 . -792) T) ((-1114 . -789) T) ((-697 . -1094) T) ((-578 . -611) 99515) ((-379 . -363) T) ((-169 . -493) 99493) ((-222 . -611) 99425) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -723) T) ((-1043 . -489) 99390) ((-141 . -425) 99372) ((-141 . -368) T) ((-1024 . -102) T) ((-512 . -509) 99351) ((-709 . -614) 99107) ((-476 . -102) T) ((-463 . -102) T) ((-1031 . -1106) T) ((-1216 . -611) 99089) ((-1175 . -1035) 99025) ((-1168 . -35) 98991) ((-1168 . -95) 98957) ((-1168 . -1197) 98923) ((-1168 . -1194) 98889) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98868) ((-1167 . -1194) 98834) ((-1167 . -1197) 98800) ((-1031 . -23) T) ((-1167 . -95) 98766) ((-571 . -493) T) ((-1167 . -35) 98732) ((-1161 . -1194) 98698) ((-1161 . -1197) 98664) ((-1161 . -95) 98630) ((-361 . -1106) T) ((-359 . -1145) 98609) ((-353 . -1145) 98588) 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((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97384) ((-96 . -102) T) ((-649 . -849) 97368) ((-1129 . -1077) T) ((-1057 . -21) T) ((-1057 . -25) T) ((-812 . -231) 97337) ((-949 . -25) T) ((-949 . -21) T) ((-619 . -1053) T) ((-1114 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1024 . -309) 97275) ((-886 . -611) 97257) ((-882 . -611) 97239) ((-251 . -847) 97190) ((-250 . -847) 97141) ((-523 . -514) 97074) ((-868 . -637) 97051) ((-476 . -309) 96989) ((-463 . -309) 96927) ((-351 . -290) T) ((-1150 . -1247) 96911) ((-1136 . -611) 96873) ((-1136 . -612) 96834) ((-1134 . -102) T) ((-996 . -1052) 96730) ((-40 . -897) 96682) ((-1150 . -602) 96659) ((-1287 . -644) 96646) ((-863 . -490) 96623) ((-1058 . -151) 96569) ((-869 . -1213) T) ((-996 . -111) 96451) ((-339 . -714) 96435) ((-863 . -611) 96397) ((-174 . -714) 96329) ((-407 . -286) 96287) ((-869 . -556) T) ((-108 . -400) 96269) ((-84 . -384) T) ((-84 . -395) T) ((-697 . -172) T) ((-615 . -611) 96251) ((-99 . -723) T) ((-482 . -102) 96041) ((-99 . -473) T) ((-116 . -172) T) ((-1107 . -38) 96011) ((-169 . -637) 95959) ((-1050 . -102) T) ((-996 . -614) 95849) ((-868 . -25) T) ((-812 . -238) 95828) ((-868 . -21) T) ((-815 . -102) T) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 95806) ((-127 . -1209) T) ((-121 . -1209) T) ((-1031 . -131) T) ((-666 . -367) 95790) ((-996 . -1046) T) ((-1232 . -637) 95738) ((-1098 . -611) 95720) ((-1000 . -611) 95702) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1094) T) ((-1000 . -612) 95686) ((-996 . -243) 95665) ((-996 . -233) 95644) ((-1287 . -723) T) ((-1251 . -145) 95623) ((-830 . -1094) T) ((-1251 . -147) 95602) ((-1244 . -147) 95581) ((-1244 . -145) 95560) ((-1243 . -1213) 95539) ((-1223 . -145) 95446) ((-1223 . -147) 95353) ((-1222 . -1213) 95332) ((-379 . -131) T) ((-564 . -883) 95314) ((0 . -1094) T) ((-174 . -172) T) ((-169 . -21) T) ((-169 . -25) T) ((-49 . -1094) T) ((-1245 . -644) 95219) ((-1243 . -556) 95170) ((-711 . -1106) T) ((-1222 . -556) 95121) ((-564 . -1035) 95103) ((-594 . -147) 95082) ((-594 . -145) 95061) ((-495 . -1035) 95004) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-869 . -363) T) ((-833 . -131) T) ((-824 . -131) T) ((-711 . -23) T) ((-506 . -611) 94970) ((-502 . -611) 94952) ((-1283 . -1053) T) ((-379 . -1055) T) ((-1023 . -1094) 94930) ((-55 . -1035) 94912) ((-898 . -34) T) ((-482 . -309) 94850) ((-591 . -102) T) ((-1150 . -612) 94811) ((-1150 . -611) 94743) ((-1166 . -847) 94722) ((-45 . -102) T) ((-1119 . -847) 94701) ((-814 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-852 . -25) T) ((-44 . -367) 94685) ((-852 . -21) T) ((-728 . -452) 94636) ((-1282 . -611) 94618) ((-1050 . -309) 94556) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -883) 94538) ((-1259 . -1209) T) ((-227 . -309) 94476) ((-144 . -368) T) ((-1043 . -612) 94418) ((-1043 . -611) 94361) ((-313 . -906) NIL) ((-1217 . -841) T) ((-695 . -1035) 94306) ((-708 . -917) T) ((-474 . -1213) 94285) ((-1167 . -452) 94264) ((-1161 . -452) 94243) ((-330 . -102) T) ((-869 . -1106) T) ((-316 . -644) 94064) ((-313 . -644) 93993) ((-474 . -556) 93944) ((-339 . -514) 93910) ((-550 . -151) 93860) ((-40 . -307) T) ((-840 . -611) 93842) ((-697 . -290) T) ((-869 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93812) ((-512 . -102) T) ((-407 . -612) 93619) ((-407 . -611) 93601) ((-263 . -611) 93583) ((-116 . -290) T) ((-1245 . -723) T) ((-1243 . -363) 93562) ((-1222 . -363) 93541) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93523) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93507) ((-734 . -34) T) ((-482 . -38) 93477) ((-141 . -34) T) ((-117 . -881) 93454) ((-117 . -883) NIL) ((-621 . -1035) 93337) ((-641 . -847) 93316) ((-1271 . -102) T) ((-295 . -102) T) ((-709 . -368) 93295) 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-23) T) ((-715 . -1106) T) ((-711 . -131) T) ((-649 . -102) T) ((-477 . -714) 92048) ((-45 . -282) 91998) ((-105 . -1094) T) ((-68 . -611) 91980) ((-967 . -102) T) ((-861 . -102) T) ((-621 . -897) 91939) ((-1283 . -1094) T) ((-381 . -1094) T) ((-1208 . -1094) T) ((-1107 . -231) 91908) ((-82 . -1209) T) ((-1057 . -847) T) ((-949 . -847) 91887) ((-117 . -897) NIL) ((-779 . -917) 91866) ((-710 . -847) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91845) ((-247 . -1213) 91824) ((-533 . -857) T) ((-481 . -847) 91803) ((-1152 . -825) T) ((-1136 . -1052) 91787) ((-390 . -758) T) ((-690 . -1209) T) ((-687 . -1035) 91771) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91702) ((-247 . -556) 91633) ((-525 . -1077) T) ((-1136 . -111) 91612) ((-453 . -741) 91582) ((-863 . -1052) 91552) ((-814 . -38) 91494) ((-690 . -881) 91476) ((-690 . -883) 91458) ((-295 . -309) 91262) ((-907 . -1213) T) ((-666 . -411) 91246) ((-863 . -111) 91211) ((-690 . -1035) 91156) ((-1001 . -452) T) ((-907 . -556) T) ((-533 . -611) 91138) ((-581 . -917) T) ((-474 . -1106) T) ((-518 . -917) T) ((-1150 . -288) 91115) ((-911 . -452) T) ((-65 . -611) 91097) ((-630 . -229) 91043) ((-474 . -23) T) ((-1114 . -791) T) ((-869 . -131) T) ((-1114 . -788) T) ((-1274 . -1276) 91022) ((-1114 . -723) T) ((-650 . -644) 90996) ((-294 . -611) 90737) ((-1136 . -614) 90655) ((-1032 . -34) T) ((-812 . -845) 90634) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -714) 90604) ((-690 . -377) 90586) ((-690 . -338) 90568) ((-477 . -172) T) ((-381 . -714) 90538) ((-863 . -614) 90473) ((-868 . -847) NIL) ((-564 . -1019) T) ((-495 . -1019) T) ((-1127 . -611) 90455) ((-1107 . -238) 90434) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90416) ((-1136 . -1046) T) ((-1172 . -38) 90313) ((-855 . -611) 90295) ((-564 . -545) T) ((-666 . -1053) T) ((-728 . -946) 90248) ((-1136 . -233) 90227) ((-1076 . -1094) T) ((-1031 . -25) T) ((-1031 . -21) T) ((-1000 . -1052) 90172) ((-902 . -102) T) ((-863 . -1046) T) ((-690 . -897) NIL) ((-355 . -329) 90156) ((-355 . -363) T) ((-352 . -329) 90140) ((-352 . -363) T) ((-344 . -329) 90124) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90094) ((-546 . -847) T) ((-523 . -683) 90044) ((-217 . -102) T) ((-1021 . -1035) 89924) ((-1000 . -111) 89853) ((-1168 . -970) 89822) ((-1167 . -970) 89784) ((-520 . -151) 89768) ((-1074 . -370) 89747) ((-351 . -611) 89729) ((-322 . -21) T) ((-354 . -1035) 89706) ((-322 . -25) T) ((-1161 . -970) 89675) ((-1120 . -970) 89642) ((-76 . -611) 89624) ((-695 . -307) T) ((-169 . -847) 89603) ((-129 . -841) T) ((-907 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-907 . -329) 89590) ((-86 . -611) 89572) ((-695 . -1019) T) ((-673 . -847) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-898 . -1007) 89556) ((-833 . -21) T) ((-48 . -1035) 89499) ((-833 . -25) T) ((-824 . -25) T) ((-824 . -21) T) ((-1281 . -1053) T) ((-549 . -102) T) ((-1279 . -1053) T) ((-650 . -723) T) ((-1098 . -616) 89402) ((-1000 . -614) 89332) ((-1282 . -1052) 89316) ((-1232 . -847) 89295) ((-812 . -411) 89264) ((-103 . -119) 89248) ((-129 . -1094) T) ((-52 . -1094) T) ((-923 . -611) 89230) ((-868 . -989) 89207) ((-820 . -102) T) ((-1282 . -111) 89186) ((-649 . -38) 89156) ((-571 . -847) T) ((-355 . -1106) T) ((-352 . -1106) T) ((-344 . -1106) T) ((-264 . -1106) T) ((-247 . -1106) T) ((-621 . -307) 89135) ((-1144 . -309) 88939) ((-524 . -1077) T) ((-311 . -1094) T) ((-660 . -23) T) ((-482 . -231) 88908) ((-152 . -1053) T) ((-355 . -23) T) ((-352 . -23) T) ((-344 . -23) T) ((-117 . -307) T) ((-264 . -23) T) ((-247 . -23) T) ((-1000 . -1046) T) ((-709 . -906) 88887) ((-1150 . -614) 88864) ((-1000 . -233) 88836) ((-1000 . -243) T) ((-117 . -1019) NIL) ((-907 . -1106) T) ((-1244 . -452) 88815) ((-1223 . -452) 88794) ((-523 . -611) 88726) ((-709 . -644) 88651) ((-407 . -1052) 88603) ((-504 . -611) 88585) ((-907 . -23) T) ((-487 . -309) NIL) ((-1282 . -614) 88541) 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-1219) 87595) ((-407 . -1046) T) ((-319 . -1053) T) ((-690 . -307) T) ((-108 . -845) T) ((-709 . -723) T) ((-407 . -243) T) ((-407 . -233) 87574) ((-487 . -38) 87524) ((-217 . -38) 87474) ((-474 . -493) 87440) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87422) ((-697 . -612) 87337) ((-711 . -21) T) ((-711 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87319) ((-116 . -611) 87301) ((-157 . -25) T) ((-1281 . -1094) T) ((-869 . -637) 87249) ((-1279 . -1094) T) ((-960 . -102) T) ((-732 . -102) T) ((-712 . -102) T) ((-453 . -102) T) ((-813 . -452) 87200) ((-44 . -1094) T) ((-1082 . -847) T) ((-660 . -131) T) ((-1058 . -309) 87051) ((-666 . -714) 87035) ((-289 . -1053) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86985) ((-955 . -847) 86964) ((-996 . -644) 86902) ((-240 . -1266) 86872) ((-1021 . -307) T) ((-294 . -1052) 86793) ((-907 . -131) T) ((-40 . -917) T) ((-487 . -400) 86775) ((-354 . -307) T) ((-217 . -400) 86757) ((-1074 . -411) 86741) ((-294 . -111) 86657) ((-1177 . -847) T) ((-1176 . -847) T) ((-869 . -25) T) ((-869 . -21) T) ((-339 . -611) 86639) ((-1245 . -47) 86583) ((-225 . -147) T) ((-174 . -611) 86565) ((-1107 . -845) 86544) ((-771 . -611) 86526) ((-128 . -847) T) ((-606 . -235) 86473) ((-475 . -235) 86423) ((-1281 . -714) 86393) ((-48 . -307) T) ((-1279 . -714) 86363) ((-65 . -614) 86292) ((-961 . -1094) T) ((-812 . -1094) 86082) ((-312 . -102) T) ((-898 . -1209) T) ((-48 . -1019) T) ((-1222 . -637) 85990) ((-685 . -102) 85968) ((-44 . -714) 85952) ((-550 . -102) T) ((-294 . -614) 85883) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -758) T) ((-1206 . -1094) 85861) ((-351 . -1052) 85806) ((-671 . -1094) 85784) ((-1057 . -147) T) ((-949 . -147) 85763) ((-949 . -145) 85742) ((-796 . -102) T) ((-152 . -714) 85726) ((-481 . -147) 85705) ((-481 . -145) 85684) ((-351 . -111) 85613) ((-1074 . -1053) T) ((-322 . -847) 85592) ((-1251 . -970) 85561) ((-625 . -1094) T) ((-1244 . -970) 85523) ((-511 . -131) T) ((-507 . -131) T) ((-295 . -229) 85473) ((-359 . -1053) T) ((-353 . -1053) T) ((-345 . -1053) T) ((-294 . -1046) 85415) ((-1223 . -970) 85384) ((-379 . -847) T) ((-108 . -1053) T) ((-996 . -723) T) ((-867 . -917) T) ((-840 . -792) 85363) ((-840 . -789) 85342) ((-418 . -309) 85281) ((-468 . -102) T) ((-594 . -970) 85250) ((-319 . -1094) T) ((-407 . -792) 85229) ((-407 . -789) 85208) ((-500 . -489) 85190) ((-1245 . -1035) 85156) ((-1243 . -21) T) ((-1243 . -25) T) ((-1222 . -21) T) ((-1222 . -25) T) ((-812 . -714) 85098) ((-351 . -614) 85028) ((-695 . -404) T) ((-1272 . -1209) T) ((-604 . -102) T) ((-1107 . -411) 84997) ((-1000 . -368) NIL) ((-667 . -102) T) ((-180 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-734 . -1209) T) ((-44 . -758) T) ((-592 . -102) T) ((-77 . -396) T) ((-77 . -395) T) ((-649 . -652) 84981) ((-141 . -1209) T) ((-868 . -147) T) ((-868 . -145) NIL) ((-1208 . -93) T) ((-351 . -1046) T) ((-70 . -383) T) ((-70 . -395) T) ((-1159 . -102) T) ((-666 . -514) 84914) ((-685 . -309) 84852) ((-960 . -38) 84749) ((-732 . -38) 84719) ((-550 . -309) 84523) ((-316 . -1209) T) ((-351 . -233) T) ((-351 . -243) T) ((-313 . -1209) T) ((-289 . -1094) T) ((-1174 . -611) 84505) ((-708 . -1213) T) ((-1150 . -647) 84489) ((-1203 . -556) 84468) ((-708 . -556) T) ((-316 . -881) 84452) ((-316 . -883) 84377) ((-313 . -881) 84338) ((-313 . -883) NIL) ((-796 . -309) 84303) ((-319 . -714) 84144) ((-324 . -323) 84121) ((-485 . -102) T) ((-474 . -25) T) ((-474 . -21) T) ((-418 . -38) 84095) ((-316 . -1035) 83758) ((-225 . -1194) T) ((-225 . -1197) T) ((-3 . -611) 83740) ((-313 . -1035) 83670) ((-2 . -1094) T) ((-2 . |RecordCategory|) T) ((-830 . -611) 83652) ((-1107 . -1053) 83582) ((-580 . -917) T) ((-564 . -817) T) ((-564 . -917) T) ((-495 . -917) T) ((-136 . -1035) 83566) ((-225 . -95) T) ((-75 . -441) T) ((-75 . -395) T) ((0 . -611) 83548) ((-169 . -147) 83527) ((-169 . -145) 83478) ((-225 . -35) T) ((-49 . -611) 83460) ((-477 . -1053) T) ((-487 . -231) 83442) ((-484 . -965) 83426) ((-482 . -845) 83405) ((-217 . -231) 83387) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-812 . -172) 83366) ((-728 . -102) T) ((-1023 . -611) 83333) ((-500 . -286) 83308) ((-316 . -377) 83277) ((-313 . -377) 83238) ((-313 . -338) 83199) ((-1079 . -611) 83181) ((-813 . -946) 83128) ((-658 . -131) T) ((-1232 . -145) 83107) ((-1232 . -147) 83086) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -714) 83073) ((-1153 . -608) 83049) ((-592 . -309) NIL) ((-484 . -1094) 83027) ((-390 . -611) 83009) ((-510 . -847) T) ((-1144 . -229) 82959) ((-1251 . -1250) 82943) ((-1251 . -1237) 82920) ((-1244 . -1242) 82881) ((-1244 . -1237) 82851) ((-1244 . -1240) 82835) ((-1223 . -1221) 82796) ((-1223 . -1237) 82773) ((-619 . -611) 82755) ((-1223 . -1219) 82739) ((-695 . -917) T) ((-1168 . -284) 82705) ((-1167 . -284) 82671) ((-1161 . -284) 82637) ((-1074 . -1094) T) ((-1056 . -1094) T) ((-48 . -302) T) ((-316 . -897) 82603) ((-313 . -897) NIL) ((-1056 . -1063) 82582) ((-1114 . -883) 82564) ((-796 . -38) 82548) ((-264 . -637) 82496) ((-247 . -637) 82444) ((-697 . -1052) 82431) ((-594 . -1237) 82408) ((-1120 . -284) 82374) ((-319 . -172) 82305) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82287) ((-1114 . -1035) 82269) ((-1096 . -151) 82253) ((-108 . -1094) T) ((-116 . -1052) 82240) ((-708 . -363) T) ((-500 . -602) 82215) ((-697 . -111) 82200) ((-436 . -102) T) ((-45 . -1143) 82150) ((-116 . -111) 82135) ((-633 . -717) T) ((-605 . -717) T) ((-812 . -514) 82068) ((-1032 . -1209) T) ((-940 . -151) 82052) ((-1217 . -611) 82034) ((-1166 . -452) 81965) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81915) ((-1136 . -644) 81889) ((-1119 . -452) 81840) ((-1081 . -1213) 81819) ((-779 . -1213) 81798) ((-777 . -1213) 81777) ((-62 . -1209) T) ((-477 . -611) 81729) ((-477 . -612) 81651) ((-1081 . -556) 81582) ((-991 . -1094) T) ((-779 . -556) 81493) ((-777 . -556) 81424) ((-482 . -411) 81393) ((-621 . -917) 81372) ((-454 . -1213) 81351) ((-728 . -309) 81338) ((-697 . -614) 81310) ((-398 . -611) 81292) ((-671 . -514) 81225) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81156) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -917) T) ((-117 . -817) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 81138) ((-116 . -614) 81110) ((-1261 . -611) 81092) ((-1215 . -847) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80977) ((-1120 . -309) 80964) ((-1074 . -714) 80832) ((-863 . -644) 80792) ((-940 . -977) 80776) ((-907 . -21) T) ((-289 . -172) T) ((-907 . -25) T) ((-311 . -93) T) ((-869 . -847) 80727) ((-708 . -1106) T) ((-708 . -23) T) ((-697 . -1046) T) ((-643 . -1094) 80705) 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. -611) 77339) ((-1076 . -612) 77320) ((-407 . -906) 77299) ((-50 . -1106) T) ((-1021 . -917) T) ((-1000 . -723) T) ((-709 . -883) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-840 . -644) 77272) ((-1203 . -131) T) ((-1161 . -400) 77224) ((-1001 . -309) NIL) ((-812 . -489) 77208) ((-354 . -917) T) ((-1150 . -34) T) ((-407 . -644) 77160) ((-50 . -23) T) ((-708 . -131) T) ((-709 . -1035) 77040) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 77011) ((-1134 . -1094) T) ((-1274 . -1273) 76995) ((-697 . -792) T) ((-697 . -789) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76977) ((-1222 . -989) 76947) ((-48 . -917) T) ((-671 . -489) 76931) ((-251 . -1266) 76901) ((-250 . -1266) 76871) ((-1170 . -847) T) ((-1107 . -172) 76850) ((-1114 . -1019) T) ((-1043 . -34) T) ((-833 . -147) 76829) ((-833 . -145) 76808) ((-734 . -107) 76792) ((-610 . -132) T) ((-482 . -1094) 76582) ((-1172 . -1053) T) ((-868 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76552) ((-141 . -107) 76534) ((-709 . -377) 76518) ((-830 . -614) 76386) ((-1114 . -545) T) ((-579 . -102) T) ((-129 . -490) 76368) ((-390 . -1052) 76352) ((-1282 . -723) T) ((-1166 . -946) 76321) ((-129 . -611) 76288) ((-52 . -611) 76270) ((-1119 . -946) 76237) ((-649 . -411) 76221) ((-1271 . -1053) T) ((-619 . -1052) 76205) ((-658 . -25) T) ((-658 . -21) T) ((-1152 . -514) NIL) ((-1251 . -102) T) ((-1244 . -102) T) ((-390 . -111) 76184) ((-222 . -254) 76168) ((-1223 . -102) T) ((-1050 . -1094) T) ((-1001 . -1145) T) ((-1050 . -1049) 76108) ((-815 . -1094) T) ((-343 . -1213) T) ((-633 . -644) 76092) ((-619 . -111) 76071) ((-605 . -644) 76055) ((-595 . -102) T) ((-311 . -490) 76036) ((-585 . -131) T) ((-594 . -102) T) ((-414 . -1094) T) ((-385 . -1094) T) ((-311 . -611) 76002) ((-227 . -1094) 75980) ((-643 . -514) 75913) ((-630 . -514) 75757) ((-830 . -1046) 75736) ((-641 . -151) 75720) ((-343 . -556) T) ((-709 . -897) 75663) ((-550 . -229) 75613) ((-1251 . -284) 75579) ((-1074 . -290) 75530) ((-487 . -845) T) ((-223 . -1106) T) ((-1244 . -284) 75496) ((-1223 . -284) 75462) ((-1001 . -38) 75412) ((-217 . -845) T) ((-1203 . -493) 75378) ((-911 . -38) 75330) ((-840 . -791) 75309) ((-840 . -788) 75288) ((-840 . -723) 75267) ((-359 . -290) T) ((-353 . -290) T) ((-345 . -290) T) ((-169 . -452) 75198) ((-427 . -38) 75182) ((-108 . -290) T) ((-223 . -23) T) ((-407 . -791) 75161) ((-407 . -788) 75140) ((-407 . -723) T) ((-500 . -288) 75115) ((-477 . -1052) 75080) ((-654 . -131) T) ((-619 . -614) 75049) ((-1107 . -514) 74982) ((-336 . -131) T) ((-169 . -402) 74961) ((-482 . -714) 74903) ((-812 . -286) 74880) ((-477 . -111) 74836) ((-649 . -1053) T) ((-1232 . -452) 74767) ((-1270 . -1077) T) ((-1269 . -1077) T) ((-1081 . -131) T) ((-1050 . -714) 74709) ((-264 . -847) 74688) ((-247 . -847) 74667) ((-779 . -131) T) ((-777 . -131) T) ((-571 . -452) T) ((-1024 . -514) 74600) ((-619 . -1046) T) ((-591 . -1094) T) ((-533 . -173) T) ((-461 . -131) T) ((-454 . -131) T) ((-45 . -1094) T) ((-385 . -714) 74570) ((-814 . -1094) T) ((-476 . -514) 74503) ((-463 . -514) 74436) ((-453 . -367) 74406) ((-45 . -608) 74385) ((-316 . -302) T) ((-477 . -614) 74335) ((-666 . -611) 74297) ((-59 . -847) 74276) ((-1223 . -309) 74161) ((-548 . -611) 74143) ((-1001 . -400) 74125) ((-812 . -602) 74102) ((-516 . -847) 74081) ((-496 . -847) 74060) ((-40 . -1213) T) ((-996 . -1035) 73956) ((-50 . -131) T) ((-581 . -131) T) ((-518 . -131) T) ((-294 . -644) 73816) ((-343 . -329) 73793) ((-343 . -363) T) ((-322 . -323) 73770) ((-319 . -286) 73755) ((-40 . -556) T) ((-379 . -1194) T) ((-379 . -1197) T) ((-1032 . -1185) 73730) ((-1182 . -235) 73680) ((-1161 . -231) 73632) ((-330 . -1094) T) ((-379 . -95) T) ((-379 . -35) T) ((-1032 . -107) 73578) ((-477 . -1046) T) ((-479 . -235) 73528) ((-1153 . -489) 73462) ((-1283 . -1052) 73446) ((-381 . -1052) 73430) ((-477 . -243) T) ((-813 . -102) T) ((-711 . -147) 73409) ((-711 . -145) 73388) ((-484 . -489) 73372) ((-485 . -335) 73341) ((-1283 . -111) 73320) ((-512 . 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((-1107 . -489) 70607) ((-60 . -309) 70545) ((-331 . -102) T) ((-1203 . -21) T) ((-1203 . -25) T) ((-40 . -1106) T) ((-708 . -21) T) ((-625 . -611) 70527) ((-515 . -323) 70506) ((-708 . -25) T) ((-439 . -102) T) ((-108 . -286) NIL) ((-918 . -1106) T) ((-40 . -23) T) ((-768 . -1106) T) ((-564 . -1213) T) ((-495 . -1213) T) ((-319 . -611) 70488) ((-1001 . -231) 70470) ((-169 . -166) 70454) ((-580 . -556) T) ((-564 . -556) T) ((-495 . -556) T) ((-768 . -23) T) ((-1243 . -147) 70433) ((-1153 . -602) 70409) ((-1243 . -145) 70388) ((-1024 . -489) 70372) ((-1222 . -145) 70297) ((-1222 . -147) 70222) ((-1274 . -1280) 70201) ((-476 . -489) 70185) ((-463 . -489) 70169) ((-523 . -34) T) ((-649 . -714) 70139) ((-112 . -964) T) ((-658 . -847) 70118) ((-1172 . -172) 70069) ((-365 . -102) T) ((-240 . -238) 70048) ((-251 . -102) T) ((-250 . -102) T) ((-1232 . -946) 70017) ((-245 . -847) 69996) ((-813 . -38) 69845) ((-45 . -514) 69637) ((-1152 . -286) 69612) ((-214 . -1094) T) ((-1144 . -1094) T) 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T) ((-1244 . -644) 4321) ((-624 . -93) T) ((-1190 . -611) 4303) ((-1082 . -611) 4285) ((-126 . -489) 4269) ((-483 . -93) T) ((-1070 . -611) 4251) ((-390 . -23) T) ((-87 . -1209) T) ((-218 . -93) T) ((-1223 . -644) 4103) ((-907 . -714) 4068) ((-619 . -23) T) ((-606 . -611) 4050) ((-606 . -612) NIL) ((-475 . -612) NIL) ((-475 . -611) 4032) ((-511 . -1094) T) ((-507 . -1094) T) ((-351 . -25) T) ((-351 . -21) T) ((-127 . -309) 3970) ((-121 . -309) 3908) ((-595 . -644) 3895) ((-225 . -1046) T) ((-594 . -644) 3820) ((-379 . -999) T) ((-225 . -243) T) ((-225 . -233) T) ((-1057 . -614) 3792) ((-1057 . -616) 3773) ((-955 . -612) 3734) ((-955 . -611) 3646) ((-949 . -614) 3435) ((-867 . -38) 3422) ((-710 . -614) 3372) ((-1243 . -290) 3323) ((-1222 . -290) 3274) ((-481 . -614) 3059) ((-1114 . -452) T) ((-502 . -847) T) ((-316 . -1133) 3038) ((-996 . -147) 3017) ((-996 . -145) 2996) ((-495 . -309) 2983) ((-295 . -1185) 2962) ((-1177 . -611) 2944) ((-1176 . -611) 2926) ((-868 . -1052) 2871) ((-477 . -1106) T) ((-139 . -832) 2853) ((-621 . -102) T) ((-1195 . -489) 2837) ((-251 . -368) 2816) ((-250 . -368) 2795) ((-1057 . -1046) T) ((-295 . -107) 2745) ((-130 . -611) 2727) ((-128 . -612) NIL) ((-128 . -611) 2671) ((-117 . -102) T) ((-949 . -1046) T) ((-868 . -111) 2600) ((-477 . -23) T) ((-481 . -1046) T) ((-1057 . -233) T) ((-949 . -326) 2569) ((-481 . -326) 2526) ((-355 . -172) T) ((-352 . -172) T) ((-344 . -172) T) ((-264 . -172) 2437) ((-247 . -172) 2348) ((-960 . -1035) 2244) ((-517 . -490) 2225) ((-732 . -1035) 2196) ((-517 . -611) 2162) ((-1099 . -102) T) ((-1086 . -611) 2129) ((-1031 . -611) 2111) ((-1272 . -151) 2095) ((-1270 . -614) 2076) ((-1264 . -611) 2058) ((-1251 . -723) T) ((-1244 . -723) T) ((-1223 . -788) NIL) ((-1223 . -791) NIL) ((-169 . -1052) 1968) ((-907 . -172) T) ((-868 . -614) 1898) ((-1223 . -723) T) ((-1269 . -614) 1879) ((-1000 . -342) 1853) ((-997 . -514) 1786) ((-840 . -847) 1765) ((-564 . -1145) T) ((-474 . -290) 1716) ((-595 . -723) T) ((-361 . -611) 1698) ((-322 . -611) 1680) ((-418 . -1035) 1576) ((-594 . -723) T) ((-407 . -847) 1527) ((-169 . -111) 1423) ((-830 . -131) 1375) ((-734 . -151) 1359) ((-1259 . -309) 1297) ((-487 . -307) T) ((-379 . -611) 1264) ((-520 . -1007) 1248) ((-379 . -612) 1162) ((-217 . -307) T) ((-141 . -151) 1144) ((-711 . -286) 1123) ((-487 . -1019) T) ((-580 . -38) 1110) ((-564 . -38) 1097) ((-495 . -38) 1062) ((-217 . -1019) T) ((-868 . -1046) T) ((-833 . -611) 1044) ((-824 . -611) 1026) ((-822 . -611) 1008) ((-813 . -906) 987) ((-1283 . -1106) T) ((-1232 . -1052) 810) ((-852 . -1052) 794) ((-868 . -243) T) ((-868 . -233) NIL) ((-685 . -1209) T) ((-1283 . -23) T) ((-813 . -644) 719) ((-550 . -1209) T) ((-418 . -338) 703) ((-571 . -1052) 690) ((-1232 . -111) 499) ((-697 . -637) 481) ((-852 . -111) 460) ((-381 . -23) T) ((-169 . -614) 238) ((-1182 . -514) 30) ((-658 . -1094) T) ((-677 . -1094) T) ((-672 . -1094) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index ecefc886..f09aa508 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3449600528) -(4414 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3450528886) +(4415 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -477,661 +477,658 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |sech2cosh| |squareFreeFactors| |xn| |isPlus| - |finiteBasis| |rightFactorCandidate| |uniform01| |hermiteH| - |addPoint2| |getCode| |child| |alternatingGroup| |shade| |update| - |tryFunctionalDecomposition| |d01asf| |s17ajf| |getProperties| - |colorDef| |noLinearFactor?| |musserTrials| |algebraicDecompose| - |internalZeroSetSplit| |Lazard| |iiGamma| |simplifyLog| - |processTemplate| |e02akf| |vspace| |bivariate?| |reducedForm| - |countRealRoots| |character?| |complexEigenvectors| |fixedPointExquo| - |entry| |indicialEquationAtInfinity| |zeroMatrix| |d02cjf| - |OMParseError?| |port| |outputList| |sum| |setTopPredicate| - |integralLastSubResultant| |scripted?| |f2st| |makeFR| |birth| - |zeroDim?| |setMinPoints| |exquo| |opeval| |flexibleArray| - |mainMonomials| |largest| |singularitiesOf| |acoshIfCan| |freeOf?| - |BasicMethod| |gcdPrimitive| |t| |div| |B1solve| |position| - |UnVectorise| |dihedral| |patternVariable| |ord| |range| - |nextNormalPoly| |generic?| |rowEchelon| |multiset| |quo| |rischDE| - |squareFreePart| |extensionDegree| |leader| |indices| |paraboloidal| - |f02adf| |pointPlot| |stFunc1| |call| |byte| |roughBase?| - |antiCommutative?| |s19aaf| |partition| |lp| |safetyMargin| - |getExplanations| |s18aff| |OMReadError?| |rem| |euler| - |startTableInvSet!| |logpart| |extractClosed| |computeInt| - |mainSquareFreePart| |imagE| |removeRoughlyRedundantFactorsInPols| - |readInt8!| |merge!| |zero| |hasHi| |clipWithRanges| |df2st| - |taylorQuoByVar| |index| |components| |tryFunctionalDecomposition?| - |unrankImproperPartitions1| |rk4qc| |plotPolar| |selectAndPolynomials| - |int| |tablePow| |lfintegrate| |rootKerSimp| |e02def| |multiple?| - |firstDenom| |top| |possiblyInfinite?| |viewPosDefault| |And| - |primintegrate| |iiasin| |primaryDecomp| |s18adf| |extractPoint| - |f02awf| |multisect| |curveColorPalette| |term?| |Or| - |expenseOfEvaluationIF| |recur| |s21bcf| |pair| |henselFact| - |setPosition| |clipParametric| |inverseIntegralMatrixAtInfinity| - |showTheFTable| |cAsech| |Not| |tValues| F2FG |lambert| - |intPatternMatch| |d02gaf| |mat| |createPrimitivePoly| |bytes| - |setValue!| |value| |startPolynomial| |numerators| |maxrank| - |laplacian| |purelyTranscendental?| |scalarTypeOf| |virtualDegree| - |pole?| |quasiAlgebraicSet| |ramified?| |pureLex| BY |modularGcd| - |pquo| |pointSizeDefault| |every?| |component| |screenResolution| - |setRow!| |combineFeatureCompatibility| |normalForm| |rangeIsFinite| - |permutations| |besselJ| |stiffnessAndStabilityOfODEIF| - |leftExactQuotient| |cAcot| |maxIndex| |intermediateResultsIF| - |idealiser| |critBonD| |charClass| |factorset| |indicialEquations| - |interpret| |deepCopy| |constantCoefficientRicDE| |lastSubResultant| - |pow| |supersub| |checkPrecision| |complexExpand| |iipow| - |innerSolve1| |unitNormalize| |numberOfChildren| |internalIntegrate| - |nsqfree| |interReduce| |radicalSimplify| |generator| |cTan| - |discreteLog| |imagk| |pseudoQuotient| |numer| |sequences| - |antisymmetric?| |mightHaveRoots| |c05nbf| |headReduced?| - |symmetricSquare| |se2rfi| |sqfree| |atrapezoidal| |denom| |even?| - |lo| |e02aef| |factorSquareFreeByRecursion| |minGbasis| |f07fdf| - |e01sff| |f01rdf| |weighted| |completeEchelonBasis| |outputFloating| - |incr| |removeSuperfluousQuasiComponents| |coercePreimagesImages| - |extractSplittingLeaf| |getMatch| |monic?| |printingInfo?| |subSet| - |subresultantSequence| |realElementary| |pi| |socf2socdf| |d01gaf| - |subspace| |rk4a| |extendedSubResultantGcd| |invertIfCan| |f04qaf| - |max| LODO2FUN |leftRegularRepresentation| |forLoop| |infinity| - |d01fcf| |plusInfinity| |f02ajf| |quoted?| |legendre| - |LazardQuotient2| |OMputEndAtp| |enterInCache| |Frobenius| |diag| - |showTypeInOutput| |leftCharacteristicPolynomial| |minusInfinity| - |cylindrical| |firstUncouplingMatrix| |mainMonomial| - |setVariableOrder| ~ |meatAxe| |iisqrt3| |setScreenResolution3D| - |belong?| |hexDigit| |cosh2sech| |monicCompleteDecompose| - |branchPointAtInfinity?| |fullPartialFraction| |notelem| |nor| - |taylorRep| |associates?| |kernel| |coefChoose| |mkcomm| - |radicalEigenvalues| |s18aef| |chiSquare1| |open| |mapSolve| - |genericPosition| |leftMult| |relativeApprox| |draw| |unravel| - |s17adf| |coHeight| |simpsono| |autoReduced?| |id| |c06gsf| - |symmetricPower| |cyclicEntries| |inverseLaplace| |matrix| |permanent| - |useEisensteinCriterion| |OMputEndError| |rightOne| |goto| |init| - |argumentListOf| |factorial| |functionIsFracPolynomial?| |f02bbf| - |type| |intersect| |df2fi| |algint| |subNode?| |diagonals| |table| - |enqueue!| |shellSort| |expandLog| |simpleBounds?| |ode1| - |strongGenerators| |odd?| |f02wef| |setStatus!| |operations| |new| - |viewWriteAvailable| |getStream| |s17agf| |sub| |makeObject| - |reciprocalPolynomial| |palgint| |primPartElseUnitCanonical| - |shallowCopy| |e02adf| |s21bbf| |search| |pushNewContour| |arbitrary| - |generalLambert| |legendreP| |normalElement| |bandedJacobian| |hi| - |f01qcf| |split| |leftRemainder| |clikeUniv| |measure| - |basisOfNucleus| |readUInt8!| |explicitlyEmpty?| |symbolTable| |coef| - |regularRepresentation| |elliptic| |lfextlimint| |reorder| - |SturmHabichtCoefficients| |untab| |acosIfCan| |integer?| |ratDsolve| - |monomRDEsys| |setleaves!| |rectangularMatrix| |inverse| |ode| - |flagFactor| |rightRank| |numberOfDivisors| |infiniteProduct| - |clearCache| |uncouplingMatrices| |skewSFunction| |checkRur| - |outlineRender| = |cot2trig| |chainSubResultants| |droot| |f04axf| - |isExpt| |shiftLeft| |linkToFortran| |omError| |packageCall| - |binaryFunction| |graeffe| |linearPart| |compound?| |ref| - |polynomialZeros| |edf2ef| |powerAssociative?| |linearDependence| < - |normalise| |variable?| |setImagSteps| |column| |OMconnOutDevice| - |fi2df| |branchPoint?| |monomialIntPoly| |numFunEvals3D| > - |signatureAst| |setProperty| |iicsc| |box| |oddlambert| |vector| - |numberOfCycles| |yellow| |rischNormalize| - |rightRegularRepresentation| |OMgetObject| |explogs2trigs| <= - |sin2csc| |reseed| |showTheSymbolTable| |iisqrt2| |reify| - |integralCoordinates| |makeTerm| |hconcat| |viewZoomDefault| >= - |removeRoughlyRedundantFactorsInPol| |child?| |e04jaf| |f02akf| - |transcendenceDegree| |getIdentifier| |presub| |s18def| - |trivialIdeal?| |rightExtendedGcd| |pToDmp| |quotedOperators| - |positive?| |endOfFile?| |normInvertible?| ~= |charpol| - |jacobiIdentity?| |coefficient| |e04naf| |algebraicCoefficients?| - |isQuotient| |factorPolynomial| |commutator| - |indiceSubResultantEuclidean| |associatedSystem| |coerce| - |trailingCoefficient| |wronskianMatrix| |normalizedAssociate| - |generalInfiniteProduct| |decompose| + |superscript| |chebyshevT| - |bat| |anticoord| |construct| |sPol| |elRow2!| |norm| - |maximumExponent| |OMgetAtp| |OMputBVar| - |unexpand| |cycles| - |minRowIndex| |rotatex| |factorByRecursion| - |setLegalFortranSourceExtensions| |numericIfCan| |integralBasis| - |unaryFunction| / |writeUInt8!| |e02bbf| |univariateSolve| |unary?| - |quotientByP| |leastAffineMultiple| |semiSubResultantGcdEuclidean1| - |genericRightTrace| |GospersMethod| |listBranches| |extractTop!| - |df2mf| |comment| |OMputAtp| |idealiserMatrix| |copies| |zCoord| - |OMputString| |create3Space| |height| |roughBasicSet| |movedPoints| - |lowerCase| |clip| |extendedint| |monicRightDivide| |innerSolve| - |head| |lists| |newLine| |digits| |adjoint| |operator| |nextPartition| - |hermite| |internalAugment| |stoseInvertible?reg| |decomposeFunc| - |complexElementary| |inspect| |genus| |Is| |constantOperator| - |nextsubResultant2| |setProperties| |stop| |unitCanonical| - |lexGroebner| |checkForZero| |balancedBinaryTree| |viewDeltaXDefault| - |collect| |llprop| |sizeMultiplication| |myDegree| |deleteRoutine!| - |associator| |eigenvector| |var2StepsDefault| |mainVariable?| - |nullary?| |stopTableGcd!| |basisOfLeftAnnihilator| |bright| - |showIntensityFunctions| |toseInvertible?| |HenselLift| |cycle| - |ParCond| |weakBiRank| |rightPower| - |solveLinearPolynomialEquationByFractions| |totalDifferential| - |cyclic?| |solveLinearPolynomialEquationByRecursion| |collectUnder| - |rightDiscriminant| |squareFreePolynomial| |move| |leftScalarTimes!| - |output| |tubeRadius| |sn| |nextNormalPrimitivePoly| |randnum| - |drawCurves| |isConnected?| |setelt| |tail| |stirling1| |sayLength| - |interactiveEnv| |normalizedDivide| |setright!| |iterationVar| - |perfectSquare?| |evenlambert| |s17dhf| |OMputAttr| |minordet| - |usingTable?| |OMmakeConn| |OMunhandledSymbol| |optpair| |identity| - |copy| |c06gqf| |contractSolve| |nand| |addmod| |currentEnv| - |infieldIntegrate| |OMUnknownCD?| |remove!| |prinb| |makeUnit| - |showClipRegion| |tanintegrate| |prem| |diophantineSystem| |mainValue| - |style| |definingPolynomial| |OMgetString| |seed| |error| |OMreceive| - |numberOfFactors| |lazyEvaluate| |selectPDERoutines| |autoCoerce| - |rightScalarTimes!| |recip| |exists?| |stoseIntegralLastSubResultant| - |infinityNorm| |super| |lazyIrreducibleFactors| |inverseColeman| - |options| |assert| |nthRoot| |OMserve| |simplifyPower| |discriminant| - |binomial| |stronglyReduced?| |credPol| |atanhIfCan| - |viewThetaDefault| |overbar| |froot| |startStats!| |initTable!| - |setOrder| |elRow1!| |unit| |fibonacci| |drawComplex| |multiEuclidean| - |li| |pack!| |semiDiscriminantEuclidean| |numerator| |besselY| - |divide| |rename!| |string| |ran| |iiperm| |isTimes| |characteristic| - |failed| |getOperator| |cCot| |sortConstraints| |partitions| - |completeSmith| |parametersOf| |medialSet| |normalDenom| |f04arf| - |resultantEuclidean| |c06ekf| |rationalIfCan| |compose| - |parabolicCylindrical| |solveInField| |parabolic| |prefixRagits| - |evaluate| |radPoly| |decrease| - |rewriteSetByReducingWithParticularGenerators| |updateStatus!| - |duplicates?| |primitiveElement| |useNagFunctions| |matrixGcd| - |OMconnInDevice| |term| |jordanAlgebra?| |shuffle| |lexTriangular| - |clipPointsDefault| |mdeg| |useEisensteinCriterion?| - |expressIdealMember| |fractionPart| |difference| |FormatArabic| - |startTable!| |numberOfVariables| |iiacosh| |delete| |OMgetEndAttr| - |universe| |readInt16!| |nthCoef| |retractIfCan| |calcRanges| - |doubleComplex?| |abs| |getVariableOrder| |submod| |repeating?| - |zeroVector| |readByte!| |mainVariable| |coord| |sh| - |integralAtInfinity?| |palginfieldint| |c05pbf| |OMcloseConn| - |commaSeparate| |integralDerivationMatrix| |iiasinh| - |symmetricDifference| |integralBasisAtInfinity| |digit?| |elliptic?| - |withPredicates| |leftOne| |moduleSum| |drawStyle| |swap| - |stoseLastSubResultant| |factorsOfCyclicGroupSize| |LyndonWordsList1| - |s17aff| |qPot| |quasiRegular?| |totalfract| |newTypeLists| UP2UTS - |equivOperands| |outputMeasure| |exponentialOrder| - |noncommutativeJordanAlgebra?| |inputBinaryFile| |generalPosition| - |quartic| |depth| |quasiComponent| |rightZero| |commutative?| - |exprToXXP| |numberOfIrreduciblePoly| |quasiMonicPolynomials| - |retract| |prindINFO| |dAndcExp| |groebner| |unparse| - |inputOutputBinaryFile| |d02kef| |factorials| |c06ebf| - |changeThreshhold| |palgintegrate| |zeroDimensional?| |eq| - |symbolTableOf| |rationalPoints| |symmetricGroup| |expintegrate| - |part?| |map| |cRationalPower| |fortranLiteral| |prod| |iter| - |resultantReduit| |leastPower| |vark| |constantIfCan| |d01aqf| - |condition| |mapGen| |coerceP| |lfunc| |graphImage| - |purelyAlgebraicLeadingMonomial?| |insert!| |listOfMonoms| - |endSubProgram| |setOfMinN| |logGamma| |numberOfComponents| - |maxColIndex| |push| |e02agf| |generate| |rootPower| |deriv| - |coerceImages| |solveLinearPolynomialEquation| |unmakeSUP| - |createMultiplicationMatrix| |isList| |stoseInternalLastSubResultant| - |f04mcf| |selectIntegrationRoutines| |minPoints3D| |quadratic?| - |leftFactor| |contract| |incrementBy| |reducedDiscriminant| - |hitherPlane| |complexZeros| |lineColorDefault| |convert| - |getMultiplicationMatrix| |mappingAst| |setPrologue!| |meshPar2Var| - |mapCoef| |cSin| |expand| |sparsityIF| |lexico| |mantissa| - |fortranDoubleComplex| |float| |intChoose| |explicitlyFinite?| - |geometric| |secIfCan| |filterWhile| |pointColorDefault| |jacobian| - |cycleRagits| |palgint0| |option?| |limitPlus| |cAsec| |exp| - |setprevious!| |outputArgs| |filterUntil| |iidsum| |iiasech| - |qualifier| |leadingIdeal| |mainCharacterization| |approximants| - |OMgetAttr| |zeroSetSplitIntoTriangularSystems| |select| |cardinality| - |const| SEGMENT |setFieldInfo| |subHeight| |bernoulliB| - |clearTheSymbolTable| |hdmpToDmp| |stirling2| |d03faf| |linearMatrix| - |modifyPointData| |testDim| |divideIfCan| |bitTruth| |twoFactor| - |generalizedInverse| |SFunction| |complex?| |primeFrobenius| - |commutativeEquality| |log| |jordanAdmissible?| |cCosh| |arity| - |primitivePart| |bitCoef| |addPoint| |transform| |coerceL| - |OMgetEndBVar| |bothWays| |triangular?| |fmecg| |drawToScale| |leaf?| - |functionIsContinuousAtEndPoints| |s15aef| |refine| - |fortranCarriageReturn| |OMgetInteger| |primitivePart!| - |setButtonValue| |pushuconst| |lookup| |redmat| |ipow| GE |power| - |monicDecomposeIfCan| |fortranTypeOf| |iiatanh| |makeRecord| |exprex| - |pointColor| |extendedIntegrate| |datalist| |compile| |dequeue!| GT - |basisOfLeftNucleus| |selectfirst| |generators| - |getMultiplicationTable| |prologue| |btwFact| |f01qdf| |outputFixed| - LE |inverseIntegralMatrix| |hostPlatform| |atom?| |any?| |e04gcf| - |pmintegrate| |lazyPseudoDivide| |compBound| LT |hostByteOrder| - |tanh2trigh| |f01qef| |addMatchRestricted| |monomRDE| |readBytes!| - |viewPhiDefault| |showScalarValues| |factor1| |printInfo!| |times| - |rewriteIdealWithRemainder| |branchIfCan| |createThreeSpace| - |applyRules| |central?| |revert| |exponential1| |order| - |createLowComplexityTable| |directory| |pointColorPalette| |polygon| - |balancedFactorisation| |createLowComplexityNormalBasis| |nil| - |precision| |bivariatePolynomials| |setPredicates| |node?| |poisson| - |cLog| |rowEchelonLocal| |f01maf| |property| |permutationGroup| |comp| - |OMgetBVar| |drawComplexVectorField| |completeEval| |pToHdmp| |rotate| - |powerSum| |copyInto!| |setelt!| |consnewpol| |colorFunction| - |littleEndian| |leftDiscriminant| |monom| |setrest!| |cycleTail| - |nary?| |addMatch| |clipBoolean| |invertibleSet| |approximate| - |multiplyExponents| |reducedContinuedFraction| |genericLeftNorm| - |LazardQuotient| |isOp| |complex| |trace2PowMod| |nextIrreduciblePoly| - |s14baf| |f01rcf| |units| |inc| |resetBadValues| - |currentCategoryFrame| |permutation| |monicRightFactorIfCan| |gderiv| - |symbolIfCan| |collectUpper| |expenseOfEvaluation| - |halfExtendedSubResultantGcd1| |times!| |toScale| |alternative?| - |common| |groebnerIdeal| |basisOfCenter| |reflect| |copy!| |addiag| - |totalGroebner| |zag| |isAbsolutelyIrreducible?| |tensorProduct| - |absolutelyIrreducible?| |toseSquareFreePart| |att2Result| - |OMputEndBind| |digit| |localReal?| |elseBranch| |c02agf| - |exactQuotient| |find| |separateFactors| |initial| |listYoungTableaus| - |loadNativeModule| |exprHasWeightCosWXorSinWX| |setProperties!| - |systemSizeIF| |key| |reindex| |code| |mr| |cycleLength| - |physicalLength| |d01bbf| |setLabelValue| |remove| |pdf2ef| |s17def| - |factors| |compdegd| |definingEquations| |infinite?| |rightRemainder| - |tree| |cAcsc| |OMreadFile| |returnType!| |filename| |schema| - |numericalOptimization| |prepareSubResAlgo| |isMult| |last| |argument| - |curry| |not?| |algebraicVariables| |complexSolve| |OMgetSymbol| - |nonLinearPart| |radicalSolve| |assoc| |antisymmetricTensors| - |function| |iiasec| |subscript| |predicates| |parse| |multinomial| - |genericLeftDiscriminant| |exprToUPS| |bombieriNorm| - |representationType| |any| |biRank| |mapBivariate| |whitePoint| - |clearTheIFTable| |Hausdorff| |npcoef| |optimize| |leftExtendedGcd| - |backOldPos| |eval| |isOpen?| |ratPoly| |hspace| |dflist| |mesh| - |characteristicSet| |gradient| |normalized?| |symbol?| |OMgetEndApp| - |makeSUP| |one?| |OMsupportsCD?| |expint| |hMonic| |divergence| - |primes| |unknownEndian| |mathieu24| |basisOfRightNucleus| |iicsch| - |showSummary| |createMultiplicationTable| |minPoly| |purelyAlgebraic?| - |numberOfPrimitivePoly| |toseInvertibleSet| |setCondition!| |separate| - |nextPrimitivePoly| |whatInfinity| |pushucoef| |totolex| |psolve| - |quatern| |float?| |showAttributes| |deleteProperty!| |relerror| - |f04jgf| |dmp2rfi| |boundOfCauchy| |stFuncN| |Ci| |closedCurve| - |perfectSqrt| |setAttributeButtonStep| |plot| - |rewriteIdealWithQuasiMonicGenerators| |basisOfCommutingElements| - |comparison| |minPol| |scalarMatrix| |c06frf| |setRealSteps| - |argscript| |exprHasAlgebraicWeight| |userOrdered?| |cAtanh| - |splitNodeOf!| |f04maf| |s19adf| |rk4| |substring?| |primlimitedint| - |radicalRoots| |linSolve| |RemainderList| |polarCoordinates| |d01apf| - |concat!| |cscIfCan| |makingStats?| |getlo| |e02bdf| - |leadingBasisTerm| |palgextint0| |in?| |midpoint| |zeroOf| |lcm| - |cyclicCopy| |suffix?| |setref| |subResultantGcdEuclidean| - |nextLatticePermutation| |sort| |OMputEndAttr| |trunc| |f02xef| - |laurentRep| |iiacoth| |changeName| |generalizedEigenvectors| - |conjugate| |oddintegers| 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|trace| |reverse| |plus!| - |e02ahf| |triangSolve| |rootSplit| |e02ddf| |smith| |ListOfTerms| - |cAcoth| |indicialEquation| |createPrimitiveElement| |sin| |rCoord| - |patternMatchTimes| |associative?| |palgRDE0| |rootBound| |OMputBind| - |leftAlternative?| |delay| |solid| |c06gbf| |next| |cos| |ef2edf| - |quotient| |truncate| |leftRankPolynomial| |eof?| |e| |OMgetBind| - |exponent| |cSec| |fglmIfCan| |host| |csch2sinh| |tan| |reduction| - |csubst| |label| |minrank| |s13acf| |asimpson| |e02daf| |sample| - |failed?| |denominator| |exprToGenUPS| |subresultantVector| |cot| - |basisOfRightNucloid| |d01amf| |setvalue!| |probablyZeroDim?| - |getOrder| |critM| |computeCycleLength| |true| |s01eaf| |po| - |HermiteIntegrate| |radicalEigenvectors| |sec| |debug3D| |lllp| - |quoByVar| |pile| |stoseInvertibleSet| |dictionary| |problemPoints| - |ip4Address| |iiacot| |halfExtendedResultant1| |csc| |arrayStack| - |ranges| |genericLeftTrace| |c02aff| |denominators| |Lazard2| |f01bsf| - |limit| |nullSpace| |distFact| |makeResult| |asin| |hash| |iicoth| - |makeop| |asecIfCan| |areEquivalent?| |decreasePrecision| |pol| - |removeCosSq| |innerint| |trigs| |changeNameToObjf| |lazyVariations| - |acos| |count| |recolor| |members| |perfectNthPower?| |prime| |conjug| - |viewport3D| |bezoutResultant| |symmetricRemainder| |imagJ| |exp1| - |middle| |atan| |rightRecip| |minimumDegree| |bubbleSort!| |sincos| - |doubleFloatFormat| |stoseInvertible?| |basisOfRightAnnihilator| - |gcdprim| |constructor| |distance| |relationsIdeal| |fTable| |acot| - |divisorCascade| |cyclePartition| |f04mbf| |asechIfCan| |empty| - |closeComponent| |e01bgf| |leaves| |multiplyCoefficients| |dimension| - |inf| |reverse!| |tower| |asec| |option| |harmonic| |fintegrate| - |changeVar| |pair?| |getSyntaxFormsFromFile| |findCycle| |infRittWu?| - |degreePartition| |showArrayValues| |red| |invertibleElseSplit?| - |acsc| |modTree| |powern| |directSum| |swapColumns!| |pleskenSplit| - |resetNew| |initiallyReduce| |optional?| |sturmSequence| - |explimitedint| |LowTriBddDenomInv| |sinh| |symmetricProduct| - |removeZeroes| |s17akf| |diagonal?| |ptFunc| |implies| |OMwrite| - |setClipValue| |mesh?| |imaginary| |nthFlag| |cosh| |cup| |read!| - |f07adf| |realEigenvalues| |maxRowIndex| |insertionSort!| - |oblateSpheroidal| |leftTrace| |cAsinh| |lazyPseudoRemainder| - |constantRight| |postfix| |tanh| |doubleResultant| |irreducible?| - |midpoints| |gethi| |numberOfImproperPartitions| |assign| - |roughSubIdeal?| |iisec| |increasePrecision| |polyRDE| |ReduceOrder| - |complexNumeric| |companionBlocks| |coth| |rightTrim| |binding| - |bottom!| |brillhartIrreducible?| |fortranLogical| - |sumOfKthPowerDivisors| |tubePointsDefault| |leadingIndex| |curryLeft| - |OMputSymbol| |or?| |readIfCan!| |s13adf| |SturmHabichtMultiple| - |sech| |leftTrim| |exponential| |subtractIfCan| |exportedOperators| - |orbit| |rroot| |realRoots| |basis| |mapUp!| |kernels| |continue| - |routines| |commonDenominator| |minset| |univariatePolynomial| |csch| - |rules| |unknown| |polCase| |selectMultiDimensionalRoutines| - |unprotectedRemoveRedundantFactors| |hue| |stosePrepareSubResAlgo| - |imagK| |identityMatrix| |rootProduct| |intcompBasis| |PDESolve| - |headRemainder| |asinh| |univariate| |test| |iiacsc| |trapezoidal| - |prepareDecompose| |realZeros| |dmpToP| |selectNonFiniteRoutines| - |has?| |binary| |orbits| |nextsousResultant2| |zero?| |acosh| - |predicate| |leftUnit| |atanIfCan| |squareFree| |partialFraction| - |exactQuotient!| |aQuartic| |basisOfCentroid| |multiEuclideanTree| - |partialDenominators| NOT |supRittWu?| |tubeRadiusDefault| |atanh| - |doubleRank| |stronglyReduce| |enterPointData| |shiftRight| |c06fuf| - |traverse| |rootRadius| |univcase| |prefix| |inconsistent?| OR - |computePowers| |d03edf| |acoth| |factor| |leviCivitaSymbol| - |frobenius| |leftNorm| |cAtan| |setnext!| |merge| |appendPoint| - |OMputVariable| AND |showRegion| |OMgetType| |localIntegralBasis| - |sqrt| |asech| |irreducibleRepresentation| |modulus| |normalizeIfCan| - |Ei| |fortranLinkerArgs| |tab| |dominantTerm| |safeFloor| |chebyshevU| - |integral?| |rangePascalTriangle| |real| |rotatez| |inRadical?| - |unit?| |quasiRegular| |pattern| |showAll?| |makeViewport2D| - |cschIfCan| |s18acf| |rename| |powmod| |qqq| |imag| |multiple| - |fixedPoints| |tubePlot| |minimumExponent| |meshFun2Var| - |karatsubaOnce| |leftDivide| |newSubProgram| |badValues| - |highCommonTerms| |errorInfo| |pade| |equiv| |directProduct| - |applyQuote| |s14abf| |nextPrimitiveNormalPoly| |f02abf| |increment| - |minIndex| |airyAi| |cot2tan| |createNormalPrimitivePoly| |log10| - |mapUnivariate| |positiveRemainder| |An| |crest| |gbasis| - |expandTrigProducts| |nextPrime| |scan| |testModulus| |rightMult| - |bitand| |mainDefiningPolynomial| |e04ycf| |wrregime| |ldf2lst| - |quickSort| |brace| |iisinh| |parameters| |rightRankPolynomial| - |twist| |message| |lazyResidueClass| |vertConcat| |rowEch| |s21baf| - |bitior| |lSpaceBasis| |OMgetEndAtp| |integralMatrix| |e04mbf| - |destruct| |ruleset| |contains?| |corrPoly| |coordinate| |powers| - |f04asf| |characteristicSerie| |extractBottom!| - |wordsForStrongGenerators| |univariatePolynomialsGcds| |writable?| - |getGoodPrime| |f07aef| |number?| |OMreadStr| |nthr| - |particularSolution| |cycleEntry| |inGroundField?| - |removeRedundantFactorsInPols| |real?| |restorePrecision| |f04adf| - |monicLeftDivide| |getButtonValue| |newReduc| |vectorise| |ODESolve| * - |listRepresentation| |algintegrate| |d01alf| |suchThat| - |divideExponents| |iitanh| |reduceLODE| |iprint| |shallowExpand| - |green| |meshPar1Var| |graphCurves| |mapExpon| |string?| |monomial| - |rdHack1| |outerProduct| |overset?| |clearDenominator| |d02raf| - |oneDimensionalArray| |moebius| |sizePascalTriangle| |setAdaptive| - |cosIfCan| |cons| |multivariate| |dot| |variationOfParameters| - |functionIsOscillatory| |rombergo| |outputBinaryFile| |cartesian| - |divideIfCan!| |s20adf| |extractIfCan| |linear| |normalize| |create| - |variables| |countable?| |tanAn| |elColumn2!| |cyclicParents| |bfKeys| - |lowerPolynomial| |roughUnitIdeal?| |chineseRemainder| - |dimensionOfIrreducibleRepresentation| |cAcos| - |lastSubResultantElseSplit| |polar| |delete!| |axes| |key?| |zerosOf| - |signature| |complexLimit| |acothIfCan| |OMputEndBVar| |polynomial| - |numberOfComposites| |typeList| |select!| |seriesSolve| |groebSolve| - |c05adf| |iroot| |rootSimp| |torsion?| |extension| |latex| Y - |splitConstant| |superHeight| |xCoord| |cycleSplit!| - |toseLastSubResultant| |zeroSquareMatrix| |c06fqf| - |cyclotomicFactorization| |makeEq| |ode2| |invertible?| |lllip| |hex| - |polyPart| |cfirst| |hasSolution?| |semiLastSubResultantEuclidean| - |coleman| |source| |taylor| |rank| |objectOf| |ramifiedAtInfinity?| - |nullity| |prevPrime| |arguments| |space| |neglist| |youngGroup| - |invmod| |nativeModuleExtension| |laurent| |makeGraphImage| - |trigs2explogs| |trapezoidalo| |lazyPremWithDefault| |identification| - |null| |shiftRoots| |OMopenString| |OMgetApp| |e02zaf| - |semiResultantEuclidean1| |arg1| |puiseux| |normalDeriv| - |selectOptimizationRoutines| |laguerreL| |and?| |leftLcm| |not| - |s17acf| |exponents| |presuper| |s21bdf| |root?| |arg2| - |constantOpIfCan| |startTableGcd!| |bumptab1| |coefficients| - |rubiksGroup| |and| |resultant| |eulerPhi| |reduced?| - |generateIrredPoly| |mpsode| |inv| |nextSubsetGray| |completeHensel| - |cap| |imagi| |or| |linearPolynomials| |integralRepresents| - |leftUnits| |physicalLength!| |duplicates| |redpps| |target| |ground?| - |conditions| |check| |eisensteinIrreducible?| |nextSublist| - |modularGcdPrimitive| |xor| |inHallBasis?| |mainKernel| |OMgetFloat| - UTS2UP |numFunEvals| |factorSFBRlcUnit| |ground| |match| - |systemCommand| |qinterval| |ellipticCylindrical| |primeFactor| - |maxPoints| |case| |conjugates| |safeCeiling| |setClosed| |write!| - |sorted?| |leadingMonomial| |lhs| |csc2sin| |semiResultantEuclidean2| - |RittWuCompare| |maxint| |Zero| |setfirst!| |UP2ifCan| |equiv?| - |nodes| |clipSurface| |leadingCoefficient| |rhs| |solve| |coth2trigh| - |One| |wholePart| |chvar| |frst| |infLex?| |simpson| - |OMUnknownSymbol?| |primitiveMonomials| |pdf2df| |normal| - |factorOfDegree| |connect| |conditionsForIdempotents| - |createGenericMatrix| |kroneckerDelta| |c06ecf| |mainVariables| - |tan2trig| |ravel| |reductum| |cCsch| |reducedQPowers| |rightTrace| - |primextintfrac| |iisin| |e04fdf| |bat1| |f02agf| |controlPanel| - |reshape| |rootOfIrreduciblePoly| |lift| |euclideanNormalForm| - |iFTable| |lyndon| |elem?| |name| |initializeGroupForWordProblem| - |sinhIfCan| |pushdown| |reduce| |solve1| |impliesOperands| |sechIfCan| - |mkAnswer| |aspFilename| |totalLex| |body| |numeric| |ParCondList| - |typeLists| |limitedint| |f01ref| |gramschmidt| |logical?| |elt| - |gcdcofact| |lifting| |removeRoughlyRedundantFactorsInContents| - |radical| |contours| |unvectorise| |zeroSetSplit| |d01ajf| |badNum| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |Record| |Union| |simpleBounds?| |nonSingularModel| |units| |inv| + |monomRDE| |minimize| |univariatePolynomial| |internalSubPolSet?| + |stronglyReduced?| |removeSuperfluousCases| |open?| |leftUnits| + |ground?| |ode1| |readBytes!| |color| |polCase| |transcendent?| + |domainOf| |credPol| |selectODEIVPRoutines| |defineProperty| + |physicalLength!| |rischDE| |ground| |useSingleFactorBound?| + |strongGenerators| |port| |viewPhiDefault| |setPoly| + |selectMultiDimensionalRoutines| |s17dcf| |atanhIfCan| |iiabs| + |mapmult| |duplicates| |squareFreePart| |odd?| |leadingMonomial| + |showScalarValues| |besselK| |unprotectedRemoveRedundantFactors| + |elements| |resetAttributeButtons| |viewThetaDefault| |cAsin| |index?| + |redpps| |factorsOfDegree| |factor1| |f02wef| |cyclotomic| |t| + |leadingCoefficient| |hue| |exquo| |bipolarCylindrical| |overbar| + |key| |OMencodingSGML| |conditionP| |code| |check| |arg1| |d02bbf| + |div| |setStatus!| |primitiveMonomials| |printInfo!| + |stosePrepareSubResAlgo| |mindeg| |basisOfLeftNucloid| |froot| + |mainPrimitivePart| |nextNormalPoly| |symmetricTensors| + |eisensteinIrreducible?| |groebgen| |arg2| |quo| |viewWriteAvailable| + |rewriteIdealWithRemainder| |reductum| |imagK| |bumptab| + |homogeneous?| |filename| |subMatrix| |polygamma| |startStats!| + |generic?| |printInfo| |nextSublist| |getStream| |bracket| + |branchIfCan| |identityMatrix| |removeCoshSq| |antiCommutator| |not?| + |initTable!| |showFortranOutputStack| |internalInfRittWu?| + |modularGcdPrimitive| |rootProduct| |exptMod| |s17agf| |rem| + |createThreeSpace| |infix| |conditions| |dimensionsOf| |parse| + |setOrder| |createZechTable| |e04dgf| |inHallBasis?| |applyRules| + |sub| |intcompBasis| |upperCase!| |inR?| |match| |scopes| |elRow1!| + |optAttributes| |expintfldpoly| |mainKernel| |reciprocalPolynomial| + |central?| |eigenvalues| |pomopo!| |PDESolve| |unit| |quadratic| |Nul| + |d02bhf| |OMgetFloat| |palgint| |leftZero| |revert| |OMclose| + |headRemainder| |differentialVariables| |fibonacci| |sequence| + |f07fef| UTS2UP |alphanumeric| |primPartElseUnitCanonical| + |partialQuotients| |exponential1| |iiacsc| |substring?| |drawComplex| + |subNodeOf?| |log2| |modifyPoint| |numFunEvals| |showSummary| + |shallowCopy| |addBadValue| |order| |trapezoidal| |univariate?| + |multiEuclidean| |flexible?| |normalizeAtInfinity| |viewWriteDefault| + |parameters| |factorSFBRlcUnit| |createLowComplexityTable| |e02adf| + |adaptive| |semiResultantEuclideannaif| |prepareDecompose| |suffix?| + |pack!| |setMinPoints3D| |elementary| |matrixConcat3D| |qinterval| + |pointColorPalette| |showAttributes| |computeBasis| |realZeros| + |integers| |semiDiscriminantEuclidean| |sinhcosh| |f02aef| + |setMaxPoints3D| |ellipticCylindrical| |result| |headReduced?| + |linearAssociatedExp| |leftMinimalPolynomial| |polygon| |dmpToP| + |prefix?| |validExponential| |numerator| BY + |tableForDiscreteLogarithm| |fracPart| |primeFactor| |symmetricSquare| + |balancedFactorisation| |writeLine!| |reset| |selectNonFiniteRoutines| + |perspective| |changeMeasure| |besselY| |simplifyExp| |BumInSepFFE| + |maxPoints| |se2rfi| |createLowComplexityNormalBasis| + |rightExactQuotient| |has?| |operators| |linearAssociatedOrder| + |numberOfNormalPoly| |tryFunctionalDecomposition?| |conjugates| + |sqfree| |squareFreePrim| |bivariatePolynomials| |write| |binary| + |sylvesterSequence| |genus| |leftRecip| |e02dcf| + |unrankImproperPartitions1| |safeCeiling| + |removeRoughlyRedundantFactorsInPols| |atrapezoidal| |edf2efi| |save| + |zero| |setPredicates| |extendedEuclidean| |orbits| |Is| + |clearTheFTable| |rk4qc| |null?| |readInt8!| |setClosed| |even?| + |node?| |rootOf| |janko2| |nextsousResultant2| |constantOperator| + |plotPolar| |nthRootIfCan| |rootDirectory| |write!| |e02aef| |nothing| + |infix?| |And| |zero?| |coth2tanh| |nextsubResultant2| |var2Steps| + |selectAndPolynomials| |lazyIntegrate| |sorted?| + |factorSquareFreeByRecursion| |FormatRoman| |pointColorDefault| + |leftUnit| |Or| |mask| |cSech| |setProperties| |setColumn!| + |alphabetic| |tablePow| |csc2sin| |minGbasis| |jacobian| + |plusInfinity| |rewriteSetWithReduction| |Not| |hasoln| |atanIfCan| + |unitCanonical| |internalIntegrate0| |critMonD1| |lfintegrate| + |semiResultantEuclidean2| |dn| |f07fdf| |minusInfinity| |cycleRagits| + |alphanumeric?| |squareFree| |lexGroebner| |rootKerSimp| |rank| + |RittWuCompare| |e01sff| |palgint0| |cAcsch| |OMputObject| + |partialFraction| |checkForZero| |ratDenom| |splitNodeOf!| |e02def| + |maxint| |f01rdf| |option?| |d02ejf| |mkIntegral| |exactQuotient!| + |balancedBinaryTree| |principalAncestors| |f04maf| |width| |multiple?| + |setfirst!| |weighted| |repeating| |limitPlus| |hdmpToP| |aQuartic| + |viewDeltaXDefault| |palgRDE| |s19adf| |firstDenom| |UP2ifCan| + |completeEchelonBasis| |cAsec| |e02dff| |flatten| |collect| |rk4| + |diagonalMatrix| |possiblyInfinite?| |equiv?| |setprevious!| + |outputFloating| |type| |hclf| |inf| |adaptive?| |llprop| + |primlimitedint| |getBadValues| |viewPosDefault| |nodes| + |removeSuperfluousQuasiComponents| |outputArgs| + |characteristicPolynomial| |reverse!| |high| |bezoutDiscriminant| + |sizeMultiplication| |numer| |radicalRoots| |primintegrate| + |clipSurface| |iidsum| |coercePreimagesImages| |harmonic| |OMputError| + |vconcat| |hasHi| |iomode| |myDegree| |linSolve| |denom| |iiasin| + |extractSplittingLeaf| |iiasech| |resultantnaif| |shrinkable| + |fintegrate| |deleteRoutine!| |showAllElements| |RemainderList| + |primaryDecomp| |axes| |getMatch| |terms| |qualifier| |changeVar| + |digamma| |polarCoordinates| |sumSquares| |associator| |pi| |optional| + |key?| |s18adf| |monic?| |leadingIdeal| |d01gbf| |iisech| |pair?| + |eigenvector| |lepol| |d01apf| |infinity| |zerosOf| |extractPoint| ~ + |printingInfo?| |isPower| |mainCharacterization| |e02ajf| + |getSyntaxFormsFromFile| |var2StepsDefault| |lowerCase?| |concat!| + |complexLimit| |f02awf| |lift| |subSet| |approximants| + |lieAdmissible?| |lflimitedint| |findCycle| = |open| |mainVariable?| + |torsionIfCan| |cscIfCan| |acothIfCan| |multisect| |categories| + |reduce| |generator| |subresultantSequence| |OMgetAttr| |cyclicEqual?| + |infRittWu?| |solveLinearlyOverQ| |nullary?| |kernel| |denomRicDE| + |makingStats?| |curveColorPalette| |OMputEndBVar| |realElementary| + |writeInt8!| |zeroSetSplitIntoTriangularSystems| |degreePartition| + |OMputEndApp| < |draw| |stopTableGcd!| |getlo| |tanhIfCan| + |numberOfComposites| |term?| |socf2socdf| |cardinality| + |selectOrPolynomials| |semicolonSeparate| |showArrayValues| > + |basisOfLeftAnnihilator| |tracePowMod| |e02bdf| + |expenseOfEvaluationIF| |typeList| |d01gaf| |critMTonD1| |const| + |monomials| |red| <= |showIntensityFunctions| |leadingBasisTerm| + |s14aaf| |select!| |recur| |operations| |subspace| |setFieldInfo| + |subResultantChain| |invertibleElseSplit?| |bounds| >= + |toseInvertible?| |palgextint0| |pastel| |seriesSolve| |s21bcf| |rk4a| + |leftPower| |subHeight| |modTree| |lyndonIfCan| |makeObject| + |HenselLift| |in?| |rightQuotient| |groebSolve| |henselFact| + |extendedSubResultantGcd| |bernoulliB| |leftFactorIfCan| |ridHack1| + |powern| |cycle| |midpoint| |algebraicOf| |setPosition| |c05adf| + |clipWithRanges| |invertIfCan| |aromberg| |clearTheSymbolTable| + |constantKernel| |directSum| + |zeroOf| |ParCond| |coef| + |resultantEuclideannaif| |iroot| |clipParametric| |currentEnv| |df2st| + |f04qaf| |hdmpToDmp| |selectSumOfSquaresRoutines| |swapColumns!| + |region| - |weakBiRank| |rightUnits| |clearCache| |cyclicCopy| + |rootSimp| |inverseIntegralMatrixAtInfinity| |taylorQuoByVar| LODO2FUN + |stirling2| |someBasis| |pleskenSplit| |matrixDimensions| / + |rightPower| |setref| |roman| |showTheFTable| |torsion?| + |leftRegularRepresentation| |components| |d03faf| |pr2dmp| |rotate!| + |resetNew| |solveLinearPolynomialEquationByFractions| |listexp| + |subResultantGcdEuclidean| |extension| |cAsech| |byte| |forLoop| + |linearMatrix| |fortranLiteralLine| |octon| |initiallyReduce| + |totalDifferential| |concat| |cyclicGroup| |nextLatticePermutation| + |latex| |tValues| |d01fcf| |hessian| |modifyPointData| |optional?| + |tanNa| |cyclic?| |s17aef| |OMputEndAttr| |splitConstant| F2FG + |f02ajf| |rootPoly| |testDim| |sturmSequence| |aCubic| + |solveLinearPolynomialEquationByRecursion| |f01mcf| |trunc| + |superHeight| |lambert| |int| |quoted?| |asinhIfCan| |divideIfCan| + |explimitedint| |OMsupportsSymbol?| |collectUnder| + |clearFortranOutputStack| |f02xef| |intPatternMatch| |xCoord| + |bitTruth| |legendre| |bright| |viewpoint| |splitSquarefree| + |LowTriBddDenomInv| |rightDiscriminant| |low| |laurentRep| |d02gaf| + |cycleSplit!| |LazardQuotient2| |supDimElseRittWu?| |twoFactor| + |symmetricProduct| |indiceSubResultant| |squareFreePolynomial| + |iiacoth| |pushdterm| |mat| |toseLastSubResultant| |keys| |reverse| + |OMputEndAtp| |generalizedInverse| |prime?| |normal?| |removeZeroes| + |list| |move| |changeName| |is?| |zeroSquareMatrix| + |createPrimitivePoly| |enterInCache| |SFunction| |primitive?| |s17akf| + |root| |car| |leftScalarTimes!| |generalizedEigenvectors| + |sturmVariationsOf| |bytes| |c06fqf| |Frobenius| |complex?| + |bernoulli| |laplace| |diagonal?| |cdr| |tubeRadius| |conjugate| + |initiallyReduced?| |cyclotomicFactorization| |diag| |primeFrobenius| + |padicFraction| |ptFunc| |stoseInvertibleSetsqfreg| |setDifference| + |sn| |e01daf| |rule| |yRange| |oddintegers| |makeEq| + |showTypeInOutput| |commutativeEquality| |definingInequation| |escape| + |implies| |setIntersection| |declare| |printCode| + |nextNormalPrimitivePoly| |zRange| |outputForm| |ode2| + |leftCharacteristicPolynomial| |jordanAdmissible?| |rk4f| |OMwrite| + |minColIndex| |setUnion| |scaleRoots| |randnum| |map!| |retractable?| + |invertible?| |cylindrical| |cCosh| |primPartElseUnitCanonical!| + |setClipValue| |headAst| |apply| |partialNumerators| |qsetelt!| + |drawCurves| |error| |negative?| |lllip| |firstUncouplingMatrix| + |arity| |iteratedInitials| |vedf2vef| |mesh?| |isConnected?| + |subResultantsChain| |writeByte!| |assert| |hex| |mainMonomial| + |baseRDEsys| |primitivePart| |imaginary| |constant?| |size| + |stirling1| |computeInt| |dec| |solveRetract| |cos2sec| |polyPart| + |setVariableOrder| |bitCoef| |stoseInvertibleSetreg| |nthFlag| + |quasiMonic?| |sayLength| |prinpolINFO| |trueEqual| |cfirst| |meatAxe| + |bipolar| |addPoint| |cup| |sts2stst| |interactiveEnv| + |mainSquareFreePart| |minimalPolynomial| |c06gcf| |hasSolution?| + |iisqrt3| |leadingSupport| |transform| |read!| |goodnessOfFit| |first| + |minus!| |normalizedDivide| |imagE| |acsch| |getMeasure| + |semiLastSubResultantEuclidean| |properties| |constantToUnaryFunction| + |setScreenResolution3D| |bandedHessian| |coerceL| |f07adf| |failed| + |rest| |setright!| |s15adf| |aLinear| |coleman| |belong?| |translate| + |e01bhf| |OMgetEndBVar| |realEigenvalues| |nextColeman| |substitute| + |iterationVar| |multMonom| |OMgetEndError| |objectOf| |hexDigit| + |bothWays| |incrementKthElement| |fortranInteger| |maxRowIndex| + |removeDuplicates| |perfectSquare?| |beauzamyBound| |viewSizeDefault| + |ramifiedAtInfinity?| |say| |delete| |cosh2sech| |triangular?| + |LiePolyIfCan| |rewriteIdealWithHeadRemainder| |insertionSort!| + |evenlambert| |genericRightNorm| |UpTriBddDenomInv| |nullity| + |monicCompleteDecompose| |finiteBound| |fmecg| |oblateSpheroidal| + |algebraicSort| |s17dhf| |rotatey| |genericRightTraceForm| |prevPrime| + |drawToScale| |fixedDivisor| |lieAlgebra?| |leftTrace| |swapRows!| + |OMputAttr| |d01asf| |laguerre| |space| |setValue!| + |rightMinimalPolynomial| |leaf?| |toroidal| |cAsinh| |linGenPos| + |euler| |minordet| |s17ajf| |rightFactorIfCan| |neglist| + |startPolynomial| |functionIsContinuousAtEndPoints| + |removeRedundantFactors| |lazyPseudoRemainder| |nlde| |getProperties| + |startTableInvSet!| |usingTable?| |d03eef| |e01sbf| |youngGroup| + |numerators| |size?| |s15aef| |constantRight| |changeBase| + |signAround| |colorDef| |bumprow| |invmod| |maxrank| |refine| + |setEmpty!| |postfix| |symFunc| |superscript| |noLinearFactor?| + |unitNormal| |curve| |nativeModuleExtension| |laplacian| |iibinom| + |fortranCarriageReturn| |doubleResultant| |f04faf| |chebyshevT| + |musserTrials| |KrullNumber| |extractProperty| |makeGraphImage| + |purelyTranscendental?| |OMgetInteger| |composites| |irreducible?| + |more?| |match?| |bat| |algebraicDecompose| |crushedSet| + |currentSubProgram| |trigs2explogs| |scalarTypeOf| |totalDegree| + |midpoints| |anticoord| |prinshINFO| |listConjugateBases| + |internalZeroSetSplit| |trapezoidalo| |virtualDegree| |double| + |generic| |symmetricGroup| |gethi| |square?| |sPol| + |pushFortranOutputStack| |integerIfCan| |f02bjf| |Lazard| + |lazyPremWithDefault| |pole?| |expintegrate| |mainExpression| + |differentiate| |numberOfImproperPartitions| |lprop| |elRow2!| + |popFortranOutputStack| |iiGamma| |imports| |pmComplexintegrate| + |identification| |quasiAlgebraicSet| |findBinding| |part?| |eulerE| + |assign| |norm| |logpart| |ramified?| |simplifyLog| |shiftRoots| + |constant| |cRationalPower| |retractIfCan| |viewport2D| |debug| + |derivationCoordinates| |roughSubIdeal?| |ratPoly| |maximumExponent| + |extractClosed| |complexNormalize| |processTemplate| |OMopenString| + |fortranLiteral| |pureLex| |useSingleFactorBound| D |iisec| |Beta| + |createNormalPoly| |OMgetAtp| |hspace| |float| |e02akf| |OMgetApp| + |modularGcd| |prod| |selectPolynomials| |increasePrecision| + |wholeRagits| |OMputBVar| |dflist| |sinIfCan| |vspace| |e02zaf| |pquo| + |monomialIntegrate| |resultantReduit| |unexpand| |deref| |mesh| + |outputAsFortran| |bivariate?| |leastPower| |semiResultantEuclidean1| + |declare!| |pointSizeDefault| |ip4Address| |selectFiniteRoutines| + |/\\| |halfExtendedResultant2| |level| |cycles| |blankSeparate| + |characteristicSet| |reducedForm| |normalDeriv| |associatedEquations| + |every?| |iiacot| |vark| |anfactor| |\\/| |minRowIndex| |gradient| + |front| |countRealRoots| |selectOptimizationRoutines| |component| + |constantIfCan| |fractRagits| |halfExtendedResultant1| |listLoops| + |rotatex| |fractionFreeGauss!| |normalized?| |character?| + |screenResolution| |d01aqf| |composite| |arrayStack| |subset?| + |factorByRecursion| |log| |fixPredicate| |symbol?| + |complexEigenvectors| |inGroundField?| |setRow!| |fprindINFO| |mapGen| + |map| |ranges| |karatsubaDivide| |setLegalFortranSourceExtensions| + |localAbs| |OMgetEndApp| |removeRedundantFactorsInPols| + |fixedPointExquo| |combineFeatureCompatibility| |equality| |coerceP| + |genericLeftTrace| |lfinfieldint| |numericIfCan| GE |splitDenominator| + |makeSUP| |real?| |indicialEquationAtInfinity| |lfunc| |normalForm| + |nthFractionalTerm| |print| |c02aff| |getPickedPoints| |entry?| + |integralBasis| |one?| GT |zeroMatrix| |restorePrecision| + |rangeIsFinite| |rightNorm| |segment| |graphImage| |resolve| + |denominators| |removeConstantTerm| |unaryFunction| |OMsupportsCD?| + |radicalEigenvector| LE |d02cjf| |f04adf| |permutations| + |purelyAlgebraicLeadingMonomial?| |extendIfCan| |exteriorDifferential| + |Lazard2| |node| |writeUInt8!| |expint| LT |unitVector| + |OMParseError?| |monicLeftDivide| |categoryFrame| |heapSort| + |mantissa| |besselJ| |insert!| |convert| |f01bsf| |retract| |e02bbf| + |hMonic| |stFunc2| |getButtonValue| |setTopPredicate| + |stiffnessAndStabilityOfODEIF| |bitLength| |listOfMonoms| + |numberOfOperations| |limit| |doublyTransitive?| |univariateSolve| + |divergence| |center| |newReduc| |integralLastSubResultant| + |leftExactQuotient| |mvar| |endSubProgram| |groebnerFactorize| + |nullSpace| |unary?| |swap!| |primes| |vectorise| |scripted?| |cAcot| + |setOfMinN| |dimensions| |distFact| |linears| |nil| |quotientByP| + |unknownEndian| |OMencodingXML| |f2st| |ODESolve| |logGamma| + |maxIndex| |curveColor| |leadingCoefficientRicDE| |makeResult| + |status| |leastAffineMultiple| |mathieu24| |readLineIfCan!| |makeFR| + |listRepresentation| |intermediateResultsIF| |structuralConstants| + |numberOfComponents| |iicoth| |permutationRepresentation| + |semiSubResultantGcdEuclidean1| |basisOfRightNucleus| |complement| + |algintegrate| |birth| |idealiser| |errorKind| |maxColIndex| |makeop| + |pointData| |iicsch| |approximate| |genericRightTrace| |zeroDim?| + |erf| |getOperands| |d01alf| |ptree| |critBonD| |sylvesterMatrix| + |push| |asecIfCan| |laurentIfCan| |complex| |GospersMethod| |insert| + |createMultiplicationTable| |intensity| |divideExponents| + |setMinPoints| |charClass| |e02agf| |getGraph| |whileLoop| + |areEquivalent?| |listBranches| |minPoly| |identitySquareMatrix| + |iitanh| |opeval| |super| |factorset| |rootPower| |module| + |decreasePrecision| |cCoth| |extractTop!| |lfextendedint| |dilog| + |purelyAlgebraic?| |flexibleArray| |reduceLODE| |indicialEquations| + GF2FG |deriv| |pol| |tanIfCan| |prolateSpheroidal| |df2mf| + |numberOfPrimitivePoly| |shift| |sin| |iprint| |mainMonomials| + |deepCopy| |tubePoints| |coerceImages| |symmetric?| |removeCosSq| + |complementaryBasis| |OMputAtp| |toseInvertibleSet| |cos| + |shallowExpand| |largest| |innerint| |constantCoefficientRicDE| + |ldf2vmf| |solveLinearPolynomialEquation| |safetyMargin| |empty?| + |integerBound| |idealiserMatrix| |setCondition!| |remove| + |loadNativeModule| |tan| |singularitiesOf| |green| |exQuo| + |getExplanations| |lastSubResultant| |unmakeSUP| |leaves| |nodeOf?| + |trigs| |copies| |rarrow| |times| |cot| |separate| |meshPar1Var| + |acoshIfCan| |changeNameToObjf| |pow| |createMultiplicationMatrix| + |s18dcf| |ratpart| |equation| |nextPrimitivePoly| |zCoord| |last| + |sec| |headReduce| |freeOf?| |graphCurves| |supersub| |isList| + |minPoints| |lazyVariations| |remainder| |comp| |assoc| |function| + |whatInfinity| |OMputString| |over| |csc| |mapExpon| |complexExpand| + |complexNumericIfCan| |stoseInternalLastSubResultant| |conical| + |recolor| |pushucoef| |create3Space| |asin| |printTypes| |string?| + |iipow| |f04mcf| |overlabel| |members| |merge!| |expt| |entry| + |totolex| |acos| |left| |monom| |roughBasicSet| |slex| |eval| + |rdHack1| |innerSolve1| |just| |selectIntegrationRoutines| + |perfectNthPower?| |acschIfCan| |optimize| |iicos| |cn| |right| + |movedPoints| |psolve| |atan| |overset?| |unitNormalize| |minPoints3D| + |putGraph| |summation| |prime| |varselect| |lowerCase| |quatern| + |acot| |clearDenominator| |numberOfChildren| |subscriptedVariables| + |quadratic?| |dualSignature| |conjug| |clip| |common| |float?| |asec| + |setEpilogue!| |d02raf| |internalIntegrate| FG2F |leftFactor| |rst| + |viewport3D| |deleteProperty!| |extendedint| |evenInfiniteProduct| + |acsc| |oneDimensionalArray| |nsqfree| |getProperty| |contract| + |bezoutResultant| |makeVariable| |relerror| |monicRightDivide| |sinh| + |magnitude| |moebius| |predicate| |interReduce| |coerceListOfPairs| + |reducedDiscriminant| |symmetricRemainder| |rationalFunction| + |innerSolve| |lazy?| |f04jgf| |cosh| |sizePascalTriangle| + |radicalSimplify| |SturmHabicht| |hitherPlane| |makeSin| |imagJ| + |e01bff| |head| |dmp2rfi| |tanh| |setAdaptive| |cTan| |complexZeros| + |nil?| |exp1| |OMputEndObject| |newLine| |B1solve| |boundOfCauchy| + |top| |integral| |coth| |cosIfCan| |discreteLog| |pushup| + |lineColorDefault| |isobaric?| |middle| |UnVectorise| |mathieu11| + |digits| |sech| |stFuncN| |dot| |getMultiplicationMatrix| |imagk| + |rightRecip| |invmultisect| |child| |removeZero| |lcm| |Ci| |adjoint| + |pop!| |csch| |variationOfParameters| |dom| |rationalApproximation| + |pseudoQuotient| |mappingAst| |alternatingGroup| |bsolve| + |minimumDegree| |principalIdeal| |operator| |closedCurve| |asinh| + |functionIsOscillatory| |sequences| |OMopenFile| |setPrologue!| + |iicot| |bubbleSort!| |perfectSqrt| |append| |symbol| |nextPartition| + |OMlistSymbols| |acosh| |rombergo| |antisymmetric?| |complexIntegrate| + |meshPar2Var| |palglimint0| |sincos| |setAttributeButtonStep| + |discriminantEuclidean| |hermite| |expression| |gcd| |atanh| + |outputBinaryFile| |mightHaveRoots| |mapCoef| |slash| + |doubleFloatFormat| |messagePrint| |sqfrFactor| |false| + |internalAugment| |integer| |plot| |acoth| |cartesian| |yCoordinates| + |c05nbf| |limitedIntegrate| |cSin| |stoseInvertible?| |tree| + |selectsecond| |stoseInvertible?reg| + |rewriteIdealWithQuasiMonicGenerators| |asech| |divideIfCan!| + |sparsityIF| |semiDegreeSubResultantEuclidean| |title| + |basisOfRightAnnihilator| |resize| |decomposeFunc| + |basisOfCommutingElements| |maxPoints3D| |s20adf| |dioSolve| |lexico| + |gcdprim| |innerEigenvectors| |comparison| |complexElementary| + |multiple| |printStats!| |extractIfCan| |fortranDoubleComplex| + |setScreenResolution| |numberOfFractionalTerms| |distance| |inspect| + |applyQuote| |minPol| |radix| |#| |normalize| |e| |intChoose| + |shufflein| |getConstant| |relationsIdeal| |recoverAfterFail| + |scalarMatrix| |create| |label| |rightAlternative?| + |explicitlyFinite?| |external?| |fTable| |variable?| |fortranDouble| + |c06frf| |countable?| |ScanFloatIgnoreSpacesIfCan| |geometric| + |generalizedContinuumHypothesisAssumed| |divisorCascade| + |setImagSteps| |setRealSteps| |specialTrigs| |ruleset| |tanAn| + |complete| |secIfCan| |cyclePartition| |transcendentalDecompose| + |column| |gensym| |idealSimplify| |argscript| |elColumn2!| |critT| + |f04mbf| |OMconnOutDevice| |exprHasAlgebraicWeight| |updatF| + |cyclicParents| |removeDuplicates!| |repeating?| |nthExpon| + |asechIfCan| |fi2df| |critpOrder| |suchThat| |userOrdered?| |bfKeys| + |zeroVector| |kmax| |bit?| |empty| |branchPoint?| |cAtanh| |chiSquare| + |lowerPolynomial| |readByte!| |internalSubQuasiComponent?| |arguments| + |closeComponent| |mirror| |constructor| |monomialIntPoly| + |roughUnitIdeal?| |f2df| |mainVariable| |stack| |iiacsch| |e01bgf| + |numFunEvals3D| |OMputEndBind| |mapdiv| |chineseRemainder| |option| + |genericRightMinimalPolynomial| |coord| |monicModulo| + |multiplyCoefficients| |rules| |signatureAst| |digit| |iflist2Result| + |dimensionOfIrreducibleRepresentation| |compactFraction| |sh| + |thenBranch| |dimension| |test| |setProperty| |localReal?| |yCoord| + |cAcos| |integralAtInfinity?| |implies?| |iicsc| |elseBranch| + |kovacic| |dim| |lastSubResultantElseSplit| |palginfieldint| |romberg| + |palglimint| |e02ddf| |oddlambert| |c02agf| |maxdeg| |polar| + |fullDisplay| |lyndon?| |c05pbf| |prefix| |smith| |outputSpacing| + |numberOfCycles| |exactQuotient| |rightTrim| |delete!| |s17ahf| + |OMcloseConn| |ListOfTerms| |weierstrass| |sort| |find| |yellow| + |element?| |leftTrim| |commaSeparate| |tube| |rightUnit| |cAcoth| + |rischNormalize| |quadraticNorm| |separateFactors| |badValues| + |integralDerivationMatrix| |OMconnectTCP| |associatorDependence| + |indicialEquation| |rightRegularRepresentation| |e02bcf| + |listYoungTableaus| |highCommonTerms| |iiasinh| |insertMatch| + |createPrimitiveElement| |lazyPseudoQuotient| |shade| |OMgetObject| + |exprHasWeightCosWXorSinWX| |shanksDiscLogAlgorithm| |errorInfo| + |stopMusserTrials| |symmetricDifference| |singleFactorBound| |rCoord| + |tryFunctionalDecomposition| |random| |explogs2trigs| |setProperties!| + |notOperand| |pade| |integralBasisAtInfinity| |karatsuba| + |genericLeftMinimalPolynomial| |patternMatchTimes| |sin2csc| + |systemSizeIF| |internalDecompose| |equiv| |elliptic?| + |linearlyDependent?| |associative?| |updatD| |reseed| + |binarySearchTree| |reindex| |s14abf| |withPredicates| |monomial?| + |palgRDE0| |primextendedint| |showTheSymbolTable| |eigenvectors| + |cycleLength| |nextPrimitiveNormalPoly| |pattern| |hexDigit?| + |leftOne| |rootBound| |fractRadix| |iisqrt2| |edf2fi| |physicalLength| + |second| |f02abf| |moduleSum| |wordInGenerators| |setErrorBound| + |OMputBind| |reify| |readInt32!| |d01bbf| |third| |increment| + |palgextint| |drawStyle| |leftAlternative?| |determinant| + |integralCoordinates| |setLabelValue| |doubleDisc| |minIndex| + |addPoint2| |outerProduct| |swap| |numberOfMonomials| |delay| + |subResultantGcd| |makeTerm| |pdf2ef| |htrigs| |getCode| |airyAi| + |message| |spherical| |stoseLastSubResultant| |solid| |perfectNthRoot| + |hconcat| |LyndonWordsList| |s17def| |cot2tan| + |factorsOfCyclicGroupSize| |removeIrreducibleRedundantFactors| + |alternating| |c06gbf| |viewZoomDefault| |factors| |adaptive3D?| + |createNormalPrimitivePoly| |makeSeries| |LyndonWordsList1| |ef2edf| + |mulmod| |removeRoughlyRedundantFactorsInPol| |factorList| |compdegd| + |mapUnivariate| |quotient| |s17aff| |normFactors| |floor| |void| + |child?| |palgLODE| |definingEquations| |positiveRemainder| |qPot| + |realEigenvectors| |extend| |truncate| |e04jaf| |e01bef| |infinite?| + |An| |factorSquareFreePolynomial| |quasiRegular?| |leftRankPolynomial| + |figureUnits| |f02akf| |cons| |bindings| |rightRemainder| |crest| + |iidprod| |totalfract| |eof?| |mainForm| |factorGroebnerBasis| + |transcendenceDegree| |cAcsc| |sum| |gbasis| |s20acf| |OMgetBind| + |newTypeLists| |curve?| |mr| |getIdentifier| |sech2cosh| |OMreadFile| + |rational| |expandTrigProducts| |mergeFactors| UP2UTS |exponent| + |internal?| |presub| |squareFreeFactors| |outputAsScript| + |returnType!| |nextPrime| |ksec| |equivOperands| |cSec| + |setsubMatrix!| |s18def| |schema| |tanh2coth| |scan| |ignore?| + |outputMeasure| |fglmIfCan| |mathieu12| |trivialIdeal?| + |numericalOptimization| |scale| |testModulus| |exponentialOrder| + |rightTraceMatrix| |squareFreeLexTriangular| |host| |lp| + |systemCommand| |rightExtendedGcd| |source| |lhs| + |scanOneDimSubspaces| |prepareSubResAlgo| |rightMult| + |noncommutativeJordanAlgebra?| |makeCrit| |lintgcd| |csch2sinh| + |extensionDegree| |pToDmp| |rhs| |isMult| |collectQuasiMonic| + |mainDefiningPolynomial| |inrootof| |inputBinaryFile| |parseString| + |reduction| |indices| |quotedOperators| |redPol| |argument| |e04ycf| + |generalPosition| |lex| |distdfact| |csubst| |curry| |positive?| + |rspace| |normal| |wrregime| |quartic| |product| |minrank| + |semiResultantReduitEuclidean| |endOfFile?| |box| |mix| + |algebraicVariables| |ldf2lst| |traceMatrix| |quasiComponent| |s13acf| + |preprocess| |normInvertible?| |target| |hypergeometric0F1| + |complexSolve| |parents| |quickSort| |rightZero| |hcrf| |returns| + |asimpson| |charpol| |df2ef| |OMgetSymbol| |iisinh| |commutative?| + |satisfy?| |e02daf| |roughEqualIdeals?| |jacobiIdentity?| |precision| + |nonLinearPart| |saturate| |rightRankPolynomial| |exprToXXP| + |leastMonomial| |subCase?| |sample| |coefficient| |radicalSolve| + |buildSyntax| |twist| |numberOfIrreduciblePoly| |setlast!| |paren| + |failed?| |e04naf| |antisymmetricTensors| |sign| |lazyResidueClass| + |cond| |leftGcd| |quasiMonicPolynomials| |solveid| |denominator| + |ravel| |algebraicCoefficients?| |iiasec| |eyeDistance| |vertConcat| + |subst| |prindINFO| |internalLastSubResultant| |exprToGenUPS| |row| + |makeFloatFunction| |factorPolynomial| |reshape| |subscript| |rowEch| + |zeroDimPrime?| |dAndcExp| |block| |subresultantVector| |commutator| + |numericalIntegration| |predicates| |s21baf| |basisOfRightNucloid| + |groebner| |simplify| |pascalTriangle| |delta| |outputList| + |indiceSubResultantEuclidean| |multinomial| |PollardSmallFactor| + |lSpaceBasis| |unparse| |quadraticForm| |d01amf| |imagI| |lists| + |associatedSystem| |genericLeftDiscriminant| |certainlySubVariety?| + |OMgetEndAtp| |linearAssociatedLog| |inputOutputBinaryFile| + |setvalue!| |loopPoints| |trailingCoefficient| |sdf2lst| |exprToUPS| + |integralMatrix| |LyndonBasis| |d02kef| |weights| |probablyZeroDim?| + |call| |bombieriNorm| |wronskianMatrix| |oddInfiniteProduct| |update| + |e04mbf| |leader| |factorials| |ScanArabic| |objects| |getOrder| + |viewDeltaYDefault| |normalizedAssociate| |rootNormalize| + |representationType| |contains?| |double?| |c06ebf| |base| ** + |byteBuffer| |critM| |generalInfiniteProduct| |biRank| + |leftTraceMatrix| |corrPoly| |fortranCompilerName| |changeThreshhold| + |computeCycleLength| |lazyPrem| |decompose| |leadingExponent| + |mapBivariate| |coordinate| |computeCycleEntry| |lambda| + |palgintegrate| |s01eaf| |argumentList!| |any| EQ |whitePoint| + |changeWeightLevel| |powers| |divisors| |zeroDimensional?| |po| + |factorSquareFree| |s21bbf| |ocf2ocdf| |clearTheIFTable| |position| + |init| |f04asf| |list?| |symbolTableOf| |HermiteIntegrate| |rational?| + |pushNewContour| |d02gbf| |Hausdorff| |characteristicSerie| + |rationalPoints| |lagrange| |radicalEigenvectors| |generalSqFr| + |arbitrary| |char| |npcoef| |orthonormalBasis| |extractBottom!| + |debug3D| |content| |generalLambert| |leftExtendedGcd| |parametric?| + |wordsForStrongGenerators| |divide| |pseudoRemainder| |rischDEsys| + |lllp| |legendreP| |backOldPos| |ScanFloatIgnoreSpaces| + |univariatePolynomialsGcds| |algSplitSimple| |index| |rename!| + |linear| |mainCoefficients| |symbolTable| |quoByVar| |normalElement| + |findConstructor| |isOpen?| |writable?| |ran| |rdregime| |pile| + |unitsColorDefault| |bandedJacobian| |BasicMethod| |getGoodPrime| + |capacity| |iiperm| |polynomial| |interpret| |stoseInvertibleSet| + |linearDependenceOverZ| |e02bef| |point| |f01qcf| |checkPrecision| + |gcdPrimitive| |poisson| |f07aef| |splitLinear| |pair| |isTimes| + |previous| |dictionary| |OMbindTCP| |split| |cLog| |aQuadratic| + |number?| |localUnquote| |characteristic| |lo| |problemPoints| + |fillPascalTriangle| |kind| |rowEchelonLocal| |leftRemainder| + |wholeRadix| |value| |OMreadStr| |repSq| |getOperator| |incr| |series| + |f01maf| |clikeUniv| |op| |showTheRoutinesTable| |nthr| |cCot| + |continuedFraction| |euclideanGroebner| |curryRight| |measure| + |permutationGroup| |stoseSquareFreePart| |particularSolution| + |sortConstraints| |OMputFloat| |expextendedint| |setStatus| + |basisOfNucleus| |OMgetBVar| |polygon?| |max| |cycleEntry| |ffactor| + |complexEigenvalues| |partitions| |s18aff| |subQuasiComponent?| + |readUInt8!| |drawComplexVectorField| |tableau| |ScanRoman| + |subPolSet?| |completeSmith| |phiCoord| |OMReadError?| |min| + |explicitlyEmpty?| |completeEval| |maxrow| |basisOfCentroid| |light| + |LiePoly| |parametersOf| |rur| |transpose| F |regularRepresentation| + |nilFactor| |varList| |pToHdmp| |multiEuclideanTree| |distribute| + |wordInStrongGenerators| |medialSet| |eq?| + |rightCharacteristicPolynomial| |elliptic| |zeroDimPrimary?| |length| + |union| |rotate| |partialDenominators| |singular?| |Aleph| + |normalDenom| |wreath| |replaceKthElement| |increase| |powerSum| + |lfextlimint| |scripts| |supRittWu?| |script| |direction| |f04arf| + |bivariateSLPEBR| |matrix| |reverseLex| RF2UTS |solve| |reorder| + |copyInto!| |degree| |nthExponent| |tubeRadiusDefault| |comment| + |compiledFunction| |resultantEuclidean| |fortranComplex| |cross| + |coth2trigh| |SturmHabichtCoefficients| |setleft!| |setelt!| + |doubleRank| |nthFactor| |close| |c06ekf| |closed?| |approxNthRoot| + |coshIfCan| |wholePart| |insertRoot!| |untab| |readable?| |consnewpol| + |tex| |stronglyReduce| |s13aaf| |rationalIfCan| + |stoseInvertible?sqfreg| |enumerate| |hi| |chvar| |acosIfCan| + |insertTop!| |colorFunction| |enterPointData| |printHeader| |display| + |round| |compose| |OMputApp| |upDateBranches| |frst| |integer?| + |littleEndian| |sinh2csch| |closedCurve?| |shiftRight| + |parabolicCylindrical| |generalizedEigenvector| |numeric| + |mergeDifference| |uniform| |infLex?| |iiacos| |ratDsolve| + |leftDiscriminant| |id| |c06fuf| |removeSinhSq| |radical| + |solveInField| |mainContent| |fill!| |singRicDE| |simpson| + |monomRDEsys| |normDeriv2| |setrest!| |traverse| |axesColorDefault| + |parabolic| |LagrangeInterpolation| |power!| |listOfLists| + |OMUnknownSymbol?| |setleaves!| |c06fpf| |table| |cycleTail| + |rootRadius| |integralMatrixAtInfinity| |prefixRagits| + |diagonalProduct| |polyRicDE| |dark| |pdf2df| |nary?| + |rectangularMatrix| |new| |back| |represents| |univcase| |input| |obj| + |sumOfSquares| |evaluate| |firstNumer| + |standardBasisOfCyclicSubmodule| |factorOfDegree| |xn| |search| + |inverse| |algDsolve| |addMatch| |bringDown| |inconsistent?| |library| + |radPoly| |outputGeneral| |e02baf| |epilogue| |cache| |connect| + |clipBoolean| |plus| |isPlus| |ode| |qelt| |mathieu22| |computePowers| + |imagj| |vector| |decrease| |mapDown!| |cPower| |member?| + |conditionsForIdempotents| |qsetelt| |finiteBasis| |flagFactor| + |choosemon| |invertibleSet| |d03edf| |abelianGroup| + |rewriteSetByReducingWithParticularGenerators| |externalList| + |rationalPoint?| |reducedSystem| |createGenericMatrix| |rightRank| + |d01akf| |rightFactorCandidate| |xRange| |multiplyExponents| + |leviCivitaSymbol| |logIfCan| |uniform01| |createPrimitiveNormalPoly| + |updateStatus!| |semiSubResultantGcdEuclidean2| |factorFraction| + |kroneckerDelta| |numberOfDivisors| |reducedContinuedFraction| |tanQ| + |firstSubsetGray| |frobenius| |set| |binaryTournament| |hermiteH| + |duplicates?| |hasTopPredicate?| |category| |fortranCharacter| + |c06ecf| |isQuotient| |infiniteProduct| |genericLeftNorm| |nullary| + |leftNorm| |linear?| |domain| |primitiveElement| |addPointLast| + |dfRange| |e02gaf| |mainVariables| |uncouplingMatrices| + |evaluateInverse| |LazardQuotient| |cAtan| |screenResolution3D| + |package| |useNagFunctions| |lighting| |horizConcat| |f04atf| + |tan2trig| |skewSFunction| |isOp| |diagonal| |setnext!| |setTex!| + |generalizedContinuumHypothesisAssumed?| |matrixGcd| |cubic| + |returnTypeOf| |cCsch| |checkRur| |trace2PowMod| + |countRealRootsMultiple| |upperCase?| |merge| |getRef| + |OMconnInDevice| |regime| |acotIfCan| |reducedQPowers| |outlineRender| + |nextIrreduciblePoly| |pseudoDivide| |radicalOfLeftTraceForm| + |appendPoint| |setLength!| |term| |stopTableInvSet!| |noKaratsuba| + |rightTrace| |height| |cot2trig| |accuracyIF| |s14baf| |binaryTree| + |OMputVariable| |jordanAlgebra?| |s17dgf| ~= |cAcosh| + |possiblyNewVariety?| |datalist| |primextintfrac| |chainSubResultants| + |f01rcf| |getDatabase| |deepExpand| |showRegion| |shuffle| + |halfExtendedSubResultantGcd2| |coerce| |bfEntry| |insertBottom!| + |iisin| |droot| |OMgetEndObject| |resetBadValues| |OMgetType| |queue| + |mapMatrixIfCan| |lexTriangular| |construct| |repeatUntilLoop| + |showTheIFTable| |e04fdf| |f04axf| |topPredicate| + |currentCategoryFrame| |heap| |localIntegralBasis| |stop| |depth| + |clipPointsDefault| |groebner?| |antiAssociative?| |graphs| |bat1| + |isExpt| |permutation| |cycleElt| |mkPrim| |irreducibleRepresentation| + |show| |mdeg| |outputAsTex| |extendedResultant| |diff| |f02agf| + |shiftLeft| |normal01| |monicRightFactorIfCan| |makeCos| |modulus| + |cyclic| |useEisensteinCriterion?| |putColorInfo| |positiveSolve| + |controlPanel| |linkToFortran| |cSinh| |gderiv| |normalizeIfCan| + |point?| |trace| |expressIdealMember| |basicSet| |build| |atoms| + |rootOfIrreduciblePoly| |omError| |symbolIfCan| |removeSinSq| |iilog| + |Ei| |digit?| |expr| |redPo| |rowEchelon| |fractionPart| |output| + |s17dlf| |asinIfCan| |euclideanNormalForm| |packageCall| |var1Steps| + |collectUpper| |fortranLinkerArgs| |interpolate| |lifting1| |multiset| + |tail| |surface| |difference| |OMsend| |roughBase?| |dihedral| + |iFTable| |expenseOfEvaluation| |binaryFunction| |true| |nextItem| + |makeprod| |tab| |schwerpunkt| |antiCommutative?| |FormatArabic| + |critB| |degreeSubResultantEuclidean| |lyndon| |patternVariable| + |pointPlot| |graeffe| |cyclicSubmodule| |halfExtendedSubResultantGcd1| + |genericLeftTraceForm| |dominantTerm| |position!| |unknown| + |startTable!| |resultantReduitEuclidean| |zoom| |elem?| |stFunc1| + |linearPart| |times!| |Gamma| |safeFloor| |OMgetEndBind| |variable| + |setMaxPoints| |numberOfVariables| |cyclotomicDecomposition| |parent| + |initializeGroupForWordProblem| |compound?| |toScale| |Si| |s19abf| + |chebyshevU| |iterators| |hash| |iiacosh| |solveLinear| |rightDivide| + |squareMatrix| |sinhIfCan| |ref| |alternative?| |graphStates| + |integral?| |andOperands| |count| |sumOfDivisors| |OMgetEndAttr| + |separateDegrees| |createRandomElement| |pushdown| |polynomialZeros| + |groebnerIdeal| |primintfldpoly| |rangePascalTriangle| + |triangularSystems| |universe| |coordinates| |setelt| |decimal| + |besselI| |solve1| |edf2ef| |basisOfCenter| |f02axf| |rotatez| + |readLine!| |readInt16!| |explicitEntries?| |weight| |polyred| + |impliesOperands| |powerAssociative?| |reflect| |sup| |measure2Result| + |inRadical?| |nthCoef| |moebiusMu| |rightGcd| |copy| |li| |subTriSet?| + |sechIfCan| |linearDependence| |leftRank| |copy!| |unit?| |coerceS| + |formula| |readUInt16!| |calcRanges| |OMlistCDs| |lazyGintegrate| + |mkAnswer| |next| |normalise| |sizeLess?| |addiag| |edf2df| + |quasiRegular| |doubleComplex?| |mathieu23| |expIfCan| |children| + |aspFilename| |finite?| |totalGroebner| |f02fjf| |showAll?| |abs| + |autoCoerce| |tanSum| |separant| |complexRoots| |totalLex| + |branchPointAtInfinity?| |createNormalElement| |zag| |bits| + |makeViewport2D| |options| |singularAtInfinity?| |getVariableOrder| + |rationalPower| |fortran| |airyBi| |ParCondList| |fullPartialFraction| + |printStatement| |isAbsolutelyIrreducible?| |moduloP| |cschIfCan| + |numberOfHues| |submod| |degreeSubResultant| |irreducibleFactors| + |nrows| |typeLists| |notelem| |extract!| |tensorProduct| |ideal| + |s18acf| |basisOfMiddleNucleus| |ddFact| |ncols| |limitedint| |nor| + |principal?| |absolutelyIrreducible?| + |semiIndiceSubResultantEuclidean| |rename| |string| |jacobi| + |OMmakeConn| |euclideanSize| |d01anf| |f01ref| |taylorRep| + |setAdaptive3D| |toseSquareFreePart| |brillhartTrials| |powmod| + |OMunhandledSymbol| |quote| |bag| |close!| |gramschmidt| |associates?| + |att2Result| |expandPower| |modularFactor| |qqq| |convergents| + |optpair| |plus!| |triangulate| |logical?| |coefChoose| |fixedPoints| + |sec2cos| |identity| |binomThmExpt| |seriesToOutputForm| |e02ahf| + |gcdcofact| |mkcomm| |solid?| |primitivePart!| NOT |tubePlot| + |Vectorise| |c06gqf| |removeRedundantFactorsInContents| + |moreAlgebraic?| |triangSolve| |lifting| |setButtonValue| + |radicalEigenvalues| |stiffnessAndStabilityFactor| |tower| OR + |minimumExponent| |OMgetVariable| |iitan| |contractSolve| |rootSplit| + |qfactor| |removeRoughlyRedundantFactorsInContents| |s18aef| + |pushuconst| |ricDsolve| AND |meshFun2Var| |mindegTerm| |nand| + |taylorIfCan| |s19aaf| |contours| |chiSquare1| |lookup| + |unrankImproperPartitions0| |approxSqrt| |karatsubaOnce| |eq| |iiatan| + |addmod| |setchildren!| |integrate| |partition| |unvectorise| |log10| + |mapSolve| |infieldint| |redmat| |gcdcofactprim| |leftDivide| |iter| + |infieldIntegrate| |squareTop| |reduceBasisAtInfinity| |f01brf| |ipow| + |operation| |zeroSetSplit| |genericPosition| |iCompose| |bitand| + |condition| |padecf| |newSubProgram| |mapExponents| |leadingTerm| + |OMUnknownCD?| |directory| |getCurve| |dequeue| |d01ajf| |leftMult| + |complexNumeric| |power| |bitior| |pdct| |remove!| |alphabetic?| + |graphState| |generate| |continue| |badNum| |relativeApprox| |blue| + |monicDecomposeIfCan| |polyRDE| |rquo| |prinb| |cothIfCan| |cTanh| + |tab1| |unravel| |kernels| |topFortranOutputStack| |fortranTypeOf| + |s19acf| |ReduceOrder| |makeUnit| |SturmHabichtSequence| |makeSketch| + |makeMulti| |incrementBy| |paraboloidal| |iiatanh| |s17adf| + |univariate| |initials| |tRange| |companionBlocks| |fortranReal| + |showClipRegion| |constDsolve| |removeSquaresIfCan| |expand| |exprex| + |coHeight| |f02adf| |hasPredicate?| |binding| |readUInt32!| + |tanintegrate| |OMencodingBinary| |morphism| |entries| |laguerreL| + |filterWhile| |bottom!| |simpsono| |pointColor| |eigenMatrix| * + |makeYoungTableau| |exp| |e01baf| |prem| |plenaryPower| |denomLODE| + |and?| |filterUntil| |extendedIntegrate| |autoReduced?| |factor| + |split!| |brillhartIrreducible?| |dmpToHdmp| |diophantineSystem| + |less?| |createIrreduciblePoly| |setFormula!| |leftLcm| |select| + |c06gsf| |gcdPolynomial| |dequeue!| |sqrt| |fortranLogical| + |acscIfCan| |derivative| |ord| |mainValue| |augment| |extractIndex| + |s17acf| |basisOfLeftNucleus| |symmetricPower| |mapUnivariateIfCan| + |real| |sncndn| |sumOfKthPowerDivisors| |range| |style| |palgLODE0| + |cCsc| |monicDivide| |exponents| |selectfirst| |cyclicEntries| |imag| + |var1StepsDefault| |lowerCase!| |tubePointsDefault| |iifact| + |definingPolynomial| |patternMatch| |points| |presuper| + |directProduct| |inverseLaplace| |e04ucf| |generators| |leadingIndex| + |pointLists| |OMgetString| |OMread| Y |factorAndSplit| |sort!| + |s21bdf| |permanent| |getMultiplicationTable| |randomR| |curryLeft| + |e01sef| |c06eaf| |seed| |interval| |numberOfComputedEntries| |root?| + |knownInfBasis| |useEisensteinCriterion| |brace| |prologue| + |OMputSymbol| |cotIfCan| |OMreceive| |deepestTail| |goodPoint| + |padicallyExpand| |constantOpIfCan| |makeRecord| |btwFact| |compile| + |fixedPoint| |OMputEndError| |destruct| SEGMENT |or?| |upperCase| + |numberOfFactors| |constantLeft| |raisePolynomial| + |linearlyDependentOverZ?| |startTableGcd!| |rightOne| |f01qdf| + |deepestInitial| |LyndonCoordinates| |readIfCan!| |lazyEvaluate| + |componentUpperBound| |iExquo| |rightLcm| |bumptab1| |null| |goto| + |outputFixed| |parts| |lazyPquo| |s13adf| |complexForm| |rootsOf| + |selectPDERoutines| |bigEndian| |connectTo| |coefficients| |not| + |argumentListOf| |inverseIntegralMatrix| |allRootsOf| + |SturmHabichtMultiple| |realSolve| |iicosh| |rightScalarTimes!| + |rowEchLocal| |completeHermite| |rubiksGroup| |and| |factorial| + |divisor| |monomial| |hostPlatform| |exponential| |replace| |iiexp| + |recip| |getZechTable| |baseRDE| |resultant| |or| + |functionIsFracPolynomial?| |hyperelliptic| |multivariate| |atom?| + |subtractIfCan| |qroot| |exists?| |clearTable!| |cExp| |lquo| + |eulerPhi| |xor| |any?| |f02bbf| |OMgetError| |variables| + |exportedOperators| |orOperands| |reopen!| |ceiling| + |stoseIntegralLastSubResultant| |overlap| |signature| |reduced?| + |case| |intersect| |e04gcf| |generalTwoFactor| |orbit| |dihedralGroup| + |infinityNorm| |resetVariableOrder| |irreducibleFactor| + |genericRightDiscriminant| |generateIrredPoly| |Zero| |df2fi| + |pmintegrate| |OMencodingUnknown| |rroot| |tan2cot| |cCos| + |lazyIrreducibleFactors| |OMsetEncoding| |stopTable!| |mpsode| |One| + |inc| |algint| |sin?| |lazyPseudoDivide| |exprHasLogarithmicWeights| + |realRoots| |inverseColeman| |viewDefaults| |writeBytes!| |cosSinInfo| + |nextSubsetGray| |compBound| |subNode?| |name| |makeViewport3D| + |basis| |thetaCoord| |callForm?| |nthRoot| |bezoutMatrix| + |reduceByQuasiMonic| |completeHensel| |f02aff| |body| |diagonals| + |hostByteOrder| |taylor| |mapUp!| |setProperty!| |OMserve| + |currentScope| |randomLC| |nonQsign| |cap| |univariatePolynomials| + |property| |enqueue!| |tanh2trigh| |laurent| |charthRoot| |routines| + |simplifyPower| |lastSubResultantEuclidean| |trim| |algebraic?| + |imagi| |initial| |shellSort| |f01qef| |OMputInteger| |puiseux| + |interpretString| |commonDenominator| |push!| |discriminant| |expPot| + |primlimintfrac| |linearPolynomials| |elt| |expandLog| |e01saf| + |addMatchRestricted| |leftQuotient| |minset| |top!| |binomial| + |f02aaf| |stripCommentsAndBlanks| |integralRepresents| |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 d60fd9a3..f0478176 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5296 +1,5296 @@ -(3199907 . 3449600551) -((-4310 (((-112) (-1 (-112) |#2| |#2|) $) 85) (((-112) $) NIL)) (-3606 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-1881 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-1226 (-564)) |#2|) 43)) (-3852 (($ $) 79)) (-4367 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 51) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 49) ((|#2| (-1 |#2| |#2| |#2|) $) 48)) (-1356 (((-564) (-1 (-112) 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -4012 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -4012 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-35) |has| |#1| (-1194)) ((-95) |has| |#1| (-1194)) ((-102) . T) ((-111 #0# #0#) -4012 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -4012 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -4012 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -4012 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-859)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1019)) ((-612 (-169 (-379))) |has| |#1| (-1019)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-889 (-379))) |has| |#1| (-612 (-889 (-379)))) ((-612 (-889 (-564))) |has| |#1| (-612 (-889 (-564)))) ((-612 #1=(-1166 |#1|)) . 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4002 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4002 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1046)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4002 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-4077 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-4367 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2082 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -4077 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4367 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2082 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-768) (-1209) (-1209)) (T -239)) -((-2082 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-4367 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-4077 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-768)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 -4077 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4367 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2082 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) -((-1754 (((-112) $ $) NIL (|has| |#2| (-1094)))) (-3976 (((-112) $) NIL (|has| |#2| (-131)))) (-3473 (($ (-918)) 65 (|has| |#2| (-1046)))) (-3476 (((-1264) $ (-564) (-564)) NIL (|has| $ (-6 -4412)))) (-3382 (($ $ $) 69 (|has| |#2| (-790)))) (-3936 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-3263 (((-112) $ (-768)) 17)) (-3042 (((-768)) NIL (|has| |#2| (-368)))) (-3438 (((-564) $) NIL (|has| |#2| (-845)))) (-1881 ((|#2| $ (-564) |#2|) NIL (|has| $ (-6 -4412)))) (-3760 (($) NIL T CONST)) (-2013 (((-3 (-564) "failed") $) NIL (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094)))) (((-3 (-407 (-564)) "failed") $) NIL (-12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094)))) (((-3 |#2| "failed") $) 34 (|has| |#2| (-1094)))) (-2064 (((-564) $) NIL (-12 (|has| |#2| (-1035 (-564))) (|has| 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(IF (|has| |t#2| (-723)) (PROGN (-6 (-723)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4409)) (-6 -4409) |%noBranch|) (IF (|has| |t#2| (-845)) (-6 (-845)) |%noBranch|) (IF (|has| |t#2| (-790)) (-6 (-790)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4012 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4012 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4012 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4012 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4012 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1046)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -4012 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4012 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4012 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4012 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4012 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4012 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4012 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4012 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4012 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1046)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -4002 (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1046))) ((-637 |#1|) |has| |#1| (-1046)) ((-714 #0#) |has| |#1| (-556)) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) |has| |#1| (-556)) ((-723) -4002 (|has| |#1| (-1106)) (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-847) . T) ((-897 (-1170)) |has| |#1| (-1046)) ((-883 (-379)) |has| |#1| (-883 (-379))) ((-883 (-564)) |has| |#1| (-883 (-564))) ((-881 |#1|) . 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NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2887442 2887555 2887585 "TRIGCAT" 2887798 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2887111 2887190 2887331 "TRIGCAT-" 2887336 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2884004 2885969 2886250 "TREE" 2886865 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2883278 2883806 2883836 "TRANFUN" 2883871 T TRANFUN (NIL) -9 NIL 2883937 NIL) (-1193 2882557 2882748 2883028 "TRANFUN-" 2883033 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2882361 2882393 2882454 "TOPSP" 2882518 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2881709 2881824 2881978 "TOOLSIGN" 2882242 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2880370 2880886 2881125 "TEXTFILE" 2881492 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2878309 2878823 2879252 "TEX" 2879963 T TEX (NIL) -8 NIL NIL NIL) (-1188 2878090 2878121 2878193 "TEX1" 2878272 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2877738 2877801 2877891 "TEMUTL" 2878022 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2875892 2876172 2876497 "TBCMPPK" 2877461 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2867780 2874052 2874108 "TBAGG" 2874508 NIL TBAGG (NIL T T) -9 NIL 2874719 NIL) (-1184 2862850 2864338 2866092 "TBAGG-" 2866097 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862234 2862341 2862486 "TANEXP" 2862739 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2855735 2862091 2862184 "TABLE" 2862189 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855147 2855246 2855384 "TABLEAU" 2855632 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2849755 2850975 2852223 "TABLBUMP" 2853933 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848977 2849124 2849305 "SYSTEM" 2849596 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845436 2846135 2846918 "SYSSOLP" 2848228 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844470 2844948 2845067 "SYSNNI" 2845253 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845338) (-1176 2843767 2844199 2844278 "SYSINT" 2844338 NIL SYSINT (NIL NIL) -8 NIL NIL 2844383) (-1175 2840126 2841045 2841755 "SYNTAX" 2843079 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837284 2837886 2838518 "SYMTAB" 2839516 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2832533 2833435 2834418 "SYMS" 2836323 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2829795 2831991 2832221 "SYMPOLY" 2832338 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829312 2829387 2829510 "SYMFUNC" 2829707 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825358 2826624 2827437 "SYMBOL" 2828521 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818897 2820586 2822306 "SWITCH" 2823660 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812158 2817718 2818021 "SUTS" 2818652 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804251 2811405 2811678 "SUPXS" 2811943 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2795766 2803869 2803995 "SUP" 2804160 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794925 2795052 2795269 "SUPFRACF" 2795634 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2794546 2794605 2794718 "SUP2" 2794860 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792959 2793233 2793596 "SUMRF" 2794245 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792273 2792339 2792538 "SUMFS" 2792880 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776267 2791450 2791701 "SULS" 2792080 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775896 2776089 2776159 "SUCHTAST" 2776219 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775218 2775421 2775561 "SUCH" 2775804 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769112 2770124 2771083 "SUBSPACE" 2774306 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2768542 2768632 2768796 "SUBRESP" 2769000 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761907 2763207 2764518 "STTF" 2767278 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2756080 2757200 2758347 "STTFNC" 2760807 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747391 2749262 2751056 "STTAYLOR" 2754321 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2740635 2747255 2747338 "STRTBL" 2747343 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2736026 2740590 2740621 "STRING" 2740626 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730914 2735399 2735429 "STRICAT" 2735488 T STRICAT (NIL) -9 NIL 2735550 NIL) (-1150 2723717 2728533 2729144 "STREAM" 2730338 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723227 2723304 2723448 "STREAM3" 2723634 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722209 2722392 2722627 "STREAM2" 2723040 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721897 2721949 2722042 "STREAM1" 2722151 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720913 2721094 2721325 "STINPROD" 2721713 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720491 2720675 2720705 "STEP" 2720785 T STEP (NIL) -9 NIL 2720863 NIL) (-1144 2714034 2720390 2720467 "STBL" 2720472 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709208 2713255 2713298 "STAGG" 2713451 NIL STAGG (NIL T) -9 NIL 2713540 NIL) (-1142 2706910 2707512 2708384 "STAGG-" 2708389 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705105 2706680 2706772 "STACK" 2706853 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697828 2703246 2703702 "SREGSET" 2704735 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690253 2691622 2693135 "SRDCMPK" 2696434 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683220 2687693 2687723 "SRAGG" 2689026 T SRAGG (NIL) -9 NIL 2689634 NIL) (-1137 2682237 2682492 2682871 "SRAGG-" 2682876 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2676724 2681184 2681605 "SQMATRIX" 2681863 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670471 2673442 2674169 "SPLTREE" 2676069 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666461 2667127 2667773 "SPLNODE" 2669897 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665508 2665741 2665771 "SPFCAT" 2666215 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664245 2664455 2664719 "SPECOUT" 2665266 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655897 2657641 2657671 "SPADXPT" 2662063 T SPADXPT (NIL) -9 NIL 2664097 NIL) (-1130 2655658 2655698 2655767 "SPADPRSR" 2655850 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653840 2655613 2655644 "SPADAST" 2655649 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2645811 2647558 2647601 "SPACEC" 2651974 NIL SPACEC (NIL T) -9 NIL 2653790 NIL) (-1127 2643968 2645743 2645792 "SPACE3" 2645797 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2642720 2642891 2643182 "SORTPAK" 2643773 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2640770 2641073 2641492 "SOLVETRA" 2642384 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2639781 2640003 2640277 "SOLVESER" 2640543 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634992 2635882 2636884 "SOLVERAD" 2638833 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2630807 2631416 2632145 "SOLVEFOR" 2634359 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625104 2630156 2630253 "SNTSCAT" 2630258 NIL SNTSCAT (NIL T T T T) -9 NIL 2630328 NIL) (-1120 2619237 2623427 2623818 "SMTS" 2624794 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2613677 2619125 2619202 "SMP" 2619207 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611836 2612137 2612535 "SMITH" 2613374 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2604723 2608887 2608990 "SMATCAT" 2610341 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610891 NIL) (-1116 2601663 2602486 2603664 "SMATCAT-" 2603669 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599376 2600899 2600942 "SKAGG" 2601203 NIL SKAGG (NIL T) -9 NIL 2601338 NIL) (-1114 2595711 2598792 2598987 "SINT" 2599174 T SINT (NIL) -8 NIL NIL 2599347) (-1113 2595483 2595521 2595587 "SIMPAN" 2595667 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2594789 2595018 2595158 "SIG" 2595365 T SIG (NIL) -8 NIL NIL NIL) (-1111 2593627 2593848 2594123 "SIGNRF" 2594548 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592432 2592583 2592874 "SIGNEF" 2593456 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2591765 2592015 2592139 "SIGAST" 2592330 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589455 2589909 2590415 "SHP" 2591306 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583355 2589356 2589432 "SHDP" 2589437 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582954 2583120 2583150 "SGROUP" 2583243 T SGROUP (NIL) -9 NIL 2583305 NIL) (-1105 2582812 2582838 2582911 "SGROUP-" 2582916 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2579647 2580345 2581068 "SGCF" 2582111 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2574042 2579094 2579191 "SFRTCAT" 2579196 NIL SFRTCAT (NIL T T T T) -9 NIL 2579235 NIL) (-1102 2567463 2568481 2569617 "SFRGCD" 2573025 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2560590 2561662 2562848 "SFQCMPK" 2566396 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560212 2560301 2560411 "SFORT" 2560531 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559357 2560052 2560173 "SEXOF" 2560178 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558491 2559238 2559306 "SEX" 2559311 T SEX (NIL) -8 NIL NIL NIL) (-1097 2554030 2554719 2554814 "SEXCAT" 2557751 NIL SEXCAT (NIL T T T T T) -9 NIL 2558329 NIL) (-1096 2551210 2553964 2554012 "SET" 2554017 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549461 2549923 2550228 "SETMN" 2550951 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2549067 2549193 2549223 "SETCAT" 2549340 T SETCAT (NIL) -9 NIL 2549425 NIL) (-1093 2548847 2548899 2548998 "SETCAT-" 2549003 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545234 2547308 2547351 "SETAGG" 2548221 NIL SETAGG (NIL T) -9 NIL 2548561 NIL) (-1091 2544692 2544808 2545045 "SETAGG-" 2545050 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544162 2544388 2544489 "SEQAST" 2544613 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543361 2543655 2543716 "SEGXCAT" 2544002 NIL SEGXCAT (NIL T T) -9 NIL 2544122 NIL) (-1088 2542415 2543027 2543209 "SEG" 2543214 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541394 2541608 2541651 "SEGCAT" 2542173 NIL SEGCAT (NIL T) -9 NIL 2542394 NIL) (-1086 2540443 2540773 2540973 "SEGBIND" 2541229 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2540064 2540123 2540236 "SEGBIND2" 2540378 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2539664 2539865 2539942 "SEGAST" 2540009 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538883 2539009 2539213 "SEG2" 2539508 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538320 2538818 2538865 "SDVAR" 2538870 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2530602 2538090 2538220 "SDPOL" 2538225 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529195 2529461 2529780 "SCPKG" 2530317 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528355 2528528 2528721 "SCOPE" 2529024 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2527575 2527709 2527888 "SCACHE" 2528210 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527247 2527407 2527437 "SASTCAT" 2527442 T SASTCAT (NIL) -9 NIL 2527455 NIL) (-1076 2526761 2527082 2527158 "SAOS" 2527193 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526326 2526361 2526534 "SAERFFC" 2526720 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520292 2526223 2526303 "SAE" 2526308 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519885 2519920 2520079 "SAEFACT" 2520251 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518206 2518520 2518921 "RURPK" 2519551 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516842 2517121 2517433 "RULESET" 2518040 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2514029 2514532 2514997 "RULE" 2516523 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2513668 2513823 2513906 "RULECOLD" 2513981 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513166 2513385 2513479 "RSTRCAST" 2513596 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2508014 2508809 2509729 "RSETGCD" 2512365 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497271 2502323 2502420 "RSETCAT" 2506539 NIL RSETCAT (NIL T T T T) -9 NIL 2507636 NIL) (-1065 2495198 2495737 2496561 "RSETCAT-" 2496566 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2487583 2488960 2490480 "RSDCMPK" 2493797 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2485588 2486029 2486103 "RRCC" 2487189 NIL RRCC (NIL T T) -9 NIL 2487533 NIL) (-1062 2484939 2485113 2485392 "RRCC-" 2485397 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484409 2484635 2484736 "RPTAST" 2484860 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458407 2468002 2468069 "RPOLCAT" 2478733 NIL RPOLCAT (NIL T T T) -9 NIL 2481892 NIL) (-1059 2449905 2452245 2455367 "RPOLCAT-" 2455372 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2440952 2448116 2448598 "ROUTINE" 2449445 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2437777 2440578 2440718 "ROMAN" 2440834 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2436048 2436637 2436897 "ROIRC" 2437582 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432433 2434684 2434714 "RNS" 2435018 T RNS (NIL) -9 NIL 2435291 NIL) (-1054 2430942 2431325 2431859 "RNS-" 2431934 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430391 2430773 2430803 "RNG" 2430808 T RNG (NIL) -9 NIL 2430829 NIL) (-1052 2429783 2430145 2430188 "RMODULE" 2430250 NIL RMODULE (NIL T) -9 NIL 2430292 NIL) (-1051 2428619 2428713 2429049 "RMCAT2" 2429684 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425496 2427965 2428262 "RMATRIX" 2428381 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418438 2420672 2420787 "RMATCAT" 2424146 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425128 NIL) (-1048 2417813 2417960 2418267 "RMATCAT-" 2418272 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417380 2417455 2417583 "RINTERP" 2417732 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416499 2417027 2417057 "RING" 2417113 T RING (NIL) -9 NIL 2417205 NIL) (-1045 2416291 2416335 2416432 "RING-" 2416437 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415132 2415369 2415627 "RIDIST" 2416055 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406448 2414600 2414806 "RGCHAIN" 2414980 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2405824 2406204 2406245 "RGBCSPC" 2406303 NIL RGBCSPC (NIL T) -9 NIL 2406355 NIL) (-1041 2405008 2405363 2405404 "RGBCMDL" 2405636 NIL RGBCMDL (NIL T) -9 NIL 2405750 NIL) (-1040 2402002 2402616 2403286 "RF" 2404372 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2401648 2401711 2401814 "RFFACTOR" 2401933 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401373 2401408 2401505 "RFFACT" 2401607 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399490 2399854 2400236 "RFDIST" 2401013 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2398943 2399035 2399198 "RETSOL" 2399392 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2398579 2398659 2398702 "RETRACT" 2398835 NIL RETRACT (NIL T) -9 NIL 2398922 NIL) (-1034 2398428 2398453 2398540 "RETRACT-" 2398545 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2398057 2398250 2398320 "RETAST" 2398380 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2390911 2397710 2397837 "RESULT" 2397952 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2389529 2390180 2390379 "RESRING" 2390814 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389165 2389214 2389312 "RESLATC" 2389466 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2388870 2388905 2389012 "REPSQ" 2389124 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386292 2386872 2387474 "REP" 2388290 T REP (NIL) -7 NIL NIL NIL) (-1027 2385989 2386024 2386135 "REPDB" 2386251 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2379889 2381278 2382501 "REP2" 2384801 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376266 2376947 2377755 "REP1" 2379116 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2368989 2374407 2374863 "REGSET" 2375896 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2367802 2368137 2368387 "REF" 2368774 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367179 2367282 2367449 "REDORDER" 2367686 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363174 2366392 2366619 "RECLOS" 2367007 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362226 2362407 2362622 "REALSOLV" 2362981 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2362072 2362113 2362143 "REAL" 2362148 T REAL (NIL) -9 NIL 2362183 NIL) (-1018 2358555 2359357 2360241 "REAL0Q" 2361237 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354156 2355144 2356205 "REAL0" 2357536 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2353654 2353873 2353967 "RDUCEAST" 2354084 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2353059 2353131 2353338 "RDIV" 2353576 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352127 2352301 2352514 "RDIST" 2352881 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2350724 2351011 2351383 "RDETRS" 2351835 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2348536 2348990 2349528 "RDETR" 2350266 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347147 2347425 2347829 "RDEEFS" 2348252 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2345642 2345948 2346380 "RDEEF" 2346835 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2339895 2342778 2342808 "RCFIELD" 2344103 T RCFIELD (NIL) -9 NIL 2344833 NIL) (-1008 2337959 2338463 2339159 "RCFIELD-" 2339234 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334275 2336060 2336103 "RCAGG" 2337187 NIL RCAGG (NIL T) -9 NIL 2337652 NIL) (-1006 2333903 2333997 2334160 "RCAGG-" 2334165 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333238 2333350 2333515 "RATRET" 2333787 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2332791 2332858 2332979 "RATFACT" 2333166 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332099 2332219 2332371 "RANDSRC" 2332661 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2331833 2331877 2331950 "RADUTIL" 2332048 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2324976 2330666 2330976 "RADIX" 2331557 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2316622 2324818 2324948 "RADFF" 2324953 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316274 2316349 2316377 "RADCAT" 2316534 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2316059 2316107 2316204 "RADCAT-" 2316209 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314210 2315834 2315923 "QUEUE" 2316003 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2310778 2314147 2314192 "QUAT" 2314197 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310416 2310459 2310586 "QUATCT2" 2310729 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304155 2307465 2307505 "QUATCAT" 2308285 NIL QUATCAT (NIL T) -9 NIL 2309051 NIL) (-993 2300299 2301336 2302723 "QUATCAT-" 2302817 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2297819 2299383 2299424 "QUAGG" 2299799 NIL QUAGG (NIL T) -9 NIL 2299974 NIL) (-991 2297451 2297644 2297712 "QQUTAST" 2297771 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296376 2296849 2297021 "QFORM" 2297323 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2287580 2292793 2292833 "QFCAT" 2293491 NIL QFCAT (NIL T) -9 NIL 2294492 NIL) (-988 2283152 2284353 2285944 "QFCAT-" 2286038 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2282790 2282833 2282960 "QFCAT2" 2283103 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282250 2282360 2282490 "QEQUAT" 2282680 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275397 2276469 2277653 "QCMPACK" 2281183 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2272973 2273394 2273822 "QALGSET" 2275052 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272218 2272392 2272624 "QALGSET2" 2272793 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2270908 2271132 2271449 "PWFFINTB" 2271991 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2269090 2269258 2269612 "PUSHVAR" 2270722 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2265008 2266062 2266103 "PTRANFN" 2267987 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263410 2263701 2264023 "PTPACK" 2264719 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2263042 2263099 2263208 "PTFUNC2" 2263347 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2257569 2261914 2261955 "PTCAT" 2262251 NIL PTCAT (NIL T) -9 NIL 2262404 NIL) (-976 2257227 2257262 2257386 "PSQFR" 2257528 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2255822 2256120 2256454 "PSEUDLIN" 2256925 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2242585 2244956 2247280 "PSETPK" 2253582 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2235629 2238343 2238439 "PSETCAT" 2241460 NIL PSETCAT (NIL T T T T) -9 NIL 2242274 NIL) (-972 2233465 2234099 2234920 "PSETCAT-" 2234925 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2232814 2232979 2233007 "PSCURVE" 2233275 T PSCURVE (NIL) -9 NIL 2233442 NIL) (-970 2229162 2230652 2230717 "PSCAT" 2231561 NIL PSCAT (NIL T T T) -9 NIL 2231801 NIL) (-969 2228225 2228441 2228841 "PSCAT-" 2228846 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2226957 2227590 2227795 "PRTITION" 2228040 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226459 2226678 2226770 "PRTDAST" 2226885 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2215549 2217763 2219951 "PRS" 2224321 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213407 2214899 2214939 "PRQAGG" 2215122 NIL PRQAGG (NIL T) -9 NIL 2215224 NIL) (-964 2212793 2213022 2213050 "PROPLOG" 2213235 T PROPLOG (NIL) -9 NIL 2213357 NIL) (-963 2209963 2210607 2211071 "PROPFRML" 2212361 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209423 2209533 2209663 "PROPERTY" 2209853 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203508 2207589 2208409 "PRODUCT" 2208649 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2200813 2202966 2203200 "PR" 2203319 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2200609 2200641 2200700 "PRINT" 2200774 T PRINT (NIL) -7 NIL NIL NIL) (-958 2199949 2200066 2200218 "PRIMES" 2200489 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2198014 2198415 2198881 "PRIMELT" 2199528 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2197743 2197792 2197820 "PRIMCAT" 2197944 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2193904 2197681 2197726 "PRIMARR" 2197731 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2192911 2193089 2193317 "PRIMARR2" 2193722 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2192554 2192610 2192721 "PREASSOC" 2192849 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2192029 2192162 2192190 "PPCURVE" 2192395 T PPCURVE (NIL) -9 NIL 2192531 NIL) (-951 2191651 2191824 2191907 "PORTNUM" 2191966 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2189010 2189409 2190001 "POLYROOT" 2191232 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2182947 2188614 2188774 "POLY" 2188883 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182330 2182388 2182622 "POLYLIFT" 2182883 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2178605 2179054 2179683 "POLYCATQ" 2181875 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165414 2170780 2170845 "POLYCAT" 2174359 NIL POLYCAT (NIL T T T) -9 NIL 2176287 NIL) (-945 2158863 2160725 2163109 "POLYCAT-" 2163114 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158450 2158518 2158638 "POLY2UP" 2158789 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2158082 2158139 2158248 "POLY2" 2158387 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2156767 2157006 2157282 "POLUTIL" 2157856 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155122 2155399 2155730 "POLTOPOL" 2156489 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2150639 2155058 2155104 "POINT" 2155109 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2148826 2149183 2149558 "PNTHEORY" 2150284 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147245 2147542 2147954 "PMTOOLS" 2148524 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2146838 2146916 2147033 "PMSYM" 2147161 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146348 2146417 2146591 "PMQFCAT" 2146763 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2145703 2145813 2145969 "PMPRED" 2146225 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145099 2145185 2145346 "PMPREDFS" 2145604 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2143742 2143950 2144335 "PMPLCAT" 2144861 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143274 2143353 2143505 "PMLSAGG" 2143657 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2142749 2142825 2143006 "PMKERNEL" 2143192 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142366 2142441 2142554 "PMINS" 2142668 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2141794 2141863 2142079 "PMFS" 2142291 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2141022 2141140 2141345 "PMDOWN" 2141671 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140185 2140344 2140526 "PMASS" 2140860 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139459 2139570 2139733 "PMASSFS" 2140071 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139114 2139182 2139276 "PLOTTOOL" 2139385 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2133721 2134925 2136073 "PLOT" 2137986 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129525 2130569 2131490 "PLOT3D" 2132820 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128437 2128614 2128849 "PLOT1" 2129329 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2103826 2108503 2113354 "PLEQN" 2123703 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103144 2103266 2103446 "PINTERP" 2103691 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2102837 2102884 2102987 "PINTERPA" 2103091 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2102085 2102606 2102693 "PI" 2102733 T PI (NIL) -8 NIL NIL 2102800) (-917 2100474 2101423 2101451 "PID" 2101633 T PID (NIL) -9 NIL 2101767 NIL) (-916 2100199 2100236 2100324 "PICOERCE" 2100431 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099519 2099658 2099834 "PGROEB" 2100055 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095106 2095920 2096825 "PGE" 2098634 T PGE (NIL) -7 NIL NIL NIL) (-913 2093229 2093476 2093842 "PGCD" 2094823 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2092567 2092670 2092831 "PFRPAC" 2093113 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089235 2091115 2091468 "PFR" 2092246 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2087624 2087868 2088193 "PFOTOOLS" 2088982 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086157 2086396 2086747 "PFOQ" 2087381 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2084630 2084842 2085205 "PFO" 2085941 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081210 2084519 2084588 "PF" 2084593 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2078636 2079881 2079909 "PFECAT" 2080494 T PFECAT (NIL) -9 NIL 2080878 NIL) (-905 2078081 2078235 2078449 "PFECAT-" 2078454 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2076684 2076936 2077237 "PFBRU" 2077830 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2074549 2074902 2075334 "PFBR" 2076335 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070458 2071925 2072601 "PERM" 2073906 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2065719 2066665 2067535 "PERMGRP" 2069621 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2063851 2064782 2064823 "PERMCAT" 2065269 NIL PERMCAT (NIL T) -9 NIL 2065574 NIL) (-899 2063504 2063545 2063669 "PERMAN" 2063804 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2061040 2063169 2063291 "PENDTREE" 2063415 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059125 2059867 2059908 "PDRING" 2060565 NIL PDRING (NIL T) -9 NIL 2060851 NIL) (-896 2058228 2058446 2058808 "PDRING-" 2058813 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055470 2056221 2056889 "PDEPROB" 2057580 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2053015 2053519 2054074 "PDEPACK" 2054935 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2051927 2052117 2052368 "PDECOMP" 2052814 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2049532 2050349 2050377 "PDECAT" 2051164 T PDECAT (NIL) -9 NIL 2051877 NIL) (-891 2049283 2049316 2049406 "PCOMP" 2049493 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047488 2048084 2048381 "PBWLB" 2049012 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2039988 2041561 2042899 "PATTERN" 2046171 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2039620 2039677 2039786 "PATTERN2" 2039925 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037377 2037765 2038222 "PATTERN1" 2039209 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2034772 2035326 2035807 "PATRES" 2036942 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034336 2034403 2034535 "PATRES2" 2034699 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032219 2032624 2033031 "PATMATCH" 2034003 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2031755 2031938 2031979 "PATMAB" 2032086 NIL PATMAB (NIL T) -9 NIL 2032169 NIL) (-882 2030300 2030609 2030867 "PATLRES" 2031560 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2029846 2029969 2030010 "PATAB" 2030015 NIL PATAB (NIL T) -9 NIL 2030187 NIL) (-880 2027327 2027859 2028432 "PARTPERM" 2029293 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2026948 2027011 2027113 "PARSURF" 2027258 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2026580 2026637 2026746 "PARSU2" 2026885 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026344 2026384 2026451 "PARSER" 2026533 T PARSER (NIL) -7 NIL NIL NIL) (-876 2025965 2026028 2026130 "PARSCURV" 2026275 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2025597 2025654 2025763 "PARSC2" 2025902 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025236 2025294 2025391 "PARPCURV" 2025533 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2024868 2024925 2025034 "PARPC2" 2025173 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024388 2024474 2024593 "PAN2EXPR" 2024769 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023192 2023509 2023737 "PALETTE" 2024180 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2021660 2022197 2022557 "PAIR" 2022878 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2015557 2020919 2021113 "PADICRC" 2021515 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2008813 2014903 2015087 "PADICRAT" 2015405 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007155 2008750 2008795 "PADIC" 2008800 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004357 2005895 2005935 "PADICCT" 2006516 NIL PADICCT (NIL NIL) -9 NIL 2006798 NIL) (-865 2003314 2003514 2003782 "PADEPAC" 2004144 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002526 2002659 2002865 "PADE" 2003176 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2000940 2001734 2002014 "OWP" 2002330 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000460 2000646 2000743 "OVERSET" 2000863 T OVERSET (NIL) -8 NIL NIL NIL) (-861 1999533 2000065 2000237 "OVAR" 2000328 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1998797 1998918 1999079 "OUT" 1999392 T OUT (NIL) -7 NIL NIL NIL) (-859 1987695 1989906 1992106 "OUTFORM" 1996617 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1987031 1987292 1987419 "OUTBFILE" 1987588 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986338 1986503 1986531 "OUTBCON" 1986849 T OUTBCON (NIL) -9 NIL 1987015 NIL) (-856 1985939 1986051 1986208 "OUTBCON-" 1986213 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985346 1985668 1985757 "OSI" 1985870 T OSI (NIL) -8 NIL NIL NIL) (-854 1984902 1985214 1985242 "OSGROUP" 1985247 T OSGROUP (NIL) -9 NIL 1985269 NIL) (-853 1983647 1983874 1984159 "ORTHPOL" 1984649 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981225 1983482 1983603 "OREUP" 1983608 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1978655 1980916 1981043 "ORESUP" 1981167 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976183 1976683 1977244 "OREPCTO" 1978144 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1969999 1972174 1972215 "OREPCAT" 1974563 NIL OREPCAT (NIL T) -9 NIL 1975667 NIL) (-848 1967146 1967928 1968986 "OREPCAT-" 1968991 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966323 1966595 1966623 "ORDSET" 1966932 T ORDSET (NIL) -9 NIL 1967096 NIL) (-846 1965842 1965964 1966157 "ORDSET-" 1966162 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964468 1965233 1965261 "ORDRING" 1965463 T ORDRING (NIL) -9 NIL 1965588 NIL) (-844 1964113 1964207 1964351 "ORDRING-" 1964356 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963519 1963956 1963984 "ORDMON" 1963989 T ORDMON (NIL) -9 NIL 1964010 NIL) (-842 1962681 1962828 1963023 "ORDFUNS" 1963368 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1962045 1962438 1962466 "ORDFIN" 1962531 T ORDFIN (NIL) -9 NIL 1962605 NIL) (-840 1958631 1960631 1961040 "ORDCOMP" 1961669 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1957897 1958024 1958210 "ORDCOMP2" 1958491 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954505 1955388 1956202 "OPTPROB" 1957103 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951307 1951946 1952650 "OPTPACK" 1953821 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1949020 1949760 1949788 "OPTCAT" 1950607 T OPTCAT (NIL) -9 NIL 1951257 NIL) (-835 1948463 1948697 1948802 "OPSIG" 1948935 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948231 1948270 1948336 "OPQUERY" 1948417 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945389 1946542 1947046 "OP" 1947760 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1944924 1945095 1945136 "OPERCAT" 1945271 NIL OPERCAT (NIL T) -9 NIL 1945339 NIL) (-831 1944770 1944797 1944883 "OPERCAT-" 1944888 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1941609 1943567 1943936 "ONECOMP" 1944434 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1940914 1941029 1941203 "ONECOMP2" 1941481 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940333 1940439 1940569 "OMSERVER" 1940804 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937221 1939773 1939813 "OMSAGG" 1939874 NIL OMSAGG (NIL T) -9 NIL 1939938 NIL) (-826 1935844 1936107 1936389 "OMPKG" 1936959 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935274 1935377 1935405 "OM" 1935704 T OM (NIL) -9 NIL NIL NIL) (-824 1933848 1934823 1934992 "OMLO" 1935155 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1932773 1932920 1933147 "OMEXPR" 1933674 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1932091 1932319 1932455 "OMERR" 1932657 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931269 1931512 1931672 "OMERRK" 1931951 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1930747 1930946 1931054 "OMENC" 1931181 T OMENC (NIL) -8 NIL NIL NIL) (-819 1924642 1925827 1926998 "OMDEV" 1929596 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1923711 1923882 1924076 "OMCONN" 1924468 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922324 1923274 1923302 "OINTDOM" 1923307 T OINTDOM (NIL) -9 NIL 1923328 NIL) (-816 1918130 1919314 1920030 "OFMONOID" 1921640 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1917568 1918067 1918112 "ODVAR" 1918117 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1915018 1917313 1917468 "ODR" 1917473 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907354 1914794 1914920 "ODPOL" 1914925 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901224 1907226 1907331 "ODP" 1907336 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1899990 1900205 1900480 "ODETOOLS" 1900998 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1896957 1897615 1898331 "ODESYS" 1899323 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1891839 1892747 1893772 "ODERTRIC" 1896032 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891265 1891347 1891541 "ODERED" 1891751 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888153 1888701 1889378 "ODERAT" 1890688 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885110 1885577 1886174 "ODEPRRIC" 1887682 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1883080 1883649 1884135 "ODEPROB" 1884644 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1879600 1880085 1880732 "ODEPRIM" 1882559 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1878849 1878951 1879211 "ODEPAL" 1879492 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1875011 1875802 1876666 "ODEPACK" 1878005 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1874044 1874151 1874380 "ODEINT" 1874900 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868145 1869570 1871017 "ODEIFTBL" 1872617 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863480 1864266 1865225 "ODEEF" 1867304 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1862815 1862904 1863134 "ODECONST" 1863385 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1860966 1861601 1861629 "ODECAT" 1862234 T ODECAT (NIL) -9 NIL 1862765 NIL) (-796 1857865 1860678 1860797 "OCT" 1860879 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857503 1857546 1857673 "OCTCT2" 1857816 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852269 1854677 1854717 "OC" 1855814 NIL OC (NIL T) -9 NIL 1856672 NIL) (-793 1849496 1850244 1851234 "OC-" 1851328 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1848874 1849316 1849344 "OCAMON" 1849349 T OCAMON (NIL) -9 NIL 1849370 NIL) (-791 1848431 1848746 1848774 "OASGP" 1848779 T OASGP (NIL) -9 NIL 1848799 NIL) (-790 1847718 1848181 1848209 "OAMONS" 1848249 T OAMONS (NIL) -9 NIL 1848292 NIL) (-789 1847158 1847565 1847593 "OAMON" 1847598 T OAMON (NIL) -9 NIL 1847618 NIL) (-788 1846462 1846954 1846982 "OAGROUP" 1846987 T OAGROUP (NIL) -9 NIL 1847007 NIL) (-787 1846152 1846202 1846290 "NUMTUBE" 1846406 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1839725 1841243 1842779 "NUMQUAD" 1844636 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835481 1836469 1837494 "NUMODE" 1838720 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1832862 1833716 1833744 "NUMINT" 1834667 T NUMINT (NIL) -9 NIL 1835431 NIL) (-783 1831810 1832007 1832225 "NUMFMT" 1832664 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818169 1821114 1823646 "NUMERIC" 1829317 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1812566 1817618 1817713 "NTSCAT" 1817718 NIL NTSCAT (NIL T T T T) -9 NIL 1817757 NIL) (-780 1811760 1811925 1812118 "NTPOLFN" 1812405 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1799592 1808585 1809397 "NSUP" 1810981 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799224 1799281 1799390 "NSUP2" 1799529 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789207 1798998 1799131 "NSMP" 1799136 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1787639 1787940 1788297 "NREP" 1788895 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786230 1786482 1786840 "NPCOEF" 1787382 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785296 1785411 1785627 "NORMRETR" 1786111 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783337 1783627 1784036 "NORMPK" 1785004 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1783022 1783050 1783174 "NORMMA" 1783303 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1782849 1782979 1783008 "NONE" 1783013 T NONE (NIL) -8 NIL NIL NIL) (-770 1782638 1782667 1782736 "NONE1" 1782813 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782121 1782183 1782369 "NODE1" 1782570 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780391 1781215 1781470 "NNI" 1781817 T NNI (NIL) -8 NIL NIL 1782052) (-767 1778811 1779124 1779488 "NLINSOL" 1780059 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1775079 1776047 1776946 "NIPROB" 1777932 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1773836 1774070 1774372 "NFINTBAS" 1774841 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1773010 1773486 1773527 "NETCLT" 1773699 NIL NETCLT (NIL T) -9 NIL 1773781 NIL) (-763 1771718 1771949 1772230 "NCODIV" 1772778 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771480 1771517 1771592 "NCNTFRAC" 1771675 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1769660 1770024 1770444 "NCEP" 1771105 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1768557 1769304 1769332 "NASRING" 1769442 T NASRING (NIL) -9 NIL 1769522 NIL) (-759 1768352 1768396 1768490 "NASRING-" 1768495 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767505 1768004 1768032 "NARNG" 1768149 T NARNG (NIL) -9 NIL 1768240 NIL) (-757 1767197 1767264 1767398 "NARNG-" 1767403 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1766076 1766283 1766518 "NAGSP" 1766982 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757348 1759032 1760705 "NAGS" 1764423 T NAGS (NIL) -7 NIL NIL NIL) (-754 1755896 1756204 1756535 "NAGF07" 1757037 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750434 1751725 1753032 "NAGF04" 1754609 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743402 1745016 1746649 "NAGF02" 1748821 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1738626 1739726 1740843 "NAGF01" 1742305 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732254 1733820 1735405 "NAGE04" 1737061 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723423 1725544 1727674 "NAGE02" 1730144 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719376 1720323 1721287 "NAGE01" 1722479 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717171 1717705 1718263 "NAGD03" 1718838 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1708921 1710849 1712803 "NAGD02" 1715237 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1702732 1704157 1705597 "NAGD01" 1707501 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1698941 1699763 1700600 "NAGC06" 1701915 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697406 1697738 1698094 "NAGC05" 1698605 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1696782 1696901 1697045 "NAGC02" 1697282 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1695842 1696399 1696439 "NAALG" 1696518 NIL NAALG (NIL T) -9 NIL 1696579 NIL) (-740 1695677 1695706 1695796 "NAALG-" 1695801 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1689627 1690735 1691922 "MULTSQFR" 1694573 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1688946 1689021 1689205 "MULTFACT" 1689539 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1682031 1685909 1685962 "MTSCAT" 1687032 NIL MTSCAT (NIL T T) -9 NIL 1687546 NIL) (-736 1681743 1681797 1681889 "MTHING" 1681971 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1681535 1681568 1681628 "MSYSCMD" 1681703 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1677644 1680290 1680610 "MSET" 1681248 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1674739 1677205 1677246 "MSETAGG" 1677251 NIL MSETAGG (NIL T) -9 NIL 1677285 NIL) (-732 1670607 1672118 1672863 "MRING" 1674039 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670173 1670240 1670371 "MRF2" 1670534 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1669791 1669826 1669970 "MRATFAC" 1670132 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667403 1667698 1668129 "MPRFF" 1669496 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661455 1667257 1667354 "MPOLY" 1667359 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1660945 1660980 1661188 "MPCPF" 1661414 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660459 1660502 1660686 "MPC3" 1660896 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1659654 1659735 1659956 "MPC2" 1660374 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657955 1658292 1658682 "MONOTOOL" 1659314 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657206 1657497 1657525 "MONOID" 1657744 T MONOID (NIL) -9 NIL 1657891 NIL) (-722 1656752 1656871 1657052 "MONOID-" 1657057 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1647603 1653519 1653578 "MONOGEN" 1654252 NIL MONOGEN (NIL T T) -9 NIL 1654708 NIL) (-720 1644821 1645556 1646556 "MONOGEN-" 1646675 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1643680 1644100 1644128 "MONADWU" 1644520 T MONADWU (NIL) -9 NIL 1644758 NIL) (-718 1643052 1643211 1643459 "MONADWU-" 1643464 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642437 1642655 1642683 "MONAD" 1642890 T MONAD (NIL) -9 NIL 1643002 NIL) (-716 1642122 1642200 1642332 "MONAD-" 1642337 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640438 1641035 1641314 "MOEBIUS" 1641875 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1639830 1640208 1640248 "MODULE" 1640253 NIL MODULE (NIL T) -9 NIL 1640279 NIL) (-713 1639398 1639494 1639684 "MODULE-" 1639689 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637105 1637762 1638089 "MODRING" 1639222 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1634076 1635210 1635731 "MODOP" 1636634 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1632691 1633143 1633420 "MODMONOM" 1633939 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622488 1630982 1631396 "MODMON" 1632328 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1619671 1621332 1621608 "MODFIELD" 1622363 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1618675 1618952 1619142 "MMLFORM" 1619501 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618201 1618244 1618423 "MMAP" 1618626 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616410 1617151 1617192 "MLO" 1617615 NIL MLO (NIL T) -9 NIL 1617857 NIL) (-704 1613776 1614292 1614894 "MLIFT" 1615891 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613167 1613251 1613405 "MKUCFUNC" 1613687 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1612766 1612836 1612959 "MKRECORD" 1613090 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1611813 1611975 1612203 "MKFUNC" 1612577 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611201 1611305 1611461 "MKFLCFN" 1611696 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1610744 1611111 1611170 "MKCHSET" 1611175 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1610021 1610123 1610308 "MKBCFUNC" 1610637 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1606755 1609575 1609711 "MINT" 1609905 T MINT (NIL) -8 NIL NIL NIL) (-696 1605567 1605810 1606087 "MHROWRED" 1606510 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1600974 1604102 1604507 "MFLOAT" 1605182 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600331 1600407 1600578 "MFINFACT" 1600886 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1596646 1597494 1598378 "MESH" 1599467 T MESH (NIL) -7 NIL NIL NIL) (-692 1595036 1595348 1595701 "MDDFACT" 1596333 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1591878 1594195 1594236 "MDAGG" 1594491 NIL MDAGG (NIL T) -9 NIL 1594634 NIL) (-690 1581648 1591171 1591378 "MCMPLX" 1591691 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1580789 1580935 1581135 "MCDEN" 1581497 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1578679 1578949 1579329 "MCALCFN" 1580519 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1577604 1577844 1578077 "MAYBE" 1578485 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575216 1575739 1576301 "MATSTOR" 1577075 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571221 1574588 1574836 "MATRIX" 1575001 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1566985 1567694 1568430 "MATLIN" 1570578 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557139 1560277 1560354 "MATCAT" 1565234 NIL MATCAT (NIL T T T) -9 NIL 1566651 NIL) (-682 1553495 1554516 1555872 "MATCAT-" 1555877 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552089 1552242 1552575 "MATCAT2" 1553330 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550201 1550525 1550909 "MAPPKG3" 1551764 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549182 1549355 1549577 "MAPPKG2" 1550025 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1547681 1547965 1548292 "MAPPKG1" 1548888 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1546787 1547087 1547264 "MAPPAST" 1547524 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546398 1546456 1546579 "MAPHACK3" 1546723 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1545990 1546051 1546165 "MAPHACK2" 1546330 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545427 1545531 1545673 "MAPHACK1" 1545881 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1543533 1544127 1544431 "MAGMA" 1545155 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543039 1543257 1543348 "MACROAST" 1543462 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539505 1541278 1541739 "M3D" 1542611 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1533659 1537874 1537915 "LZSTAGG" 1538697 NIL LZSTAGG (NIL T) -9 NIL 1538992 NIL) (-669 1529616 1530790 1532247 "LZSTAGG-" 1532252 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1526730 1527507 1527994 "LWORD" 1529161 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526333 1526534 1526609 "LSTAST" 1526675 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519526 1526104 1526238 "LSQM" 1526243 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1518750 1518889 1519117 "LSPP" 1519381 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1516562 1516863 1517319 "LSMP" 1518439 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513341 1514015 1514745 "LSMP1" 1515864 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507266 1512508 1512549 "LSAGG" 1512611 NIL LSAGG (NIL T) -9 NIL 1512689 NIL) (-661 1503961 1504885 1506098 "LSAGG-" 1506103 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1501587 1503105 1503354 "LPOLY" 1503756 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501169 1501254 1501377 "LPEFRAC" 1501496 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499516 1500263 1500516 "LO" 1501001 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499168 1499280 1499308 "LOGIC" 1499419 T LOGIC (NIL) -9 NIL 1499500 NIL) (-656 1499030 1499053 1499124 "LOGIC-" 1499129 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498223 1498363 1498556 "LODOOPS" 1498886 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1495673 1498139 1498205 "LODO" 1498210 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494211 1494446 1494799 "LODOF" 1495420 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1490559 1492964 1493005 "LODOCAT" 1493443 NIL LODOCAT (NIL T) -9 NIL 1493654 NIL) (-651 1490292 1490350 1490477 "LODOCAT-" 1490482 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1487639 1490133 1490251 "LODO2" 1490256 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485101 1487576 1487621 "LODO1" 1487626 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1483961 1484126 1484438 "LODEEF" 1484924 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479247 1482091 1482132 "LNAGG" 1483079 NIL LNAGG (NIL T) -9 NIL 1483523 NIL) (-646 1478394 1478608 1478950 "LNAGG-" 1478955 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1474557 1475319 1475958 "LMOPS" 1477809 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1473952 1474314 1474355 "LMODULE" 1474416 NIL LMODULE (NIL T) -9 NIL 1474458 NIL) (-643 1471198 1473597 1473720 "LMDICT" 1473862 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1470924 1471106 1471166 "LITERAL" 1471171 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464155 1469870 1470168 "LIST" 1470659 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1463680 1463754 1463893 "LIST3" 1464075 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1462687 1462865 1463093 "LIST2" 1463498 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1460821 1461133 1461532 "LIST2MAP" 1462334 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1459543 1460187 1460228 "LINEXP" 1460483 NIL LINEXP (NIL T) -9 NIL 1460632 NIL) (-636 1458190 1458450 1458747 "LINDEP" 1459295 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1454957 1455676 1456453 "LIMITRF" 1457445 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453232 1453528 1453944 "LIMITPS" 1454652 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1447687 1452743 1452971 "LIE" 1453053 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1446736 1447179 1447219 "LIECAT" 1447359 NIL LIECAT (NIL T) -9 NIL 1447510 NIL) (-631 1446577 1446604 1446692 "LIECAT-" 1446697 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439189 1446026 1446191 "LIB" 1446432 T LIB (NIL) -8 NIL NIL NIL) (-629 1434824 1435707 1436642 "LGROBP" 1438306 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1432690 1432964 1433326 "LF" 1434545 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1431530 1432222 1432250 "LFCAT" 1432457 T LFCAT (NIL) -9 NIL 1432596 NIL) (-626 1428432 1429062 1429750 "LEXTRIPK" 1430894 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425203 1426002 1426505 "LEXP" 1428012 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1424706 1424924 1425016 "LETAST" 1425131 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423104 1423417 1423818 "LEADCDET" 1424388 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422294 1422368 1422597 "LAZM3PK" 1423025 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417238 1420371 1420909 "LAUPOL" 1421806 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1416803 1416847 1417015 "LAPLACE" 1417188 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1414769 1415904 1416155 "LA" 1416636 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1413842 1414400 1414441 "LALG" 1414503 NIL LALG (NIL T) -9 NIL 1414562 NIL) (-617 1413556 1413615 1413751 "LALG-" 1413756 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413391 1413415 1413456 "KVTFROM" 1413518 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412191 1412608 1412837 "KTVLOGIC" 1413182 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412026 1412050 1412091 "KRCFROM" 1412153 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1410930 1411117 1411416 "KOVACIC" 1411826 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1410765 1410789 1410830 "KONVERT" 1410892 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1410600 1410624 1410665 "KOERCE" 1410727 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408334 1409094 1409487 "KERNEL" 1410239 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1407836 1407917 1408047 "KERNEL2" 1408248 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1401687 1406375 1406429 "KDAGG" 1406806 NIL KDAGG (NIL T T) -9 NIL 1407012 NIL) (-607 1401216 1401340 1401545 "KDAGG-" 1401550 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394391 1400877 1401032 "KAFILE" 1401094 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1388846 1393902 1394130 "JORDAN" 1394212 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388252 1388495 1388616 "JOINAST" 1388745 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388098 1388157 1388212 "JAVACODE" 1388217 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384397 1386303 1386357 "IXAGG" 1387286 NIL IXAGG (NIL T T) -9 NIL 1387745 NIL) (-601 1383316 1383622 1384041 "IXAGG-" 1384046 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1378896 1383238 1383297 "IVECTOR" 1383302 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1377662 1377899 1378165 "ITUPLE" 1378663 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376098 1376275 1376581 "ITRIGMNP" 1377484 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1374843 1375047 1375330 "ITFUN3" 1375874 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374475 1374532 1374641 "ITFUN2" 1374780 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372304 1373337 1373636 "ITAYLOR" 1374209 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361276 1366441 1367604 "ISUPS" 1371174 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360380 1360520 1360756 "ISUMP" 1361123 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1355644 1360181 1360260 "ISTRING" 1360333 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355147 1355365 1355457 "ISAST" 1355572 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354357 1354438 1354654 "IRURPK" 1355061 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353293 1353494 1353734 "IRSN" 1354137 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351322 1351677 1352113 "IRRF2F" 1352931 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351069 1351107 1351183 "IRREDFFX" 1351278 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1349684 1349943 1350242 "IROOT" 1350802 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346315 1347368 1348060 "IR" 1349024 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1343928 1344423 1344989 "IR2" 1345793 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343000 1343113 1343334 "IR2F" 1343811 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1342791 1342825 1342885 "IPRNTPK" 1342960 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339398 1342680 1342749 "IPF" 1342754 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1337752 1339323 1339380 "IPADIC" 1339385 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337091 1337312 1337442 "IP4ADDR" 1337642 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1336591 1336795 1336905 "IOMODE" 1337001 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1335664 1336188 1336315 "IOBFILE" 1336484 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335152 1335568 1335596 "IOBCON" 1335601 T IOBCON (NIL) -9 NIL 1335622 NIL) (-575 1334649 1334707 1334897 "INVLAPLA" 1335088 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324297 1326651 1329037 "INTTR" 1332313 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1320641 1321383 1322247 "INTTOOLS" 1323482 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320227 1320318 1320435 "INTSLPE" 1320544 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318208 1320150 1320209 "INTRVL" 1320214 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1315810 1316322 1316897 "INTRF" 1317693 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315221 1315318 1315460 "INTRET" 1315708 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313218 1313607 1314077 "INTRAT" 1314829 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310446 1311029 1311655 "INTPM" 1312703 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307148 1307748 1308493 "INTPAF" 1309832 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302327 1303289 1304340 "INTPACK" 1306117 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299231 1302056 1302183 "INT" 1302220 T INT (NIL) -8 NIL NIL NIL) (-563 1298483 1298635 1298843 "INTHERTR" 1299073 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1297922 1298002 1298190 "INTHERAL" 1298397 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1295768 1296211 1296668 "INTHEORY" 1297485 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287076 1288697 1290476 "INTG0" 1294120 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1267649 1272439 1277249 "INTFTBL" 1282286 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1266898 1267036 1267209 "INTFACT" 1267508 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264283 1264729 1265293 "INTEF" 1266452 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1262742 1263455 1263483 "INTDOM" 1263784 T INTDOM (NIL) -9 NIL 1263991 NIL) (-555 1262111 1262285 1262527 "INTDOM-" 1262532 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1258598 1260495 1260549 "INTCAT" 1261348 NIL INTCAT (NIL T) -9 NIL 1261668 NIL) (-553 1258070 1258173 1258301 "INTBIT" 1258490 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1256741 1256895 1257209 "INTALG" 1257915 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256198 1256288 1256458 "INTAF" 1256645 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1249652 1256008 1256148 "INTABL" 1256153 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1248983 1249422 1249487 "INT8" 1249521 T INT8 (NIL) -8 NIL NIL 1249566) (-548 1248313 1248752 1248817 "INT64" 1248851 T INT64 (NIL) -8 NIL NIL 1248896) (-547 1247643 1248082 1248147 "INT32" 1248181 T INT32 (NIL) -8 NIL NIL 1248226) (-546 1246973 1247412 1247477 "INT16" 1247511 T INT16 (NIL) -8 NIL NIL 1247556) (-545 1241980 1244662 1244690 "INS" 1245624 T INS (NIL) -9 NIL 1246289 NIL) (-544 1239220 1239991 1240965 "INS-" 1241038 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237995 1238222 1238520 "INPSIGN" 1238973 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237113 1237230 1237427 "INPRODPF" 1237875 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236007 1236124 1236361 "INPRODFF" 1236993 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235007 1235159 1235419 "INNMFACT" 1235843 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234204 1234301 1234489 "INMODGCD" 1234906 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232712 1232957 1233281 "INFSP" 1233949 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231896 1232013 1232196 "INFPROD0" 1232592 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228778 1229961 1230476 "INFORM" 1231389 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228388 1228448 1228546 "INFORM1" 1228713 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227911 1228000 1228114 "INFINITY" 1228294 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227087 1227631 1227732 "INETCLTS" 1227830 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225703 1225953 1226274 "INEP" 1226835 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224979 1225600 1225665 "INDE" 1225670 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224543 1224611 1224728 "INCRMAPS" 1224906 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223361 1223812 1224018 "INBFILE" 1224357 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218661 1219597 1220541 "INBFF" 1222449 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217569 1217838 1217866 "INBCON" 1218379 T INBCON (NIL) -9 NIL 1218645 NIL) (-526 1216821 1217044 1217320 "INBCON-" 1217325 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216327 1216545 1216636 "INAST" 1216750 T INAST (NIL) -8 NIL NIL NIL) (-524 1215781 1216006 1216112 "IMPTAST" 1216241 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212275 1215625 1215729 "IMATRIX" 1215734 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210987 1211110 1211425 "IMATQF" 1212131 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209207 1209434 1209771 "IMATLIN" 1210743 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203833 1209131 1209189 "ILIST" 1209194 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201786 1203693 1203806 "IIARRAY2" 1203811 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197211 1201697 1201761 "IFF" 1201766 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196585 1196828 1196944 "IFAST" 1197115 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191628 1195877 1196065 "IFARRAY" 1196442 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190835 1191532 1191605 "IFAMON" 1191610 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190419 1190484 1190538 "IEVALAB" 1190745 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190094 1190162 1190322 "IEVALAB-" 1190327 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189752 1190008 1190071 "IDPO" 1190076 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189029 1189641 1189716 "IDPOAMS" 1189721 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188363 1188918 1188993 "IDPOAM" 1188998 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187448 1187698 1187751 "IDPC" 1188164 NIL IDPC (NIL T T) -9 NIL 1188313 NIL) (-508 1186944 1187340 1187413 "IDPAM" 1187418 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186347 1186836 1186909 "IDPAG" 1186914 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186019 1186183 1186258 "IDENT" 1186292 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182274 1183122 1184017 "IDECOMP" 1185176 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175138 1176197 1177244 "IDEAL" 1181310 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174302 1174414 1174613 "ICDEN" 1175022 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173400 1173782 1173929 "ICARD" 1174175 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171460 1171773 1172178 "IBPTOOLS" 1173077 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167094 1171080 1171193 "IBITS" 1171379 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163817 1164393 1165088 "IBATOOL" 1166511 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161596 1162058 1162591 "IBACHIN" 1163352 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159473 1161442 1161545 "IARRAY2" 1161550 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155626 1159399 1159456 "IARRAY1" 1159461 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149610 1154038 1154519 "IAN" 1155165 T IAN (NIL) -8 NIL NIL NIL) (-494 1149121 1149178 1149351 "IALGFACT" 1149547 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148649 1148762 1148790 "HYPCAT" 1148997 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148187 1148304 1148490 "HYPCAT-" 1148495 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147809 1147982 1148065 "HOSTNAME" 1148124 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147654 1147691 1147732 "HOMOTOP" 1147737 NIL HOMOTOP (NIL T) -9 NIL 1147770 NIL) (-489 1144333 1145664 1145705 "HOAGG" 1146686 NIL HOAGG (NIL T) -9 NIL 1147365 NIL) (-488 1142927 1143326 1143852 "HOAGG-" 1143857 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136958 1142522 1142671 "HEXADEC" 1142798 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135706 1135928 1136191 "HEUGCD" 1136735 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134809 1135543 1135673 "HELLFDIV" 1135678 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133036 1134586 1134674 "HEAP" 1134753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132326 1132588 1132722 "HEADAST" 1132922 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126240 1132241 1132303 "HDP" 1132308 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119983 1125875 1126027 "HDMP" 1126141 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119307 1119447 1119611 "HB" 1119839 T HB (NIL) -7 NIL NIL NIL) (-479 1112804 1119153 1119257 "HASHTBL" 1119262 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112307 1112525 1112617 "HASAST" 1112732 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110112 1111929 1112111 "HACKPI" 1112145 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105807 1109965 1110078 "GTSET" 1110083 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099333 1105685 1105783 "GSTBL" 1105788 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091638 1098364 1098629 "GSERIES" 1099124 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090805 1091196 1091224 "GROUP" 1091427 T GROUP (NIL) -9 NIL 1091561 NIL) (-472 1090171 1090330 1090581 "GROUP-" 1090586 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088538 1088859 1089246 "GROEBSOL" 1089848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087478 1087740 1087791 "GRMOD" 1088320 NIL GRMOD (NIL T T) -9 NIL 1088488 NIL) (-469 1087246 1087282 1087410 "GRMOD-" 1087415 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082563 1083600 1084600 "GRIMAGE" 1086266 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081029 1081290 1081614 "GRDEF" 1082259 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080473 1080589 1080730 "GRAY" 1080908 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079686 1080066 1080117 "GRALG" 1080270 NIL GRALG (NIL T T) -9 NIL 1080363 NIL) (-464 1079347 1079420 1079583 "GRALG-" 1079588 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076151 1078932 1079110 "GPOLSET" 1079254 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075505 1075562 1075820 "GOSPER" 1076088 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071264 1071943 1072469 "GMODPOL" 1075204 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070269 1070453 1070691 "GHENSEL" 1071076 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064320 1065163 1066190 "GENUPS" 1069353 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064017 1064068 1064157 "GENUFACT" 1064263 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063429 1063506 1063671 "GENPGCD" 1063935 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062903 1062938 1063151 "GENMFACT" 1063388 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061469 1061726 1062033 "GENEEZ" 1062646 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055370 1061080 1061242 "GDMP" 1061392 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044739 1049141 1050247 "GCNAALG" 1054353 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043158 1043994 1044022 "GCDDOM" 1044277 T GCDDOM (NIL) -9 NIL 1044434 NIL) (-451 1042628 1042755 1042970 "GCDDOM-" 1042975 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041300 1041485 1041789 "GB" 1042407 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029916 1032246 1034638 "GBINTERN" 1038991 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027753 1028045 1028466 "GBF" 1029591 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026534 1026699 1026966 "GBEUCLID" 1027569 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025883 1026008 1026157 "GAUSSFAC" 1026405 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024250 1024552 1024866 "GALUTIL" 1025602 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022558 1022832 1023156 "GALPOLYU" 1023977 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019923 1020213 1020620 "GALFACTU" 1022255 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011729 1013228 1014836 "GALFACT" 1018355 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009117 1009775 1009803 "FVFUN" 1010959 T FVFUN (NIL) -9 NIL 1011679 NIL) (-440 1008383 1008565 1008593 "FVC" 1008884 T FVC (NIL) -9 NIL 1009067 NIL) (-439 1008053 1008208 1008276 "FUNDESC" 1008335 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007695 1007850 1007931 "FUNCTION" 1008005 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005466 1006017 1006483 "FT" 1007249 T FT (NIL) -8 NIL NIL NIL) (-436 1004284 1004767 1004970 "FTEM" 1005283 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002540 1002829 1003233 "FSUPFACT" 1003975 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000937 1001226 1001558 "FST" 1002228 T FST (NIL) -8 NIL NIL NIL) (-433 1000108 1000214 1000409 "FSRED" 1000819 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998786 999042 999396 "FSPRMELT" 999823 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995871 996309 996808 "FSPECF" 998349 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977925 986374 986414 "FS" 990262 NIL FS (NIL T) -9 NIL 992551 NIL) (-429 966572 969565 973621 "FS-" 973918 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966086 966140 966317 "FSINT" 966513 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964405 965079 965382 "FSERIES" 965865 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963419 963535 963766 "FSCINT" 964285 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959653 962363 962404 "FSAGG" 962774 NIL FSAGG (NIL T) -9 NIL 963033 NIL) (-424 957415 958016 958812 "FSAGG-" 958907 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956457 956600 956827 "FSAGG2" 957268 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954111 954391 954945 "FS2UPS" 956175 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953693 953736 953891 "FS2" 954062 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952550 952721 953030 "FS2EXPXP" 953518 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951976 952091 952243 "FRUTIL" 952430 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943416 947471 948829 "FR" 950650 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938491 941134 941174 "FRNAALG" 942570 NIL FRNAALG (NIL T) -9 NIL 943177 NIL) (-416 934164 935240 936515 "FRNAALG-" 937265 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933802 933845 933972 "FRNAAF2" 934115 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932209 932656 932951 "FRMOD" 933614 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929987 930592 930909 "FRIDEAL" 932000 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929182 929269 929558 "FRIDEAL2" 929894 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928315 928729 928770 "FRETRCT" 928775 NIL FRETRCT (NIL T) -9 NIL 928951 NIL) (-410 927427 927658 928009 "FRETRCT-" 928014 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924631 925815 925874 "FRAMALG" 926756 NIL FRAMALG (NIL T T) -9 NIL 927048 NIL) (-408 922765 923220 923850 "FRAMALG-" 924073 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916713 922240 922516 "FRAC" 922521 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916349 916406 916513 "FRAC2" 916650 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915985 916042 916149 "FR2" 916286 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910650 913510 913538 "FPS" 914657 T FPS (NIL) -9 NIL 915214 NIL) (-403 910099 910208 910372 "FPS-" 910518 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907545 909188 909216 "FPC" 909441 T FPC (NIL) -9 NIL 909583 NIL) (-401 907338 907378 907475 "FPC-" 907480 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906216 906826 906867 "FPATMAB" 906872 NIL FPATMAB (NIL T) -9 NIL 907024 NIL) (-399 903916 904392 904818 "FPARFRAC" 905853 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899309 899808 900490 "FORTRAN" 903348 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897025 897525 898064 "FORT" 898790 T FORT (NIL) -7 NIL NIL NIL) (-396 894701 895263 895291 "FORTFN" 896351 T FORTFN (NIL) -9 NIL 896975 NIL) (-395 894465 894515 894543 "FORTCAT" 894602 T FORTCAT (NIL) -9 NIL 894664 NIL) (-394 892598 893081 893471 "FORMULA" 894095 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892386 892416 892485 "FORMULA1" 892562 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891909 891961 892134 "FORDER" 892328 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891005 891169 891362 "FOP" 891736 T FOP (NIL) -7 NIL NIL NIL) (-390 889613 890285 890459 "FNLA" 890887 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888368 888757 888785 "FNCAT" 889245 T FNCAT (NIL) -9 NIL 889505 NIL) (-388 887934 888327 888355 "FNAME" 888360 T FNAME (NIL) -8 NIL NIL NIL) (-387 886589 887526 887554 "FMTC" 887559 T FMTC (NIL) -9 NIL 887595 NIL) (-386 882949 884112 884741 "FMONOID" 885993 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882168 882691 882840 "FM" 882845 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879592 880238 880266 "FMFUN" 881410 T FMFUN (NIL) -9 NIL 882118 NIL) (-383 878861 879042 879070 "FMC" 879360 T FMC (NIL) -9 NIL 879542 NIL) (-382 876055 876889 876943 "FMCAT" 878138 NIL FMCAT (NIL T T) -9 NIL 878633 NIL) (-381 874948 875821 875921 "FM1" 876000 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872722 873138 873632 "FLOATRP" 874499 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866323 870451 871072 "FLOAT" 872121 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863761 864261 864839 "FLOATCP" 865790 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862562 863374 863415 "FLINEXP" 863420 NIL FLINEXP (NIL T) -9 NIL 863513 NIL) (-376 861716 861951 862279 "FLINEXP-" 862284 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860792 860936 861160 "FLASORT" 861568 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858009 858851 858903 "FLALG" 860130 NIL FLALG (NIL T T) -9 NIL 860597 NIL) (-373 851793 855495 855536 "FLAGG" 856798 NIL FLAGG (NIL T) -9 NIL 857450 NIL) (-372 850519 850858 851348 "FLAGG-" 851353 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849561 849704 849931 "FLAGG2" 850372 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846528 847510 847569 "FINRALG" 848697 NIL FINRALG (NIL T T) -9 NIL 849205 NIL) (-369 845688 845917 846256 "FINRALG-" 846261 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845094 845307 845335 "FINITE" 845531 T FINITE (NIL) -9 NIL 845638 NIL) (-367 837552 839713 839753 "FINAALG" 843420 NIL FINAALG (NIL T) -9 NIL 844873 NIL) (-366 832884 833934 835078 "FINAALG-" 836457 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832279 832639 832742 "FILE" 832814 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830963 831275 831329 "FILECAT" 832013 NIL FILECAT (NIL T T) -9 NIL 832229 NIL) (-363 828823 830325 830353 "FIELD" 830393 T FIELD (NIL) -9 NIL 830473 NIL) (-362 827443 827828 828339 "FIELD-" 828344 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825320 826078 826425 "FGROUP" 827129 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824410 824574 824794 "FGLMICPK" 825152 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820269 824335 824392 "FFX" 824397 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819870 819931 820066 "FFSLPE" 820202 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815859 816642 817438 "FFPOLY" 819106 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815363 815399 815608 "FFPOLY2" 815817 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811233 815282 815345 "FFP" 815350 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806658 811144 811208 "FF" 811213 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801811 806001 806191 "FFNBX" 806512 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796767 800946 801204 "FFNBP" 801665 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791427 796051 796262 "FFNB" 796600 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790259 790457 790772 "FFINTBAS" 791224 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786479 788666 788694 "FFIELDC" 789314 T FFIELDC (NIL) -9 NIL 789690 NIL) (-348 785141 785512 786009 "FFIELDC-" 786014 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784710 784756 784880 "FFHOM" 785083 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782405 782892 783409 "FFF" 784225 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778050 782147 782248 "FFCGX" 782348 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773698 777782 777889 "FFCGP" 777993 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768908 773425 773533 "FFCG" 773634 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750733 759779 759865 "FFCAT" 765030 NIL FFCAT (NIL T T T) -9 NIL 766481 NIL) (-341 745931 746978 748292 "FFCAT-" 749522 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745342 745385 745620 "FFCAT2" 745882 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734539 738314 739534 "FEXPR" 744194 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733539 733974 734015 "FEVALAB" 734099 NIL FEVALAB (NIL T) -9 NIL 734360 NIL) (-337 732698 732908 733246 "FEVALAB-" 733251 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731291 732081 732284 "FDIV" 732597 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728357 729072 729187 "FDIVCAT" 730755 NIL FDIVCAT (NIL T T T T) -9 NIL 731192 NIL) (-334 728119 728146 728316 "FDIVCAT-" 728321 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727339 727426 727703 "FDIV2" 728026 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726025 726284 726573 "FCPAK1" 727070 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725151 725525 725666 "FCOMP" 725916 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708880 712301 715839 "FC" 721633 T FC (NIL) -8 NIL NIL NIL) (-329 701451 705444 705484 "FAXF" 707286 NIL FAXF (NIL T) -9 NIL 707978 NIL) (-328 698727 699385 700210 "FAXF-" 700675 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693827 698103 698279 "FARRAY" 698584 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689072 691112 691165 "FAMR" 692188 NIL FAMR (NIL T T) -9 NIL 692648 NIL) (-325 687962 688264 688699 "FAMR-" 688704 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687158 687884 687937 "FAMONOID" 687942 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684970 685654 685707 "FAMONC" 686648 NIL FAMONC (NIL T T) -9 NIL 687034 NIL) (-322 683662 684724 684861 "FAGROUP" 684866 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681457 681776 682179 "FACUTIL" 683343 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680556 680741 680963 "FACTFUNC" 681267 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672953 679807 680019 "EXPUPXS" 680412 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670436 670976 671562 "EXPRTUBE" 672387 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666630 667222 667959 "EXPRODE" 669775 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651996 665285 665713 "EXPR" 666234 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646403 646990 647803 "EXPR2UPS" 651294 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646039 646096 646203 "EXPR2" 646340 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637436 645171 645468 "EXPEXPAN" 645876 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637263 637393 637422 "EXIT" 637427 T EXIT (NIL) -8 NIL NIL NIL) (-311 636770 636987 637078 "EXITAST" 637192 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636397 636459 636572 "EVALCYC" 636702 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635938 636056 636097 "EVALAB" 636267 NIL EVALAB (NIL T) -9 NIL 636371 NIL) (-308 635419 635541 635762 "EVALAB-" 635767 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632879 634155 634183 "EUCDOM" 634738 T EUCDOM (NIL) -9 NIL 635088 NIL) (-306 631284 631726 632316 "EUCDOM-" 632321 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618822 621582 624332 "ESTOOLS" 628554 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618454 618511 618620 "ESTOOLS2" 618759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618205 618247 618327 "ESTOOLS1" 618406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612110 613838 613866 "ES" 616634 T ES (NIL) -9 NIL 618043 NIL) (-301 607057 608344 610161 "ES-" 610325 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603431 604192 604972 "ESCONT" 606297 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603176 603208 603290 "ESCONT1" 603393 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602851 602901 603001 "ES2" 603120 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602481 602539 602648 "ES1" 602787 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601697 601826 602002 "ERROR" 602325 T ERROR (NIL) -7 NIL NIL NIL) (-295 595200 601556 601647 "EQTBL" 601652 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587751 590514 591963 "EQ" 593784 NIL -3205 (NIL T) -8 NIL NIL NIL) (-293 587383 587440 587549 "EQ2" 587688 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582672 583721 584814 "EP" 586322 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581250 581547 581859 "ENV" 582380 T ENV (NIL) -8 NIL NIL NIL) (-290 580421 580949 580977 "ENTIRER" 580982 T ENTIRER (NIL) -9 NIL 581028 NIL) (-289 576915 578376 578746 "EMR" 580220 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576059 576244 576298 "ELTAGG" 576678 NIL ELTAGG (NIL T T) -9 NIL 576889 NIL) (-287 575778 575840 575981 "ELTAGG-" 575986 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575567 575596 575650 "ELTAB" 575734 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574693 574839 575038 "ELFUTS" 575418 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574435 574491 574519 "ELEMFUN" 574624 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574305 574326 574394 "ELEMFUN-" 574399 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569196 572405 572446 "ELAGG" 573386 NIL ELAGG (NIL T) -9 NIL 573849 NIL) (-281 567481 567915 568578 "ELAGG-" 568583 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566146 566424 566717 "ELABEXPR" 567208 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559010 560813 561640 "EFUPXS" 565422 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552460 554261 555071 "EFULS" 558286 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549882 550240 550719 "EFSTRUC" 552092 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538953 540519 542079 "EF" 548397 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538054 538438 538587 "EAB" 538824 T EAB (NIL) -8 NIL NIL NIL) (-274 537263 538013 538041 "E04UCFA" 538046 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536472 537222 537250 "E04NAFA" 537255 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535681 536431 536459 "E04MBFA" 536464 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534890 535640 535668 "E04JAFA" 535673 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534101 534849 534877 "E04GCFA" 534882 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533312 534060 534088 "E04FDFA" 534093 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532521 533271 533299 "E04DGFA" 533304 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526694 528046 529410 "E04AGNT" 531177 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525400 525880 525920 "DVARCAT" 526395 NIL DVARCAT (NIL T) -9 NIL 526594 NIL) (-265 524604 524816 525130 "DVARCAT-" 525135 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517496 524403 524532 "DSMP" 524537 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512305 513441 514509 "DROPT" 516448 T DROPT (NIL) -8 NIL NIL NIL) (-262 511970 512029 512127 "DROPT1" 512240 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507085 508211 509348 "DROPT0" 510853 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505430 505755 506141 "DRAWPT" 506719 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500017 500940 502019 "DRAW" 504404 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499650 499703 499821 "DRAWHACK" 499958 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498381 498650 498941 "DRAWCX" 499379 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497896 497965 498116 "DRAWCURV" 498307 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488364 490326 492441 "DRAWCFUN" 495801 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485177 487059 487100 "DQAGG" 487729 NIL DQAGG (NIL T) -9 NIL 488002 NIL) (-253 473448 480155 480238 "DPOLCAT" 482090 NIL DPOLCAT (NIL T T T T) -9 NIL 482635 NIL) (-252 468284 469633 471591 "DPOLCAT-" 471596 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461433 468145 468243 "DPMO" 468248 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454485 461213 461380 "DPMM" 461385 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454117 454404 454452 "DOMCTOR" 454457 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453412 453639 453776 "DOMAIN" 454000 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447155 453047 453199 "DMP" 453313 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446755 446811 446955 "DLP" 447093 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440625 446082 446272 "DLIST" 446597 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437469 439478 439519 "DLAGG" 440069 NIL DLAGG (NIL T) -9 NIL 440299 NIL) (-243 436274 436912 436940 "DIVRING" 437032 T DIVRING (NIL) -9 NIL 437115 NIL) (-242 435511 435701 436001 "DIVRING-" 436006 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433613 433970 434376 "DISPLAY" 435125 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427549 433527 433590 "DIRPROD" 433595 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426397 426600 426865 "DIRPROD2" 427342 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415654 421612 421665 "DIRPCAT" 422075 NIL DIRPCAT (NIL NIL T) -9 NIL 422915 NIL) (-237 412980 413622 414503 "DIRPCAT-" 414840 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412267 412427 412613 "DIOSP" 412814 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408969 411179 411220 "DIOPS" 411654 NIL DIOPS (NIL T) -9 NIL 411883 NIL) (-234 408518 408632 408823 "DIOPS-" 408828 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407402 408004 408032 "DIFRING" 408219 T DIFRING (NIL) -9 NIL 408329 NIL) (-232 407048 407125 407277 "DIFRING-" 407282 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404845 406091 406132 "DIFEXT" 406495 NIL DIFEXT (NIL T) -9 NIL 406789 NIL) (-230 403130 403558 404224 "DIFEXT-" 404229 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400452 402662 402703 "DIAGG" 402708 NIL DIAGG (NIL T) -9 NIL 402728 NIL) (-228 399836 399993 400245 "DIAGG-" 400250 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395301 398795 399072 "DHMATRIX" 399605 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390913 391822 392832 "DFSFUN" 394311 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386018 389844 390156 "DFLOAT" 390621 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384246 384527 384923 "DFINTTLS" 385726 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381302 382267 382667 "DERHAM" 383912 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379151 381077 381166 "DEQUEUE" 381246 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378366 378499 378695 "DEGRED" 379013 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374761 375506 376359 "DEFINTRF" 377594 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372288 372757 373356 "DEFINTEF" 374280 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371665 371908 372023 "DEFAST" 372193 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365696 371260 371409 "DECIMAL" 371536 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363206 363666 364172 "DDFACT" 365240 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362802 362845 362996 "DBLRESP" 363157 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360701 361035 361395 "DBASE" 362569 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359970 360181 360327 "DATAARY" 360600 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359103 359929 359957 "D03FAFA" 359962 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358237 359062 359090 "D03EEFA" 359095 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356187 356653 357142 "D03AGNT" 357768 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355503 356146 356174 "D02EJFA" 356179 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354819 355462 355490 "D02CJFA" 355495 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354135 354778 354806 "D02BHFA" 354811 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353451 354094 354122 "D02BBFA" 354127 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346648 348237 349843 "D02AGNT" 351865 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344416 344939 345485 "D01WGTS" 346122 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343510 344375 344403 "D01TRNS" 344408 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342605 343469 343497 "D01GBFA" 343502 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341700 342564 342592 "D01FCFA" 342597 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340795 341659 341687 "D01ASFA" 341692 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339890 340754 340782 "D01AQFA" 340787 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338985 339849 339877 "D01APFA" 339882 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338080 338944 338972 "D01ANFA" 338977 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337175 338039 338067 "D01AMFA" 338072 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336270 337134 337162 "D01ALFA" 337167 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335365 336229 336257 "D01AKFA" 336262 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334460 335324 335352 "D01AJFA" 335357 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327755 329308 330869 "D01AGNT" 332919 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327092 327220 327372 "CYCLOTOM" 327623 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323827 324540 325267 "CYCLES" 326385 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323139 323273 323444 "CVMP" 323688 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320910 321168 321544 "CTRIGMNP" 322867 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320401 320701 320775 "CTOR" 320856 T CTOR (NIL) -8 NIL NIL NIL) (-186 319937 320132 320233 "CTORKIND" 320320 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319285 319544 319572 "CTORCAT" 319754 T CTORCAT (NIL) -9 NIL 319867 NIL) (-184 318883 318994 319153 "CTORCAT-" 319158 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318399 318586 318684 "CTORCALL" 318805 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317773 317872 318025 "CSTTOOLS" 318296 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313572 314229 314987 "CRFP" 317085 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313074 313293 313385 "CRCEAST" 313500 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312121 312306 312534 "CRAPACK" 312878 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311505 311606 311810 "CPMATCH" 311997 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311230 311258 311364 "CPIMA" 311471 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307594 308266 308984 "COORDSYS" 310565 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307002 307124 307267 "CONTOUR" 307471 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302920 305005 305497 "CONTFRAC" 306542 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302800 302821 302849 "CONDUIT" 302886 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301965 302493 302521 "COMRING" 302526 T COMRING (NIL) -9 NIL 302578 NIL) (-171 301046 301323 301507 "COMPPROP" 301801 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300707 300742 300870 "COMPLPAT" 301005 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290756 300516 300625 "COMPLEX" 300630 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290392 290449 290556 "COMPLEX2" 290693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290110 290145 290243 "COMPFACT" 290351 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274264 284492 284532 "COMPCAT" 285536 NIL COMPCAT (NIL T) -9 NIL 286932 NIL) (-165 263775 266703 270330 "COMPCAT-" 270686 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263504 263532 263635 "COMMUPC" 263741 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263299 263332 263391 "COMMONOP" 263465 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262882 263050 263137 "COMM" 263232 T COMM (NIL) -8 NIL NIL NIL) (-161 262485 262686 262761 "COMMAAST" 262827 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261734 261928 261956 "COMBOPC" 262294 T COMBOPC (NIL) -9 NIL 262469 NIL) (-159 260630 260840 261082 "COMBINAT" 261524 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256827 257401 258041 "COMBF" 260052 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255612 255943 256178 "COLOR" 256612 T COLOR (NIL) -8 NIL NIL NIL) (-156 255115 255333 255425 "COLONAST" 255540 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254755 254802 254927 "CMPLXRT" 255062 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254230 254455 254554 "CLLCTAST" 254676 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249730 250760 251840 "CLIP" 253170 T CLIP (NIL) -7 NIL NIL NIL) (-152 248103 248836 249075 "CLIF" 249557 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244325 246249 246290 "CLAGG" 247219 NIL CLAGG (NIL T) -9 NIL 247755 NIL) (-150 242747 243204 243787 "CLAGG-" 243792 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242291 242376 242516 "CINTSLPE" 242656 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239792 240263 240811 "CHVAR" 241819 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239027 239555 239583 "CHARZ" 239588 T CHARZ (NIL) -9 NIL 239603 NIL) (-146 238781 238821 238899 "CHARPOL" 238981 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237900 238461 238489 "CHARNZ" 238536 T CHARNZ (NIL) -9 NIL 238592 NIL) (-144 235889 236590 236925 "CHAR" 237585 T CHAR (NIL) -8 NIL NIL NIL) (-143 235615 235676 235704 "CFCAT" 235815 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234860 234971 235153 "CDEN" 235499 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230852 234013 234293 "CCLASS" 234600 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230159 230302 230465 "CATEGORY" 230709 T -10 (NIL) -8 NIL NIL NIL) (-139 229791 230078 230126 "CATCTOR" 230131 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229269 229494 229592 "CATAST" 229713 T CATAST (NIL) -8 NIL NIL NIL) (-137 228772 228990 229082 "CASEAST" 229197 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223808 224801 225554 "CARTEN" 228075 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222916 223064 223285 "CARTEN2" 223655 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221258 222066 222323 "CARD" 222679 T CARD (NIL) -8 NIL NIL NIL) (-133 220861 221062 221137 "CAPSLAST" 221203 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220233 220561 220589 "CACHSET" 220721 T CACHSET (NIL) -9 NIL 220798 NIL) (-131 219729 220025 220053 "CABMON" 220103 T CABMON (NIL) -9 NIL 220159 NIL) (-130 219229 219433 219543 "BYTEORD" 219639 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218232 218763 218905 "BYTE" 219068 T BYTE (NIL) -8 NIL NIL 219190) (-128 213632 217737 217909 "BYTEBUF" 218080 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211189 213324 213431 "BTREE" 213558 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208686 210837 210959 "BTOURN" 211099 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206103 208156 208197 "BTCAT" 208265 NIL BTCAT (NIL T) -9 NIL 208342 NIL) (-124 205770 205850 205999 "BTCAT-" 206004 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201062 204913 204941 "BTAGG" 205163 T BTAGG (NIL) -9 NIL 205324 NIL) (-122 200552 200677 200883 "BTAGG-" 200888 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197595 199830 200045 "BSTREE" 200369 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196733 196859 197043 "BRILL" 197451 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193432 195459 195500 "BRAGG" 196149 NIL BRAGG (NIL T) -9 NIL 196407 NIL) (-118 191961 192367 192922 "BRAGG-" 192927 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185217 191307 191491 "BPADICRT" 191809 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183559 185154 185199 "BPADIC" 185204 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183257 183287 183401 "BOUNDZRO" 183523 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178772 179863 180730 "BOP" 182410 T BOP (NIL) -8 NIL NIL NIL) (-113 176393 176837 177357 "BOP1" 178285 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175095 175817 176010 "BOOLEAN" 176220 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174457 174835 174889 "BMODULE" 174894 NIL BMODULE (NIL T T) -9 NIL 174959 NIL) (-110 170285 174255 174328 "BITS" 174404 T BITS (NIL) -8 NIL NIL NIL) (-109 169697 169819 169961 "BINDING" 170163 T BINDING (NIL) -8 NIL NIL NIL) (-108 163731 169294 169442 "BINARY" 169569 T BINARY (NIL) -8 NIL NIL NIL) (-107 161558 162986 163027 "BGAGG" 163287 NIL BGAGG (NIL T) -9 NIL 163424 NIL) (-106 161389 161421 161512 "BGAGG-" 161517 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160487 160773 160978 "BFUNCT" 161204 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159177 159355 159643 "BEZOUT" 160311 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155694 158029 158359 "BBTREE" 158880 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155428 155481 155509 "BASTYPE" 155628 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155281 155309 155382 "BASTYPE-" 155387 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154715 154791 154943 "BALFACT" 155192 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153598 154130 154316 "AUTOMOR" 154560 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153324 153329 153355 "ATTREG" 153360 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151603 152021 152373 "ATTRBUT" 152990 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151238 151431 151497 "ATTRAST" 151555 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150774 150887 150913 "ATRIG" 151114 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150583 150624 150711 "ATRIG-" 150716 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150254 150414 150440 "ASTCAT" 150445 T ASTCAT (NIL) -9 NIL 150475 NIL) (-92 149981 150040 150159 "ASTCAT-" 150164 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148178 149757 149845 "ASTACK" 149924 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146683 146980 147345 "ASSOCEQ" 147860 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145715 146342 146466 "ASP9" 146590 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145478 145663 145702 "ASP8" 145707 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144346 145083 145225 "ASP80" 145367 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143244 143981 144113 "ASP7" 144245 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142198 142921 143039 "ASP78" 143157 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141167 141878 141995 "ASP77" 142112 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140079 140805 140936 "ASP74" 141067 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138979 139714 139846 "ASP73" 139978 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138083 138805 138905 "ASP6" 138910 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137027 137760 137878 "ASP55" 137996 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135976 136701 136820 "ASP50" 136939 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135064 135677 135787 "ASP4" 135897 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134152 134765 134875 "ASP49" 134985 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132936 133691 133859 "ASP42" 134041 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131712 132469 132639 "ASP41" 132823 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130662 131389 131507 "ASP35" 131625 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130427 130610 130649 "ASP34" 130654 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130164 130231 130307 "ASP33" 130382 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129057 129799 129931 "ASP31" 130063 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128822 129005 129044 "ASP30" 129049 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128557 128626 128702 "ASP29" 128777 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128322 128505 128544 "ASP28" 128549 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128087 128270 128309 "ASP27" 128314 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127171 127785 127896 "ASP24" 128007 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126247 126973 127085 "ASP20" 127090 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125335 125948 126058 "ASP1" 126168 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124277 125009 125128 "ASP19" 125247 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124014 124081 124157 "ASP12" 124232 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122866 123613 123757 "ASP10" 123901 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120765 122710 122801 "ARRAY2" 122806 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116579 120413 120527 "ARRAY1" 120682 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115611 115784 116005 "ARRAY12" 116402 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109970 111841 111916 "ARR2CAT" 114546 NIL ARR2CAT (NIL T T T) -9 NIL 115304 NIL) (-56 107404 108148 109102 "ARR2CAT-" 109107 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107231 107310 "ARITY" 107343 T ARITY (NIL) -8 NIL NIL NIL) (-54 105744 105896 106202 "APPRULE" 106832 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105395 105443 105562 "APPLYORE" 105690 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104369 104660 104855 "ANY" 105218 T ANY (NIL) -8 NIL NIL NIL) (-51 103647 103770 103927 "ANY1" 104243 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101204 102084 102411 "ANTISYM" 103371 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100911 101007 "ANON" 101126 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3200364 3200369 3200374 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3200349 3200354 3200359 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3200334 3200339 3200344 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3200319 3200324 3200329 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3199488 3200194 3200271 "ZMOD" 3200276 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3198598 3198762 3198971 "ZLINDEP" 3199320 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3187898 3189666 3191638 "ZDSOLVE" 3196728 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3187144 3187285 3187474 "YSTREAM" 3187744 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3184945 3186445 3186649 "XRPOLY" 3186987 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3181525 3182816 3183391 "XPR" 3184417 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3179273 3180856 3181060 "XPOLY" 3181356 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3177056 3178398 3178453 "XPOLYC" 3178741 NIL XPOLYC (NIL T T) -9 NIL 3178854 NIL) (-1279 3173459 3175573 3175961 "XPBWPOLY" 3176714 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3169362 3171622 3171664 "XF" 3172285 NIL XF (NIL T) -9 NIL 3172685 NIL) (-1277 3168983 3169071 3169240 "XF-" 3169245 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3164309 3165572 3165627 "XFALG" 3167799 NIL XFALG (NIL T T) -9 NIL 3168588 NIL) (-1275 3163442 3163546 3163751 "XEXPPKG" 3164201 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3161578 3163292 3163388 "XDPOLY" 3163393 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3160515 3161089 3161132 "XALG" 3161137 NIL XALG (NIL T) -9 NIL 3161248 NIL) (-1272 3153984 3158492 3158986 "WUTSET" 3160107 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3152267 3153036 3153359 "WP" 3153795 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3151896 3152089 3152159 "WHILEAST" 3152219 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3151395 3151613 3151707 "WHEREAST" 3151824 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3150281 3150479 3150774 "WFFINTBS" 3151192 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3148185 3148612 3149074 "WEIER" 3149853 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3147332 3147756 3147798 "VSPACE" 3147934 NIL VSPACE (NIL T) -9 NIL 3148008 NIL) (-1265 3147170 3147197 3147288 "VSPACE-" 3147293 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3146978 3147021 3147089 "VOID" 3147124 T VOID (NIL) -8 NIL NIL NIL) (-1263 3145114 3145473 3145879 "VIEW" 3146594 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3141538 3142177 3142914 "VIEWDEF" 3144399 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3130869 3133086 3135259 "VIEW3D" 3139387 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3123147 3124780 3126359 "VIEW2D" 3129312 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3118549 3122917 3123009 "VECTOR" 3123090 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3117126 3117385 3117703 "VECTOR2" 3118279 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3110653 3114910 3114953 "VECTCAT" 3115946 NIL VECTCAT (NIL T) -9 NIL 3116532 NIL) (-1256 3109667 3109921 3110311 "VECTCAT-" 3110316 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3109148 3109318 3109438 "VARIABLE" 3109582 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3109081 3109086 3109116 "UTYPE" 3109121 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3107911 3108065 3108327 "UTSODETL" 3108907 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3105351 3105811 3106335 "UTSODE" 3107452 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3097215 3102977 3103466 "UTS" 3104920 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3088450 3093782 3093825 "UTSCAT" 3094937 NIL UTSCAT (NIL T) -9 NIL 3095694 NIL) (-1249 3085798 3086520 3087509 "UTSCAT-" 3087514 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3085425 3085468 3085601 "UTS2" 3085749 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3079698 3082263 3082306 "URAGG" 3084376 NIL URAGG (NIL T) -9 NIL 3085099 NIL) (-1246 3076637 3077500 3078623 "URAGG-" 3078628 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3072353 3075251 3075723 "UPXSSING" 3076301 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3064446 3071600 3071873 "UPXS" 3072138 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3057546 3064350 3064422 "UPXSCONS" 3064427 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3047783 3054541 3054603 "UPXSCCA" 3055177 NIL UPXSCCA (NIL T T) -9 NIL 3055410 NIL) (-1241 3047421 3047506 3047680 "UPXSCCA-" 3047685 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3037511 3044042 3044085 "UPXSCAT" 3044733 NIL UPXSCAT (NIL T) -9 NIL 3045341 NIL) (-1239 3036941 3037020 3037199 "UPXS2" 3037426 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3035595 3035848 3036199 "UPSQFREE" 3036684 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3029375 3032397 3032452 "UPSCAT" 3033613 NIL UPSCAT (NIL T T) -9 NIL 3034387 NIL) (-1236 3028579 3028786 3029113 "UPSCAT-" 3029118 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3014421 3022427 3022470 "UPOLYC" 3024571 NIL UPOLYC (NIL T) -9 NIL 3025792 NIL) (-1234 3005749 3008175 3011322 "UPOLYC-" 3011327 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3005376 3005419 3005552 "UPOLYC2" 3005700 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2996942 3005059 3005188 "UP" 3005295 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2996281 2996388 2996552 "UPMP" 2996831 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2995834 2995915 2996054 "UPDIVP" 2996194 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2994402 2994651 2994967 "UPDECOMP" 2995583 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2993637 2993749 2993934 "UPCDEN" 2994286 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2993156 2993225 2993374 "UP2" 2993562 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2991671 2992360 2992637 "UNISEG" 2992914 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2990886 2991013 2991218 "UNISEG2" 2991514 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2989946 2990126 2990352 "UNIFACT" 2990702 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2973905 2989123 2989374 "ULS" 2989753 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2961931 2973809 2973881 "ULSCONS" 2973886 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2944539 2956489 2956551 "ULSCCAT" 2957189 NIL ULSCCAT (NIL T T) -9 NIL 2957477 NIL) (-1220 2943589 2943834 2944222 "ULSCCAT-" 2944227 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2933456 2939901 2939944 "ULSCAT" 2940807 NIL ULSCAT (NIL T) -9 NIL 2941537 NIL) (-1218 2932886 2932965 2933144 "ULS2" 2933371 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2932003 2932486 2932593 "UINT8" 2932704 T UINT8 (NIL) -8 NIL NIL 2932789) (-1216 2931119 2931602 2931709 "UINT64" 2931820 T UINT64 (NIL) -8 NIL NIL 2931905) (-1215 2930235 2930718 2930825 "UINT32" 2930936 T UINT32 (NIL) -8 NIL NIL 2931021) (-1214 2929351 2929834 2929941 "UINT16" 2930052 T UINT16 (NIL) -8 NIL NIL 2930137) (-1213 2927746 2928677 2928707 "UFD" 2928919 T UFD (NIL) -9 NIL 2929033 NIL) (-1212 2927540 2927586 2927681 "UFD-" 2927686 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2926622 2926805 2927021 "UDVO" 2927346 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2924438 2924847 2925318 "UDPO" 2926186 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2924371 2924376 2924406 "TYPE" 2924411 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2924158 2924326 2924357 "TYPEAST" 2924362 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2923129 2923331 2923571 "TWOFACT" 2923952 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2922200 2922538 2922773 "TUPLE" 2922929 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2919891 2920410 2920949 "TUBETOOL" 2921683 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2918740 2918945 2919186 "TUBE" 2919684 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2913496 2917712 2917995 "TS" 2918492 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2902163 2906255 2906352 "TSETCAT" 2911621 NIL TSETCAT (NIL T T T T) -9 NIL 2913152 NIL) (-1201 2896895 2898495 2900386 "TSETCAT-" 2900391 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2891157 2892004 2892946 "TRMANIP" 2896031 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2890598 2890661 2890824 "TRIMAT" 2891089 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2888394 2888631 2888995 "TRIGMNIP" 2890347 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2887914 2888027 2888057 "TRIGCAT" 2888270 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2887583 2887662 2887803 "TRIGCAT-" 2887808 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2884476 2886441 2886722 "TREE" 2887337 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2883750 2884278 2884308 "TRANFUN" 2884343 T TRANFUN (NIL) -9 NIL 2884409 NIL) (-1193 2883029 2883220 2883500 "TRANFUN-" 2883505 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2882833 2882865 2882926 "TOPSP" 2882990 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2882181 2882296 2882450 "TOOLSIGN" 2882714 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2880842 2881358 2881597 "TEXTFILE" 2881964 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2878781 2879295 2879724 "TEX" 2880435 T TEX (NIL) -8 NIL NIL NIL) (-1188 2878562 2878593 2878665 "TEX1" 2878744 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2878210 2878273 2878363 "TEMUTL" 2878494 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2876364 2876644 2876969 "TBCMPPK" 2877933 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2868252 2874524 2874580 "TBAGG" 2874980 NIL TBAGG (NIL T T) -9 NIL 2875191 NIL) (-1184 2863322 2864810 2866564 "TBAGG-" 2866569 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862706 2862813 2862958 "TANEXP" 2863211 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2856207 2862563 2862656 "TABLE" 2862661 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855619 2855718 2855856 "TABLEAU" 2856104 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2850227 2851447 2852695 "TABLBUMP" 2854405 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2849449 2849596 2849777 "SYSTEM" 2850068 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845908 2846607 2847390 "SYSSOLP" 2848700 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844942 2845420 2845539 "SYSNNI" 2845725 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845810) (-1176 2844239 2844671 2844750 "SYSINT" 2844810 NIL SYSINT (NIL NIL) -8 NIL NIL 2844855) (-1175 2840598 2841517 2842227 "SYNTAX" 2843551 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837756 2838358 2838990 "SYMTAB" 2839988 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2833005 2833907 2834890 "SYMS" 2836795 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2830267 2832463 2832693 "SYMPOLY" 2832810 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829784 2829859 2829982 "SYMFUNC" 2830179 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825830 2827096 2827909 "SYMBOL" 2828993 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2819369 2821058 2822778 "SWITCH" 2824132 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812630 2818190 2818493 "SUTS" 2819124 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804723 2811877 2812150 "SUPXS" 2812415 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2796238 2804341 2804467 "SUP" 2804632 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2795397 2795524 2795741 "SUPFRACF" 2796106 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2795018 2795077 2795190 "SUP2" 2795332 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2793431 2793705 2794068 "SUMRF" 2794717 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792745 2792811 2793010 "SUMFS" 2793352 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776739 2791922 2792173 "SULS" 2792552 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2776368 2776561 2776631 "SUCHTAST" 2776691 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775690 2775893 2776033 "SUCH" 2776276 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769584 2770596 2771555 "SUBSPACE" 2774778 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2769014 2769104 2769268 "SUBRESP" 2769472 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2762379 2763679 2764990 "STTF" 2767750 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2756552 2757672 2758819 "STTFNC" 2761279 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747863 2749734 2751528 "STTAYLOR" 2754793 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2741107 2747727 2747810 "STRTBL" 2747815 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2736498 2741062 2741093 "STRING" 2741098 T STRING (NIL) -8 NIL NIL NIL) (-1151 2731386 2735871 2735901 "STRICAT" 2735960 T STRICAT (NIL) -9 NIL 2736022 NIL) (-1150 2724189 2729005 2729616 "STREAM" 2730810 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723699 2723776 2723920 "STREAM3" 2724106 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722681 2722864 2723099 "STREAM2" 2723512 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2722369 2722421 2722514 "STREAM1" 2722623 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2721385 2721566 2721797 "STINPROD" 2722185 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720963 2721147 2721177 "STEP" 2721257 T STEP (NIL) -9 NIL 2721335 NIL) (-1144 2714506 2720862 2720939 "STBL" 2720944 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709680 2713727 2713770 "STAGG" 2713923 NIL STAGG (NIL T) -9 NIL 2714012 NIL) (-1142 2707382 2707984 2708856 "STAGG-" 2708861 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705577 2707152 2707244 "STACK" 2707325 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2698300 2703718 2704174 "SREGSET" 2705207 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690725 2692094 2693607 "SRDCMPK" 2696906 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683692 2688165 2688195 "SRAGG" 2689498 T SRAGG (NIL) -9 NIL 2690106 NIL) (-1137 2682709 2682964 2683343 "SRAGG-" 2683348 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2677196 2681656 2682077 "SQMATRIX" 2682335 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670943 2673914 2674641 "SPLTREE" 2676541 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666933 2667599 2668245 "SPLNODE" 2670369 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665980 2666213 2666243 "SPFCAT" 2666687 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664717 2664927 2665191 "SPECOUT" 2665738 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2656369 2658113 2658143 "SPADXPT" 2662535 T SPADXPT (NIL) -9 NIL 2664569 NIL) (-1130 2656130 2656170 2656239 "SPADPRSR" 2656322 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2654312 2656085 2656116 "SPADAST" 2656121 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2646283 2648030 2648073 "SPACEC" 2652446 NIL SPACEC (NIL T) -9 NIL 2654262 NIL) (-1127 2644440 2646215 2646264 "SPACE3" 2646269 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2643192 2643363 2643654 "SORTPAK" 2644245 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2641242 2641545 2641964 "SOLVETRA" 2642856 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2640253 2640475 2640749 "SOLVESER" 2641015 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2635464 2636354 2637356 "SOLVERAD" 2639305 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2631279 2631888 2632617 "SOLVEFOR" 2634831 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625576 2630628 2630725 "SNTSCAT" 2630730 NIL SNTSCAT (NIL T T T T) -9 NIL 2630800 NIL) (-1120 2619709 2623899 2624290 "SMTS" 2625266 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2614149 2619597 2619674 "SMP" 2619679 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2612308 2612609 2613007 "SMITH" 2613846 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2605195 2609359 2609462 "SMATCAT" 2610813 NIL SMATCAT (NIL NIL T T T) -9 NIL 2611363 NIL) (-1116 2602135 2602958 2604136 "SMATCAT-" 2604141 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599848 2601371 2601414 "SKAGG" 2601675 NIL SKAGG (NIL T) -9 NIL 2601810 NIL) (-1114 2596183 2599264 2599459 "SINT" 2599646 T SINT (NIL) -8 NIL NIL 2599819) (-1113 2595955 2595993 2596059 "SIMPAN" 2596139 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2595261 2595490 2595630 "SIG" 2595837 T SIG (NIL) -8 NIL NIL NIL) (-1111 2594099 2594320 2594595 "SIGNRF" 2595020 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592904 2593055 2593346 "SIGNEF" 2593928 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2592237 2592487 2592611 "SIGAST" 2592802 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589927 2590381 2590887 "SHP" 2591778 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583827 2589828 2589904 "SHDP" 2589909 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2583426 2583592 2583622 "SGROUP" 2583715 T SGROUP (NIL) -9 NIL 2583777 NIL) (-1105 2583284 2583310 2583383 "SGROUP-" 2583388 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2580119 2580817 2581540 "SGCF" 2582583 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2574514 2579566 2579663 "SFRTCAT" 2579668 NIL SFRTCAT (NIL T T T T) -9 NIL 2579707 NIL) (-1102 2567935 2568953 2570089 "SFRGCD" 2573497 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2561062 2562134 2563320 "SFQCMPK" 2566868 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560684 2560773 2560883 "SFORT" 2561003 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559829 2560524 2560645 "SEXOF" 2560650 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558963 2559710 2559778 "SEX" 2559783 T SEX (NIL) -8 NIL NIL NIL) (-1097 2554502 2555191 2555286 "SEXCAT" 2558223 NIL SEXCAT (NIL T T T T T) -9 NIL 2558801 NIL) (-1096 2551682 2554436 2554484 "SET" 2554489 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549933 2550395 2550700 "SETMN" 2551423 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2549539 2549665 2549695 "SETCAT" 2549812 T SETCAT (NIL) -9 NIL 2549897 NIL) (-1093 2549319 2549371 2549470 "SETCAT-" 2549475 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545706 2547780 2547823 "SETAGG" 2548693 NIL SETAGG (NIL T) -9 NIL 2549033 NIL) (-1091 2545164 2545280 2545517 "SETAGG-" 2545522 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544634 2544860 2544961 "SEQAST" 2545085 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543833 2544127 2544188 "SEGXCAT" 2544474 NIL SEGXCAT (NIL T T) -9 NIL 2544594 NIL) (-1088 2542887 2543499 2543681 "SEG" 2543686 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541866 2542080 2542123 "SEGCAT" 2542645 NIL SEGCAT (NIL T) -9 NIL 2542866 NIL) (-1086 2540915 2541245 2541445 "SEGBIND" 2541701 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2540536 2540595 2540708 "SEGBIND2" 2540850 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2540136 2540337 2540414 "SEGAST" 2540481 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2539355 2539481 2539685 "SEG2" 2539980 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538792 2539290 2539337 "SDVAR" 2539342 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2531074 2538562 2538692 "SDPOL" 2538697 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529667 2529933 2530252 "SCPKG" 2530789 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528827 2529000 2529193 "SCOPE" 2529496 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2528047 2528181 2528360 "SCACHE" 2528682 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527719 2527879 2527909 "SASTCAT" 2527914 T SASTCAT (NIL) -9 NIL 2527927 NIL) (-1076 2527233 2527554 2527630 "SAOS" 2527665 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526798 2526833 2527006 "SAERFFC" 2527192 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520764 2526695 2526775 "SAE" 2526780 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2520357 2520392 2520551 "SAEFACT" 2520723 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518678 2518992 2519393 "RURPK" 2520023 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2517314 2517593 2517905 "RULESET" 2518512 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2514501 2515004 2515469 "RULE" 2516995 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2514140 2514295 2514378 "RULECOLD" 2514453 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513638 2513857 2513951 "RSTRCAST" 2514068 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2508486 2509281 2510201 "RSETGCD" 2512837 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497743 2502795 2502892 "RSETCAT" 2507011 NIL RSETCAT (NIL T T T T) -9 NIL 2508108 NIL) (-1065 2495670 2496209 2497033 "RSETCAT-" 2497038 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2488055 2489432 2490952 "RSDCMPK" 2494269 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2486060 2486501 2486575 "RRCC" 2487661 NIL RRCC (NIL T T) -9 NIL 2488005 NIL) (-1062 2485411 2485585 2485864 "RRCC-" 2485869 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484881 2485107 2485208 "RPTAST" 2485332 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458879 2468474 2468541 "RPOLCAT" 2479205 NIL RPOLCAT (NIL T T T) -9 NIL 2482364 NIL) (-1059 2450377 2452717 2455839 "RPOLCAT-" 2455844 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2441424 2448588 2449070 "ROUTINE" 2449917 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2438249 2441050 2441190 "ROMAN" 2441306 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2436520 2437109 2437369 "ROIRC" 2438054 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432905 2435156 2435186 "RNS" 2435490 T RNS (NIL) -9 NIL 2435763 NIL) (-1054 2431414 2431797 2432331 "RNS-" 2432406 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430863 2431245 2431275 "RNG" 2431280 T RNG (NIL) -9 NIL 2431301 NIL) (-1052 2430255 2430617 2430660 "RMODULE" 2430722 NIL RMODULE (NIL T) -9 NIL 2430764 NIL) (-1051 2429091 2429185 2429521 "RMCAT2" 2430156 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425968 2428437 2428734 "RMATRIX" 2428853 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418910 2421144 2421259 "RMATCAT" 2424618 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425600 NIL) (-1048 2418285 2418432 2418739 "RMATCAT-" 2418744 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417852 2417927 2418055 "RINTERP" 2418204 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416971 2417499 2417529 "RING" 2417585 T RING (NIL) -9 NIL 2417677 NIL) (-1045 2416763 2416807 2416904 "RING-" 2416909 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415604 2415841 2416099 "RIDIST" 2416527 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406920 2415072 2415278 "RGCHAIN" 2415452 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2406296 2406676 2406717 "RGBCSPC" 2406775 NIL RGBCSPC (NIL T) -9 NIL 2406827 NIL) (-1041 2405480 2405835 2405876 "RGBCMDL" 2406108 NIL RGBCMDL (NIL T) -9 NIL 2406222 NIL) (-1040 2402474 2403088 2403758 "RF" 2404844 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2402120 2402183 2402286 "RFFACTOR" 2402405 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401845 2401880 2401977 "RFFACT" 2402079 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399962 2400326 2400708 "RFDIST" 2401485 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2399415 2399507 2399670 "RETSOL" 2399864 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2399051 2399131 2399174 "RETRACT" 2399307 NIL RETRACT (NIL T) -9 NIL 2399394 NIL) (-1034 2398900 2398925 2399012 "RETRACT-" 2399017 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2398529 2398722 2398792 "RETAST" 2398852 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2391383 2398182 2398309 "RESULT" 2398424 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2390001 2390652 2390851 "RESRING" 2391286 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389637 2389686 2389784 "RESLATC" 2389938 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2389342 2389377 2389484 "REPSQ" 2389596 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386764 2387344 2387946 "REP" 2388762 T REP (NIL) -7 NIL NIL NIL) (-1027 2386461 2386496 2386607 "REPDB" 2386723 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2380361 2381750 2382973 "REP2" 2385273 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376738 2377419 2378227 "REP1" 2379588 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2369461 2374879 2375335 "REGSET" 2376368 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2368274 2368609 2368859 "REF" 2369246 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367651 2367754 2367921 "REDORDER" 2368158 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363646 2366864 2367091 "RECLOS" 2367479 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362698 2362879 2363094 "REALSOLV" 2363453 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2362544 2362585 2362615 "REAL" 2362620 T REAL (NIL) -9 NIL 2362655 NIL) (-1018 2359027 2359829 2360713 "REAL0Q" 2361709 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354628 2355616 2356677 "REAL0" 2358008 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2354126 2354345 2354439 "RDUCEAST" 2354556 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2353531 2353603 2353810 "RDIV" 2354048 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352599 2352773 2352986 "RDIST" 2353353 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2351196 2351483 2351855 "RDETRS" 2352307 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2349008 2349462 2350000 "RDETR" 2350738 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347619 2347897 2348301 "RDEEFS" 2348724 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2346114 2346420 2346852 "RDEEF" 2347307 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2340367 2343250 2343280 "RCFIELD" 2344575 T RCFIELD (NIL) -9 NIL 2345305 NIL) (-1008 2338431 2338935 2339631 "RCFIELD-" 2339706 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334747 2336532 2336575 "RCAGG" 2337659 NIL RCAGG (NIL T) -9 NIL 2338124 NIL) (-1006 2334375 2334469 2334632 "RCAGG-" 2334637 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333710 2333822 2333987 "RATRET" 2334259 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2333263 2333330 2333451 "RATFACT" 2333638 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332571 2332691 2332843 "RANDSRC" 2333133 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2332305 2332349 2332422 "RADUTIL" 2332520 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2325448 2331138 2331448 "RADIX" 2332029 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2317094 2325290 2325420 "RADFF" 2325425 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316746 2316821 2316849 "RADCAT" 2317006 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2316531 2316579 2316676 "RADCAT-" 2316681 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314682 2316306 2316395 "QUEUE" 2316475 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2311250 2314619 2314664 "QUAT" 2314669 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310888 2310931 2311058 "QUATCT2" 2311201 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304627 2307937 2307977 "QUATCAT" 2308757 NIL QUATCAT (NIL T) -9 NIL 2309523 NIL) (-993 2300771 2301808 2303195 "QUATCAT-" 2303289 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2298291 2299855 2299896 "QUAGG" 2300271 NIL QUAGG (NIL T) -9 NIL 2300446 NIL) (-991 2297923 2298116 2298184 "QQUTAST" 2298243 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296848 2297321 2297493 "QFORM" 2297795 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2288052 2293265 2293305 "QFCAT" 2293963 NIL QFCAT (NIL T) -9 NIL 2294964 NIL) (-988 2283624 2284825 2286416 "QFCAT-" 2286510 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2283262 2283305 2283432 "QFCAT2" 2283575 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282722 2282832 2282962 "QEQUAT" 2283152 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275869 2276941 2278125 "QCMPACK" 2281655 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2273445 2273866 2274294 "QALGSET" 2275524 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272690 2272864 2273096 "QALGSET2" 2273265 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2271380 2271604 2271921 "PWFFINTB" 2272463 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2269562 2269730 2270084 "PUSHVAR" 2271194 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2265480 2266534 2266575 "PTRANFN" 2268459 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263882 2264173 2264495 "PTPACK" 2265191 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2263514 2263571 2263680 "PTFUNC2" 2263819 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2258041 2262386 2262427 "PTCAT" 2262723 NIL PTCAT (NIL T) -9 NIL 2262876 NIL) (-976 2257699 2257734 2257858 "PSQFR" 2258000 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2256294 2256592 2256926 "PSEUDLIN" 2257397 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2243057 2245428 2247752 "PSETPK" 2254054 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2236101 2238815 2238911 "PSETCAT" 2241932 NIL PSETCAT (NIL T T T T) -9 NIL 2242746 NIL) (-972 2233937 2234571 2235392 "PSETCAT-" 2235397 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2233286 2233451 2233479 "PSCURVE" 2233747 T PSCURVE (NIL) -9 NIL 2233914 NIL) (-970 2229634 2231124 2231189 "PSCAT" 2232033 NIL PSCAT (NIL T T T) -9 NIL 2232273 NIL) (-969 2228697 2228913 2229313 "PSCAT-" 2229318 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2227429 2228062 2228267 "PRTITION" 2228512 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226931 2227150 2227242 "PRTDAST" 2227357 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2216021 2218235 2220423 "PRS" 2224793 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213879 2215371 2215411 "PRQAGG" 2215594 NIL PRQAGG (NIL T) -9 NIL 2215696 NIL) (-964 2213265 2213494 2213522 "PROPLOG" 2213707 T PROPLOG (NIL) -9 NIL 2213829 NIL) (-963 2210435 2211079 2211543 "PROPFRML" 2212833 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209895 2210005 2210135 "PROPERTY" 2210325 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203980 2208061 2208881 "PRODUCT" 2209121 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2201285 2203438 2203672 "PR" 2203791 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2201081 2201113 2201172 "PRINT" 2201246 T PRINT (NIL) -7 NIL NIL NIL) (-958 2200421 2200538 2200690 "PRIMES" 2200961 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2198486 2198887 2199353 "PRIMELT" 2200000 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2198215 2198264 2198292 "PRIMCAT" 2198416 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2194378 2198153 2198198 "PRIMARR" 2198203 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2193385 2193563 2193791 "PRIMARR2" 2194196 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2193028 2193084 2193195 "PREASSOC" 2193323 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2192503 2192636 2192664 "PPCURVE" 2192869 T PPCURVE (NIL) -9 NIL 2193005 NIL) (-951 2192125 2192298 2192381 "PORTNUM" 2192440 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2189484 2189883 2190475 "POLYROOT" 2191706 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2183421 2189088 2189248 "POLY" 2189357 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182804 2182862 2183096 "POLYLIFT" 2183357 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2179079 2179528 2180157 "POLYCATQ" 2182349 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165888 2171254 2171319 "POLYCAT" 2174833 NIL POLYCAT (NIL T T T) -9 NIL 2176761 NIL) (-945 2159337 2161199 2163583 "POLYCAT-" 2163588 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158924 2158992 2159112 "POLY2UP" 2159263 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2158556 2158613 2158722 "POLY2" 2158861 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2157241 2157480 2157756 "POLUTIL" 2158330 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155596 2155873 2156204 "POLTOPOL" 2156963 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2151111 2155532 2155578 "POINT" 2155583 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2149298 2149655 2150030 "PNTHEORY" 2150756 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147717 2148014 2148426 "PMTOOLS" 2148996 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2147310 2147388 2147505 "PMSYM" 2147633 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146820 2146889 2147063 "PMQFCAT" 2147235 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2146175 2146285 2146441 "PMPRED" 2146697 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145571 2145657 2145818 "PMPREDFS" 2146076 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2144214 2144422 2144807 "PMPLCAT" 2145333 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143746 2143825 2143977 "PMLSAGG" 2144129 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2143221 2143297 2143478 "PMKERNEL" 2143664 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142838 2142913 2143026 "PMINS" 2143140 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2142266 2142335 2142551 "PMFS" 2142763 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2141494 2141612 2141817 "PMDOWN" 2142143 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140657 2140816 2140998 "PMASS" 2141332 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139931 2140042 2140205 "PMASSFS" 2140543 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139586 2139654 2139748 "PLOTTOOL" 2139857 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2134193 2135397 2136545 "PLOT" 2138458 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129997 2131041 2131962 "PLOT3D" 2133292 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128909 2129086 2129321 "PLOT1" 2129801 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2104298 2108975 2113826 "PLEQN" 2124175 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103616 2103738 2103918 "PINTERP" 2104163 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2103309 2103356 2103459 "PINTERPA" 2103563 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2102557 2103078 2103165 "PI" 2103205 T PI (NIL) -8 NIL NIL 2103272) (-917 2100946 2101895 2101923 "PID" 2102105 T PID (NIL) -9 NIL 2102239 NIL) (-916 2100671 2100708 2100796 "PICOERCE" 2100903 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099991 2100130 2100306 "PGROEB" 2100527 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095578 2096392 2097297 "PGE" 2099106 T PGE (NIL) -7 NIL NIL NIL) (-913 2093701 2093948 2094314 "PGCD" 2095295 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2093039 2093142 2093303 "PFRPAC" 2093585 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089707 2091587 2091940 "PFR" 2092718 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2088096 2088340 2088665 "PFOTOOLS" 2089454 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086629 2086868 2087219 "PFOQ" 2087853 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2085102 2085314 2085677 "PFO" 2086413 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081682 2084991 2085060 "PF" 2085065 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2079108 2080353 2080381 "PFECAT" 2080966 T PFECAT (NIL) -9 NIL 2081350 NIL) (-905 2078553 2078707 2078921 "PFECAT-" 2078926 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2077156 2077408 2077709 "PFBRU" 2078302 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2075021 2075374 2075806 "PFBR" 2076807 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070930 2072397 2073073 "PERM" 2074378 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2066191 2067137 2068007 "PERMGRP" 2070093 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2064323 2065254 2065295 "PERMCAT" 2065741 NIL PERMCAT (NIL T) -9 NIL 2066046 NIL) (-899 2063976 2064017 2064141 "PERMAN" 2064276 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2061512 2063641 2063763 "PENDTREE" 2063887 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059597 2060339 2060380 "PDRING" 2061037 NIL PDRING (NIL T) -9 NIL 2061323 NIL) (-896 2058700 2058918 2059280 "PDRING-" 2059285 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055942 2056693 2057361 "PDEPROB" 2058052 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2053487 2053991 2054546 "PDEPACK" 2055407 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2052399 2052589 2052840 "PDECOMP" 2053286 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2050004 2050821 2050849 "PDECAT" 2051636 T PDECAT (NIL) -9 NIL 2052349 NIL) (-891 2049755 2049788 2049878 "PCOMP" 2049965 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047960 2048556 2048853 "PBWLB" 2049484 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2040460 2042033 2043371 "PATTERN" 2046643 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2040092 2040149 2040258 "PATTERN2" 2040397 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037849 2038237 2038694 "PATTERN1" 2039681 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2035244 2035798 2036279 "PATRES" 2037414 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034808 2034875 2035007 "PATRES2" 2035171 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032691 2033096 2033503 "PATMATCH" 2034475 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2032227 2032410 2032451 "PATMAB" 2032558 NIL PATMAB (NIL T) -9 NIL 2032641 NIL) (-882 2030772 2031081 2031339 "PATLRES" 2032032 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2030318 2030441 2030482 "PATAB" 2030487 NIL PATAB (NIL T) -9 NIL 2030659 NIL) (-880 2027799 2028331 2028904 "PARTPERM" 2029765 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2027420 2027483 2027585 "PARSURF" 2027730 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2027052 2027109 2027218 "PARSU2" 2027357 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026816 2026856 2026923 "PARSER" 2027005 T PARSER (NIL) -7 NIL NIL NIL) (-876 2026437 2026500 2026602 "PARSCURV" 2026747 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2026069 2026126 2026235 "PARSC2" 2026374 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025708 2025766 2025863 "PARPCURV" 2026005 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2025340 2025397 2025506 "PARPC2" 2025645 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024860 2024946 2025065 "PAN2EXPR" 2025241 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023664 2023981 2024209 "PALETTE" 2024652 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2022132 2022669 2023029 "PAIR" 2023350 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2016029 2021391 2021585 "PADICRC" 2021987 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2009285 2015375 2015559 "PADICRAT" 2015877 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007627 2009222 2009267 "PADIC" 2009272 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004829 2006367 2006407 "PADICCT" 2006988 NIL PADICCT (NIL NIL) -9 NIL 2007270 NIL) (-865 2003786 2003986 2004254 "PADEPAC" 2004616 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002998 2003131 2003337 "PADE" 2003648 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2001412 2002206 2002486 "OWP" 2002802 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000932 2001118 2001215 "OVERSET" 2001335 T OVERSET (NIL) -8 NIL NIL NIL) (-861 2000005 2000537 2000709 "OVAR" 2000800 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1999269 1999390 1999551 "OUT" 1999864 T OUT (NIL) -7 NIL NIL NIL) (-859 1988167 1990378 1992578 "OUTFORM" 1997089 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1987503 1987764 1987891 "OUTBFILE" 1988060 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986810 1986975 1987003 "OUTBCON" 1987321 T OUTBCON (NIL) -9 NIL 1987487 NIL) (-856 1986411 1986523 1986680 "OUTBCON-" 1986685 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985818 1986140 1986229 "OSI" 1986342 T OSI (NIL) -8 NIL NIL NIL) (-854 1985374 1985686 1985714 "OSGROUP" 1985719 T OSGROUP (NIL) -9 NIL 1985741 NIL) (-853 1984119 1984346 1984631 "ORTHPOL" 1985121 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981697 1983954 1984075 "OREUP" 1984080 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1979127 1981388 1981515 "ORESUP" 1981639 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976655 1977155 1977716 "OREPCTO" 1978616 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1970471 1972646 1972687 "OREPCAT" 1975035 NIL OREPCAT (NIL T) -9 NIL 1976139 NIL) (-848 1967618 1968400 1969458 "OREPCAT-" 1969463 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966795 1967067 1967095 "ORDSET" 1967404 T ORDSET (NIL) -9 NIL 1967568 NIL) (-846 1966314 1966436 1966629 "ORDSET-" 1966634 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964940 1965705 1965733 "ORDRING" 1965935 T ORDRING (NIL) -9 NIL 1966060 NIL) (-844 1964585 1964679 1964823 "ORDRING-" 1964828 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963991 1964428 1964456 "ORDMON" 1964461 T ORDMON (NIL) -9 NIL 1964482 NIL) (-842 1963153 1963300 1963495 "ORDFUNS" 1963840 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1962517 1962910 1962938 "ORDFIN" 1963003 T ORDFIN (NIL) -9 NIL 1963077 NIL) (-840 1959103 1961103 1961512 "ORDCOMP" 1962141 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1958369 1958496 1958682 "ORDCOMP2" 1958963 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954977 1955860 1956674 "OPTPROB" 1957575 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951779 1952418 1953122 "OPTPACK" 1954293 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1949492 1950232 1950260 "OPTCAT" 1951079 T OPTCAT (NIL) -9 NIL 1951729 NIL) (-835 1948935 1949169 1949274 "OPSIG" 1949407 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948703 1948742 1948808 "OPQUERY" 1948889 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945861 1947014 1947518 "OP" 1948232 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1945396 1945567 1945608 "OPERCAT" 1945743 NIL OPERCAT (NIL T) -9 NIL 1945811 NIL) (-831 1945242 1945269 1945355 "OPERCAT-" 1945360 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1942081 1944039 1944408 "ONECOMP" 1944906 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1941386 1941501 1941675 "ONECOMP2" 1941953 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940805 1940911 1941041 "OMSERVER" 1941276 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937693 1940245 1940285 "OMSAGG" 1940346 NIL OMSAGG (NIL T) -9 NIL 1940410 NIL) (-826 1936316 1936579 1936861 "OMPKG" 1937431 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935746 1935849 1935877 "OM" 1936176 T OM (NIL) -9 NIL NIL NIL) (-824 1934320 1935295 1935464 "OMLO" 1935627 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1933245 1933392 1933619 "OMEXPR" 1934146 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1932563 1932791 1932927 "OMERR" 1933129 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931741 1931984 1932144 "OMERRK" 1932423 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1931219 1931418 1931526 "OMENC" 1931653 T OMENC (NIL) -8 NIL NIL NIL) (-819 1925114 1926299 1927470 "OMDEV" 1930068 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1924183 1924354 1924548 "OMCONN" 1924940 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922796 1923746 1923774 "OINTDOM" 1923779 T OINTDOM (NIL) -9 NIL 1923800 NIL) (-816 1918602 1919786 1920502 "OFMONOID" 1922112 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1918040 1918539 1918584 "ODVAR" 1918589 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1915490 1917785 1917940 "ODR" 1917945 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907826 1915266 1915392 "ODPOL" 1915397 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901696 1907698 1907803 "ODP" 1907808 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1900462 1900677 1900952 "ODETOOLS" 1901470 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1897429 1898087 1898803 "ODESYS" 1899795 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1892311 1893219 1894244 "ODERTRIC" 1896504 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891737 1891819 1892013 "ODERED" 1892223 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888625 1889173 1889850 "ODERAT" 1891160 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885582 1886049 1886646 "ODEPRRIC" 1888154 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1883552 1884121 1884607 "ODEPROB" 1885116 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1880072 1880557 1881204 "ODEPRIM" 1883031 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1879321 1879423 1879683 "ODEPAL" 1879964 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1875483 1876274 1877138 "ODEPACK" 1878477 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1874516 1874623 1874852 "ODEINT" 1875372 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868617 1870042 1871489 "ODEIFTBL" 1873089 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863952 1864738 1865697 "ODEEF" 1867776 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1863287 1863376 1863606 "ODECONST" 1863857 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1861438 1862073 1862101 "ODECAT" 1862706 T ODECAT (NIL) -9 NIL 1863237 NIL) (-796 1858337 1861150 1861269 "OCT" 1861351 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857975 1858018 1858145 "OCTCT2" 1858288 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852741 1855149 1855189 "OC" 1856286 NIL OC (NIL T) -9 NIL 1857144 NIL) (-793 1849968 1850716 1851706 "OC-" 1851800 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1849346 1849788 1849816 "OCAMON" 1849821 T OCAMON (NIL) -9 NIL 1849842 NIL) (-791 1848903 1849218 1849246 "OASGP" 1849251 T OASGP (NIL) -9 NIL 1849271 NIL) (-790 1848190 1848653 1848681 "OAMONS" 1848721 T OAMONS (NIL) -9 NIL 1848764 NIL) (-789 1847630 1848037 1848065 "OAMON" 1848070 T OAMON (NIL) -9 NIL 1848090 NIL) (-788 1846934 1847426 1847454 "OAGROUP" 1847459 T OAGROUP (NIL) -9 NIL 1847479 NIL) (-787 1846624 1846674 1846762 "NUMTUBE" 1846878 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1840197 1841715 1843251 "NUMQUAD" 1845108 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835953 1836941 1837966 "NUMODE" 1839192 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1833334 1834188 1834216 "NUMINT" 1835139 T NUMINT (NIL) -9 NIL 1835903 NIL) (-783 1832282 1832479 1832697 "NUMFMT" 1833136 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818641 1821586 1824118 "NUMERIC" 1829789 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1813038 1818090 1818185 "NTSCAT" 1818190 NIL NTSCAT (NIL T T T T) -9 NIL 1818229 NIL) (-780 1812232 1812397 1812590 "NTPOLFN" 1812877 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1800064 1809057 1809869 "NSUP" 1811453 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799696 1799753 1799862 "NSUP2" 1800001 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789679 1799470 1799603 "NSMP" 1799608 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1788111 1788412 1788769 "NREP" 1789367 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786702 1786954 1787312 "NPCOEF" 1787854 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785768 1785883 1786099 "NORMRETR" 1786583 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783809 1784099 1784508 "NORMPK" 1785476 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1783494 1783522 1783646 "NORMMA" 1783775 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1783321 1783451 1783480 "NONE" 1783485 T NONE (NIL) -8 NIL NIL NIL) (-770 1783110 1783139 1783208 "NONE1" 1783285 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782593 1782655 1782841 "NODE1" 1783042 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780863 1781687 1781942 "NNI" 1782289 T NNI (NIL) -8 NIL NIL 1782524) (-767 1779283 1779596 1779960 "NLINSOL" 1780531 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1775551 1776519 1777418 "NIPROB" 1778404 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1774308 1774542 1774844 "NFINTBAS" 1775313 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1773482 1773958 1773999 "NETCLT" 1774171 NIL NETCLT (NIL T) -9 NIL 1774253 NIL) (-763 1772190 1772421 1772702 "NCODIV" 1773250 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771952 1771989 1772064 "NCNTFRAC" 1772147 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1770132 1770496 1770916 "NCEP" 1771577 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1769029 1769776 1769804 "NASRING" 1769914 T NASRING (NIL) -9 NIL 1769994 NIL) (-759 1768824 1768868 1768962 "NASRING-" 1768967 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767977 1768476 1768504 "NARNG" 1768621 T NARNG (NIL) -9 NIL 1768712 NIL) (-757 1767669 1767736 1767870 "NARNG-" 1767875 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1766548 1766755 1766990 "NAGSP" 1767454 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757820 1759504 1761177 "NAGS" 1764895 T NAGS (NIL) -7 NIL NIL NIL) (-754 1756368 1756676 1757007 "NAGF07" 1757509 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750906 1752197 1753504 "NAGF04" 1755081 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743874 1745488 1747121 "NAGF02" 1749293 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1739098 1740198 1741315 "NAGF01" 1742777 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732726 1734292 1735877 "NAGE04" 1737533 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723895 1726016 1728146 "NAGE02" 1730616 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719848 1720795 1721759 "NAGE01" 1722951 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717643 1718177 1718735 "NAGD03" 1719310 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1709393 1711321 1713275 "NAGD02" 1715709 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1703204 1704629 1706069 "NAGD01" 1707973 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1699413 1700235 1701072 "NAGC06" 1702387 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697878 1698210 1698566 "NAGC05" 1699077 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1697254 1697373 1697517 "NAGC02" 1697754 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1696314 1696871 1696911 "NAALG" 1696990 NIL NAALG (NIL T) -9 NIL 1697051 NIL) (-740 1696149 1696178 1696268 "NAALG-" 1696273 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1690099 1691207 1692394 "MULTSQFR" 1695045 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1689418 1689493 1689677 "MULTFACT" 1690011 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1682503 1686381 1686434 "MTSCAT" 1687504 NIL MTSCAT (NIL T T) -9 NIL 1688018 NIL) (-736 1682215 1682269 1682361 "MTHING" 1682443 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1682007 1682040 1682100 "MSYSCMD" 1682175 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1678116 1680762 1681082 "MSET" 1681720 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1675211 1677677 1677718 "MSETAGG" 1677723 NIL MSETAGG (NIL T) -9 NIL 1677757 NIL) (-732 1671079 1672590 1673335 "MRING" 1674511 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670645 1670712 1670843 "MRF2" 1671006 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1670263 1670298 1670442 "MRATFAC" 1670604 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667875 1668170 1668601 "MPRFF" 1669968 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661927 1667729 1667826 "MPOLY" 1667831 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1661417 1661452 1661660 "MPCPF" 1661886 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660931 1660974 1661158 "MPC3" 1661368 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1660126 1660207 1660428 "MPC2" 1660846 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1658427 1658764 1659154 "MONOTOOL" 1659786 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657678 1657969 1657997 "MONOID" 1658216 T MONOID (NIL) -9 NIL 1658363 NIL) (-722 1657224 1657343 1657524 "MONOID-" 1657529 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1648075 1653991 1654050 "MONOGEN" 1654724 NIL MONOGEN (NIL T T) -9 NIL 1655180 NIL) (-720 1645293 1646028 1647028 "MONOGEN-" 1647147 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1644152 1644572 1644600 "MONADWU" 1644992 T MONADWU (NIL) -9 NIL 1645230 NIL) (-718 1643524 1643683 1643931 "MONADWU-" 1643936 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642909 1643127 1643155 "MONAD" 1643362 T MONAD (NIL) -9 NIL 1643474 NIL) (-716 1642594 1642672 1642804 "MONAD-" 1642809 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640910 1641507 1641786 "MOEBIUS" 1642347 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1640302 1640680 1640720 "MODULE" 1640725 NIL MODULE (NIL T) -9 NIL 1640751 NIL) (-713 1639870 1639966 1640156 "MODULE-" 1640161 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637577 1638234 1638561 "MODRING" 1639694 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1634548 1635682 1636203 "MODOP" 1637106 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1633163 1633615 1633892 "MODMONOM" 1634411 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622960 1631454 1631868 "MODMON" 1632800 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1620143 1621804 1622080 "MODFIELD" 1622835 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1619147 1619424 1619614 "MMLFORM" 1619973 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618673 1618716 1618895 "MMAP" 1619098 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616882 1617623 1617664 "MLO" 1618087 NIL MLO (NIL T) -9 NIL 1618329 NIL) (-704 1614248 1614764 1615366 "MLIFT" 1616363 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613639 1613723 1613877 "MKUCFUNC" 1614159 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1613238 1613308 1613431 "MKRECORD" 1613562 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1612285 1612447 1612675 "MKFUNC" 1613049 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611673 1611777 1611933 "MKFLCFN" 1612168 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1611216 1611583 1611642 "MKCHSET" 1611647 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1610493 1610595 1610780 "MKBCFUNC" 1611109 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607227 1610047 1610183 "MINT" 1610377 T MINT (NIL) -8 NIL NIL NIL) (-696 1606039 1606282 1606559 "MHROWRED" 1606982 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601446 1604574 1604979 "MFLOAT" 1605654 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600803 1600879 1601050 "MFINFACT" 1601358 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597118 1597966 1598850 "MESH" 1599939 T MESH (NIL) -7 NIL NIL NIL) (-692 1595508 1595820 1596173 "MDDFACT" 1596805 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592350 1594667 1594708 "MDAGG" 1594963 NIL MDAGG (NIL T) -9 NIL 1595106 NIL) (-690 1582120 1591643 1591850 "MCMPLX" 1592163 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581261 1581407 1581607 "MCDEN" 1581969 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579151 1579421 1579801 "MCALCFN" 1580991 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578076 1578316 1578549 "MAYBE" 1578957 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575688 1576211 1576773 "MATSTOR" 1577547 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571693 1575060 1575308 "MATRIX" 1575473 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567457 1568166 1568902 "MATLIN" 1571050 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557611 1560749 1560826 "MATCAT" 1565706 NIL MATCAT (NIL T T T) -9 NIL 1567123 NIL) (-682 1553967 1554988 1556344 "MATCAT-" 1556349 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552561 1552714 1553047 "MATCAT2" 1553802 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550673 1550997 1551381 "MAPPKG3" 1552236 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549654 1549827 1550049 "MAPPKG2" 1550497 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548153 1548437 1548764 "MAPPKG1" 1549360 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547259 1547559 1547736 "MAPPAST" 1547996 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546870 1546928 1547051 "MAPHACK3" 1547195 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546462 1546523 1546637 "MAPHACK2" 1546802 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545899 1546003 1546145 "MAPHACK1" 1546353 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544005 1544599 1544903 "MAGMA" 1545627 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543511 1543729 1543820 "MACROAST" 1543934 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539977 1541750 1542211 "M3D" 1543083 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534131 1538346 1538387 "LZSTAGG" 1539169 NIL LZSTAGG (NIL T) -9 NIL 1539464 NIL) (-669 1530088 1531262 1532719 "LZSTAGG-" 1532724 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527202 1527979 1528466 "LWORD" 1529633 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526805 1527006 1527081 "LSTAST" 1527147 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519998 1526576 1526710 "LSQM" 1526715 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519222 1519361 1519589 "LSPP" 1519853 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517034 1517335 1517791 "LSMP" 1518911 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513813 1514487 1515217 "LSMP1" 1516336 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507738 1512980 1513021 "LSAGG" 1513083 NIL LSAGG (NIL T) -9 NIL 1513161 NIL) (-661 1504433 1505357 1506570 "LSAGG-" 1506575 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502059 1503577 1503826 "LPOLY" 1504228 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501641 1501726 1501849 "LPEFRAC" 1501968 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499988 1500735 1500988 "LO" 1501473 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499640 1499752 1499780 "LOGIC" 1499891 T LOGIC (NIL) -9 NIL 1499972 NIL) (-656 1499502 1499525 1499596 "LOGIC-" 1499601 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498695 1498835 1499028 "LODOOPS" 1499358 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496145 1498611 1498677 "LODO" 1498682 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494683 1494918 1495271 "LODOF" 1495892 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491031 1493436 1493477 "LODOCAT" 1493915 NIL LODOCAT (NIL T) -9 NIL 1494126 NIL) (-651 1490764 1490822 1490949 "LODOCAT-" 1490954 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488111 1490605 1490723 "LODO2" 1490728 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485573 1488048 1488093 "LODO1" 1488098 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484433 1484598 1484910 "LODEEF" 1485396 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479719 1482563 1482604 "LNAGG" 1483551 NIL LNAGG (NIL T) -9 NIL 1483995 NIL) (-646 1478866 1479080 1479422 "LNAGG-" 1479427 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475029 1475791 1476430 "LMOPS" 1478281 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474424 1474786 1474827 "LMODULE" 1474888 NIL LMODULE (NIL T) -9 NIL 1474930 NIL) (-643 1471670 1474069 1474192 "LMDICT" 1474334 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471396 1471578 1471638 "LITERAL" 1471643 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464627 1470342 1470640 "LIST" 1471131 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464152 1464226 1464365 "LIST3" 1464547 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463159 1463337 1463565 "LIST2" 1463970 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461293 1461605 1462004 "LIST2MAP" 1462806 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460015 1460659 1460700 "LINEXP" 1460955 NIL LINEXP (NIL T) -9 NIL 1461104 NIL) (-636 1458662 1458922 1459219 "LINDEP" 1459767 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455429 1456148 1456925 "LIMITRF" 1457917 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453704 1454000 1454416 "LIMITPS" 1455124 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448159 1453215 1453443 "LIE" 1453525 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447208 1447651 1447691 "LIECAT" 1447831 NIL LIECAT (NIL T) -9 NIL 1447982 NIL) (-631 1447049 1447076 1447164 "LIECAT-" 1447169 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439661 1446498 1446663 "LIB" 1446904 T LIB (NIL) -8 NIL NIL NIL) (-629 1435296 1436179 1437114 "LGROBP" 1438778 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433162 1433436 1433798 "LF" 1435017 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432002 1432694 1432722 "LFCAT" 1432929 T LFCAT (NIL) -9 NIL 1433068 NIL) (-626 1428904 1429534 1430222 "LEXTRIPK" 1431366 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425675 1426474 1426977 "LEXP" 1428484 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425178 1425396 1425488 "LETAST" 1425603 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423576 1423889 1424290 "LEADCDET" 1424860 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422766 1422840 1423069 "LAZM3PK" 1423497 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417710 1420843 1421381 "LAUPOL" 1422278 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417275 1417319 1417487 "LAPLACE" 1417660 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415241 1416376 1416627 "LA" 1417108 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414314 1414872 1414913 "LALG" 1414975 NIL LALG (NIL T) -9 NIL 1415034 NIL) (-617 1414028 1414087 1414223 "LALG-" 1414228 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413863 1413887 1413928 "KVTFROM" 1413990 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412663 1413080 1413309 "KTVLOGIC" 1413654 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412498 1412522 1412563 "KRCFROM" 1412625 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411402 1411589 1411888 "KOVACIC" 1412298 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411237 1411261 1411302 "KONVERT" 1411364 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411072 1411096 1411137 "KOERCE" 1411199 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408806 1409566 1409959 "KERNEL" 1410711 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408308 1408389 1408519 "KERNEL2" 1408720 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402159 1406847 1406901 "KDAGG" 1407278 NIL KDAGG (NIL T T) -9 NIL 1407484 NIL) (-607 1401688 1401812 1402017 "KDAGG-" 1402022 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394863 1401349 1401504 "KAFILE" 1401566 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389318 1394374 1394602 "JORDAN" 1394684 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388724 1388967 1389088 "JOINAST" 1389217 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388570 1388629 1388684 "JAVACODE" 1388689 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384869 1386775 1386829 "IXAGG" 1387758 NIL IXAGG (NIL T T) -9 NIL 1388217 NIL) (-601 1383788 1384094 1384513 "IXAGG-" 1384518 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379368 1383710 1383769 "IVECTOR" 1383774 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378134 1378371 1378637 "ITUPLE" 1379135 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376570 1376747 1377053 "ITRIGMNP" 1377956 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375315 1375519 1375802 "ITFUN3" 1376346 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374947 1375004 1375113 "ITFUN2" 1375252 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372776 1373809 1374108 "ITAYLOR" 1374681 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361748 1366913 1368076 "ISUPS" 1371646 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360852 1360992 1361228 "ISUMP" 1361595 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356116 1360653 1360732 "ISTRING" 1360805 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355619 1355837 1355929 "ISAST" 1356044 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354829 1354910 1355126 "IRURPK" 1355533 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353765 1353966 1354206 "IRSN" 1354609 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351794 1352149 1352585 "IRRF2F" 1353403 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351541 1351579 1351655 "IRREDFFX" 1351750 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350156 1350415 1350714 "IROOT" 1351274 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346787 1347840 1348532 "IR" 1349496 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344400 1344895 1345461 "IR2" 1346265 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343472 1343585 1343806 "IR2F" 1344283 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343263 1343297 1343357 "IPRNTPK" 1343432 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339870 1343152 1343221 "IPF" 1343226 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338224 1339795 1339852 "IPADIC" 1339857 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337563 1337784 1337914 "IP4ADDR" 1338114 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337063 1337267 1337377 "IOMODE" 1337473 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336136 1336660 1336787 "IOBFILE" 1336956 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335624 1336040 1336068 "IOBCON" 1336073 T IOBCON (NIL) -9 NIL 1336094 NIL) (-575 1335121 1335179 1335369 "INVLAPLA" 1335560 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324769 1327123 1329509 "INTTR" 1332785 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321113 1321855 1322719 "INTTOOLS" 1323954 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320699 1320790 1320907 "INTSLPE" 1321016 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318680 1320622 1320681 "INTRVL" 1320686 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316282 1316794 1317369 "INTRF" 1318165 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315693 1315790 1315932 "INTRET" 1316180 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313690 1314079 1314549 "INTRAT" 1315301 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310918 1311501 1312127 "INTPM" 1313175 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307620 1308220 1308965 "INTPAF" 1310304 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302799 1303761 1304812 "INTPACK" 1306589 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299703 1302528 1302655 "INT" 1302692 T INT (NIL) -8 NIL NIL NIL) (-563 1298955 1299107 1299315 "INTHERTR" 1299545 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298394 1298474 1298662 "INTHERAL" 1298869 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296240 1296683 1297140 "INTHEORY" 1297957 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287548 1289169 1290948 "INTG0" 1294592 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268121 1272911 1277721 "INTFTBL" 1282758 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267370 1267508 1267681 "INTFACT" 1267980 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264755 1265201 1265765 "INTEF" 1266924 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263214 1263927 1263955 "INTDOM" 1264256 T INTDOM (NIL) -9 NIL 1264463 NIL) (-555 1262583 1262757 1262999 "INTDOM-" 1263004 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259070 1260967 1261021 "INTCAT" 1261820 NIL INTCAT (NIL T) -9 NIL 1262140 NIL) (-553 1258542 1258645 1258773 "INTBIT" 1258962 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257213 1257367 1257681 "INTALG" 1258387 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256670 1256760 1256930 "INTAF" 1257117 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250124 1256480 1256620 "INTABL" 1256625 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249455 1249894 1249959 "INT8" 1249993 T INT8 (NIL) -8 NIL NIL 1250038) (-548 1248785 1249224 1249289 "INT64" 1249323 T INT64 (NIL) -8 NIL NIL 1249368) (-547 1248115 1248554 1248619 "INT32" 1248653 T INT32 (NIL) -8 NIL NIL 1248698) (-546 1247445 1247884 1247949 "INT16" 1247983 T INT16 (NIL) -8 NIL NIL 1248028) (-545 1242452 1245134 1245162 "INS" 1246096 T INS (NIL) -9 NIL 1246761 NIL) (-544 1239692 1240463 1241437 "INS-" 1241510 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238467 1238694 1238992 "INPSIGN" 1239445 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237585 1237702 1237899 "INPRODPF" 1238347 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236479 1236596 1236833 "INPRODFF" 1237465 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235479 1235631 1235891 "INNMFACT" 1236315 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234676 1234773 1234961 "INMODGCD" 1235378 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233184 1233429 1233753 "INFSP" 1234421 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232368 1232485 1232668 "INFPROD0" 1233064 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229250 1230433 1230948 "INFORM" 1231861 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228860 1228920 1229018 "INFORM1" 1229185 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228383 1228472 1228586 "INFINITY" 1228766 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227559 1228103 1228204 "INETCLTS" 1228302 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226175 1226425 1226746 "INEP" 1227307 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225451 1226072 1226137 "INDE" 1226142 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225015 1225083 1225200 "INCRMAPS" 1225378 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223833 1224284 1224490 "INBFILE" 1224829 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219133 1220069 1221013 "INBFF" 1222921 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218041 1218310 1218338 "INBCON" 1218851 T INBCON (NIL) -9 NIL 1219117 NIL) (-526 1217293 1217516 1217792 "INBCON-" 1217797 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216799 1217017 1217108 "INAST" 1217222 T INAST (NIL) -8 NIL NIL NIL) (-524 1216253 1216478 1216584 "IMPTAST" 1216713 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212747 1216097 1216201 "IMATRIX" 1216206 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211459 1211582 1211897 "IMATQF" 1212603 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209679 1209906 1210243 "IMATLIN" 1211215 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204305 1209603 1209661 "ILIST" 1209666 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202258 1204165 1204278 "IIARRAY2" 1204283 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197683 1202169 1202233 "IFF" 1202238 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197057 1197300 1197416 "IFAST" 1197587 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192100 1196349 1196537 "IFARRAY" 1196914 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191307 1192004 1192077 "IFAMON" 1192082 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190891 1190956 1191010 "IEVALAB" 1191217 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190566 1190634 1190794 "IEVALAB-" 1190799 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190224 1190480 1190543 "IDPO" 1190548 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189501 1190113 1190188 "IDPOAMS" 1190193 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188835 1189390 1189465 "IDPOAM" 1189470 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187920 1188170 1188223 "IDPC" 1188636 NIL IDPC (NIL T T) -9 NIL 1188785 NIL) (-508 1187416 1187812 1187885 "IDPAM" 1187890 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186819 1187308 1187381 "IDPAG" 1187386 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186491 1186655 1186730 "IDENT" 1186764 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182746 1183594 1184489 "IDECOMP" 1185648 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175610 1176669 1177716 "IDEAL" 1181782 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174774 1174886 1175085 "ICDEN" 1175494 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173872 1174254 1174401 "ICARD" 1174647 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171932 1172245 1172650 "IBPTOOLS" 1173549 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167566 1171552 1171665 "IBITS" 1171851 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164289 1164865 1165560 "IBATOOL" 1166983 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162068 1162530 1163063 "IBACHIN" 1163824 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159945 1161914 1162017 "IARRAY2" 1162022 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156099 1159871 1159928 "IARRAY1" 1159933 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150083 1154511 1154992 "IAN" 1155638 T IAN (NIL) -8 NIL NIL NIL) (-494 1149594 1149651 1149824 "IALGFACT" 1150020 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149122 1149235 1149263 "HYPCAT" 1149470 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148660 1148777 1148963 "HYPCAT-" 1148968 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148282 1148455 1148538 "HOSTNAME" 1148597 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148127 1148164 1148205 "HOMOTOP" 1148210 NIL HOMOTOP (NIL T) -9 NIL 1148243 NIL) (-489 1144806 1146137 1146178 "HOAGG" 1147159 NIL HOAGG (NIL T) -9 NIL 1147838 NIL) (-488 1143400 1143799 1144325 "HOAGG-" 1144330 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137431 1142995 1143144 "HEXADEC" 1143271 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136179 1136401 1136664 "HEUGCD" 1137208 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135282 1136016 1136146 "HELLFDIV" 1136151 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133509 1135059 1135147 "HEAP" 1135226 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132799 1133061 1133195 "HEADAST" 1133395 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126713 1132714 1132776 "HDP" 1132781 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120456 1126348 1126500 "HDMP" 1126614 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119780 1119920 1120084 "HB" 1120312 T HB (NIL) -7 NIL NIL NIL) (-479 1113277 1119626 1119730 "HASHTBL" 1119735 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112780 1112998 1113090 "HASAST" 1113205 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110585 1112402 1112584 "HACKPI" 1112618 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106280 1110438 1110551 "GTSET" 1110556 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099806 1106158 1106256 "GSTBL" 1106261 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092111 1098837 1099102 "GSERIES" 1099597 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091278 1091669 1091697 "GROUP" 1091900 T GROUP (NIL) -9 NIL 1092034 NIL) (-472 1090644 1090803 1091054 "GROUP-" 1091059 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089011 1089332 1089719 "GROEBSOL" 1090321 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087951 1088213 1088264 "GRMOD" 1088793 NIL GRMOD (NIL T T) -9 NIL 1088961 NIL) (-469 1087719 1087755 1087883 "GRMOD-" 1087888 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083036 1084073 1085073 "GRIMAGE" 1086739 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081502 1081763 1082087 "GRDEF" 1082732 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080946 1081062 1081203 "GRAY" 1081381 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080159 1080539 1080590 "GRALG" 1080743 NIL GRALG (NIL T T) -9 NIL 1080836 NIL) (-464 1079820 1079893 1080056 "GRALG-" 1080061 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076624 1079405 1079583 "GPOLSET" 1079727 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075978 1076035 1076293 "GOSPER" 1076561 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071737 1072416 1072942 "GMODPOL" 1075677 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070742 1070926 1071164 "GHENSEL" 1071549 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064793 1065636 1066663 "GENUPS" 1069826 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064490 1064541 1064630 "GENUFACT" 1064736 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063902 1063979 1064144 "GENPGCD" 1064408 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063376 1063411 1063624 "GENMFACT" 1063861 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061942 1062199 1062506 "GENEEZ" 1063119 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055843 1061553 1061715 "GDMP" 1061865 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045212 1049614 1050720 "GCNAALG" 1054826 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043631 1044467 1044495 "GCDDOM" 1044750 T GCDDOM (NIL) -9 NIL 1044907 NIL) (-451 1043101 1043228 1043443 "GCDDOM-" 1043448 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041773 1041958 1042262 "GB" 1042880 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030389 1032719 1035111 "GBINTERN" 1039464 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028226 1028518 1028939 "GBF" 1030064 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027007 1027172 1027439 "GBEUCLID" 1028042 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026356 1026481 1026630 "GAUSSFAC" 1026878 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024723 1025025 1025339 "GALUTIL" 1026075 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023031 1023305 1023629 "GALPOLYU" 1024450 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020396 1020686 1021093 "GALFACTU" 1022728 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012202 1013701 1015309 "GALFACT" 1018828 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009590 1010248 1010276 "FVFUN" 1011432 T FVFUN (NIL) -9 NIL 1012152 NIL) (-440 1008856 1009038 1009066 "FVC" 1009357 T FVC (NIL) -9 NIL 1009540 NIL) (-439 1008526 1008681 1008749 "FUNDESC" 1008808 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008168 1008323 1008404 "FUNCTION" 1008478 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005939 1006490 1006956 "FT" 1007722 T FT (NIL) -8 NIL NIL NIL) (-436 1004757 1005240 1005443 "FTEM" 1005756 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003013 1003302 1003706 "FSUPFACT" 1004448 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001410 1001699 1002031 "FST" 1002701 T FST (NIL) -8 NIL NIL NIL) (-433 1000581 1000687 1000882 "FSRED" 1001292 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999259 999515 999869 "FSPRMELT" 1000296 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996344 996782 997281 "FSPECF" 998822 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978398 986847 986887 "FS" 990735 NIL FS (NIL T) -9 NIL 993024 NIL) (-429 967045 970038 974094 "FS-" 974391 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966559 966613 966790 "FSINT" 966986 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964878 965552 965855 "FSERIES" 966338 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963892 964008 964239 "FSCINT" 964758 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960126 962836 962877 "FSAGG" 963247 NIL FSAGG (NIL T) -9 NIL 963506 NIL) (-424 957888 958489 959285 "FSAGG-" 959380 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956930 957073 957300 "FSAGG2" 957741 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954584 954864 955418 "FS2UPS" 956648 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954166 954209 954364 "FS2" 954535 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953023 953194 953503 "FS2EXPXP" 953991 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952449 952564 952716 "FRUTIL" 952903 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943889 947944 949302 "FR" 951123 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938964 941607 941647 "FRNAALG" 943043 NIL FRNAALG (NIL T) -9 NIL 943650 NIL) (-416 934637 935713 936988 "FRNAALG-" 937738 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934275 934318 934445 "FRNAAF2" 934588 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932682 933129 933424 "FRMOD" 934087 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930460 931065 931382 "FRIDEAL" 932473 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929655 929742 930031 "FRIDEAL2" 930367 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928788 929202 929243 "FRETRCT" 929248 NIL FRETRCT (NIL T) -9 NIL 929424 NIL) (-410 927900 928131 928482 "FRETRCT-" 928487 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925104 926288 926347 "FRAMALG" 927229 NIL FRAMALG (NIL T T) -9 NIL 927521 NIL) (-408 923238 923693 924323 "FRAMALG-" 924546 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917186 922713 922989 "FRAC" 922994 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916822 916879 916986 "FRAC2" 917123 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916458 916515 916622 "FR2" 916759 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911123 913983 914011 "FPS" 915130 T FPS (NIL) -9 NIL 915687 NIL) (-403 910572 910681 910845 "FPS-" 910991 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908018 909661 909689 "FPC" 909914 T FPC (NIL) -9 NIL 910056 NIL) (-401 907811 907851 907948 "FPC-" 907953 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906689 907299 907340 "FPATMAB" 907345 NIL FPATMAB (NIL T) -9 NIL 907497 NIL) (-399 904389 904865 905291 "FPARFRAC" 906326 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899782 900281 900963 "FORTRAN" 903821 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897498 897998 898537 "FORT" 899263 T FORT (NIL) -7 NIL NIL NIL) (-396 895174 895736 895764 "FORTFN" 896824 T FORTFN (NIL) -9 NIL 897448 NIL) (-395 894938 894988 895016 "FORTCAT" 895075 T FORTCAT (NIL) -9 NIL 895137 NIL) (-394 893071 893554 893944 "FORMULA" 894568 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892859 892889 892958 "FORMULA1" 893035 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892382 892434 892607 "FORDER" 892801 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891478 891642 891835 "FOP" 892209 T FOP (NIL) -7 NIL NIL NIL) (-390 890086 890758 890932 "FNLA" 891360 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888841 889230 889258 "FNCAT" 889718 T FNCAT (NIL) -9 NIL 889978 NIL) (-388 888407 888800 888828 "FNAME" 888833 T FNAME (NIL) -8 NIL NIL NIL) (-387 887062 887999 888027 "FMTC" 888032 T FMTC (NIL) -9 NIL 888068 NIL) (-386 883422 884585 885214 "FMONOID" 886466 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882641 883164 883313 "FM" 883318 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880065 880711 880739 "FMFUN" 881883 T FMFUN (NIL) -9 NIL 882591 NIL) (-383 879334 879515 879543 "FMC" 879833 T FMC (NIL) -9 NIL 880015 NIL) (-382 876528 877362 877416 "FMCAT" 878611 NIL FMCAT (NIL T T) -9 NIL 879106 NIL) (-381 875421 876294 876394 "FM1" 876473 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873195 873611 874105 "FLOATRP" 874972 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866796 870924 871545 "FLOAT" 872594 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864234 864734 865312 "FLOATCP" 866263 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863035 863847 863888 "FLINEXP" 863893 NIL FLINEXP (NIL T) -9 NIL 863986 NIL) (-376 862189 862424 862752 "FLINEXP-" 862757 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861265 861409 861633 "FLASORT" 862041 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858482 859324 859376 "FLALG" 860603 NIL FLALG (NIL T T) -9 NIL 861070 NIL) (-373 852266 855968 856009 "FLAGG" 857271 NIL FLAGG (NIL T) -9 NIL 857923 NIL) (-372 850992 851331 851821 "FLAGG-" 851826 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850034 850177 850404 "FLAGG2" 850845 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847001 847983 848042 "FINRALG" 849170 NIL FINRALG (NIL T T) -9 NIL 849678 NIL) (-369 846161 846390 846729 "FINRALG-" 846734 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845567 845780 845808 "FINITE" 846004 T FINITE (NIL) -9 NIL 846111 NIL) (-367 838025 840186 840226 "FINAALG" 843893 NIL FINAALG (NIL T) -9 NIL 845346 NIL) (-366 833357 834407 835551 "FINAALG-" 836930 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832752 833112 833215 "FILE" 833287 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831436 831748 831802 "FILECAT" 832486 NIL FILECAT (NIL T T) -9 NIL 832702 NIL) (-363 829296 830798 830826 "FIELD" 830866 T FIELD (NIL) -9 NIL 830946 NIL) (-362 827916 828301 828812 "FIELD-" 828817 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825793 826551 826898 "FGROUP" 827602 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824883 825047 825267 "FGLMICPK" 825625 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820742 824808 824865 "FFX" 824870 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820343 820404 820539 "FFSLPE" 820675 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816332 817115 817911 "FFPOLY" 819579 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815836 815872 816081 "FFPOLY2" 816290 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811706 815755 815818 "FFP" 815823 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807131 811617 811681 "FF" 811686 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802284 806474 806664 "FFNBX" 806985 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797240 801419 801677 "FFNBP" 802138 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791900 796524 796735 "FFNB" 797073 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790732 790930 791245 "FFINTBAS" 791697 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786952 789139 789167 "FFIELDC" 789787 T FFIELDC (NIL) -9 NIL 790163 NIL) (-348 785614 785985 786482 "FFIELDC-" 786487 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785183 785229 785353 "FFHOM" 785556 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782878 783365 783882 "FFF" 784698 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778523 782620 782721 "FFCGX" 782821 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774171 778255 778362 "FFCGP" 778466 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769381 773898 774006 "FFCG" 774107 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751206 760252 760338 "FFCAT" 765503 NIL FFCAT (NIL T T T) -9 NIL 766954 NIL) (-341 746404 747451 748765 "FFCAT-" 749995 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745815 745858 746093 "FFCAT2" 746355 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735012 738787 740007 "FEXPR" 744667 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734012 734447 734488 "FEVALAB" 734572 NIL FEVALAB (NIL T) -9 NIL 734833 NIL) (-337 733171 733381 733719 "FEVALAB-" 733724 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731764 732554 732757 "FDIV" 733070 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728830 729545 729660 "FDIVCAT" 731228 NIL FDIVCAT (NIL T T T T) -9 NIL 731665 NIL) (-334 728592 728619 728789 "FDIVCAT-" 728794 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727812 727899 728176 "FDIV2" 728499 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726498 726757 727046 "FCPAK1" 727543 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725624 725998 726139 "FCOMP" 726389 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709353 712774 716312 "FC" 722106 T FC (NIL) -8 NIL NIL NIL) (-329 701924 705917 705957 "FAXF" 707759 NIL FAXF (NIL T) -9 NIL 708451 NIL) (-328 699200 699858 700683 "FAXF-" 701148 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694300 698576 698752 "FARRAY" 699057 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689545 691585 691638 "FAMR" 692661 NIL FAMR (NIL T T) -9 NIL 693121 NIL) (-325 688435 688737 689172 "FAMR-" 689177 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687631 688357 688410 "FAMONOID" 688415 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685443 686127 686180 "FAMONC" 687121 NIL FAMONC (NIL T T) -9 NIL 687507 NIL) (-322 684135 685197 685334 "FAGROUP" 685339 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681930 682249 682652 "FACUTIL" 683816 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681029 681214 681436 "FACTFUNC" 681740 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673426 680280 680492 "EXPUPXS" 680885 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670909 671449 672035 "EXPRTUBE" 672860 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667103 667695 668432 "EXPRODE" 670248 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652469 665758 666186 "EXPR" 666707 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646876 647463 648276 "EXPR2UPS" 651767 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646512 646569 646676 "EXPR2" 646813 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637909 645644 645941 "EXPEXPAN" 646349 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637736 637866 637895 "EXIT" 637900 T EXIT (NIL) -8 NIL NIL NIL) (-311 637243 637460 637551 "EXITAST" 637665 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636870 636932 637045 "EVALCYC" 637175 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636411 636529 636570 "EVALAB" 636740 NIL EVALAB (NIL T) -9 NIL 636844 NIL) (-308 635892 636014 636235 "EVALAB-" 636240 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633352 634628 634656 "EUCDOM" 635211 T EUCDOM (NIL) -9 NIL 635561 NIL) (-306 631757 632199 632789 "EUCDOM-" 632794 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619295 622055 624805 "ESTOOLS" 629027 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618927 618984 619093 "ESTOOLS2" 619232 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618678 618720 618800 "ESTOOLS1" 618879 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612583 614311 614339 "ES" 617107 T ES (NIL) -9 NIL 618516 NIL) (-301 607530 608817 610634 "ES-" 610798 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603904 604665 605445 "ESCONT" 606770 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603649 603681 603763 "ESCONT1" 603866 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603324 603374 603474 "ES2" 603593 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602954 603012 603121 "ES1" 603260 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602170 602299 602475 "ERROR" 602798 T ERROR (NIL) -7 NIL NIL NIL) (-295 595673 602029 602120 "EQTBL" 602125 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588224 590987 592436 "EQ" 594257 NIL -3292 (NIL T) -8 NIL NIL NIL) (-293 587856 587913 588022 "EQ2" 588161 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583145 584194 585287 "EP" 586795 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581723 582020 582332 "ENV" 582853 T ENV (NIL) -8 NIL NIL NIL) (-290 580894 581422 581450 "ENTIRER" 581455 T ENTIRER (NIL) -9 NIL 581501 NIL) (-289 577388 578849 579219 "EMR" 580693 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576532 576717 576771 "ELTAGG" 577151 NIL ELTAGG (NIL T T) -9 NIL 577362 NIL) (-287 576251 576313 576454 "ELTAGG-" 576459 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576040 576069 576123 "ELTAB" 576207 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575166 575312 575511 "ELFUTS" 575891 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574908 574964 574992 "ELEMFUN" 575097 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574778 574799 574867 "ELEMFUN-" 574872 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569669 572878 572919 "ELAGG" 573859 NIL ELAGG (NIL T) -9 NIL 574322 NIL) (-281 567954 568388 569051 "ELAGG-" 569056 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566619 566897 567190 "ELABEXPR" 567681 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559483 561286 562113 "EFUPXS" 565895 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552933 554734 555544 "EFULS" 558759 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550355 550713 551192 "EFSTRUC" 552565 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539426 540992 542552 "EF" 548870 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538527 538911 539060 "EAB" 539297 T EAB (NIL) -8 NIL NIL NIL) (-274 537736 538486 538514 "E04UCFA" 538519 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536945 537695 537723 "E04NAFA" 537728 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536154 536904 536932 "E04MBFA" 536937 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535363 536113 536141 "E04JAFA" 536146 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534574 535322 535350 "E04GCFA" 535355 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533785 534533 534561 "E04FDFA" 534566 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532994 533744 533772 "E04DGFA" 533777 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527167 528519 529883 "E04AGNT" 531650 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525873 526353 526393 "DVARCAT" 526868 NIL DVARCAT (NIL T) -9 NIL 527067 NIL) (-265 525077 525289 525603 "DVARCAT-" 525608 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517969 524876 525005 "DSMP" 525010 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512778 513914 514982 "DROPT" 516921 T DROPT (NIL) -8 NIL NIL NIL) (-262 512443 512502 512600 "DROPT1" 512713 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507558 508684 509821 "DROPT0" 511326 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505903 506228 506614 "DRAWPT" 507192 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500490 501413 502492 "DRAW" 504877 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500123 500176 500294 "DRAWHACK" 500431 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498854 499123 499414 "DRAWCX" 499852 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498369 498438 498589 "DRAWCURV" 498780 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488837 490799 492914 "DRAWCFUN" 496274 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485650 487532 487573 "DQAGG" 488202 NIL DQAGG (NIL T) -9 NIL 488475 NIL) (-253 473921 480628 480711 "DPOLCAT" 482563 NIL DPOLCAT (NIL T T T T) -9 NIL 483108 NIL) (-252 468757 470106 472064 "DPOLCAT-" 472069 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461906 468618 468716 "DPMO" 468721 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454958 461686 461853 "DPMM" 461858 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454590 454877 454925 "DOMCTOR" 454930 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453885 454112 454249 "DOMAIN" 454473 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447628 453520 453672 "DMP" 453786 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447228 447284 447428 "DLP" 447566 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441098 446555 446745 "DLIST" 447070 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437942 439951 439992 "DLAGG" 440542 NIL DLAGG (NIL T) -9 NIL 440772 NIL) (-243 436747 437385 437413 "DIVRING" 437505 T DIVRING (NIL) -9 NIL 437588 NIL) (-242 435984 436174 436474 "DIVRING-" 436479 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434086 434443 434849 "DISPLAY" 435598 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428022 434000 434063 "DIRPROD" 434068 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426870 427073 427338 "DIRPROD2" 427815 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416127 422085 422138 "DIRPCAT" 422548 NIL DIRPCAT (NIL NIL T) -9 NIL 423388 NIL) (-237 413453 414095 414976 "DIRPCAT-" 415313 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412740 412900 413086 "DIOSP" 413287 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409442 411652 411693 "DIOPS" 412127 NIL DIOPS (NIL T) -9 NIL 412356 NIL) (-234 408991 409105 409296 "DIOPS-" 409301 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407875 408477 408505 "DIFRING" 408692 T DIFRING (NIL) -9 NIL 408802 NIL) (-232 407521 407598 407750 "DIFRING-" 407755 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405318 406564 406605 "DIFEXT" 406968 NIL DIFEXT (NIL T) -9 NIL 407262 NIL) (-230 403603 404031 404697 "DIFEXT-" 404702 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400925 403135 403176 "DIAGG" 403181 NIL DIAGG (NIL T) -9 NIL 403201 NIL) (-228 400309 400466 400718 "DIAGG-" 400723 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395774 399268 399545 "DHMATRIX" 400078 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391386 392295 393305 "DFSFUN" 394784 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386491 390317 390629 "DFLOAT" 391094 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384719 385000 385396 "DFINTTLS" 386199 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381775 382740 383140 "DERHAM" 384385 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379624 381550 381639 "DEQUEUE" 381719 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378839 378972 379168 "DEGRED" 379486 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375234 375979 376832 "DEFINTRF" 378067 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372761 373230 373829 "DEFINTEF" 374753 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372138 372381 372496 "DEFAST" 372666 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366169 371733 371882 "DECIMAL" 372009 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363679 364139 364645 "DDFACT" 365713 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363275 363318 363469 "DBLRESP" 363630 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361174 361508 361868 "DBASE" 363042 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360443 360654 360800 "DATAARY" 361073 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359576 360402 360430 "D03FAFA" 360435 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358710 359535 359563 "D03EEFA" 359568 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356660 357126 357615 "D03AGNT" 358241 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355976 356619 356647 "D02EJFA" 356652 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355292 355935 355963 "D02CJFA" 355968 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354608 355251 355279 "D02BHFA" 355284 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353924 354567 354595 "D02BBFA" 354600 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347121 348710 350316 "D02AGNT" 352338 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344889 345412 345958 "D01WGTS" 346595 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343983 344848 344876 "D01TRNS" 344881 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343078 343942 343970 "D01GBFA" 343975 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342173 343037 343065 "D01FCFA" 343070 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341268 342132 342160 "D01ASFA" 342165 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340363 341227 341255 "D01AQFA" 341260 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339458 340322 340350 "D01APFA" 340355 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338553 339417 339445 "D01ANFA" 339450 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337648 338512 338540 "D01AMFA" 338545 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336743 337607 337635 "D01ALFA" 337640 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335838 336702 336730 "D01AKFA" 336735 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334933 335797 335825 "D01AJFA" 335830 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328228 329781 331342 "D01AGNT" 333392 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327565 327693 327845 "CYCLOTOM" 328096 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324300 325013 325740 "CYCLES" 326858 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323612 323746 323917 "CVMP" 324161 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321383 321641 322017 "CTRIGMNP" 323340 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320878 321177 321250 "CTOR" 321330 T CTOR (NIL) -8 NIL NIL NIL) (-186 320414 320609 320710 "CTORKIND" 320797 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319762 320021 320049 "CTORCAT" 320231 T CTORCAT (NIL) -9 NIL 320344 NIL) (-184 319360 319471 319630 "CTORCAT-" 319635 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318876 319063 319161 "CTORCALL" 319282 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318250 318349 318502 "CSTTOOLS" 318773 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314049 314706 315464 "CRFP" 317562 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313551 313770 313862 "CRCEAST" 313977 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312598 312783 313011 "CRAPACK" 313355 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311982 312083 312287 "CPMATCH" 312474 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311707 311735 311841 "CPIMA" 311948 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308071 308743 309461 "COORDSYS" 311042 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307479 307601 307744 "CONTOUR" 307948 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303397 305482 305974 "CONTFRAC" 307019 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303277 303298 303326 "CONDUIT" 303363 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302442 302970 302998 "COMRING" 303003 T COMRING (NIL) -9 NIL 303055 NIL) (-171 301523 301800 301984 "COMPPROP" 302278 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301184 301219 301347 "COMPLPAT" 301482 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291233 300993 301102 "COMPLEX" 301107 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290869 290926 291033 "COMPLEX2" 291170 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290587 290622 290720 "COMPFACT" 290828 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274741 284969 285009 "COMPCAT" 286013 NIL COMPCAT (NIL T) -9 NIL 287409 NIL) (-165 264252 267180 270807 "COMPCAT-" 271163 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263981 264009 264112 "COMMUPC" 264218 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263776 263809 263868 "COMMONOP" 263942 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263359 263527 263614 "COMM" 263709 T COMM (NIL) -8 NIL NIL NIL) (-161 262962 263163 263238 "COMMAAST" 263304 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262211 262405 262433 "COMBOPC" 262771 T COMBOPC (NIL) -9 NIL 262946 NIL) (-159 261107 261317 261559 "COMBINAT" 262001 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 257304 257878 258518 "COMBF" 260529 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256089 256420 256655 "COLOR" 257089 T COLOR (NIL) -8 NIL NIL NIL) (-156 255592 255810 255902 "COLONAST" 256017 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255232 255279 255404 "CMPLXRT" 255539 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254707 254932 255031 "CLLCTAST" 255153 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250207 251237 252317 "CLIP" 253647 T CLIP (NIL) -7 NIL NIL NIL) (-152 248580 249313 249552 "CLIF" 250034 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244802 246726 246767 "CLAGG" 247696 NIL CLAGG (NIL T) -9 NIL 248232 NIL) (-150 243224 243681 244264 "CLAGG-" 244269 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242768 242853 242993 "CINTSLPE" 243133 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240269 240740 241288 "CHVAR" 242296 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239504 240032 240060 "CHARZ" 240065 T CHARZ (NIL) -9 NIL 240080 NIL) (-146 239258 239298 239376 "CHARPOL" 239458 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238377 238938 238966 "CHARNZ" 239013 T CHARNZ (NIL) -9 NIL 239069 NIL) (-144 236366 237067 237402 "CHAR" 238062 T CHAR (NIL) -8 NIL NIL NIL) (-143 236092 236153 236181 "CFCAT" 236292 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235337 235448 235630 "CDEN" 235976 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231329 234490 234770 "CCLASS" 235077 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230636 230779 230942 "CATEGORY" 231186 T -10 (NIL) -8 NIL NIL NIL) (-139 230268 230555 230603 "CATCTOR" 230608 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229746 229971 230069 "CATAST" 230190 T CATAST (NIL) -8 NIL NIL NIL) (-137 229249 229467 229559 "CASEAST" 229674 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224285 225278 226031 "CARTEN" 228552 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 223393 223541 223762 "CARTEN2" 224132 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221735 222543 222800 "CARD" 223156 T CARD (NIL) -8 NIL NIL NIL) (-133 221338 221539 221614 "CAPSLAST" 221680 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220710 221038 221066 "CACHSET" 221198 T CACHSET (NIL) -9 NIL 221275 NIL) (-131 220206 220502 220530 "CABMON" 220580 T CABMON (NIL) -9 NIL 220636 NIL) (-130 219706 219910 220020 "BYTEORD" 220116 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218709 219240 219382 "BYTE" 219545 T BYTE (NIL) -8 NIL NIL 219667) (-128 214109 218214 218386 "BYTEBUF" 218557 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211666 213801 213908 "BTREE" 214035 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209163 211314 211436 "BTOURN" 211576 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206580 208633 208674 "BTCAT" 208742 NIL BTCAT (NIL T) -9 NIL 208819 NIL) (-124 206247 206327 206476 "BTCAT-" 206481 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201539 205390 205418 "BTAGG" 205640 T BTAGG (NIL) -9 NIL 205801 NIL) (-122 201029 201154 201360 "BTAGG-" 201365 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198072 200307 200522 "BSTREE" 200846 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197210 197336 197520 "BRILL" 197928 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193909 195936 195977 "BRAGG" 196626 NIL BRAGG (NIL T) -9 NIL 196884 NIL) (-118 192438 192844 193399 "BRAGG-" 193404 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185694 191784 191968 "BPADICRT" 192286 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184036 185631 185676 "BPADIC" 185681 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183734 183764 183878 "BOUNDZRO" 184000 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178773 179938 180899 "BOP" 182793 T BOP (NIL) -8 NIL NIL NIL) (-113 176394 176838 177358 "BOP1" 178286 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175096 175818 176011 "BOOLEAN" 176221 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174458 174836 174890 "BMODULE" 174895 NIL BMODULE (NIL T T) -9 NIL 174960 NIL) (-110 170286 174256 174329 "BITS" 174405 T BITS (NIL) -8 NIL NIL NIL) (-109 169698 169820 169962 "BINDING" 170164 T BINDING (NIL) -8 NIL NIL NIL) (-108 163732 169295 169443 "BINARY" 169570 T BINARY (NIL) -8 NIL NIL NIL) (-107 161559 162987 163028 "BGAGG" 163288 NIL BGAGG (NIL T) -9 NIL 163425 NIL) (-106 161390 161422 161513 "BGAGG-" 161518 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160488 160774 160979 "BFUNCT" 161205 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159178 159356 159644 "BEZOUT" 160312 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155695 158030 158360 "BBTREE" 158881 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155429 155482 155510 "BASTYPE" 155629 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155282 155310 155383 "BASTYPE-" 155388 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154716 154792 154944 "BALFACT" 155193 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153599 154131 154317 "AUTOMOR" 154561 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153325 153330 153356 "ATTREG" 153361 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151604 152022 152374 "ATTRBUT" 152991 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151239 151432 151498 "ATTRAST" 151556 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150775 150888 150914 "ATRIG" 151115 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150584 150625 150712 "ATRIG-" 150717 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150255 150415 150441 "ASTCAT" 150446 T ASTCAT (NIL) -9 NIL 150476 NIL) (-92 149982 150041 150160 "ASTCAT-" 150165 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148179 149758 149846 "ASTACK" 149925 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146684 146981 147346 "ASSOCEQ" 147861 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145716 146343 146467 "ASP9" 146591 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145479 145664 145703 "ASP8" 145708 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144347 145084 145226 "ASP80" 145368 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143245 143982 144114 "ASP7" 144246 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142199 142922 143040 "ASP78" 143158 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141168 141879 141996 "ASP77" 142113 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140080 140806 140937 "ASP74" 141068 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138980 139715 139847 "ASP73" 139979 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138084 138806 138906 "ASP6" 138911 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137028 137761 137879 "ASP55" 137997 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135977 136702 136821 "ASP50" 136940 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135065 135678 135788 "ASP4" 135898 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134153 134766 134876 "ASP49" 134986 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132937 133692 133860 "ASP42" 134042 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131713 132470 132640 "ASP41" 132824 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130663 131390 131508 "ASP35" 131626 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130428 130611 130650 "ASP34" 130655 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130165 130232 130308 "ASP33" 130383 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129058 129800 129932 "ASP31" 130064 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128823 129006 129045 "ASP30" 129050 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128558 128627 128703 "ASP29" 128778 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128323 128506 128545 "ASP28" 128550 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128088 128271 128310 "ASP27" 128315 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127172 127786 127897 "ASP24" 128008 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126248 126974 127086 "ASP20" 127091 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125336 125949 126059 "ASP1" 126169 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124278 125010 125129 "ASP19" 125248 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124015 124082 124158 "ASP12" 124233 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122867 123614 123758 "ASP10" 123902 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120766 122711 122802 "ARRAY2" 122807 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116579 120414 120528 "ARRAY1" 120683 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115611 115784 116005 "ARRAY12" 116402 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109970 111841 111916 "ARR2CAT" 114546 NIL ARR2CAT (NIL T T T) -9 NIL 115304 NIL) (-56 107404 108148 109102 "ARR2CAT-" 109107 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107231 107310 "ARITY" 107343 T ARITY (NIL) -8 NIL NIL NIL) (-54 105744 105896 106202 "APPRULE" 106832 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105395 105443 105562 "APPLYORE" 105690 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104369 104660 104855 "ANY" 105218 T ANY (NIL) -8 NIL NIL NIL) (-51 103647 103770 103927 "ANY1" 104243 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101204 102084 102411 "ANTISYM" 103371 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100911 101007 "ANON" 101126 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 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 b9bc2cb0..669422dc 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,84 +1,38 @@ -(735988 . 3449600532) -(((*1 *2 *3) - (-12 (-4 *3 (-1235 (-407 (-564)))) - (-5 *2 (-2 (|:| |den| (-564)) (|:| |gcdnum| (-564)))) - (-5 *1 (-910 *3 *4)) (-4 *4 (-1235 (-407 *3))))) - ((*1 *2 *3) - (-12 (-4 *4 (-1235 (-407 *2))) (-5 *2 (-564)) (-5 *1 (-910 *4 *3)) - (-4 *3 (-1235 (-407 *4)))))) -(((*1 *2 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-564)) - (-5 *5 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 -3378)))) - (-5 *2 (-1032)) (-5 *1 (-745))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) (-5 *2 (-641 *10)) - (-5 *1 (-622 *5 *6 *7 *8 *9 *10)) (-4 *9 (-1066 *5 *6 *7 *8)) - (-4 *10 (-1103 *5 *6 *7 *8)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-777 *5 (-861 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-1043 *5 *6))) - (-5 *1 (-626 *5 *6)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 (-777 *5 (-861 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) - (-5 *2 - (-641 (-1140 *5 (-531 (-861 *6)) (-861 *6) (-777 *5 (-861 *6))))) - (-5 *1 (-626 *5 *6)))) - ((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1024 *5 *6 *7 *8))) (-5 *1 (-1024 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1024 *5 *6 *7 *8))) (-5 *1 (-1024 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 (-777 *5 (-861 *6)))) (-5 *4 (-112)) (-4 *5 (-452)) - (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-1043 *5 *6))) - (-5 *1 (-1043 *5 *6)))) +(736189 . 3450528890) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1259 *3)) (-4 *3 (-1235 *4)) (-4 *4 (-1213)) + (-4 *1 (-342 *4 *3 *5)) (-4 *5 (-1235 (-407 *3)))))) +(((*1 *2 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-1187))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1032)) + (-5 *1 (-752))))) +(((*1 *1 *1 *1) (-4 *1 (-143))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-158 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *2 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545)))) + ((*1 *1 *1 *1) (-5 *1 (-859))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) (-5 *2 (-641 *1)) - (-4 *1 (-1066 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) - ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-641 *8)) (-5 *4 (-112)) (-4 *8 (-1060 *5 *6 *7)) - (-4 *5 (-452)) (-4 *6 (-790)) (-4 *7 (-847)) - (-5 *2 (-641 (-1140 *5 *6 *7 *8))) (-5 *1 (-1140 *5 *6 *7 *8)))) - ((*1 *2 *3) - (-12 (-5 *3 (-641 *7)) (-4 *7 (-1060 *4 *5 *6)) (-4 *4 (-556)) - (-4 *5 (-790)) (-4 *6 (-847)) (-5 *2 (-641 *1)) - (-4 *1 (-1202 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1259 *4)) (-4 *4 (-1046)) (-4 *2 (-1235 *4)) - (-5 *1 (-444 *4 *2)))) - ((*1 *2 *3 *2 *4) - (-12 (-5 *2 (-407 (-1166 (-316 *5)))) (-5 *3 (-1259 (-316 *5))) - (-5 *4 (-564)) (-4 *5 (-13 (-556) (-847))) (-5 *1 (-1124 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-641 (-175))) (-5 *1 (-1079))))) + (-12 (-5 *4 |RationalNumber|) (-5 *2 (-1 (-564))) (-5 *1 (-1044)) + (-5 *3 (-564))))) +(((*1 *2 *1) (-12 (-4 *1 (-254 *2)) (-4 *2 (-1209))))) (((*1 *2 *2) - (-12 - (-5 *2 - (-504 (-407 (-564)) (-240 *4 (-768)) (-861 *3) - (-247 *3 (-407 (-564))))) - (-14 *3 (-641 (-1170))) (-14 *4 (-768)) (-5 *1 (-505 *3 *4))))) + (-12 (-5 *2 (-641 (-641 *6))) (-4 *6 (-946 *3 *5 *4)) + (-4 *3 (-13 (-307) (-147))) (-4 *4 (-13 (-847) (-612 (-1170)))) + (-4 *5 (-790)) (-5 *1 (-921 *3 *4 *5 *6))))) (((*1 *2 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1060 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-556)) (-4 *4 (-790)) (-4 *5 (-847)) - (-5 *1 (-974 *3 *4 *5 *6))))) -(((*1 *2 *3 *4 *5 *6 *7 *8 *9) - (|partial| -12 (-5 *4 (-641 *11)) (-5 *5 (-641 (-1166 *9))) - (-5 *6 (-641 *9)) (-5 *7 (-641 *12)) (-5 *8 (-641 (-768))) - (-4 *11 (-847)) (-4 *9 (-307)) (-4 *12 (-946 *9 *10 *11)) - (-4 *10 (-790)) (-5 *2 (-641 (-1166 *12))) - (-5 *1 (-704 *10 *11 *9 *12)) (-5 *3 (-1166 *12))))) + (-12 (-4 *3 (-363)) (-5 *1 (-763 *2 *3)) (-4 *2 (-705 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-849 *2)) (-4 *2 (-1046)) (-4 *2 (-363))))) +(((*1 *1 *2 *3 *1 *3) + (-12 (-5 *2 (-889 *4)) (-4 *4 (-1094)) (-5 *1 (-886 *4 *3)) + (-4 *3 (-1094))))) +(((*1 *2 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-564)) (-5 *4 (-685 (-225))) (-5 *2 (-1032)) + (-5 *1 (-748))))) (((*1 *2 *2) - (-12 (-5 *2 (-641 *3)) (-4 *3 (-1235 (-564))) (-5 *1 (-486 *3))))) + (-12 (-4 *3 (-13 (-847) (-452))) (-5 *1 (-1200 *3 *2)) + (-4 *2 (-13 (-430 *3) (-1194)))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1209)) (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) @@ -110,14 +64,14 @@ (-12 (-5 *3 (-1170)) (-5 *2 (-245 (-1152))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-847) - (-10 -8 (-15 -4382 ((-1152) $ *3)) (-15 -3463 ((-1264) $)) - (-15 -3092 ((-1264) $))))))) + (-10 -8 (-15 -4382 ((-1152) $ *3)) (-15 -3512 ((-1264) $)) + (-15 -2890 ((-1264) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-986)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-847) - (-10 -8 (-15 -4382 ((-1152) $ (-1170))) (-15 -3463 ((-1264) $)) - (-15 -3092 ((-1264) $))))))) + (-10 -8 (-15 -4382 ((-1152) $ (-1170))) (-15 -3512 ((-1264) $)) + (-15 -2890 ((-1264) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-768)) (-5 *1 (-245 *4)) (-4 *4 (-847)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-847)))) @@ -203,62 +157,231 @@ (-12 (-5 *2 "rest") (-4 *1 (-1247 *3)) (-4 *3 (-1209)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-434))))) -(((*1 *2 *2) (-12 (-5 *2 (-641 (-685 (-316 (-564))))) (-5 *1 (-1028))))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5 *4) - (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-169 (-225)))) - (-5 *2 (-1032)) (-5 *1 (-751))))) -(((*1 *2 *3 *4) - (|partial| -12 (-5 *4 (-641 (-407 *6))) (-5 *3 (-407 *6)) - (-4 *6 (-1235 *5)) (-4 *5 (-13 (-363) (-147) (-1035 (-564)))) +(((*1 *2 *3) + (-12 (-4 *4 (-556)) (-4 *5 (-790)) (-4 *6 (-847)) + (-4 *7 (-1060 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-641 *7)) (|:| |badPols| (-641 *7)))) + (-5 *1 (-974 *4 *5 *6 *7)) (-5 *3 (-641 *7))))) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-641 (-407 *7))) + (-4 *7 (-1235 *6)) (-5 *3 (-407 *7)) (-4 *6 (-363)) (-5 *2 (-2 (|:| |mainpart| *3) (|:| |limitedlogs| (-641 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-568 *5 *6))))) -(((*1 *2 *1) - (-12 - (-5 *2 - (-641 - (-641 - (-3 (|:| -4363 (-1170)) - (|:| -2792 (-641 (-3 (|:| S (-1170)) (|:| P (-949 (-564)))))))))) - (-5 *1 (-1174))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-685 *8)) (-4 *8 (-946 *5 *7 *6)) - (-4 *5 (-13 (-307) (-147))) (-4 *6 (-13 (-847) (-612 (-1170)))) - (-4 *7 (-790)) - (-5 *2 - (-641 - (-2 (|:| -4224 (-768)) - (|:| |eqns| - (-641 - (-2 (|:| |det| *8) (|:| |rows| (-641 (-564))) - (|:| |cols| (-641 (-564)))))) - (|:| |fgb| (-641 *8))))) - (-5 *1 (-921 *5 *6 *7 *8)) (-5 *4 (-768))))) -(((*1 *2 *3) (-12 (-5 *2 (-379)) (-5 *1 (-782 *3)) (-4 *3 (-612 *2)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-918)) (-5 *2 (-379)) (-5 *1 (-782 *3)) - (-4 *3 (-612 *2)))) + (-5 *1 (-574 *6 *7))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1259 *4)) (-5 *3 (-1114)) (-4 *4 (-349)) + (-5 *1 (-528 *4))))) +(((*1 *2) (-12 (-4 *2 (-172)) (-5 *1 (-165 *3 *2)) (-4 *3 (-166 *2)))) ((*1 *2 *3) - (-12 (-5 *3 (-949 *4)) (-4 *4 (-1046)) (-4 *4 (-612 *2)) - (-5 *2 (-379)) (-5 *1 (-782 *4)))) + (-12 (-5 *3 (-1259 *1)) (-4 *1 (-370 *2 *4)) (-4 *4 (-1235 *2)) + (-4 *2 (-172)))) + ((*1 *2) + (-12 (-4 *4 (-1235 *2)) (-4 *2 (-172)) (-5 *1 (-408 *3 *2 *4)) 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(-15 -3832 ((-3 $ "failed") (-1170)))))) (-4 *5 (-790)) (-4 *7 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-456 *4 *5 *6 *7 *3)) (-4 *6 (-556)) (-4 *3 (-946 *7 *5 *4)))) @@ -2758,13 +1615,13 @@ (-12 (-4 *4 (-790)) (-4 *5 (-13 (-847) - (-10 -8 (-15 -2127 ((-1170) $)) - (-15 -3657 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -2374 ((-1170) $)) + (-15 -3832 ((-3 $ "failed") (-1170)))))) (-4 *6 (-307)) (-5 *2 (-418 *3)) (-5 *1 (-727 *4 *5 *6 *3)) (-4 *3 (-946 (-949 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-790)) - (-4 *5 (-13 (-847) (-10 -8 (-15 -2127 ((-1170) $))))) (-4 *6 (-556)) + (-4 *5 (-13 (-847) (-10 -8 (-15 -2374 ((-1170) $))))) (-4 *6 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-729 *4 *5 *6 *3)) (-4 *3 (-946 (-407 (-949 *6)) *4 *5)))) ((*1 *2 *3) @@ -2800,70 +1657,44 @@ ((*1 *2 *1) (-12 (-5 *2 (-418 *1)) (-4 *1 (-1213)))) ((*1 *2 *3) (-12 (-5 *2 (-418 *3)) (-5 *1 (-1224 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *1 *1) (-4 *1 (-35))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-276 *3 *2)) - 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|wcond| (-641 (-949 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *5)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *5)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *5)))))))))) (-5 *1 (-921 *5 *6 *7 *8)) (-5 *4 (-641 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-685 *8)) (-5 *4 (-641 (-1170))) (-4 *8 (-946 *5 *7 *6)) @@ -10560,7 +10294,7 @@ (|:| |wcond| (-641 (-949 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *5)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *5)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *5)))))))))) (-5 *1 (-921 *5 *6 *7 *8)))) ((*1 *2 *3) (-12 (-5 *3 (-685 *7)) (-4 *7 (-946 *4 *6 *5)) @@ -10572,7 +10306,7 @@ (|:| |wcond| (-641 (-949 *4))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *4)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *4)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *4)))))))))) (-5 *1 (-921 *4 *5 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-685 *9)) (-5 *5 (-918)) (-4 *9 (-946 *6 *8 *7)) @@ -10584,7 +10318,7 @@ (|:| |wcond| (-641 (-949 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *6)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *6)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *6)))))))))) (-5 *1 (-921 *6 *7 *8 *9)) (-5 *4 (-641 *9)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-685 *9)) (-5 *4 (-641 (-1170))) (-5 *5 (-918)) @@ -10596,7 +10330,7 @@ (|:| |wcond| (-641 (-949 *6))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *6)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *6)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *6)))))))))) (-5 *1 (-921 *6 *7 *8 *9)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-685 *8)) (-5 *4 (-918)) (-4 *8 (-946 *5 *7 *6)) @@ -10608,7 +10342,7 @@ (|:| |wcond| (-641 (-949 *5))) (|:| |bsoln| (-2 (|:| |partsol| (-1259 (-407 (-949 *5)))) - (|:| -3941 (-641 (-1259 (-407 (-949 *5)))))))))) + (|:| -4339 (-641 (-1259 (-407 (-949 *5)))))))))) (-5 *1 (-921 *5 *6 *7 *8)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-685 *9)) (-5 *4 (-641 *9)) (-5 *5 (-1152)) @@ -10639,149 +10373,53 @@ (-4 *9 (-946 *6 *8 *7)) (-4 *6 (-13 (-307) 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(-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1046)) (-4 *4 (-790)) (-4 *5 (-847))) (-12 (-5 *2 (-949 (-564))) (-4 *1 (-1060 *3 *4 *5)) @@ -12249,12 +11808,12 @@ (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170))) (-4 *3 (-1046)) (-4 *4 (-790)) (-4 *5 (-847)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3853 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -4011 *8))) (-4 *7 (-1060 *4 *5 *6)) (-4 *8 (-1066 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-790)) (-4 *6 (-847)) (-5 *2 (-1152)) (-5 *1 (-1064 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3853 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -4011 *8))) (-4 *7 (-1060 *4 *5 *6)) (-4 *8 (-1103 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-790)) (-4 *6 (-847)) (-5 *2 (-1152)) (-5 *1 (-1139 *4 *5 *6 *7 *8)))) @@ -12286,120 +11845,6 @@ (-4 *4 (-13 (-845) (-307) (-147) (-1019))) (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-777 *4 (-861 *6)))) (-5 *1 (-1285 *4 *5 *6)) (-14 *5 (-641 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- (-4 *5 (-373 *3)) (-5 *2 (-564)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1049 *3 *4 *5 *6 *7)) (-4 *5 (-1046)) - (-4 *6 (-238 *4 *5)) (-4 *7 (-238 *3 *5)) (-5 *2 (-564))))) -(((*1 *2) - (-12 (-4 *4 (-1213)) (-4 *5 (-1235 *4)) (-4 *6 (-1235 (-407 *5))) - (-5 *2 (-768)) (-5 *1 (-341 *3 *4 *5 *6)) (-4 *3 (-342 *4 *5 *6)))) - ((*1 *2) - (-12 (-4 *1 (-342 *3 *4 *5)) (-4 *3 (-1213)) (-4 *4 (-1235 *3)) - (-4 *5 (-1235 (-407 *4))) (-5 *2 (-768)))) - ((*1 *2 *1) (-12 (-4 *1 (-1128 *3)) (-4 *3 (-1046)) (-5 *2 (-768))))) -(((*1 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226))))) -(((*1 *1 *2) - (-12 (-5 *2 (-641 (-918))) (-5 *1 (-1095 *3 *4)) (-14 *3 (-918)) - (-14 *4 (-918))))) -(((*1 *2) (-12 (-5 *2 (-1170)) (-5 *1 (-1173))))) -(((*1 *2 *1) - (-12 (-5 *2 (-641 (-2 (|:| |gen| *3) (|:| -2152 *4)))) - (-5 *1 (-645 *3 *4 *5)) (-4 *3 (-1094)) (-4 *4 (-23)) (-14 *5 *4)))) (((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1209)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-847)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-847)))) @@ -12411,11 +11856,11 @@ (-12 (-5 *2 (-2 - (|:| -2351 + (|:| -1350 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1361 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) + (|:| -4167 (-1088 (-840 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) - (|:| -1327 + (|:| -2575 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") @@ -12431,7 +11876,7 @@ (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -1361 + (|:| -4167 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") @@ -12446,12 +11891,12 @@ (-12 (-5 *2 (-2 - (|:| -2351 + (|:| -1350 (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) (|:| |fn| (-1259 (-316 (-225)))) (|:| |yinit| (-641 (-225))) (|:| |intvals| (-641 (-225))) (|:| |g| (-316 (-225))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) - (|:| -1327 + (|:| -2575 (-2 (|:| |stiffness| (-379)) (|:| |stability| (-379)) (|:| |expense| (-379)) (|:| |accuracy| (-379)) (|:| |intermediateResults| (-379)))))) @@ -12459,55 +11904,290 @@ ((*1 *2 *3 *4) (-12 (-5 *2 (-1264)) (-5 *1 (-1186 *3 *4)) (-4 *3 (-1094)) (-4 *4 (-1094))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-847) (-556))) (-5 *1 (-431 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1133)))) +(((*1 *2 *1) (-12 (-4 *1 (-404)) (-5 *2 (-564)))) + ((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-695))))) +(((*1 *2 *3 *2) + (-12 (-5 *3 (-1 (-112) *4 *4)) (-4 *4 (-1209)) (-5 *1 (-375 *4 *2)) + (-4 *2 (-13 (-373 *4) (-10 -7 (-6 -4413))))))) +(((*1 *1) (-5 *1 (-291)))) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-556)) (-4 *3 (-1046)) + (-5 *2 (-2 (|:| -3031 *1) (|:| -2550 *1))) (-4 *1 (-849 *3)))) + ((*1 *2 *3 *3 *4) + (-12 (-5 *4 (-99 *5)) (-4 *5 (-556)) (-4 *5 (-1046)) + (-5 *2 (-2 (|:| -3031 *3) (|:| 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\ No newline at end of file |