diff options
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 2 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/net.spad.pamphlet | 68 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1422 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1329 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1323 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8969 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27575 |
9 files changed, 20399 insertions, 20296 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index dff4a1fd..af661a23 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2009-01-13 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/net.spad.pamphlet (InputByteConduit): Add readInt8!, + readInt16!, readInt32!, readUInt8!, readUInt16!, readUInt32!. + 2009-01-12 Gabriel Dos Reis <gdr@cs.tamu.edu> * interp/category.boot: Miscellaneous cleanup. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 6f2f5a6d..206fe452 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -458,7 +458,7 @@ axiom_algebra_layer_6_objects = \ axiom_algebra_layer_7 = \ BTCAT BTCAT- LNAGG LNAGG- FMCAT IDPOAM \ IFAMON GRALG GRALG- FLAGG FLAGG- \ - INT8 INT16 INT32 UNIT6 UINT16 UINT32 + INT8 INT16 INT32 UINT8 UINT16 UINT32 axiom_algebra_layer_7_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_7)) diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 1041c6b1..43631245 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -361,7 +361,7 @@ axiom_algebra_layer_6_objects = \ axiom_algebra_layer_7 = \ BTCAT BTCAT- LNAGG LNAGG- FMCAT IDPOAM \ IFAMON GRALG GRALG- FLAGG FLAGG- \ - INT8 INT16 INT32 UNIT6 UINT16 UINT32 + INT8 INT16 INT32 UINT8 UINT16 UINT32 axiom_algebra_layer_7_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_7)) diff --git a/src/algebra/net.spad.pamphlet b/src/algebra/net.spad.pamphlet index 21ca3f39..ee5e8326 100644 --- a/src/algebra/net.spad.pamphlet +++ b/src/algebra/net.spad.pamphlet @@ -41,11 +41,65 @@ InputByteConduit(): Category == Conduit with ++ readByte!(cond) attempts to read a byte from the ++ input conduit `cond'. Returns the read byte if successful, ++ otherwise \spad{nothing}. + readInt8!: % -> Maybe Int8 + ++ readInt8!(cond) attempts to read an Int8 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. + readUInt8!: % -> Maybe UInt8 + ++ readUInt8!(cond) attempts to read a UInt8 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. + readInt16!: % -> Maybe Int16 + ++ readInt16!(cond) attempts to read an Int16 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. + readUInt16!: % -> Maybe UInt16 + ++ readUInt16!(cond) attempts to read a UInt16 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. + readInt32!: % -> Maybe Int32 + ++ readInt32!(cond) attempts to read an Int32 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. + readUInt32!: % -> Maybe UInt32 + ++ readUInt32!(cond) attempts to read a UInt32 value from the + ++ input conduit `cond'. Returns the value if successful, + ++ otherwise \spad{nothing}. readBytes!: (%,ByteBuffer) -> NonNegativeInteger ++ readBytes!(c,b) reads byte sequences from conduit `c' into ++ the byte buffer `b'. The actual number of bytes written ++ is returned, and the length of `b' is set to that amount. add + NNI == NonNegativeInteger + nni(b: UInt8): NNI == b::NNI + + readInt8! cond == + -- OK, because we are using two's complement. + readByte!(cond) pretend Maybe(Int8) + + readUInt8! cond == + -- UInt8 and Byte are representationally conformant. + readByte!(cond) pretend Maybe(UInt8) + + readUInt16! cond == + (b1 := readUInt8! cond) case nothing => nothing + (b0 := readUInt8! cond) case nothing => nothing + just((shift(nni b1,8) + nni b0)::UInt16) + + readInt16! cond == + readUInt16!(cond) pretend Maybe(Int16) + + readUInt32! cond == + (b3 := readUInt8! cond) case nothing => nothing + (b2 := readUInt8! cond) case nothing => nothing + (b1 := readUInt8! cond) case nothing => nothing + (b0 := readUInt8! cond) case nothing => nothing + just((shift(nni b3,24) + shift(nni b2,16) + + shift(nni b1,8) + nni b0)::UInt32) + + readInt32! cond == + readUInt32!(cond) pretend Maybe(Int32) + readBytes!(cond,buf) == count := 0@NonNegativeInteger while count < capacity buf repeat @@ -72,11 +126,25 @@ OutputByteConduit(): Category == Conduit with ++ writeByte!(c,b) attempts to write the byte `b' on ++ the conduit `c'. Returns the written byte if successful, ++ otherwise, returns \spad{nothing}. + writeInt8!: (%,Int8) -> Maybe Int8 + ++ writeInt8!(c,b) attempts to write the 8-bit value `v' on + ++ the conduit `c'. Returns the written value if successful, + ++ otherwise, returns \spad{nothing}. + writeUInt8!: (%,UInt8) -> Maybe UInt8 + ++ writeUInt8!(c,b) attempts to write the unsigned 8-bit value `v' + ++ on the conduit `c'. Returns the written value if successful, + ++ otherwise, returns \spad{nothing}. writeBytes!: (%,ByteBuffer) -> NonNegativeInteger ++ writeBytes!(c,b) write bytes from buffer `b' ++ onto the conduit `c'. The actual number of written ++ bytes is returned. add + writeInt8!(cond,val) == + writeByte!(cond, val pretend Byte) pretend Maybe(Int8) + + writeUInt8!(cond,val) == + writeByte!(cond, val pretend Byte) pretend Maybe(UInt8) + writeBytes!(cond,buf) == count := 0@NonNegativeInteger while count < capacity buf and diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 2a1ed37d..86afad48 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2277573 . 3440472337) +(2280968 . 3440812768) (-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."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . 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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . 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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4387 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4383 . T) (-4388 . T) (-4382 . T)) +((-4396 . T) (-4394 . T) (-4393 . T) ((-4401 "*") . T) (-4392 . T) (-4397 . T) (-4391 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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 -3214) +(-32 R -3249) ((|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 -1031) (QUOTE (-561))))) (-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 -4390))) +((|HasAttribute| |#1| (QUOTE -4399))) (-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}."))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . 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"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . 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 -3214 UP UPUP -2912) +(-40 -3249 UP UPUP -1448) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4007 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4007 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4007 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3214) +((-4392 |has| (-406 |#2|) (-362)) (-4397 |has| (-406 |#2|) (-362)) (-4391 |has| (-406 |#2|) (-362)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4050 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4050 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4050 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4050 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-41 R -3249) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-306)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|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."))) -((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) +((-4396 |has| |#1| (-553)) (-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-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."))) -((-4390 . T) (-4391 . T)) -((-4007 (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|))))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|))))))) +((-4399 . T) (-4400 . T)) +((-4050 (-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|))))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4387 . T)) +((-4396 . 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 -3214) +(-54 |Base| R -3249) ((|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"))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . 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}"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) -(-61 -3269) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-61 -3305) ((|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 -3269) +(-62 -3305) ((|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 -3269) +(-63 -3305) ((|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 -3269) +(-64 -3305) ((|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 -3269) +(-65 -3305) ((|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 -3269) +(-66 -3305) ((|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 -3269) +(-67 -3305) ((|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 -3269) +(-68 -3305) ((|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 -3269) +(-69 -3305) ((|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 -3269) +(-70 -3305) ((|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 -3269) +(-71 -3305) ((|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 -3269) +(-72 -3305) ((|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 -3269) +(-73 -3305) ((|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 -3269) +(-74 -3305) ((|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 -3269) +(-77 -3305) ((|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 -3269) +(-78 -3305) ((|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 -3269) +(-79 -3305) ((|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 -3269) +(-80 -3305) ((|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 -3269) +(-81 -3305) ((|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 -3269) +(-82 -3305) ((|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 -3269) +(-83 -3305) ((|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 -3269) +(-84 -3305) ((|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 -3269) +(-85 -3305) ((|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 -3269) +(-86 -3305) ((|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 -3269) +(-87 -3305) ((|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 -3269) +(-88 -3305) ((|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 -3269) +(-89 -3305) ((|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 (-362)))) (-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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-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\"."))) -((-4390 . T)) +((-4399 . 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."))) -((-4390 . T) ((-4392 "*") . T) (-4391 . T) (-4387 . T) (-4385 . T) (-4384 . T) (-4383 . T) (-4388 . T) (-4382 . T) (-4381 . T) (-4380 . T) (-4379 . T) (-4378 . T) (-4386 . T) (-4389 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4377 . T)) +((-4399 . T) ((-4401 "*") . T) (-4400 . T) (-4396 . T) (-4394 . T) (-4393 . T) (-4392 . T) (-4397 . T) (-4391 . T) (-4390 . T) (-4389 . T) (-4388 . T) (-4387 . T) (-4395 . T) (-4398 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4386 . 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}."))) -((-4387 . T)) +((-4396 . 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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-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 (-4392 "*")))) +((|HasAttribute| |#1| (QUOTE (-4401 "*")))) (-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"))) -((-4390 . T)) +((-4399 . 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."))) -((-4391 . T)) +((-4400 . 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4050 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-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}"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -608) (QUOTE (-856))))) (-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}"))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . 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| (($) "\\spad{true} is a logical constant."))) @@ -388,22 +388,22 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3214 UP) +(-115 -3249 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}."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . 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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-902))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1015))) (|HasCategory| (-116 |#1|) (QUOTE (-814))) (-4007 (|HasCategory| (-116 |#1|) (QUOTE (-814))) (|HasCategory| (-116 |#1|) (QUOTE (-844)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-1141))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-902))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1015))) (|HasCategory| (-116 |#1|) (QUOTE (-814))) (-4050 (|HasCategory| (-116 |#1|) (QUOTE (-814))) (|HasCategory| (-116 |#1|) (QUOTE (-844)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-1141))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-306))) (|HasCategory| (-116 |#1|) (QUOTE (-543))) (|HasCategory| (-116 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-902)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) (-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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4391))) +((|HasAttribute| |#1| (QUOTE -4400))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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"))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#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| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#buf} returns the number of active elements in the buffer.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-4007 (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090)))) (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-4050 (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-129) (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090)))) (|HasCategory| (-129) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-129) (QUOTE (-1090))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample()} returns a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -462,13 +462,13 @@ NIL NIL (-133) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4392 "*") . T)) +(((-4401 "*") . T)) NIL -(-134 |minix| -2164 S T$) +(-134 |minix| -2192 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -2164 R) +(-135 |minix| -2192 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -490,8 +490,8 @@ NIL NIL (-140) ((|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}."))) -((-4390 . T) (-4380 . T) (-4391 . T)) -((-4007 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4399 . T) (-4389 . T) (-4400 . T)) +((-4050 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-141 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 @@ -506,7 +506,7 @@ NIL NIL (-144) ((|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."))) -((-4387 . T)) +((-4396 . T)) NIL (-145 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}."))) @@ -514,9 +514,9 @@ NIL NIL (-146) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4387 . T)) +((-4396 . T)) NIL -(-147 -3214 UP UPUP) +(-147 -3249 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 @@ -527,14 +527,14 @@ NIL (-149 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 -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasAttribute| |#1| (QUOTE -4390))) +((|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasAttribute| |#1| (QUOTE -4399))) (-150 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-151 |n| K Q) ((|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."))) -((-4385 . T) (-4384 . T) (-4387 . T)) +((-4394 . T) (-4393 . T) (-4396 . T)) NIL (-152) ((|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."))) @@ -556,7 +556,7 @@ 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 -(-157 R -3214) +(-157 R -3249) ((|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 @@ -587,10 +587,10 @@ NIL (-164 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) NIL -((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4386)) (|HasAttribute| |#2| (QUOTE -4389)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-844)))) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4395)) (|HasAttribute| |#2| (QUOTE -4398)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-844)))) (-165 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}."))) -((-4383 -4007 (|has| |#1| (-553)) (-12 (|has| |#1| (-306)) (|has| |#1| (-902)))) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4386 |has| |#1| (-6 -4386)) (-4389 |has| |#1| (-6 -4389)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 -4050 (|has| |#1| (-553)) (-12 (|has| |#1| (-306)) (|has| |#1| (-902)))) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4395 |has| |#1| (-6 -4395)) (-4398 |has| |#1| (-6 -4398)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-166 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."))) @@ -602,8 +602,8 @@ NIL NIL (-168 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}."))) -((-4383 -4007 (|has| |#1| (-553)) (-12 (|has| |#1| (-306)) (|has| |#1| (-902)))) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4386 |has| |#1| (-6 -4386)) (-4389 |has| |#1| (-6 -4389)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-844)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1015)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-902))))) (-4007 (-12 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(|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-348))))) +((-4392 -4050 (|has| |#1| (-553)) (-12 (|has| |#1| (-306)) (|has| |#1| (-902)))) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4395 |has| |#1| (-6 -4395)) (-4398 |has| |#1| (-6 -4398)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-822)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-844)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1015)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1190)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -609) 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(QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-1051))) (-12 (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-1190)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasAttribute| |#1| (QUOTE -4395)) (|HasAttribute| |#1| (QUOTE -4398)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-348))))) (-169 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 @@ -614,7 +614,7 @@ NIL NIL (-171) ((|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."))) -(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-172) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -622,7 +622,7 @@ NIL NIL (-173 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|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}."))) -(((-4392 "*") . T) (-4383 . T) (-4388 . T) (-4382 . T) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") . T) (-4392 . T) (-4397 . T) (-4391 . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-174) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors."))) NIL NIL -(-187 R -3214) +(-187 R -3249) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -784,23 +784,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -(-214 -3214 UP UPUP R) +(-214 -3249 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-215 -3214 FP) +(-215 -3249 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-216) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4050 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-217) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3214) +(-218 R -3249) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -814,19 +814,19 @@ NIL NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-222 |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}."))) -((-4387 . T)) +((-4396 . T)) NIL -(-223 R -3214) +(-223 R -3249) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-224) ((|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}."))) -((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-1408 . T) (-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-225) ((|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)}.}"))) @@ -834,15 +834,15 @@ NIL NIL (-226 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}"))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4401 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-227 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-228 S) ((|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."))) -((-4391 . T)) +((-4400 . T)) NIL (-229 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}."))) @@ -850,7 +850,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (-230 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}."))) -((-4387 . T)) +((-4396 . T)) NIL (-231 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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -858,36 +858,36 @@ NIL NIL (-232) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|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}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4387 . T)) +((-4396 . T)) NIL (-233 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4390))) +((|HasAttribute| |#1| (QUOTE -4399))) (-234 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}."))) -((-4391 . T)) +((-4400 . T)) NIL (-235) ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-236 S -2164 R) +(-236 S -2192 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (QUOTE (-842))) (|HasAttribute| |#3| (QUOTE -4387)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (QUOTE (-1090)))) -(-237 -2164 R) +((|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (QUOTE (-842))) (|HasAttribute| |#3| (QUOTE -4396)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (QUOTE (-1090)))) +(-237 -2192 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"))) -((-4384 |has| |#2| (-1042)) (-4385 |has| |#2| (-1042)) (-4387 |has| |#2| (-6 -4387)) ((-4392 "*") |has| |#2| (-171)) (-4390 . T)) +((-4393 |has| |#2| (-1042)) (-4394 |has| |#2| (-1042)) (-4396 |has| |#2| (-6 -4396)) ((-4401 "*") |has| |#2| (-171)) (-4399 . T)) NIL -(-238 -2164 A B) +(-238 -2192 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-239 -2164 R) +(-239 -2192 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."))) -((-4384 |has| |#2| (-1042)) (-4385 |has| |#2| (-1042)) (-4387 |has| |#2| (-6 -4387)) ((-4392 "*") |has| |#2| (-171)) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-720))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-787))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (-4007 (-12 (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1042)))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) 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(|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 @@ -898,7 +898,7 @@ NIL NIL (-242) ((|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}."))) -((-4383 . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-243 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."))) @@ -906,16 +906,16 @@ NIL NIL (-244 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}"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-245 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-246 |vl| R) ((|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"))) -(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#2| (QUOTE (-902))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4401 "*") |has| |#2| (-171)) (-4392 |has| |#2| (-553)) (-4397 |has| |#2| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4397)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-247) ((|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)) -((-4007 (-12 (|HasCategory| |#4| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-232))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-720))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-787))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-842))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1042))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (-12 (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|))) 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(QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1042)))) (-4050 (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1042)))) (|HasCategory| |#3| (QUOTE (-720))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166)))))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-4050 (|HasCategory| |#3| (QUOTE (-1042))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#3| (QUOTE (-1090)))) (-4050 (|HasAttribute| |#3| (QUOTE -4396)) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1042)))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-251 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 (-232)))) (-252 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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL (-253 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}."))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-254) ((|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."))) @@ -982,8 +982,8 @@ NIL NIL (-263 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"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#3| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-264 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 @@ -1028,11 +1028,11 @@ 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 -(-275 R -3214) +(-275 R -3249) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-276 R -3214) +(-276 R -3249) ((|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 @@ -1054,7 +1054,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090)))) (-281 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}."))) -((-4391 . T)) +((-4400 . T)) NIL (-282 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}."))) @@ -1075,18 +1075,18 @@ NIL (-286 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 -4391))) +((|HasAttribute| |#1| (QUOTE -4400))) (-287 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-288 S R |Mod| -3471 -1407 |exactQuo|) +(-288 S R |Mod| -4047 -3405 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-289) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4383 . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-290) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1102,21 +1102,21 @@ NIL NIL (-293 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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-295) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-296 -3214 S) +(-296 -3249 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f,{} p,{} k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-297 E -3214) +(-297 E -3249) ((|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 @@ -1154,7 +1154,7 @@ NIL NIL (-306) ((|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|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-307 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|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}."))) @@ -1164,7 +1164,7 @@ 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 -(-309 -3214) +(-309 -3249) ((|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 @@ -1178,8 +1178,8 @@ NIL NIL (-312 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}.")) 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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 @@ -1190,9 +1190,9 @@ NIL NIL (-315 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."))) -((-4387 -4007 (-2170 (|has| |#1| (-1042)) (|has| |#1| (-634 (-561)))) (-12 (|has| |#1| (-553)) (-4007 (-2170 (|has| |#1| (-1042)) (|has| |#1| (-634 (-561)))) (|has| |#1| (-1042)) (|has| |#1| (-471)))) (|has| |#1| (-1042)) (|has| |#1| (-471))) (-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) ((-4392 "*") |has| |#1| (-553)) (-4383 |has| |#1| (-553)) (-4388 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(|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\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 @@ -1202,8 +1202,8 @@ NIL NIL (-318 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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-319 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 @@ -1214,7 +1214,7 @@ NIL NIL (-321 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."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-786)))) (-322 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| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1230,19 +1230,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171)))) (-325 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-326 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."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3214) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-327 S -3249) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-367)))) -(-328 -3214) +(-328 -3249) ((|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-329) ((|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."))) @@ -1260,15 +1260,15 @@ 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 -(-333 S -3214 UP UPUP R) +(-333 S -3249 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-334 -3214 UP UPUP R) +(-334 -3249 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-335 -3214 UP UPUP R) +(-335 -3249 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 @@ -1282,32 +1282,32 @@ NIL NIL (-338 |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.}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-378)))) (|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-339 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-340 S -3214 UP UPUP) +(-340 S -3249 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-362)))) -(-341 -3214 UP UPUP) +(-341 -3249 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."))) -((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 |has| (-406 |#2|) (-362)) (-4397 |has| (-406 |#2|) (-362)) (-4391 |has| (-406 |#2|) (-362)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-342 |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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-343 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-344 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-345 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 @@ -1322,33 +1322,33 @@ NIL NIL (-348) ((|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-349 R UP -3214) +(-349 R UP -3249) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-350 |p| |extdeg|) ((|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-351 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-352 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-353 |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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| (-903 |#1|) (QUOTE (-144))) (|HasCategory| (-903 |#1|) (QUOTE (-367)))) (|HasCategory| (-903 |#1|) (QUOTE (-146))) (|HasCategory| (-903 |#1|) (QUOTE (-367))) (|HasCategory| (-903 |#1|) (QUOTE (-144)))) (-354 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3214 GF) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +(-355 -3249 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 @@ -1356,21 +1356,21 @@ 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 -(-357 -3214 FP FPP) +(-357 -3249 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-358 GF |n|) ((|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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) (-359 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-360 S) ((|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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4387 . T)) +((-4396 . T)) NIL (-361 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1378,7 +1378,7 @@ NIL NIL (-362) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-363 |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."))) @@ -1394,7 +1394,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-553)))) (-366 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| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) +((-4396 |has| |#1| (-553)) (-4394 . T) (-4393 . T)) NIL (-367) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1406,7 +1406,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-362)))) (-369 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| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL (-370 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$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."))) @@ -1415,14 +1415,14 @@ NIL (-371 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090)))) (-372 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4390 . T)) +((-4399 . T)) NIL (-373 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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) (-4385 . T) (-4384 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4394 . T) (-4393 . T)) NIL (-374 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."))) @@ -1434,7 +1434,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-376 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}"))) -((-4387 . T)) +((-4396 . T)) NIL (-377 |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}."))) @@ -1442,7 +1442,7 @@ NIL NIL (-378) ((|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}."))) -((-4373 . T) (-4381 . T) (-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4382 . T) (-4390 . T) (-1408 . T) (-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-379 |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}."))) @@ -1450,11 +1450,11 @@ NIL NIL (-380 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}"))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-381 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}."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL (-382) ((|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}."))) @@ -1466,7 +1466,7 @@ NIL NIL (-384 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."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (QUOTE (-171)))) (-385 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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1474,7 +1474,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-844)))) (-386) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-387) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1486,13 +1486,13 @@ NIL NIL (-389 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL (-390) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-391 -3214 UP UPUP R) +(-391 -3249 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 @@ -1516,11 +1516,11 @@ 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 -(-397 -3269 |returnType| -2243 |symbols|) +(-397 -3305 |returnType| -1642 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-398 -3214 UP) +(-398 -3249 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1534,15 +1534,15 @@ NIL NIL (-401) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-402 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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 -4373)) (|HasAttribute| |#1| (QUOTE -4381))) +((|HasAttribute| |#1| (QUOTE -4382)) (|HasAttribute| |#1| (QUOTE -4390))) (-403) ((|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\"."))) -((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-1408 . T) (-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-404 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."))) @@ -1554,15 +1554,15 @@ NIL NIL (-406 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."))) -((-4377 -12 (|has| |#1| (-6 -4388)) (|has| |#1| (-450)) (|has| |#1| (-6 -4377))) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-814))) (-4007 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (QUOTE (-844)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4388)) (|HasAttribute| |#1| (QUOTE -4377)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +((-4386 -12 (|has| |#1| (-6 -4397)) (|has| |#1| (-450)) (|has| |#1| (-6 -4386))) (-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (QUOTE (-814))) (-4050 (|HasCategory| |#1| (QUOTE (-814))) (|HasCategory| |#1| (QUOTE (-844)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#1| (QUOTE -4386)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-407 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-408 R UP) ((|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL (-409 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3214 UP A) +(-412 R -3249 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4387 . T)) +((-4396 . T)) NIL -(-413 R -3214 UP A |ibasis|) +(-413 R -3249 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1031) (|devaluate| |#2|)))) @@ -1594,12 +1594,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-416 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|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."))) -((-4387 |has| |#1| (-553)) (-4385 . T) (-4384 . T)) +((-4396 |has| |#1| (-553)) (-4394 . T) (-4393 . T)) NIL (-417 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1209))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1209))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1209)))) (|HasCategory| |#1| (QUOTE (-1015))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) (-418 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 @@ -1626,17 +1626,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-367)))) (-424 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4390 . T) (-4380 . T) (-4391 . T)) +((-4399 . T) (-4389 . T) (-4400 . T)) NIL -(-425 R -3214) +(-425 R -3249) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-426 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4377 -12 (|has| |#1| (-6 -4377)) (|has| |#2| (-6 -4377))) (-4384 . T) (-4385 . T) (-4387 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4377)) (|HasAttribute| |#2| (QUOTE -4377)))) -(-427 R -3214) +((-4386 -12 (|has| |#1| (-6 -4386)) (|has| |#2| (-6 -4386))) (-4393 . T) (-4394 . T) (-4396 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4386)) (|HasAttribute| |#2| (QUOTE -4386)))) +(-427 R -3249) ((|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 @@ -1646,17 +1646,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1102))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (-429 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}."))) -((-4387 -4007 (|has| |#1| (-1042)) (|has| |#1| (-471))) (-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) ((-4392 "*") |has| |#1| (-553)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-553)) (-4382 |has| |#1| (-553))) +((-4396 -4050 (|has| |#1| (-1042)) (|has| |#1| (-471))) (-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) ((-4401 "*") |has| |#1| (-553)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-553)) (-4391 |has| |#1| (-553))) NIL -(-430 R -3214) +(-430 R -3249) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,{}y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,{}y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,{}y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,{}y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,{}y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,{}y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,{}x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-431 R -3214) +(-431 R -3249) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-432 R -3214) +(-432 R -3249) ((|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 @@ -1664,7 +1664,7 @@ 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 -(-434 R -3214 UP) +(-434 R -3249 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 -1031) (QUOTE (-48))))) @@ -1692,7 +1692,7 @@ 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 -(-441 R UP -3214) +(-441 R UP -3249) ((|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 @@ -1730,16 +1730,16 @@ NIL NIL (-450) ((|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}."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-451 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"))) -((-4387 |has| (-406 (-945 |#1|)) (-553)) (-4385 . T) (-4384 . T)) +((-4396 |has| (-406 (-945 |#1|)) (-553)) (-4394 . T) (-4393 . T)) ((|HasCategory| (-406 (-945 |#1|)) (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| (-406 (-945 |#1|)) (QUOTE (-553)))) (-452 |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"))) -(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#2| (QUOTE (-902))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4007 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(((-4401 "*") |has| |#2| (-171)) (-4392 |has| |#2| (-553)) (-4397 |has| |#2| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4397)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-453 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 @@ -1766,7 +1766,7 @@ NIL NIL (-459 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL (-460 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1774,7 +1774,7 @@ NIL NIL (-461 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-462 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}."))) @@ -1804,7 +1804,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-469 |lv| -3214 R) +(-469 |lv| -3249 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1814,23 +1814,23 @@ NIL NIL (-471) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4387 . T)) +((-4396 . T)) NIL (-472 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-473 |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."))) -((-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090)))) +((-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090)))) (-474 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)}"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-475) ((|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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-476) ((|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'."))) @@ -1838,29 +1838,29 @@ NIL NIL (-477 |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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-478) ((|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 (-479 |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"))) -(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . 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(|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 (-482 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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) -(-483 -3214 UP UPUP R) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +(-483 -3249 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 @@ -1870,12 +1870,12 @@ NIL NIL (-485) ((|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4050 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-486 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 -4390)) (|HasAttribute| |#1| (QUOTE -4391)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) +((|HasAttribute| |#1| (QUOTE -4399)) (|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (-487 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1896,33 +1896,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-492 -3214 UP |AlExt| |AlPol|) +(-492 -3249 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-493) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| $ (QUOTE (-1042))) (|HasCategory| $ (LIST (QUOTE -1031) (QUOTE (-561))))) (-494 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-495 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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-496 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 -(-497 R UP -3214) +(-497 R UP -3249) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-498 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -308) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-112) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-112) (QUOTE (-1090))) (|HasCategory| (-112) (LIST (QUOTE -608) (QUOTE (-856))))) (-499 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)}."))) @@ -1936,7 +1936,7 @@ 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 -(-502 -3214 |Expon| |VarSet| |DPoly|) +(-502 -3249 |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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-1166))))) @@ -1986,36 +1986,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-786)))) (-514 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-515) ((|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 (-516 |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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((-4007 (|HasCategory| (-578 |#1|) (QUOTE (-144))) (|HasCategory| (-578 |#1|) (QUOTE (-367)))) (|HasCategory| (-578 |#1|) (QUOTE (-146))) (|HasCategory| (-578 |#1|) (QUOTE (-367))) (|HasCategory| (-578 |#1|) (QUOTE (-144)))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((-4050 (|HasCategory| (-578 |#1|) (QUOTE (-144))) (|HasCategory| (-578 |#1|) (QUOTE (-367)))) (|HasCategory| (-578 |#1|) (QUOTE (-146))) (|HasCategory| (-578 |#1|) (QUOTE (-367))) (|HasCategory| (-578 |#1|) (QUOTE (-144)))) (-517 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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-518 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."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-519 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 -4391))) +((|HasAttribute| |#3| (QUOTE -4400))) (-520 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 -4391))) +((|HasAttribute| |#7| (QUOTE -4400))) (-521 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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4401 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-522) ((|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 @@ -2025,11 +2025,11 @@ NIL NIL NIL (-524 S) -((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) +((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL (-525) -((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) +((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,{}b)} reads byte sequences from conduit \\spad{`c'} into the byte buffer \\spad{`b'}. The actual number of bytes written is returned,{} and the length of \\spad{`b'} is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a UInt32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an Int32 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a UInt16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an Int16 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a UInt8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an Int8 value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL (-526 GF) @@ -2048,7 +2048,7 @@ 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 -(-530 K -3214 |Par|) +(-530 K -3249 |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 @@ -2072,7 +2072,7 @@ 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 -(-536 K -3214 |Par|) +(-536 K -3249 |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 @@ -2102,7 +2102,7 @@ NIL NIL (-543) ((|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."))) -((-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4397 . T) (-4398 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-544) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) @@ -2118,13 +2118,13 @@ NIL NIL (-547 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) -(-548 R -3214) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +(-548 R -3249) ((|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 -(-549 R0 -3214 UP UPUP R) +(-549 R0 -3249 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 @@ -2134,7 +2134,7 @@ NIL NIL (-551 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."))) -((-1417 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-1408 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-552 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."))) @@ -2142,9 +2142,9 @@ NIL NIL (-553) ((|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."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-554 R -3214) +(-554 R -3249) ((|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 @@ -2156,7 +2156,7 @@ 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 -(-557 R -3214 L) +(-557 R -3249 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 -649) (|devaluate| |#2|)))) @@ -2164,31 +2164,31 @@ 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 -(-559 -3214 UP UPUP R) +(-559 -3249 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 -(-560 -3214 UP) +(-560 -3249 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 (-561) ((|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}."))) -((-4372 . T) (-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4381 . T) (-4387 . T) (-4391 . T) (-4386 . T) (-4397 . T) (-4398 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-562) ((|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 -(-563 R -3214 L) +(-563 R -3249 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 -649) (|devaluate| |#2|)))) -(-564 R -3214) +(-564 R -3249) ((|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 -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1129)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-624))))) -(-565 -3214 UP) +(-565 -3249 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 @@ -2196,27 +2196,27 @@ 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 -(-567 -3214) +(-567 -3249) ((|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 (-568 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."))) -((-1417 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-1408 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-569) ((|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 -(-570 R -3214) +(-570 R -3249) ((|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 -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-624))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-553)))) -(-571 -3214 UP) +(-571 -3249 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 -(-572 R -3214) +(-572 R -3249) ((|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 @@ -2238,27 +2238,27 @@ NIL NIL (-577 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-578 |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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) (-579) ((|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 -(-580 R -3214) +(-580 R -3249) ((|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 -(-581 E -3214) +(-581 E -3249) ((|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 -(-582 -3214) +(-582 -3249) ((|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}."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-1166))))) (-583 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"))) @@ -2286,19 +2286,19 @@ NIL NIL (-589 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-4007 (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-4050 (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-590 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 (-591 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|)))) (|HasCategory| (-561) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561)))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-561)) (|devaluate| |#1|)))) (|HasCategory| (-561) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-561)))))) (-592 |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.}"))) -((-4385 |has| |#1| (-553)) (-4384 |has| |#1| (-553)) ((-4392 "*") |has| |#1| (-553)) (-4383 |has| |#1| (-553)) (-4387 . T)) +((-4394 |has| |#1| (-553)) (-4393 |has| |#1| (-553)) ((-4401 "*") |has| |#1| (-553)) (-4392 |has| |#1| (-553)) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-553)))) (-593 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),{}..]}."))) @@ -2308,7 +2308,7 @@ 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 -(-595 R -3214 FG) +(-595 R -3249 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 @@ -2318,12 +2318,12 @@ NIL NIL (-597 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-598 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 -4391)) (|HasCategory| |#2| (QUOTE (-844))) (|HasAttribute| |#1| (QUOTE -4390)) (|HasCategory| |#3| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-844))) (|HasAttribute| |#1| (QUOTE -4399)) (|HasCategory| |#3| (QUOTE (-1090)))) (-599 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2338,19 +2338,19 @@ NIL NIL (-602 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4387 -4007 (-2170 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4385 . T) (-4384 . T)) -((-4007 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4396 -4050 (-2198 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4394 . T) (-4393 . T)) +((-4050 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-603 |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."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-604 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 (-605 |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}."))) -((-4391 . T)) +((-4400 . T)) NIL (-606 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"))) @@ -2368,7 +2368,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-610 -3214 UP) +(-610 -3249 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2390,19 +2390,19 @@ NIL NIL (-615 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."))) -((-4387 . T)) +((-4396 . T)) NIL (-616 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}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-842)))) -(-617 R -3214) +(-617 R -3249) ((|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 (-618 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"))) -((-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4383 . T) (-4387 . T)) +((-4394 . T) (-4393 . T) ((-4401 "*") . T) (-4392 . T) (-4396 . T)) ((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (-619 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."))) @@ -2418,7 +2418,7 @@ NIL NIL (-622 |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}}."))) -((-4387 . T)) +((-4396 . T)) NIL (-623 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}}."))) @@ -2428,30 +2428,30 @@ 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 -(-625 R -3214) +(-625 R -3249) ((|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 -(-626 |lv| -3214) +(-626 |lv| -3249) ((|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 (-627) ((|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."))) -((-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1148) (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (QUOTE (-1090)))) +((-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2677) (QUOTE (-52))))))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1148) (QUOTE (-844))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (QUOTE (-1090)))) (-628 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-629 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4385 . T) (-4384 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4394 . T) (-4393 . T)) NIL (-630 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4387 -4007 (-2170 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4385 . T) (-4384 . T)) -((-4007 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4396 -4050 (-2198 (|has| |#2| (-366 |#1|)) (|has| |#1| (-553))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-553)))) (-4394 . T) (-4393 . T)) +((-4050 (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-631 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 @@ -2463,10 +2463,10 @@ NIL (-633 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 -((-2159 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +((-2186 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) (-634 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}."))) -((-4387 . T)) +((-4396 . T)) NIL (-635 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}."))) @@ -2482,16 +2482,16 @@ NIL NIL (-638 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."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-639 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-640 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-641 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2503,22 +2503,22 @@ NIL (-643 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 -4391))) +((|HasAttribute| |#1| (QUOTE -4400))) (-644 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 -(-645 R -3214 L) +(-645 R -3249 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 (-646 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}}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-647 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-648 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2526,15 +2526,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-362)))) (-649 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}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-650 -3214 UP) +(-650 -3249 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)))) -(-651 A -1558) +(-651 A -1734) ((|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}}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) (-652 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."))) @@ -2550,7 +2550,7 @@ NIL NIL (-655 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}."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) ((|HasCategory| |#1| (QUOTE (-785)))) (-656 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."))) @@ -2558,7 +2558,7 @@ NIL NIL (-657 |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) (-4385 . T) (-4384 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4394 . T) (-4393 . T)) ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-171)))) (-658 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}."))) @@ -2566,13 +2566,13 @@ NIL NIL (-659 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}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL -(-660 -3214) +(-660 -3249) ((|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 -(-661 -3214 |Row| |Col| M) +(-661 -3249 |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 @@ -2582,8 +2582,8 @@ NIL NIL (-663 |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."))) -((-4387 . T) (-4390 . T) (-4384 . T) (-4385 . T)) -((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553))) (-4007 (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4396 . T) (-4399 . T) (-4393 . T) (-4394 . T)) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4401 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553))) (-4050 (|HasAttribute| |#2| (QUOTE (-4401 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-664) ((|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 @@ -2603,7 +2603,7 @@ NIL (-668 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 -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (QUOTE (-1042))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-669) ((|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 @@ -2647,10 +2647,10 @@ NIL (-679 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 (-4392 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553)))) +((|HasAttribute| |#2| (QUOTE (-4401 "*"))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-553)))) (-680 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"))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-681 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."))) @@ -2658,8 +2658,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553)))) (-682 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."))) -((-4390 . T) (-4391 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4392 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4399 . T) (-4400 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-553))) (|HasAttribute| |#1| (QUOTE (-4401 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-683 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 @@ -2668,7 +2668,7 @@ 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 -(-685 S -3214 FLAF FLAS) +(-685 S -3249 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 @@ -2678,11 +2678,11 @@ NIL NIL (-687) ((|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"))) -((-4383 . T) (-4388 |has| (-692) (-362)) (-4382 |has| (-692) (-362)) (-4389 |has| (-692) (-6 -4389)) (-4386 |has| (-692) (-6 -4386)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-692) (QUOTE (-146))) (|HasCategory| (-692) (QUOTE (-144))) (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-367))) (|HasCategory| (-692) (QUOTE (-362))) (-4007 (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-232))) (-4007 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (LIST (QUOTE -285) (QUOTE (-692)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -308) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4007 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-692) (QUOTE (-1015))) (|HasCategory| (-692) (QUOTE (-1190))) (-12 (|HasCategory| (-692) (QUOTE (-995))) (|HasCategory| (-692) (QUOTE (-1190)))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (|HasCategory| (-692) (QUOTE (-543))) (-12 (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-1190)))) (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362)))) (-4007 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-553)))) (-12 (|HasCategory| (-692) (QUOTE (-232))) (|HasCategory| (-692) (QUOTE (-362)))) (-12 (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-844))) (|HasCategory| (-692) (QUOTE (-553))) (|HasAttribute| (-692) (QUOTE -4389)) (|HasAttribute| (-692) (QUOTE -4386)) (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-144)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-348))))) +((-4392 . T) (-4397 |has| (-692) (-362)) (-4391 |has| (-692) (-362)) (-4398 |has| (-692) (-6 -4398)) (-4395 |has| (-692) (-6 -4395)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-692) (QUOTE (-146))) (|HasCategory| (-692) (QUOTE (-144))) (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-367))) (|HasCategory| (-692) (QUOTE (-362))) (-4050 (|HasCategory| (-692) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-232))) (-4050 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (LIST (QUOTE -285) (QUOTE (-692)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -308) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-692)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-692) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-692) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (-4050 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-348)))) (|HasCategory| (-692) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-692) (QUOTE (-1015))) (|HasCategory| (-692) (QUOTE (-1190))) (-12 (|HasCategory| (-692) (QUOTE (-995))) (|HasCategory| (-692) (QUOTE (-1190)))) (-4050 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (-4050 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-362))) (|HasCategory| (-692) (QUOTE (-902)))) (-12 (|HasCategory| (-692) (QUOTE (-348))) (|HasCategory| (-692) (QUOTE (-902))))) (|HasCategory| (-692) (QUOTE (-543))) (-12 (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-1190)))) (|HasCategory| (-692) (QUOTE (-1051))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902))) (-4050 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-362)))) (-4050 (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-553)))) (-12 (|HasCategory| (-692) (QUOTE (-232))) (|HasCategory| (-692) (QUOTE (-362)))) (-12 (|HasCategory| (-692) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-692) (QUOTE (-362)))) (|HasCategory| (-692) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-692) (QUOTE (-844))) (|HasCategory| (-692) (QUOTE (-553))) (|HasAttribute| (-692) (QUOTE -4398)) (|HasAttribute| (-692) (QUOTE -4395)) (-12 (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-144)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-692) (QUOTE (-306))) (|HasCategory| (-692) (QUOTE (-902)))) (|HasCategory| (-692) (QUOTE (-348))))) (-688 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}."))) -((-4391 . T)) +((-4400 . T)) NIL (-689 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}."))) @@ -2692,13 +2692,13 @@ 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 -(-691 OV E -3214 PG) +(-691 OV E -3249 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 (-692) ((|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}"))) -((-1417 . T) (-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-1408 . T) (-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-693 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."))) @@ -2706,7 +2706,7 @@ NIL NIL (-694) ((|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}"))) -((-4389 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4398 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-695 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"))) @@ -2728,7 +2728,7 @@ 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 -(-700 S -3122 I) +(-700 S -3154 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 @@ -2738,7 +2738,7 @@ NIL NIL (-702 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)}.}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL (-703 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}."))) @@ -2748,25 +2748,25 @@ 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 -(-705 R |Mod| -3471 -1407 |exactQuo|) +(-705 R |Mod| -4047 -3405 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-706 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4386 |has| |#1| (-362)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4395 |has| |#1| (-362)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . 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(|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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-709 R |Mod| -3471 -1407 |exactQuo|) +(-709 R |Mod| -4047 -3405 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4387 . T)) +((-4396 . T)) NIL (-710 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2774,11 +2774,11 @@ NIL NIL (-711 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL -(-712 -3214) +(-712 -3249) ((|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]]}."))) -((-4387 . T)) +((-4396 . T)) NIL (-713 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."))) @@ -2802,7 +2802,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-348))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-367)))) (-718 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."))) -((-4383 |has| |#1| (-362)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 |has| |#1| (-362)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-719 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."))) @@ -2812,7 +2812,7 @@ 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 -(-721 -3214 UP) +(-721 -3249 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 @@ -2830,8 +2830,8 @@ NIL NIL (-725 |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."))) -(((-4392 "*") |has| |#2| (-171)) (-4383 |has| |#2| (-553)) (-4388 |has| |#2| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . 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T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-858 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4397)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-726 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2846,15 +2846,15 @@ NIL NIL (-729 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) (-4396 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-844)))) (-730 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4380 . T) (-4391 . T)) +((-4389 . T) (-4400 . T)) NIL (-731 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}."))) -((-4390 . T) (-4380 . T) (-4391 . T)) +((-4399 . T) (-4389 . T) (-4400 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-732) ((|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."))) @@ -2866,7 +2866,7 @@ NIL NIL (-734 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL (-735 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"))) @@ -2882,7 +2882,7 @@ NIL NIL (-738 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}."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL (-739) ((|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}."))) @@ -2964,11 +2964,11 @@ 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 -(-759 -3214) +(-759 -3249) ((|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 -(-760 P -3214) +(-760 P -3249) ((|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 @@ -2976,7 +2976,7 @@ NIL NIL NIL NIL -(-762 UP -3214) +(-762 UP -3249) ((|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 @@ -2990,9 +2990,9 @@ NIL NIL (-765) ((|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."))) -(((-4392 "*") . T)) +(((-4401 "*") . T)) NIL -(-766 R -3214) +(-766 R -3249) ((|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 @@ -3012,7 +3012,7 @@ 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 -(-771 -3214 |ExtF| |SUEx| |ExtP| |n|) +(-771 -3249 |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 @@ -3026,23 +3026,23 @@ NIL NIL (-774 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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . 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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 (-776 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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T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-777 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-778 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.}"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-779 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}."))) @@ -3094,25 +3094,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-367)))) (-791 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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-792 -4007 R OS S) +(-792 -4050 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-793 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-4007 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) +((-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-4050 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-992 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (-794) ((|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 -(-795 R -3214 L) +(-795 R -3249 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 -(-796 R -3214) +(-796 R -3249) ((|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 @@ -3120,7 +3120,7 @@ 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 -(-798 R -3214) +(-798 R -3249) ((|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 @@ -3128,11 +3128,11 @@ 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 -(-800 -3214 UP UPUP R) +(-800 -3249 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 -(-801 -3214 UP L LQ) +(-801 -3249 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 @@ -3140,41 +3140,41 @@ 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 -(-803 -3214 UP L LQ) +(-803 -3249 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 -(-804 -3214 UP) +(-804 -3249 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 -(-805 -3214 L UP A LO) +(-805 -3249 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 -(-806 -3214 UP) +(-806 -3249 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)))) -(-807 -3214 LO) +(-807 -3249 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 -(-808 -3214 LODO) +(-808 -3249 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) NIL NIL -(-809 -2164 S |f|) +(-809 -2192 S |f|) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The ordering on the type is determined by its third argument which represents the less than function on vectors. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4384 |has| |#2| (-1042)) (-4385 |has| |#2| (-1042)) (-4387 |has| |#2| (-6 -4387)) ((-4392 "*") |has| |#2| (-171)) (-4390 . 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(LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-720))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-787))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))))) (|HasCategory| (-561) (QUOTE (-844))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1042)))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4050 (|HasCategory| |#2| (QUOTE (-1042))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-1090)))) (|HasAttribute| |#2| (QUOTE -4396)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-810 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-812 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-811 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) -(((-4392 "*") |has| |#2| (-362)) (-4383 |has| |#2| (-362)) (-4388 |has| |#2| (-362)) (-4382 |has| |#2| (-362)) (-4387 . T) (-4385 . T) (-4384 . T)) +(((-4401 "*") |has| |#2| (-362)) (-4392 |has| |#2| (-362)) (-4397 |has| |#2| (-362)) (-4391 |has| |#2| (-362)) (-4396 . T) (-4394 . T) (-4393 . T)) ((|HasCategory| |#2| (QUOTE (-362)))) (-812 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}))."))) @@ -3186,7 +3186,7 @@ NIL NIL (-814) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-815) ((|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}"))) @@ -3214,7 +3214,7 @@ NIL NIL (-821 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}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-232)))) (-822) ((|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."))) @@ -3226,7 +3226,7 @@ NIL NIL (-824 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4390 . T) (-4380 . T) (-4391 . T)) +((-4399 . T) (-4389 . T) (-4400 . T)) NIL (-825) ((|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."))) @@ -3238,8 +3238,8 @@ NIL NIL (-827 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."))) -((-4387 |has| |#1| (-842))) -((|HasCategory| |#1| (QUOTE (-842))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4396 |has| |#1| (-842))) +((|HasCategory| |#1| (QUOTE (-842))) (-4050 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4050 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-828 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 @@ -3250,7 +3250,7 @@ NIL NIL (-830 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) (-831) ((|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)."))) @@ -3278,13 +3278,13 @@ NIL NIL (-837 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-4387 |has| |#1| (-842))) -((|HasCategory| |#1| (QUOTE (-842))) (-4007 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4007 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4396 |has| |#1| (-842))) +((|HasCategory| |#1| (QUOTE (-842))) (-4050 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-842)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4050 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-838) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-839 -2164 S) +(-839 -2192 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3298,7 +3298,7 @@ NIL NIL (-842) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4387 . T)) +((-4396 . T)) NIL (-843 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3314,19 +3314,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171)))) (-846 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL (-847 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) -(-848 R |sigma| -3790) +(-848 R |sigma| -1965) ((|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."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-849 |x| R |sigma| -3790) +(-849 |x| R |sigma| -1965) ((|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}."))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) (-850 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..)}."))) @@ -3341,11 +3341,11 @@ NIL NIL NIL (-853 S) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) +((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL (-854) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) +((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,{}b)} attempts to write the unsigned 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,{}b)} attempts to write the 8-bit value \\spad{`v'} on the conduit \\spad{`c'}. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL (-855) @@ -3366,7 +3366,7 @@ NIL NIL (-859 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") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)"))) -((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) (-860 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3378,24 +3378,24 @@ NIL NIL (-862 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-863 |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)."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-864 |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)."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-863 |#1|) (QUOTE (-902))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-146))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-863 |#1|) (QUOTE (-1015))) (|HasCategory| (-863 |#1|) (QUOTE (-814))) (-4007 (|HasCategory| (-863 |#1|) (QUOTE (-814))) (|HasCategory| (-863 |#1|) (QUOTE (-844)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-1141))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-232))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -863) (|devaluate| |#1|)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (QUOTE (-306))) (|HasCategory| (-863 |#1|) (QUOTE (-543))) (|HasCategory| (-863 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-863 |#1|) (QUOTE (-902))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-146))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-863 |#1|) (QUOTE (-1015))) (|HasCategory| (-863 |#1|) (QUOTE (-814))) (-4050 (|HasCategory| (-863 |#1|) (QUOTE (-814))) (|HasCategory| (-863 |#1|) (QUOTE (-844)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-1141))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| (-863 |#1|) (QUOTE (-232))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -512) (QUOTE (-1166)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -863) (|devaluate| |#1|)) (LIST (QUOTE -863) (|devaluate| |#1|)))) (|HasCategory| (-863 |#1|) (QUOTE (-306))) (|HasCategory| (-863 |#1|) (QUOTE (-543))) (|HasCategory| (-863 |#1|) (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-863 |#1|) (QUOTE (-902)))) (|HasCategory| (-863 |#1|) (QUOTE (-144))))) (-865 |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)}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-814))) (-4007 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-814))) (-4050 (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-844)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -285) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-844))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) (-866 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 (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))))) (-867) ((|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 @@ -3451,7 +3451,7 @@ NIL (-880 |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 (-2159 (|HasCategory| |#2| (QUOTE (-1042)))) (-2159 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (-2159 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166))))) +((-12 (-2186 (|HasCategory| |#2| (QUOTE (-1042)))) (-2186 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (-12 (|HasCategory| |#2| (QUOTE (-1042))) (-2186 (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166))))) (-881 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 @@ -3460,7 +3460,7 @@ 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 -(-883 R -3122) +(-883 R -3154) ((|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 @@ -3484,7 +3484,7 @@ 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 -(-889 UP -3214) +(-889 UP -3249) ((|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 @@ -3502,19 +3502,19 @@ NIL NIL (-893 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}."))) -((-4387 . T)) +((-4396 . T)) NIL (-894 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 (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-895 |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 (-896 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."))) -((-4387 . T)) +((-4396 . T)) NIL (-897 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|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3522,8 +3522,8 @@ NIL NIL (-898 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) -((-4387 . T)) -((-4007 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) +((-4396 . T)) +((-4050 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-844)))) (-899 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 @@ -3538,13 +3538,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-144)))) (-902) ((|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}."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-903 |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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-904 R0 -3214 UP UPUP R) +(-904 R0 -3249 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 @@ -3558,7 +3558,7 @@ NIL NIL (-907 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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-908 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."))) @@ -3572,7 +3572,7 @@ 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 -(-911 -3214) +(-911 -3249) ((|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 @@ -3582,17 +3582,17 @@ NIL NIL (-913) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-914) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4392 "*") . T)) +(((-4401 "*") . T)) NIL -(-915 -3214 P) +(-915 -3249 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-916 |xx| -3214) +(-916 |xx| -3249) ((|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 @@ -3616,7 +3616,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-922 R -3214) +(-922 R -3249) ((|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 @@ -3628,7 +3628,7 @@ 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 -(-925 S R -3214) +(-925 S R -3249) ((|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 @@ -3648,11 +3648,11 @@ 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 -879) (|devaluate| |#1|)))) -(-930 R -3214 -3122) +(-930 R -3249 -3154) ((|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 -(-931 -3122) +(-931 -3154) ((|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 @@ -3674,8 +3674,8 @@ NIL NIL (-936 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-937 |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 @@ -3695,12 +3695,12 @@ NIL (-941 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 (-902))) (|HasAttribute| |#2| (QUOTE -4388)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-844)))) +((|HasCategory| |#2| (QUOTE (-902))) (|HasAttribute| |#2| (QUOTE -4397)) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#4| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#4| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-844)))) (-942 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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL -(-943 E V R P -3214) +(-943 E V R P -3249) ((|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 @@ -3710,9 +3710,9 @@ NIL NIL (-945 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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-946 E V R P -3214) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1166) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-946 E V R P -3249) ((|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 (-450)))) @@ -3734,13 +3734,13 @@ NIL NIL (-951 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"))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-952) ((|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 -(-953 -3214) +(-953 -3249) ((|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 @@ -3754,12 +3754,12 @@ NIL NIL (-956 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}"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4388))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4397))) (-957 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"))) -((-4387 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787)))) (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-844))))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE 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(-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-471)))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720)))) (-12 (|HasCategory| |#1| (QUOTE (-787))) (|HasCategory| |#2| (QUOTE (-787))))) (-12 (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-720)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-844))))) (-958) ((|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|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3774,7 +3774,7 @@ NIL NIL (-961 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-962 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}}"))) @@ -3794,7 +3794,7 @@ NIL NIL (-966 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-967) ((|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}."))) @@ -3806,7 +3806,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-553)))) (-969 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."))) -((-4390 . T)) +((-4399 . T)) NIL (-970 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."))) @@ -3822,7 +3822,7 @@ NIL NIL (-973 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}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-974 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3840,7 +3840,7 @@ 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 -(-978 K R UP -3214) +(-978 K R UP -3249) ((|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 @@ -3870,7 +3870,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1015))) (|HasCategory| |#2| (QUOTE (-814))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-1141)))) (-985 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}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-986 |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}."))) @@ -3882,7 +3882,7 @@ NIL NIL (-988 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."))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-989 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}."))) @@ -3890,7 +3890,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-289)))) (-990 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}."))) -((-4383 |has| |#1| (-289)) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 |has| |#1| (-289)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-991 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}."))) @@ -3898,12 +3898,12 @@ NIL NIL (-992 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.}"))) -((-4383 |has| |#1| (-289)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543)))) +((-4392 |has| |#1| (-289)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1166)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-543)))) (-993 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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-994 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3912,14 +3912,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-996 -3214 UP UPUP |radicnd| |n|) +(-996 -3249 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4383 |has| (-406 |#2|) (-362)) (-4388 |has| (-406 |#2|) (-362)) (-4382 |has| (-406 |#2|) (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4007 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4007 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4007 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +((-4392 |has| (-406 |#2|) (-362)) (-4397 |has| (-406 |#2|) (-362)) (-4391 |has| (-406 |#2|) (-362)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-4050 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-4050 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-4050 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -634) (QUOTE (-561)))) (-4050 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) (-997 |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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4007 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-561) (QUOTE (-902))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-1166)))) (|HasCategory| (-561) (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-146))) (|HasCategory| (-561) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-1015))) (|HasCategory| (-561) (QUOTE (-814))) (-4050 (|HasCategory| (-561) (QUOTE (-814))) (|HasCategory| (-561) (QUOTE (-844)))) (|HasCategory| (-561) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-1141))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| (-561) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| (-561) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| (-561) (QUOTE (-232))) (|HasCategory| (-561) (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| (-561) (LIST (QUOTE -512) (QUOTE (-1166)) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -308) (QUOTE (-561)))) (|HasCategory| (-561) (LIST (QUOTE -285) (QUOTE (-561)) (QUOTE (-561)))) (|HasCategory| (-561) (QUOTE (-306))) (|HasCategory| (-561) (QUOTE (-543))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-561) (LIST (QUOTE -634) (QUOTE (-561)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-561) (QUOTE (-902)))) (|HasCategory| (-561) (QUOTE (-144))))) (-998) ((|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 @@ -3939,7 +3939,7 @@ NIL (-1002 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 -4391)) (|HasCategory| |#2| (QUOTE (-1090)))) +((|HasAttribute| |#1| (QUOTE -4400)) (|HasCategory| |#2| (QUOTE (-1090)))) (-1003 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 @@ -3950,21 +3950,21 @@ NIL NIL (-1005) ((|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}}"))) -((-4383 . T) (-4388 . T) (-4382 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4387 . T)) +((-4392 . T) (-4397 . T) (-4391 . T) (-4394 . T) (-4393 . T) ((-4401 "*") . T) (-4396 . T)) NIL -(-1006 R -3214) +(-1006 R -3249) ((|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 -(-1007 R -3214) +(-1007 R -3249) ((|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 -(-1008 -3214 UP) +(-1008 -3249 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 -(-1009 -3214 UP) +(-1009 -3249 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 @@ -3998,9 +3998,9 @@ NIL NIL (-1017 |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"))) -((-4383 . T) (-4388 . T) (-4382 . T) (-4385 . T) (-4384 . T) ((-4392 "*") . T) (-4387 . T)) -((-4007 (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561))))) -(-1018 -3214 L) +((-4392 . T) (-4397 . T) (-4391 . T) (-4394 . T) (-4393 . T) ((-4401 "*") . T) (-4396 . T)) +((-4050 (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-406 (-561)) (LIST (QUOTE -1031) (QUOTE (-561))))) +(-1018 -3249 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 @@ -4010,12 +4010,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1090)))) (-1020 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."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-1021 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 (-4392 "*")))) +((|HasAttribute| |#1| (QUOTE (-4401 "*")))) (-1022 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 @@ -4036,14 +4036,14 @@ 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 -(-1027 -3214 |Expon| |VarSet| |FPol| |LFPol|) +(-1027 -3249 |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"))) -(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1028) ((|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.}"))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2677) (QUOTE (-52))))))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) (-1029) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4086,7 +4086,7 @@ NIL NIL (-1039 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}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| (-774 |#1| (-858 |#2|)) (QUOTE (-1090))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -774) (|devaluate| |#1|) (LIST (QUOTE -858) (|devaluate| |#2|)))))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-774 |#1| (-858 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| (-858 |#2|) (QUOTE (-367))) (|HasCategory| (-774 |#1| (-858 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-1040) ((|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"))) @@ -4098,9 +4098,9 @@ NIL NIL (-1042) ((|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."))) -((-4387 . T)) +((-4396 . T)) NIL -(-1043 |xx| -3214) +(-1043 |xx| -3249) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4110,12 +4110,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-306))) (|HasCategory| |#4| (QUOTE (-362))) (|HasCategory| |#4| (QUOTE (-553))) (|HasCategory| |#4| (QUOTE (-171)))) (-1045 |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"))) -((-4390 . T) (-4385 . T) (-4384 . T)) +((-4399 . T) (-4394 . T) (-4393 . T)) NIL (-1046 |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}."))) -((-4390 . T) (-4385 . T) (-4384 . T)) -((-4007 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4394 . T) (-4393 . T)) +((-4050 (-12 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856))))) (-1047 |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 @@ -4134,7 +4134,7 @@ NIL NIL (-1051) ((|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."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1052 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4142,19 +4142,19 @@ NIL NIL (-1053) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|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."))) -((-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4387 . T) (-4391 . T) (-4386 . T) (-4397 . T) (-4398 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1054) ((|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}"))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2654) (QUOTE (-52))))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (QUOTE (-1166))) (LIST (QUOTE |:|) (QUOTE -2677) (QUOTE (-52))))))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-52) (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1090))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (QUOTE (-1090))) (|HasCategory| (-1166) (QUOTE (-844))) (|HasCategory| (-52) (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-52) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (LIST (QUOTE -608) (QUOTE (-856))))) (-1055 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| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -985) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-1166))))) (-1056 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\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}}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL (-1057) ((|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'."))) @@ -4178,7 +4178,7 @@ NIL NIL (-1062 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}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-1063 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."))) @@ -4192,11 +4192,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1066 |Base| R -3214) +(-1066 |Base| R -3249) ((|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 -(-1067 |Base| R -3214) +(-1067 |Base| R -3249) ((|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 @@ -4210,8 +4210,8 @@ NIL NIL (-1070 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."))) -((-4383 |has| |#1| (-362)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) +((-4392 |has| |#1| (-362)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) (-1071 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 @@ -4238,8 +4238,8 @@ NIL NIL (-1077 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"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-902))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4388)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4007 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1078 (-1166)) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1078 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 @@ -4282,7 +4282,7 @@ NIL NIL (-1088 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}."))) -((-4380 . T)) +((-4389 . T)) NIL (-1089 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}."))) @@ -4298,8 +4298,8 @@ NIL NIL (-1092 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)}}"))) -((-4390 . T) (-4380 . T) (-4391 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-4399 . T) (-4389 . T) (-4400 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1093 |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 @@ -4326,7 +4326,7 @@ NIL NIL (-1099 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.}"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-1100) ((|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."))) @@ -4342,8 +4342,8 @@ NIL NIL (-1103 |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. 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(LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-720))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-787))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-842))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (|HasCategory| (-561) (QUOTE (-844))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1042)))) (-12 (|HasCategory| |#3| (QUOTE (-1042))) (|HasCategory| |#3| (LIST (QUOTE -893) (QUOTE (-1166))))) (-4050 (|HasCategory| |#3| (QUOTE (-1042))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561)))))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -1031) (QUOTE (-561))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#3| (QUOTE (-1090)))) (|HasAttribute| |#3| (QUOTE -4396)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#3| (QUOTE (-1090))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-1104 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4352,7 +4352,7 @@ 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 -(-1106 R -3214) +(-1106 R -3249) ((|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 @@ -4370,19 +4370,19 @@ NIL NIL (-1110) ((|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."))) -((-4378 . T) (-4382 . T) (-4377 . T) (-4388 . T) (-4389 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4387 . T) (-4391 . T) (-4386 . T) (-4397 . T) (-4398 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1111 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4390 . T) (-4391 . T)) +((-4399 . T) (-4400 . T)) NIL (-1112 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4392 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) +((|HasCategory| |#3| (QUOTE (-362))) (|HasAttribute| |#3| (QUOTE (-4401 "*"))) (|HasCategory| |#3| (QUOTE (-171)))) (-1113 |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."))) -((-4390 . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4399 . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1114 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}."))) @@ -4390,17 +4390,17 @@ NIL NIL (-1115 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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . 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T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-902))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1116 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) (-1117 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}"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL -(-1118 UP -3214) +(-1118 UP -3249) ((|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 @@ -4454,19 +4454,19 @@ NIL NIL (-1131 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))) (-4007 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))))) (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))) (-4050 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1130) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1130 |#1| |#2|) (QUOTE (-1090))))) (|HasCategory| (-1130 |#1| |#2|) (LIST (QUOTE -608) (QUOTE (-856))))) (-1132 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) -((-4387 . T) (-4379 |has| |#2| (-6 (-4392 "*"))) (-4390 . T) (-4384 . T) (-4385 . T)) -((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4007 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (-4007 (|HasAttribute| |#2| (QUOTE (-4392 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((-4396 . T) (-4388 |has| |#2| (-6 (-4401 "*"))) (-4399 . T) (-4393 . T) (-4394 . T)) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4401 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-362))) (-4050 (|HasAttribute| |#2| (QUOTE (-4401 "*"))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-1133 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1134) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-1135 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.}"))) @@ -4474,12 +4474,12 @@ NIL NIL (-1136 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."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) (-1137 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}."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-1138 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 @@ -4490,8 +4490,8 @@ NIL NIL (-1140 |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."))) -((-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090)))) +((-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-844))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090)))) (-1141) ((|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 @@ -4514,20 +4514,20 @@ NIL NIL (-1146 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."))) -((-4391 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4400 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-1147) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-1148) NIL -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| (-143) (QUOTE (-1090))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-1149 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#1|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (QUOTE (-1148))) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#1|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (QUOTE (-1090))) (|HasCategory| (-1148) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-1150 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 @@ -4558,9 +4558,9 @@ NIL NIL (-1157 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4392 "*") -4007 (-2170 (|has| |#1| (-362)) (|has| (-1164 |#1| |#2| |#3|) (-814))) (|has| |#1| (-171)) (-2170 (|has| |#1| (-362)) (|has| (-1164 |#1| |#2| |#3|) (-902)))) (-4383 -4007 (-2170 (|has| |#1| (-362)) (|has| (-1164 |#1| |#2| |#3|) (-814))) (|has| |#1| (-553)) (-2170 (|has| |#1| (-362)) (|has| (-1164 |#1| |#2| |#3|) (-902)))) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . 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T)) +((|HasCategory| |#1| (QUOTE (-902))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#1| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1141))) (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4397)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-902)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1163 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} 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{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-1164 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|)))) (|HasCategory| (-765) (QUOTE (-1102))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|)))) (|HasCategory| (-765) (QUOTE (-1102))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) (-1165) ((|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 @@ -4602,8 +4602,8 @@ NIL NIL (-1168 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-6 -4388)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4007 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-964) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasAttribute| |#1| (QUOTE -4388))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-6 -4397)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-4050 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| (-964) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasAttribute| |#1| (QUOTE -4397))) (-1169) ((|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 @@ -4642,8 +4642,8 @@ NIL NIL (-1178 |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}"))) -((-4390 . T) (-4391 . T)) -((-12 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2252) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2654) (|devaluate| |#2|)))))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4007 (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) +((-4399 . T) (-4400 . T)) +((-12 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2285) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2677) (|devaluate| |#2|)))))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#2| (QUOTE (-1090)))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -609) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1090))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#2| (QUOTE (-1090))) (-4050 (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#2| (LIST (QUOTE -608) (QUOTE (-856)))) (|HasCategory| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (LIST (QUOTE -608) (QUOTE (-856))))) (-1179 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 @@ -4654,7 +4654,7 @@ NIL NIL (-1181 |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})}."))) -((-4391 . T)) +((-4400 . T)) NIL (-1182 |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."))) @@ -4694,8 +4694,8 @@ NIL NIL (-1191 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-4391 . T) (-4390 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) +((-4400 . T) (-4399 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1090))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (-1192 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4704,7 +4704,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1194 R -3214) +(-1194 R -3249) ((|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 @@ -4712,7 +4712,7 @@ 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 -(-1196 R -3214) +(-1196 R -3249) ((|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 -609) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -879) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -879) (|devaluate| |#1|))))) @@ -4722,12 +4722,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-367)))) (-1198 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL (-1199 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-362)))) (-1200 |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 @@ -4740,7 +4740,7 @@ 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 (-1090))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) -(-1203 -3214) +(-1203 -3249) ((|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 @@ -4766,7 +4766,7 @@ NIL NIL (-1209) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL (-1210) ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 16 bits."))) @@ -4776,285 +4776,289 @@ NIL ((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 32 bits."))) NIL NIL -(-1212 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1212) +((|constructor| (NIL "This domain is a datatype for (unsigned) integer values of precision 8 bits."))) +NIL +NIL +(-1213 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1213 |Coef|) +(-1214 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1214 S |Coef| UTS) +(-1215 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-362)))) -(-1215 |Coef| UTS) +(-1216 |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)}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1216 |Coef| UTS) +(-1217 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1219 R S) +(-1220 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) 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(|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1223 R UP) +(-1224 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) 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T)) +((|HasCategory| |#2| (QUOTE (-902))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-553)))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-378))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -879) (QUOTE (-561)))) (|HasCategory| |#2| (LIST (QUOTE -879) (QUOTE (-561))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-378)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -609) (LIST (QUOTE -885) (QUOTE (-561)))))) (-12 (|HasCategory| (-1072) (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -609) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -634) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (QUOTE (-561)))) (-4050 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| |#2| (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (-4050 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-1141))) (|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE -4397)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (-4050 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-902)))) (|HasCategory| |#2| (QUOTE (-144))))) +(-1228 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1228 S R) +(-1229 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-553))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-1141)))) -(-1229 R) +(-1230 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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4386 |has| |#1| (-362)) (-4388 |has| |#1| (-6 -4388)) (-4385 . T) (-4384 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4395 |has| |#1| (-362)) (-4397 |has| |#1| (-6 -4397)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL -(-1230 S |Coef| |Expon|) +(-1231 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 -893) (QUOTE (-1166)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4022) (LIST (|devaluate| |#2|) (QUOTE (-1166)))))) -(-1231 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1102))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -4064) (LIST (|devaluate| |#2|) (QUOTE (-1166)))))) +(-1232 |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|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1232 RC P) +(-1233 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1233 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1234 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1234 |Coef|) +(-1235 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1235 S |Coef| ULS) +(-1236 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1236 |Coef| ULS) +(-1237 |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)}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1237 |Coef| ULS) +(-1238 |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)}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) -(-1238 |Coef| |var| |cen|) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) +(-1239 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4388 |has| |#1| (-362)) (-4382 |has| |#1| (-362)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4007 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) -(-1239 R FE |var| |cen|) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4397 |has| |#1| (-362)) (-4391 |has| |#1| (-362)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#1| (QUOTE (-171))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-561)) (QUOTE (-1102))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-4050 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-553)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-561)))))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(-1240 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))}."))) -(((-4392 "*") |has| (-1238 |#2| |#3| |#4|) (-171)) (-4383 |has| (-1238 |#2| |#3| |#4|) (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-171))) (-4007 (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1238 |#2| |#3| |#4|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1238 |#2| |#3| |#4|) (QUOTE (-553)))) -(-1240 A S) +(((-4401 "*") |has| (-1239 |#2| |#3| |#4|) (-171)) (-4392 |has| (-1239 |#2| |#3| |#4|) (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| (-1239 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-171))) (-4050 (|HasCategory| (-1239 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1239 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561)))))) (|HasCategory| (-1239 |#2| |#3| |#4|) (LIST (QUOTE -1031) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| (-1239 |#2| |#3| |#4|) (LIST (QUOTE -1031) (QUOTE (-561)))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1239 |#2| |#3| |#4|) (QUOTE (-553)))) +(-1241 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4391))) -(-1241 S) +((|HasAttribute| |#1| (QUOTE -4400))) +(-1242 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1242 |Coef1| |Coef2| UTS1 UTS2) +(-1243 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1243 S |Coef|) +(-1244 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-561)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasSignature| |#2| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1842) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1166))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362)))) -(-1244 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#2| (QUOTE (-952))) (|HasCategory| |#2| (QUOTE (-1190))) (|HasSignature| |#2| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2563) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1166))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#2| (QUOTE (-362)))) +(-1245 |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."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1245 |Coef| |var| |cen|) +(-1246 |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}."))) -(((-4392 "*") |has| |#1| (-171)) (-4383 |has| |#1| (-553)) (-4384 . T) (-4385 . T) (-4387 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4007 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|)))) (|HasCategory| (-765) (QUOTE (-1102))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasSignature| |#1| (LIST (QUOTE -4022) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-362))) (-4007 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -1842) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1412) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) -(-1246 |Coef| UTS) +(((-4401 "*") |has| |#1| (-171)) (-4392 |has| |#1| (-553)) (-4393 . T) (-4394 . T) (-4396 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasCategory| |#1| (QUOTE (-553))) (-4050 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-553)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -893) (QUOTE (-1166)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-765)) (|devaluate| |#1|)))) (|HasCategory| (-765) (QUOTE (-1102))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasSignature| |#1| (LIST (QUOTE -4064) (LIST (|devaluate| |#1|) (QUOTE (-1166)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-765))))) (|HasCategory| |#1| (QUOTE (-362))) (-4050 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-561)))) (|HasCategory| |#1| (QUOTE (-952))) (|HasCategory| |#1| (QUOTE (-1190))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasSignature| |#1| (LIST (QUOTE -2563) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1166))))) (|HasSignature| |#1| (LIST (QUOTE -1405) (LIST (LIST (QUOTE -638) (QUOTE (-1166))) (|devaluate| |#1|))))))) +(-1247 |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 -(-1247 -3214 UP L UTS) +(-1248 -3249 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 (-553)))) -(-1248) +(-1249) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1249 |sym|) +(-1250 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1250 S R) +(-1251 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL ((|HasCategory| |#2| (QUOTE (-995))) (|HasCategory| |#2| (QUOTE (-1042))) (|HasCategory| |#2| (QUOTE (-720))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1251 R) +(-1252 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) NIL -(-1252 A B) +(-1253 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1253 R) +(-1254 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4391 . T) (-4390 . T)) -((-4007 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4007 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4007 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-1254) +((-4400 . T) (-4399 . T)) +((-4050 (-12 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-4050 (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856))))) (|HasCategory| |#1| (LIST (QUOTE -609) (QUOTE (-534)))) (-4050 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090)))) (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| (-561) (QUOTE (-844))) (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-720))) (|HasCategory| |#1| (QUOTE (-1042))) (-12 (|HasCategory| |#1| (QUOTE (-995))) (|HasCategory| |#1| (QUOTE (-1042)))) (|HasCategory| |#1| (LIST (QUOTE -608) (QUOTE (-856)))) (-12 (|HasCategory| |#1| (QUOTE (-1090))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-1255) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1255) +(-1256) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1256) +(-1257) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1257) +(-1258) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1258) +(-1259) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1259 A S) +(-1260 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1260 S) +(-1261 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}."))) -((-4385 . T) (-4384 . T)) +((-4394 . T) (-4393 . T)) NIL -(-1261 R) +(-1262 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 -(-1262 K R UP -3214) +(-1263 K R UP -3249) ((|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 -(-1263) +(-1264) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1264) +(-1265) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1265 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1266 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)"))) -((-4385 |has| |#1| (-171)) (-4384 |has| |#1| (-171)) (-4387 . T)) +((-4394 |has| |#1| (-171)) (-4393 |has| |#1| (-171)) (-4396 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362)))) -(-1266 R E V P) +(-1267 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}}."))) -((-4391 . T) (-4390 . T)) +((-4400 . T) (-4399 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#4| (LIST (QUOTE -308) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -609) (QUOTE (-534)))) (|HasCategory| |#4| (QUOTE (-1090))) (|HasCategory| |#1| (QUOTE (-553))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#4| (LIST (QUOTE -608) (QUOTE (-856))))) -(-1267 R) +(-1268 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})"))) -((-4384 . T) (-4385 . T) (-4387 . T)) +((-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1268 |vl| R) +(-1269 |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."))) -((-4387 . T) (-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4383))) -(-1269 R |VarSet| XPOLY) +((-4396 . T) (-4392 |has| |#2| (-6 -4392)) (-4394 . T) (-4393 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4392))) +(-1270 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 -(-1270 |vl| R) +(-1271 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) +((-4392 |has| |#2| (-6 -4392)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL -(-1271 S -3214) +(-1272 S -3249) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1272 -3214) +(-1273 -3249) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4382 . T) (-4388 . T) (-4383 . T) ((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +((-4391 . T) (-4397 . T) (-4392 . T) ((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL -(-1273 |VarSet| R) +(-1274 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|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}}."))) -((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -711) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasAttribute| |#2| (QUOTE -4383))) -(-1274 |vl| R) +((-4392 |has| |#2| (-6 -4392)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -711) (LIST (QUOTE -406) (QUOTE (-561))))) (|HasAttribute| |#2| (QUOTE -4392))) +(-1275 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) +((-4392 |has| |#2| (-6 -4392)) (-4394 . T) (-4393 . T) (-4396 . T)) NIL -(-1275 R) +(-1276 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4383 |has| |#1| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4383))) -(-1276 R E) +((-4392 |has| |#1| (-6 -4392)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasAttribute| |#1| (QUOTE -4392))) +(-1277 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#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}."))) -((-4387 . T) (-4388 |has| |#1| (-6 -4388)) (-4383 |has| |#1| (-6 -4383)) (-4385 . T) (-4384 . T)) -((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4387)) (|HasAttribute| |#1| (QUOTE -4388)) (|HasAttribute| |#1| (QUOTE -4383))) -(-1277 |VarSet| R) +((-4396 . T) (-4397 |has| |#1| (-6 -4397)) (-4392 |has| |#1| (-6 -4392)) (-4394 . T) (-4393 . T)) +((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4396)) (|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#1| (QUOTE -4392))) +(-1278 |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."))) -((-4383 |has| |#2| (-6 -4383)) (-4385 . T) (-4384 . T) (-4387 . T)) -((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4383))) -(-1278 A) +((-4392 |has| |#2| (-6 -4392)) (-4394 . T) (-4393 . T) (-4396 . T)) +((|HasCategory| |#2| (QUOTE (-171))) (|HasAttribute| |#2| (QUOTE -4392))) +(-1279 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1279 R |ls| |ls2|) +(-1280 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1280 R) +(-1281 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1281 |p|) +(-1282 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4392 "*") . T) (-4384 . T) (-4385 . T) (-4387 . T)) +(((-4401 "*") . T) (-4393 . T) (-4394 . T) (-4396 . T)) NIL NIL NIL @@ -5072,4 +5076,4 @@ NIL NIL NIL NIL -((-3 NIL 2277553 2277558 2277563 2277568) (-2 NIL 2277533 2277538 2277543 2277548) (-1 NIL 2277513 2277518 2277523 2277528) (0 NIL 2277493 2277498 2277503 2277508) (-1281 "ZMOD.spad" 2277302 2277315 2277431 2277488) (-1280 "ZLINDEP.spad" 2276346 2276357 2277292 2277297) (-1279 "ZDSOLVE.spad" 2266195 2266217 2276336 2276341) (-1278 "YSTREAM.spad" 2265688 2265699 2266185 2266190) (-1277 "XRPOLY.spad" 2264908 2264928 2265544 2265613) (-1276 "XPR.spad" 2262699 2262712 2264626 2264725) (-1275 "XPOLY.spad" 2262254 2262265 2262555 2262624) (-1274 "XPOLYC.spad" 2261571 2261587 2262180 2262249) (-1273 "XPBWPOLY.spad" 2260008 2260028 2261351 2261420) (-1272 "XF.spad" 2258469 2258484 2259910 2260003) (-1271 "XF.spad" 2256910 2256927 2258353 2258358) (-1270 "XFALG.spad" 2253934 2253950 2256836 2256905) (-1269 "XEXPPKG.spad" 2253185 2253211 2253924 2253929) (-1268 "XDPOLY.spad" 2252799 2252815 2253041 2253110) (-1267 "XALG.spad" 2252459 2252470 2252755 2252794) (-1266 "WUTSET.spad" 2248298 2248315 2252105 2252132) (-1265 "WP.spad" 2247497 2247541 2248156 2248223) (-1264 "WHILEAST.spad" 2247295 2247304 2247487 2247492) (-1263 "WHEREAST.spad" 2246966 2246975 2247285 2247290) (-1262 "WFFINTBS.spad" 2244529 2244551 2246956 2246961) (-1261 "WEIER.spad" 2242743 2242754 2244519 2244524) (-1260 "VSPACE.spad" 2242416 2242427 2242711 2242738) (-1259 "VSPACE.spad" 2242109 2242122 2242406 2242411) (-1258 "VOID.spad" 2241786 2241795 2242099 2242104) (-1257 "VIEW.spad" 2239408 2239417 2241776 2241781) (-1256 "VIEWDEF.spad" 2234605 2234614 2239398 2239403) (-1255 "VIEW3D.spad" 2218440 2218449 2234595 2234600) (-1254 "VIEW2D.spad" 2206177 2206186 2218430 2218435) (-1253 "VECTOR.spad" 2204852 2204863 2205103 2205130) (-1252 "VECTOR2.spad" 2203479 2203492 2204842 2204847) (-1251 "VECTCAT.spad" 2201379 2201390 2203447 2203474) (-1250 "VECTCAT.spad" 2199087 2199100 2201157 2201162) (-1249 "VARIABLE.spad" 2198867 2198882 2199077 2199082) (-1248 "UTYPE.spad" 2198511 2198520 2198857 2198862) (-1247 "UTSODETL.spad" 2197804 2197828 2198467 2198472) (-1246 "UTSODE.spad" 2195992 2196012 2197794 2197799) (-1245 "UTS.spad" 2190781 2190809 2194459 2194556) (-1244 "UTSCAT.spad" 2188232 2188248 2190679 2190776) (-1243 "UTSCAT.spad" 2185327 2185345 2187776 2187781) (-1242 "UTS2.spad" 2184920 2184955 2185317 2185322) (-1241 "URAGG.spad" 2179552 2179563 2184910 2184915) (-1240 "URAGG.spad" 2174148 2174161 2179508 2179513) (-1239 "UPXSSING.spad" 2171791 2171817 2173229 2173362) (-1238 "UPXS.spad" 2168939 2168967 2169923 2170072) (-1237 "UPXSCONS.spad" 2166696 2166716 2167071 2167220) (-1236 "UPXSCCA.spad" 2165261 2165281 2166542 2166691) (-1235 "UPXSCCA.spad" 2163968 2163990 2165251 2165256) (-1234 "UPXSCAT.spad" 2162549 2162565 2163814 2163963) (-1233 "UPXS2.spad" 2162090 2162143 2162539 2162544) (-1232 "UPSQFREE.spad" 2160502 2160516 2162080 2162085) (-1231 "UPSCAT.spad" 2158095 2158119 2160400 2160497) (-1230 "UPSCAT.spad" 2155394 2155420 2157701 2157706) (-1229 "UPOLYC.spad" 2150372 2150383 2155236 2155389) (-1228 "UPOLYC.spad" 2145242 2145255 2150108 2150113) (-1227 "UPOLYC2.spad" 2144711 2144730 2145232 2145237) (-1226 "UP.spad" 2141868 2141883 2142261 2142414) (-1225 "UPMP.spad" 2140758 2140771 2141858 2141863) (-1224 "UPDIVP.spad" 2140321 2140335 2140748 2140753) (-1223 "UPDECOMP.spad" 2138558 2138572 2140311 2140316) (-1222 "UPCDEN.spad" 2137765 2137781 2138548 2138553) (-1221 "UP2.spad" 2137127 2137148 2137755 2137760) (-1220 "UNISEG.spad" 2136480 2136491 2137046 2137051) (-1219 "UNISEG2.spad" 2135973 2135986 2136436 2136441) (-1218 "UNIFACT.spad" 2135074 2135086 2135963 2135968) (-1217 "ULS.spad" 2125626 2125654 2126719 2127148) (-1216 "ULSCONS.spad" 2118020 2118040 2118392 2118541) (-1215 "ULSCCAT.spad" 2115749 2115769 2117866 2118015) (-1214 "ULSCCAT.spad" 2113586 2113608 2115705 2115710) (-1213 "ULSCAT.spad" 2111802 2111818 2113432 2113581) (-1212 "ULS2.spad" 2111314 2111367 2111792 2111797) (-1211 "UINT32.spad" 2111190 2111199 2111304 2111309) (-1210 "UINT16.spad" 2111066 2111075 2111180 2111185) (-1209 "UFD.spad" 2110131 2110140 2110992 2111061) (-1208 "UFD.spad" 2109258 2109269 2110121 2110126) (-1207 "UDVO.spad" 2108105 2108114 2109248 2109253) (-1206 "UDPO.spad" 2105532 2105543 2108061 2108066) (-1205 "TYPE.spad" 2105464 2105473 2105522 2105527) (-1204 "TYPEAST.spad" 2105383 2105392 2105454 2105459) (-1203 "TWOFACT.spad" 2104033 2104048 2105373 2105378) (-1202 "TUPLE.spad" 2103517 2103528 2103932 2103937) (-1201 "TUBETOOL.spad" 2100354 2100363 2103507 2103512) (-1200 "TUBE.spad" 2098995 2099012 2100344 2100349) (-1199 "TS.spad" 2097584 2097600 2098560 2098657) (-1198 "TSETCAT.spad" 2084711 2084728 2097552 2097579) (-1197 "TSETCAT.spad" 2071824 2071843 2084667 2084672) (-1196 "TRMANIP.spad" 2066190 2066207 2071530 2071535) (-1195 "TRIMAT.spad" 2065149 2065174 2066180 2066185) (-1194 "TRIGMNIP.spad" 2063666 2063683 2065139 2065144) (-1193 "TRIGCAT.spad" 2063178 2063187 2063656 2063661) (-1192 "TRIGCAT.spad" 2062688 2062699 2063168 2063173) (-1191 "TREE.spad" 2061259 2061270 2062295 2062322) (-1190 "TRANFUN.spad" 2061090 2061099 2061249 2061254) (-1189 "TRANFUN.spad" 2060919 2060930 2061080 2061085) (-1188 "TOPSP.spad" 2060593 2060602 2060909 2060914) (-1187 "TOOLSIGN.spad" 2060256 2060267 2060583 2060588) (-1186 "TEXTFILE.spad" 2058813 2058822 2060246 2060251) (-1185 "TEX.spad" 2055945 2055954 2058803 2058808) (-1184 "TEX1.spad" 2055501 2055512 2055935 2055940) (-1183 "TEMUTL.spad" 2055056 2055065 2055491 2055496) (-1182 "TBCMPPK.spad" 2053149 2053172 2055046 2055051) (-1181 "TBAGG.spad" 2052185 2052208 2053129 2053144) (-1180 "TBAGG.spad" 2051229 2051254 2052175 2052180) (-1179 "TANEXP.spad" 2050605 2050616 2051219 2051224) (-1178 "TABLE.spad" 2049016 2049039 2049286 2049313) (-1177 "TABLEAU.spad" 2048497 2048508 2049006 2049011) (-1176 "TABLBUMP.spad" 2045280 2045291 2048487 2048492) (-1175 "SYSTEM.spad" 2044554 2044563 2045270 2045275) (-1174 "SYSSOLP.spad" 2042027 2042038 2044544 2044549) (-1173 "SYSNNI.spad" 2041203 2041214 2042017 2042022) (-1172 "SYSINT.spad" 2040676 2040687 2041193 2041198) (-1171 "SYNTAX.spad" 2036946 2036955 2040666 2040671) (-1170 "SYMTAB.spad" 2035002 2035011 2036936 2036941) (-1169 "SYMS.spad" 2030987 2030996 2034992 2034997) (-1168 "SYMPOLY.spad" 2029994 2030005 2030076 2030203) (-1167 "SYMFUNC.spad" 2029469 2029480 2029984 2029989) (-1166 "SYMBOL.spad" 2026896 2026905 2029459 2029464) (-1165 "SWITCH.spad" 2023653 2023662 2026886 2026891) (-1164 "SUTS.spad" 2020552 2020580 2022120 2022217) (-1163 "SUPXS.spad" 2017687 2017715 2018684 2018833) (-1162 "SUP.spad" 2014456 2014467 2015237 2015390) (-1161 "SUPFRACF.spad" 2013561 2013579 2014446 2014451) (-1160 "SUP2.spad" 2012951 2012964 2013551 2013556) (-1159 "SUMRF.spad" 2011917 2011928 2012941 2012946) (-1158 "SUMFS.spad" 2011550 2011567 2011907 2011912) (-1157 "SULS.spad" 2002089 2002117 2003195 2003624) (-1156 "SUCHTAST.spad" 2001858 2001867 2002079 2002084) (-1155 "SUCH.spad" 2001538 2001553 2001848 2001853) (-1154 "SUBSPACE.spad" 1993545 1993560 2001528 2001533) (-1153 "SUBRESP.spad" 1992705 1992719 1993501 1993506) (-1152 "STTF.spad" 1988804 1988820 1992695 1992700) (-1151 "STTFNC.spad" 1985272 1985288 1988794 1988799) (-1150 "STTAYLOR.spad" 1977670 1977681 1985153 1985158) (-1149 "STRTBL.spad" 1976175 1976192 1976324 1976351) (-1148 "STRING.spad" 1975584 1975593 1975598 1975625) (-1147 "STRICAT.spad" 1975372 1975381 1975552 1975579) (-1146 "STREAM.spad" 1972230 1972241 1974897 1974912) (-1145 "STREAM3.spad" 1971775 1971790 1972220 1972225) (-1144 "STREAM2.spad" 1970843 1970856 1971765 1971770) (-1143 "STREAM1.spad" 1970547 1970558 1970833 1970838) (-1142 "STINPROD.spad" 1969453 1969469 1970537 1970542) (-1141 "STEP.spad" 1968654 1968663 1969443 1969448) (-1140 "STBL.spad" 1967180 1967208 1967347 1967362) (-1139 "STAGG.spad" 1966255 1966266 1967170 1967175) (-1138 "STAGG.spad" 1965328 1965341 1966245 1966250) (-1137 "STACK.spad" 1964679 1964690 1964935 1964962) (-1136 "SREGSET.spad" 1962383 1962400 1964325 1964352) (-1135 "SRDCMPK.spad" 1960928 1960948 1962373 1962378) (-1134 "SRAGG.spad" 1956025 1956034 1960896 1960923) (-1133 "SRAGG.spad" 1951142 1951153 1956015 1956020) (-1132 "SQMATRIX.spad" 1948758 1948776 1949674 1949761) (-1131 "SPLTREE.spad" 1943310 1943323 1948194 1948221) (-1130 "SPLNODE.spad" 1939898 1939911 1943300 1943305) (-1129 "SPFCAT.spad" 1938675 1938684 1939888 1939893) (-1128 "SPECOUT.spad" 1937225 1937234 1938665 1938670) (-1127 "SPADXPT.spad" 1929364 1929373 1937215 1937220) (-1126 "spad-parser.spad" 1928829 1928838 1929354 1929359) (-1125 "SPADAST.spad" 1928530 1928539 1928819 1928824) (-1124 "SPACEC.spad" 1912543 1912554 1928520 1928525) (-1123 "SPACE3.spad" 1912319 1912330 1912533 1912538) (-1122 "SORTPAK.spad" 1911864 1911877 1912275 1912280) (-1121 "SOLVETRA.spad" 1909621 1909632 1911854 1911859) (-1120 "SOLVESER.spad" 1908141 1908152 1909611 1909616) (-1119 "SOLVERAD.spad" 1904151 1904162 1908131 1908136) (-1118 "SOLVEFOR.spad" 1902571 1902589 1904141 1904146) (-1117 "SNTSCAT.spad" 1902171 1902188 1902539 1902566) (-1116 "SMTS.spad" 1900431 1900457 1901736 1901833) (-1115 "SMP.spad" 1897870 1897890 1898260 1898387) (-1114 "SMITH.spad" 1896713 1896738 1897860 1897865) (-1113 "SMATCAT.spad" 1894823 1894853 1896657 1896708) (-1112 "SMATCAT.spad" 1892865 1892897 1894701 1894706) (-1111 "SKAGG.spad" 1891826 1891837 1892833 1892860) (-1110 "SINT.spad" 1890652 1890661 1891692 1891821) (-1109 "SIMPAN.spad" 1890380 1890389 1890642 1890647) (-1108 "SIG.spad" 1889708 1889717 1890370 1890375) (-1107 "SIGNRF.spad" 1888816 1888827 1889698 1889703) (-1106 "SIGNEF.spad" 1888085 1888102 1888806 1888811) (-1105 "SIGAST.spad" 1887466 1887475 1888075 1888080) (-1104 "SHP.spad" 1885384 1885399 1887422 1887427) (-1103 "SHDP.spad" 1875095 1875122 1875604 1875735) (-1102 "SGROUP.spad" 1874703 1874712 1875085 1875090) (-1101 "SGROUP.spad" 1874309 1874320 1874693 1874698) (-1100 "SGCF.spad" 1867190 1867199 1874299 1874304) (-1099 "SFRTCAT.spad" 1866118 1866135 1867158 1867185) (-1098 "SFRGCD.spad" 1865181 1865201 1866108 1866113) (-1097 "SFQCMPK.spad" 1859818 1859838 1865171 1865176) (-1096 "SFORT.spad" 1859253 1859267 1859808 1859813) (-1095 "SEXOF.spad" 1859096 1859136 1859243 1859248) (-1094 "SEX.spad" 1858988 1858997 1859086 1859091) (-1093 "SEXCAT.spad" 1856539 1856579 1858978 1858983) (-1092 "SET.spad" 1854839 1854850 1855960 1855999) (-1091 "SETMN.spad" 1853273 1853290 1854829 1854834) (-1090 "SETCAT.spad" 1852758 1852767 1853263 1853268) (-1089 "SETCAT.spad" 1852241 1852252 1852748 1852753) (-1088 "SETAGG.spad" 1848762 1848773 1852221 1852236) (-1087 "SETAGG.spad" 1845291 1845304 1848752 1848757) (-1086 "SEQAST.spad" 1844994 1845003 1845281 1845286) (-1085 "SEGXCAT.spad" 1844116 1844129 1844984 1844989) (-1084 "SEG.spad" 1843929 1843940 1844035 1844040) (-1083 "SEGCAT.spad" 1842836 1842847 1843919 1843924) (-1082 "SEGBIND.spad" 1841908 1841919 1842791 1842796) (-1081 "SEGBIND2.spad" 1841604 1841617 1841898 1841903) (-1080 "SEGAST.spad" 1841318 1841327 1841594 1841599) (-1079 "SEG2.spad" 1840743 1840756 1841274 1841279) (-1078 "SDVAR.spad" 1840019 1840030 1840733 1840738) (-1077 "SDPOL.spad" 1837409 1837420 1837700 1837827) (-1076 "SCPKG.spad" 1835488 1835499 1837399 1837404) (-1075 "SCOPE.spad" 1834633 1834642 1835478 1835483) (-1074 "SCACHE.spad" 1833315 1833326 1834623 1834628) (-1073 "SASTCAT.spad" 1833224 1833233 1833305 1833310) (-1072 "SAOS.spad" 1833096 1833105 1833214 1833219) (-1071 "SAERFFC.spad" 1832809 1832829 1833086 1833091) (-1070 "SAE.spad" 1830984 1831000 1831595 1831730) (-1069 "SAEFACT.spad" 1830685 1830705 1830974 1830979) (-1068 "RURPK.spad" 1828326 1828342 1830675 1830680) (-1067 "RULESET.spad" 1827767 1827791 1828316 1828321) (-1066 "RULE.spad" 1825971 1825995 1827757 1827762) (-1065 "RULECOLD.spad" 1825823 1825836 1825961 1825966) (-1064 "RSTRCAST.spad" 1825540 1825549 1825813 1825818) (-1063 "RSETGCD.spad" 1821918 1821938 1825530 1825535) (-1062 "RSETCAT.spad" 1811702 1811719 1821886 1821913) (-1061 "RSETCAT.spad" 1801506 1801525 1811692 1811697) (-1060 "RSDCMPK.spad" 1799958 1799978 1801496 1801501) (-1059 "RRCC.spad" 1798342 1798372 1799948 1799953) (-1058 "RRCC.spad" 1796724 1796756 1798332 1798337) (-1057 "RPTAST.spad" 1796426 1796435 1796714 1796719) (-1056 "RPOLCAT.spad" 1775786 1775801 1796294 1796421) (-1055 "RPOLCAT.spad" 1754860 1754877 1775370 1775375) (-1054 "ROUTINE.spad" 1750723 1750732 1753507 1753534) (-1053 "ROMAN.spad" 1750051 1750060 1750589 1750718) (-1052 "ROIRC.spad" 1749131 1749163 1750041 1750046) (-1051 "RNS.spad" 1748034 1748043 1749033 1749126) (-1050 "RNS.spad" 1747023 1747034 1748024 1748029) (-1049 "RNG.spad" 1746758 1746767 1747013 1747018) (-1048 "RMODULE.spad" 1746396 1746407 1746748 1746753) (-1047 "RMCAT2.spad" 1745804 1745861 1746386 1746391) (-1046 "RMATRIX.spad" 1744628 1744647 1744971 1745010) (-1045 "RMATCAT.spad" 1740161 1740192 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488733 488760) (-325 "FAMR.spad" 485816 485828 487594 487691) (-324 "FAMR.spad" 483920 483934 485700 485705) (-323 "FAMONOID.spad" 483570 483580 483874 483879) (-322 "FAMONC.spad" 481792 481804 483560 483565) (-321 "FAGROUP.spad" 481398 481408 481688 481715) (-320 "FACUTIL.spad" 479594 479611 481388 481393) (-319 "FACTFUNC.spad" 478770 478780 479584 479589) (-318 "EXPUPXS.spad" 475603 475626 476902 477051) (-317 "EXPRTUBE.spad" 472831 472839 475593 475598) (-316 "EXPRODE.spad" 469703 469719 472821 472826) (-315 "EXPR.spad" 464978 464988 465692 466099) (-314 "EXPR2UPS.spad" 461070 461083 464968 464973) (-313 "EXPR2.spad" 460773 460785 461060 461065) (-312 "EXPEXPAN.spad" 457711 457736 458345 458438) (-311 "EXIT.spad" 457382 457390 457701 457706) (-310 "EXITAST.spad" 457118 457126 457372 457377) (-309 "EVALCYC.spad" 456576 456590 457108 457113) (-308 "EVALAB.spad" 456140 456150 456566 456571) (-307 "EVALAB.spad" 455702 455714 456130 456135) (-306 "EUCDOM.spad" 453244 453252 455628 455697) (-305 "EUCDOM.spad" 450848 450858 453234 453239) (-304 "ESTOOLS.spad" 442688 442696 450838 450843) (-303 "ESTOOLS2.spad" 442289 442303 442678 442683) (-302 "ESTOOLS1.spad" 441974 441985 442279 442284) (-301 "ES.spad" 434521 434529 441964 441969) (-300 "ES.spad" 426974 426984 434419 434424) (-299 "ESCONT.spad" 423747 423755 426964 426969) (-298 "ESCONT1.spad" 423496 423508 423737 423742) (-297 "ES2.spad" 422991 423007 423486 423491) (-296 "ES1.spad" 422557 422573 422981 422986) (-295 "ERROR.spad" 419878 419886 422547 422552) (-294 "EQTBL.spad" 418350 418372 418559 418586) (-293 "EQ.spad" 413224 413234 416023 416135) (-292 "EQ2.spad" 412940 412952 413214 413219) (-291 "EP.spad" 409254 409264 412930 412935) (-290 "ENV.spad" 407956 407964 409244 409249) (-289 "ENTIRER.spad" 407624 407632 407900 407951) (-288 "EMR.spad" 406825 406866 407550 407619) (-287 "ELTAGG.spad" 405065 405084 406815 406820) (-286 "ELTAGG.spad" 403269 403290 405021 405026) (-285 "ELTAB.spad" 402716 402734 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296544 297138 297165) (-243 "DLAGG.spad" 294945 294955 296524 296529) (-242 "DIVRING.spad" 294487 294495 294889 294940) (-241 "DIVRING.spad" 294073 294083 294477 294482) (-240 "DISPLAY.spad" 292253 292261 294063 294068) (-239 "DIRPROD.spad" 281833 281849 282473 282604) (-238 "DIRPROD2.spad" 280641 280659 281823 281828) (-237 "DIRPCAT.spad" 279583 279599 280505 280636) (-236 "DIRPCAT.spad" 278254 278272 279178 279183) (-235 "DIOSP.spad" 277079 277087 278244 278249) (-234 "DIOPS.spad" 276063 276073 277059 277074) (-233 "DIOPS.spad" 275021 275033 276019 276024) (-232 "DIFRING.spad" 274313 274321 275001 275016) (-231 "DIFRING.spad" 273613 273623 274303 274308) (-230 "DIFEXT.spad" 272772 272782 273593 273608) (-229 "DIFEXT.spad" 271848 271860 272671 272676) (-228 "DIAGG.spad" 271478 271488 271828 271843) (-227 "DIAGG.spad" 271116 271128 271468 271473) (-226 "DHMATRIX.spad" 269420 269430 270573 270600) (-225 "DFSFUN.spad" 262828 262836 269410 269415) (-224 "DFLOAT.spad" 259549 259557 262718 262823) (-223 "DFINTTLS.spad" 257758 257774 259539 259544) (-222 "DERHAM.spad" 255668 255700 257738 257753) (-221 "DEQUEUE.spad" 254986 254996 255275 255302) (-220 "DEGRED.spad" 254601 254615 254976 254981) (-219 "DEFINTRF.spad" 252126 252136 254591 254596) (-218 "DEFINTEF.spad" 250622 250638 252116 252121) (-217 "DEFAST.spad" 249990 249998 250612 250617) (-216 "DECIMAL.spad" 248096 248104 248457 248550) (-215 "DDFACT.spad" 245895 245912 248086 248091) (-214 "DBLRESP.spad" 245493 245517 245885 245890) (-213 "DBASE.spad" 244147 244157 245483 245488) (-212 "DATAARY.spad" 243609 243622 244137 244142) (-211 "D03FAFA.spad" 243437 243445 243599 243604) (-210 "D03EEFA.spad" 243257 243265 243427 243432) (-209 "D03AGNT.spad" 242337 242345 243247 243252) (-208 "D02EJFA.spad" 241799 241807 242327 242332) (-207 "D02CJFA.spad" 241277 241285 241789 241794) (-206 "D02BHFA.spad" 240767 240775 241267 241272) (-205 "D02BBFA.spad" 240257 240265 240757 240762) (-204 "D02AGNT.spad" 235061 235069 240247 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218134) (-183 "CTORCAT.spad" 217047 217057 217584 217589) (-182 "CTORCALL.spad" 216627 216635 217037 217042) (-181 "CSTTOOLS.spad" 215870 215883 216617 216622) (-180 "CRFP.spad" 209574 209587 215860 215865) (-179 "CRCEAST.spad" 209294 209302 209564 209569) (-178 "CRAPACK.spad" 208337 208347 209284 209289) (-177 "CPMATCH.spad" 207837 207852 208262 208267) (-176 "CPIMA.spad" 207542 207561 207827 207832) (-175 "COORDSYS.spad" 202435 202445 207532 207537) (-174 "CONTOUR.spad" 201837 201845 202425 202430) (-173 "CONTFRAC.spad" 197449 197459 201739 201832) (-172 "CONDUIT.spad" 197207 197215 197439 197444) (-171 "COMRING.spad" 196881 196889 197145 197202) (-170 "COMPPROP.spad" 196395 196403 196871 196876) (-169 "COMPLPAT.spad" 196162 196177 196385 196390) (-168 "COMPLEX.spad" 190198 190208 190442 190691) (-167 "COMPLEX2.spad" 189911 189923 190188 190193) (-166 "COMPFACT.spad" 189513 189527 189901 189906) (-165 "COMPCAT.spad" 187651 187661 189259 189508) (-164 "COMPCAT.spad" 185470 185482 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(-143 "CHAR.spad" 159232 159240 161354 161359) (-142 "CFCAT.spad" 158548 158556 159222 159227) (-141 "CDEN.spad" 157706 157720 158538 158543) (-140 "CCLASS.spad" 155855 155863 157117 157156) (-139 "CATEGORY.spad" 154945 154953 155845 155850) (-138 "CATCTOR.spad" 154836 154844 154935 154940) (-137 "CATAST.spad" 154463 154471 154826 154831) (-136 "CASEAST.spad" 154177 154185 154453 154458) (-135 "CARTEN.spad" 149280 149304 154167 154172) (-134 "CARTEN2.spad" 148666 148693 149270 149275) (-133 "CARD.spad" 145955 145963 148640 148661) (-132 "CAPSLAST.spad" 145729 145737 145945 145950) (-131 "CACHSET.spad" 145351 145359 145719 145724) (-130 "CABMON.spad" 144904 144912 145341 145346) (-129 "BYTE.spad" 144325 144333 144894 144899) (-128 "BYTEBUF.spad" 142157 142165 143494 143521) (-127 "BTREE.spad" 141226 141236 141764 141791) (-126 "BTOURN.spad" 140229 140239 140833 140860) (-125 "BTCAT.spad" 139617 139627 140197 140224) (-124 "BTCAT.spad" 139025 139037 139607 139612) (-123 "BTAGG.spad" 138147 138155 138993 139020) (-122 "BTAGG.spad" 137289 137299 138137 138142) (-121 "BSTREE.spad" 136024 136034 136896 136923) (-120 "BRILL.spad" 134219 134230 136014 136019) (-119 "BRAGG.spad" 133143 133153 134209 134214) (-118 "BRAGG.spad" 132031 132043 133099 133104) (-117 "BPADICRT.spad" 130012 130024 130267 130360) (-116 "BPADIC.spad" 129676 129688 129938 130007) (-115 "BOUNDZRO.spad" 129332 129349 129666 129671) (-114 "BOP.spad" 124796 124804 129322 129327) (-113 "BOP1.spad" 122182 122192 124752 124757) (-112 "BOOLEAN.spad" 121506 121514 122172 122177) (-111 "BMODULE.spad" 121218 121230 121474 121501) (-110 "BITS.spad" 120637 120645 120854 120881) (-109 "BINDING.spad" 120056 120064 120627 120632) (-108 "BINARY.spad" 118167 118175 118523 118616) (-107 "BGAGG.spad" 117364 117374 118147 118162) (-106 "BGAGG.spad" 116569 116581 117354 117359) (-105 "BFUNCT.spad" 116133 116141 116549 116564) (-104 "BEZOUT.spad" 115267 115294 116083 116088) (-103 "BBTREE.spad" 112086 112096 114874 114901) (-102 "BASTYPE.spad" 111758 111766 112076 112081) (-101 "BASTYPE.spad" 111428 111438 111748 111753) (-100 "BALFACT.spad" 110867 110880 111418 111423) (-99 "AUTOMOR.spad" 110314 110323 110847 110862) (-98 "ATTREG.spad" 107033 107040 110066 110309) (-97 "ATTRBUT.spad" 103056 103063 107013 107028) (-96 "ATTRAST.spad" 102773 102780 103046 103051) (-95 "ATRIG.spad" 102243 102250 102763 102768) (-94 "ATRIG.spad" 101711 101720 102233 102238) (-93 "ASTCAT.spad" 101615 101622 101701 101706) (-92 "ASTCAT.spad" 101517 101526 101605 101610) (-91 "ASTACK.spad" 100850 100859 101124 101151) (-90 "ASSOCEQ.spad" 99650 99661 100806 100811) (-89 "ASP9.spad" 98731 98744 99640 99645) (-88 "ASP8.spad" 97774 97787 98721 98726) (-87 "ASP80.spad" 97096 97109 97764 97769) (-86 "ASP7.spad" 96256 96269 97086 97091) (-85 "ASP78.spad" 95707 95720 96246 96251) (-84 "ASP77.spad" 95076 95089 95697 95702) (-83 "ASP74.spad" 94168 94181 95066 95071) (-82 "ASP73.spad" 93439 93452 94158 94163) (-81 "ASP6.spad" 92306 92319 93429 93434) (-80 "ASP55.spad" 90815 90828 92296 92301) (-79 "ASP50.spad" 88632 88645 90805 90810) (-78 "ASP4.spad" 87927 87940 88622 88627) (-77 "ASP49.spad" 86926 86939 87917 87922) (-76 "ASP42.spad" 85333 85372 86916 86921) (-75 "ASP41.spad" 83912 83951 85323 85328) (-74 "ASP35.spad" 82900 82913 83902 83907) (-73 "ASP34.spad" 82201 82214 82890 82895) (-72 "ASP33.spad" 81761 81774 82191 82196) (-71 "ASP31.spad" 80901 80914 81751 81756) (-70 "ASP30.spad" 79793 79806 80891 80896) (-69 "ASP29.spad" 79259 79272 79783 79788) (-68 "ASP28.spad" 70532 70545 79249 79254) (-67 "ASP27.spad" 69429 69442 70522 70527) (-66 "ASP24.spad" 68516 68529 69419 69424) (-65 "ASP20.spad" 67980 67993 68506 68511) (-64 "ASP1.spad" 67361 67374 67970 67975) (-63 "ASP19.spad" 62047 62060 67351 67356) (-62 "ASP12.spad" 61461 61474 62037 62042) (-61 "ASP10.spad" 60732 60745 61451 61456) (-60 "ARRAY2.spad" 60092 60101 60339 60366) (-59 "ARRAY1.spad" 58927 58936 59275 59302) (-58 "ARRAY12.spad" 57596 57607 58917 58922) (-57 "ARR2CAT.spad" 53258 53279 57564 57591) (-56 "ARR2CAT.spad" 48940 48963 53248 53253) (-55 "ARITY.spad" 48508 48515 48930 48935) (-54 "APPRULE.spad" 47752 47774 48498 48503) (-53 "APPLYORE.spad" 47367 47380 47742 47747) (-52 "ANY.spad" 45709 45716 47357 47362) (-51 "ANY1.spad" 44780 44789 45699 45704) (-50 "ANTISYM.spad" 43219 43235 44760 44775) (-49 "ANON.spad" 42916 42923 43209 43214) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2280948 2280953 2280958 2280963) (-2 NIL 2280928 2280933 2280938 2280943) (-1 NIL 2280908 2280913 2280918 2280923) (0 NIL 2280888 2280893 2280898 2280903) (-1282 "ZMOD.spad" 2280697 2280710 2280826 2280883) (-1281 "ZLINDEP.spad" 2279741 2279752 2280687 2280692) (-1280 "ZDSOLVE.spad" 2269590 2269612 2279731 2279736) (-1279 "YSTREAM.spad" 2269083 2269094 2269580 2269585) (-1278 "XRPOLY.spad" 2268303 2268323 2268939 2269008) (-1277 "XPR.spad" 2266094 2266107 2268021 2268120) (-1276 "XPOLY.spad" 2265649 2265660 2265950 2266019) (-1275 "XPOLYC.spad" 2264966 2264982 2265575 2265644) (-1274 "XPBWPOLY.spad" 2263403 2263423 2264746 2264815) (-1273 "XF.spad" 2261864 2261879 2263305 2263398) (-1272 "XF.spad" 2260305 2260322 2261748 2261753) (-1271 "XFALG.spad" 2257329 2257345 2260231 2260300) (-1270 "XEXPPKG.spad" 2256580 2256606 2257319 2257324) (-1269 "XDPOLY.spad" 2256194 2256210 2256436 2256505) (-1268 "XALG.spad" 2255854 2255865 2256150 2256189) (-1267 "WUTSET.spad" 2251693 2251710 2255500 2255527) (-1266 "WP.spad" 2250892 2250936 2251551 2251618) (-1265 "WHILEAST.spad" 2250690 2250699 2250882 2250887) (-1264 "WHEREAST.spad" 2250361 2250370 2250680 2250685) (-1263 "WFFINTBS.spad" 2247924 2247946 2250351 2250356) (-1262 "WEIER.spad" 2246138 2246149 2247914 2247919) (-1261 "VSPACE.spad" 2245811 2245822 2246106 2246133) (-1260 "VSPACE.spad" 2245504 2245517 2245801 2245806) (-1259 "VOID.spad" 2245181 2245190 2245494 2245499) (-1258 "VIEW.spad" 2242803 2242812 2245171 2245176) (-1257 "VIEWDEF.spad" 2238000 2238009 2242793 2242798) (-1256 "VIEW3D.spad" 2221835 2221844 2237990 2237995) (-1255 "VIEW2D.spad" 2209572 2209581 2221825 2221830) (-1254 "VECTOR.spad" 2208247 2208258 2208498 2208525) (-1253 "VECTOR2.spad" 2206874 2206887 2208237 2208242) (-1252 "VECTCAT.spad" 2204774 2204785 2206842 2206869) (-1251 "VECTCAT.spad" 2202482 2202495 2204552 2204557) (-1250 "VARIABLE.spad" 2202262 2202277 2202472 2202477) (-1249 "UTYPE.spad" 2201906 2201915 2202252 2202257) (-1248 "UTSODETL.spad" 2201199 2201223 2201862 2201867) (-1247 "UTSODE.spad" 2199387 2199407 2201189 2201194) (-1246 "UTS.spad" 2194176 2194204 2197854 2197951) (-1245 "UTSCAT.spad" 2191627 2191643 2194074 2194171) (-1244 "UTSCAT.spad" 2188722 2188740 2191171 2191176) (-1243 "UTS2.spad" 2188315 2188350 2188712 2188717) (-1242 "URAGG.spad" 2182947 2182958 2188305 2188310) (-1241 "URAGG.spad" 2177543 2177556 2182903 2182908) (-1240 "UPXSSING.spad" 2175186 2175212 2176624 2176757) (-1239 "UPXS.spad" 2172334 2172362 2173318 2173467) (-1238 "UPXSCONS.spad" 2170091 2170111 2170466 2170615) (-1237 "UPXSCCA.spad" 2168656 2168676 2169937 2170086) (-1236 "UPXSCCA.spad" 2167363 2167385 2168646 2168651) (-1235 "UPXSCAT.spad" 2165944 2165960 2167209 2167358) (-1234 "UPXS2.spad" 2165485 2165538 2165934 2165939) (-1233 "UPSQFREE.spad" 2163897 2163911 2165475 2165480) (-1232 "UPSCAT.spad" 2161490 2161514 2163795 2163892) (-1231 "UPSCAT.spad" 2158789 2158815 2161096 2161101) (-1230 "UPOLYC.spad" 2153767 2153778 2158631 2158784) (-1229 "UPOLYC.spad" 2148637 2148650 2153503 2153508) (-1228 "UPOLYC2.spad" 2148106 2148125 2148627 2148632) (-1227 "UP.spad" 2145263 2145278 2145656 2145809) (-1226 "UPMP.spad" 2144153 2144166 2145253 2145258) (-1225 "UPDIVP.spad" 2143716 2143730 2144143 2144148) (-1224 "UPDECOMP.spad" 2141953 2141967 2143706 2143711) (-1223 "UPCDEN.spad" 2141160 2141176 2141943 2141948) (-1222 "UP2.spad" 2140522 2140543 2141150 2141155) (-1221 "UNISEG.spad" 2139875 2139886 2140441 2140446) (-1220 "UNISEG2.spad" 2139368 2139381 2139831 2139836) (-1219 "UNIFACT.spad" 2138469 2138481 2139358 2139363) (-1218 "ULS.spad" 2129021 2129049 2130114 2130543) (-1217 "ULSCONS.spad" 2121415 2121435 2121787 2121936) (-1216 "ULSCCAT.spad" 2119144 2119164 2121261 2121410) (-1215 "ULSCCAT.spad" 2116981 2117003 2119100 2119105) (-1214 "ULSCAT.spad" 2115197 2115213 2116827 2116976) (-1213 "ULS2.spad" 2114709 2114762 2115187 2115192) (-1212 "UINT8.spad" 2114586 2114595 2114699 2114704) (-1211 "UINT32.spad" 2114462 2114471 2114576 2114581) (-1210 "UINT16.spad" 2114338 2114347 2114452 2114457) (-1209 "UFD.spad" 2113403 2113412 2114264 2114333) (-1208 "UFD.spad" 2112530 2112541 2113393 2113398) (-1207 "UDVO.spad" 2111377 2111386 2112520 2112525) (-1206 "UDPO.spad" 2108804 2108815 2111333 2111338) (-1205 "TYPE.spad" 2108736 2108745 2108794 2108799) (-1204 "TYPEAST.spad" 2108655 2108664 2108726 2108731) (-1203 "TWOFACT.spad" 2107305 2107320 2108645 2108650) (-1202 "TUPLE.spad" 2106789 2106800 2107204 2107209) (-1201 "TUBETOOL.spad" 2103626 2103635 2106779 2106784) (-1200 "TUBE.spad" 2102267 2102284 2103616 2103621) (-1199 "TS.spad" 2100856 2100872 2101832 2101929) (-1198 "TSETCAT.spad" 2087983 2088000 2100824 2100851) (-1197 "TSETCAT.spad" 2075096 2075115 2087939 2087944) (-1196 "TRMANIP.spad" 2069462 2069479 2074802 2074807) (-1195 "TRIMAT.spad" 2068421 2068446 2069452 2069457) (-1194 "TRIGMNIP.spad" 2066938 2066955 2068411 2068416) (-1193 "TRIGCAT.spad" 2066450 2066459 2066928 2066933) (-1192 "TRIGCAT.spad" 2065960 2065971 2066440 2066445) (-1191 "TREE.spad" 2064531 2064542 2065567 2065594) (-1190 "TRANFUN.spad" 2064362 2064371 2064521 2064526) (-1189 "TRANFUN.spad" 2064191 2064202 2064352 2064357) (-1188 "TOPSP.spad" 2063865 2063874 2064181 2064186) (-1187 "TOOLSIGN.spad" 2063528 2063539 2063855 2063860) (-1186 "TEXTFILE.spad" 2062085 2062094 2063518 2063523) (-1185 "TEX.spad" 2059217 2059226 2062075 2062080) (-1184 "TEX1.spad" 2058773 2058784 2059207 2059212) (-1183 "TEMUTL.spad" 2058328 2058337 2058763 2058768) (-1182 "TBCMPPK.spad" 2056421 2056444 2058318 2058323) (-1181 "TBAGG.spad" 2055457 2055480 2056401 2056416) (-1180 "TBAGG.spad" 2054501 2054526 2055447 2055452) (-1179 "TANEXP.spad" 2053877 2053888 2054491 2054496) (-1178 "TABLE.spad" 2052288 2052311 2052558 2052585) (-1177 "TABLEAU.spad" 2051769 2051780 2052278 2052283) (-1176 "TABLBUMP.spad" 2048552 2048563 2051759 2051764) (-1175 "SYSTEM.spad" 2047826 2047835 2048542 2048547) (-1174 "SYSSOLP.spad" 2045299 2045310 2047816 2047821) (-1173 "SYSNNI.spad" 2044475 2044486 2045289 2045294) (-1172 "SYSINT.spad" 2043948 2043959 2044465 2044470) (-1171 "SYNTAX.spad" 2040218 2040227 2043938 2043943) (-1170 "SYMTAB.spad" 2038274 2038283 2040208 2040213) (-1169 "SYMS.spad" 2034259 2034268 2038264 2038269) (-1168 "SYMPOLY.spad" 2033266 2033277 2033348 2033475) (-1167 "SYMFUNC.spad" 2032741 2032752 2033256 2033261) (-1166 "SYMBOL.spad" 2030168 2030177 2032731 2032736) (-1165 "SWITCH.spad" 2026925 2026934 2030158 2030163) (-1164 "SUTS.spad" 2023824 2023852 2025392 2025489) (-1163 "SUPXS.spad" 2020959 2020987 2021956 2022105) (-1162 "SUP.spad" 2017728 2017739 2018509 2018662) (-1161 "SUPFRACF.spad" 2016833 2016851 2017718 2017723) (-1160 "SUP2.spad" 2016223 2016236 2016823 2016828) (-1159 "SUMRF.spad" 2015189 2015200 2016213 2016218) (-1158 "SUMFS.spad" 2014822 2014839 2015179 2015184) (-1157 "SULS.spad" 2005361 2005389 2006467 2006896) (-1156 "SUCHTAST.spad" 2005130 2005139 2005351 2005356) (-1155 "SUCH.spad" 2004810 2004825 2005120 2005125) (-1154 "SUBSPACE.spad" 1996817 1996832 2004800 2004805) (-1153 "SUBRESP.spad" 1995977 1995991 1996773 1996778) (-1152 "STTF.spad" 1992076 1992092 1995967 1995972) (-1151 "STTFNC.spad" 1988544 1988560 1992066 1992071) (-1150 "STTAYLOR.spad" 1980942 1980953 1988425 1988430) (-1149 "STRTBL.spad" 1979447 1979464 1979596 1979623) (-1148 "STRING.spad" 1978856 1978865 1978870 1978897) (-1147 "STRICAT.spad" 1978644 1978653 1978824 1978851) (-1146 "STREAM.spad" 1975502 1975513 1978169 1978184) (-1145 "STREAM3.spad" 1975047 1975062 1975492 1975497) (-1144 "STREAM2.spad" 1974115 1974128 1975037 1975042) (-1143 "STREAM1.spad" 1973819 1973830 1974105 1974110) (-1142 "STINPROD.spad" 1972725 1972741 1973809 1973814) (-1141 "STEP.spad" 1971926 1971935 1972715 1972720) (-1140 "STBL.spad" 1970452 1970480 1970619 1970634) (-1139 "STAGG.spad" 1969527 1969538 1970442 1970447) (-1138 "STAGG.spad" 1968600 1968613 1969517 1969522) (-1137 "STACK.spad" 1967951 1967962 1968207 1968234) (-1136 "SREGSET.spad" 1965655 1965672 1967597 1967624) (-1135 "SRDCMPK.spad" 1964200 1964220 1965645 1965650) (-1134 "SRAGG.spad" 1959297 1959306 1964168 1964195) (-1133 "SRAGG.spad" 1954414 1954425 1959287 1959292) (-1132 "SQMATRIX.spad" 1952030 1952048 1952946 1953033) (-1131 "SPLTREE.spad" 1946582 1946595 1951466 1951493) (-1130 "SPLNODE.spad" 1943170 1943183 1946572 1946577) (-1129 "SPFCAT.spad" 1941947 1941956 1943160 1943165) (-1128 "SPECOUT.spad" 1940497 1940506 1941937 1941942) (-1127 "SPADXPT.spad" 1932636 1932645 1940487 1940492) (-1126 "spad-parser.spad" 1932101 1932110 1932626 1932631) (-1125 "SPADAST.spad" 1931802 1931811 1932091 1932096) (-1124 "SPACEC.spad" 1915815 1915826 1931792 1931797) (-1123 "SPACE3.spad" 1915591 1915602 1915805 1915810) (-1122 "SORTPAK.spad" 1915136 1915149 1915547 1915552) (-1121 "SOLVETRA.spad" 1912893 1912904 1915126 1915131) (-1120 "SOLVESER.spad" 1911413 1911424 1912883 1912888) (-1119 "SOLVERAD.spad" 1907423 1907434 1911403 1911408) (-1118 "SOLVEFOR.spad" 1905843 1905861 1907413 1907418) (-1117 "SNTSCAT.spad" 1905443 1905460 1905811 1905838) (-1116 "SMTS.spad" 1903703 1903729 1905008 1905105) (-1115 "SMP.spad" 1901142 1901162 1901532 1901659) (-1114 "SMITH.spad" 1899985 1900010 1901132 1901137) (-1113 "SMATCAT.spad" 1898095 1898125 1899929 1899980) (-1112 "SMATCAT.spad" 1896137 1896169 1897973 1897978) (-1111 "SKAGG.spad" 1895098 1895109 1896105 1896132) (-1110 "SINT.spad" 1893924 1893933 1894964 1895093) (-1109 "SIMPAN.spad" 1893652 1893661 1893914 1893919) (-1108 "SIG.spad" 1892980 1892989 1893642 1893647) (-1107 "SIGNRF.spad" 1892088 1892099 1892970 1892975) (-1106 "SIGNEF.spad" 1891357 1891374 1892078 1892083) (-1105 "SIGAST.spad" 1890738 1890747 1891347 1891352) (-1104 "SHP.spad" 1888656 1888671 1890694 1890699) (-1103 "SHDP.spad" 1878367 1878394 1878876 1879007) (-1102 "SGROUP.spad" 1877975 1877984 1878357 1878362) (-1101 "SGROUP.spad" 1877581 1877592 1877965 1877970) (-1100 "SGCF.spad" 1870462 1870471 1877571 1877576) (-1099 "SFRTCAT.spad" 1869390 1869407 1870430 1870457) (-1098 "SFRGCD.spad" 1868453 1868473 1869380 1869385) (-1097 "SFQCMPK.spad" 1863090 1863110 1868443 1868448) (-1096 "SFORT.spad" 1862525 1862539 1863080 1863085) (-1095 "SEXOF.spad" 1862368 1862408 1862515 1862520) (-1094 "SEX.spad" 1862260 1862269 1862358 1862363) (-1093 "SEXCAT.spad" 1859811 1859851 1862250 1862255) (-1092 "SET.spad" 1858111 1858122 1859232 1859271) (-1091 "SETMN.spad" 1856545 1856562 1858101 1858106) (-1090 "SETCAT.spad" 1856030 1856039 1856535 1856540) (-1089 "SETCAT.spad" 1855513 1855524 1856020 1856025) (-1088 "SETAGG.spad" 1852034 1852045 1855493 1855508) (-1087 "SETAGG.spad" 1848563 1848576 1852024 1852029) (-1086 "SEQAST.spad" 1848266 1848275 1848553 1848558) (-1085 "SEGXCAT.spad" 1847388 1847401 1848256 1848261) (-1084 "SEG.spad" 1847201 1847212 1847307 1847312) (-1083 "SEGCAT.spad" 1846108 1846119 1847191 1847196) (-1082 "SEGBIND.spad" 1845180 1845191 1846063 1846068) (-1081 "SEGBIND2.spad" 1844876 1844889 1845170 1845175) (-1080 "SEGAST.spad" 1844590 1844599 1844866 1844871) (-1079 "SEG2.spad" 1844015 1844028 1844546 1844551) (-1078 "SDVAR.spad" 1843291 1843302 1844005 1844010) (-1077 "SDPOL.spad" 1840681 1840692 1840972 1841099) (-1076 "SCPKG.spad" 1838760 1838771 1840671 1840676) (-1075 "SCOPE.spad" 1837905 1837914 1838750 1838755) (-1074 "SCACHE.spad" 1836587 1836598 1837895 1837900) (-1073 "SASTCAT.spad" 1836496 1836505 1836577 1836582) (-1072 "SAOS.spad" 1836368 1836377 1836486 1836491) (-1071 "SAERFFC.spad" 1836081 1836101 1836358 1836363) (-1070 "SAE.spad" 1834256 1834272 1834867 1835002) (-1069 "SAEFACT.spad" 1833957 1833977 1834246 1834251) (-1068 "RURPK.spad" 1831598 1831614 1833947 1833952) (-1067 "RULESET.spad" 1831039 1831063 1831588 1831593) (-1066 "RULE.spad" 1829243 1829267 1831029 1831034) (-1065 "RULECOLD.spad" 1829095 1829108 1829233 1829238) (-1064 "RSTRCAST.spad" 1828812 1828821 1829085 1829090) (-1063 "RSETGCD.spad" 1825190 1825210 1828802 1828807) (-1062 "RSETCAT.spad" 1814974 1814991 1825158 1825185) (-1061 "RSETCAT.spad" 1804778 1804797 1814964 1814969) (-1060 "RSDCMPK.spad" 1803230 1803250 1804768 1804773) (-1059 "RRCC.spad" 1801614 1801644 1803220 1803225) (-1058 "RRCC.spad" 1799996 1800028 1801604 1801609) (-1057 "RPTAST.spad" 1799698 1799707 1799986 1799991) (-1056 "RPOLCAT.spad" 1779058 1779073 1799566 1799693) (-1055 "RPOLCAT.spad" 1758132 1758149 1778642 1778647) (-1054 "ROUTINE.spad" 1753995 1754004 1756779 1756806) (-1053 "ROMAN.spad" 1753323 1753332 1753861 1753990) (-1052 "ROIRC.spad" 1752403 1752435 1753313 1753318) (-1051 "RNS.spad" 1751306 1751315 1752305 1752398) (-1050 "RNS.spad" 1750295 1750306 1751296 1751301) (-1049 "RNG.spad" 1750030 1750039 1750285 1750290) (-1048 "RMODULE.spad" 1749668 1749679 1750020 1750025) (-1047 "RMCAT2.spad" 1749076 1749133 1749658 1749663) (-1046 "RMATRIX.spad" 1747900 1747919 1748243 1748282) (-1045 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1726302 1726846 1726903) (-1026 "RESLATC.spad" 1725579 1725590 1726245 1726250) (-1025 "REPSQ.spad" 1725308 1725319 1725569 1725574) (-1024 "REP.spad" 1722860 1722869 1725298 1725303) (-1023 "REPDB.spad" 1722565 1722576 1722850 1722855) (-1022 "REP2.spad" 1712137 1712148 1722407 1722412) (-1021 "REP1.spad" 1706127 1706138 1712087 1712092) (-1020 "REGSET.spad" 1703924 1703941 1705773 1705800) (-1019 "REF.spad" 1703253 1703264 1703879 1703884) (-1018 "REDORDER.spad" 1702429 1702446 1703243 1703248) (-1017 "RECLOS.spad" 1701212 1701232 1701916 1702009) (-1016 "REALSOLV.spad" 1700344 1700353 1701202 1701207) (-1015 "REAL.spad" 1700216 1700225 1700334 1700339) (-1014 "REAL0Q.spad" 1697498 1697513 1700206 1700211) (-1013 "REAL0.spad" 1694326 1694341 1697488 1697493) (-1012 "RDUCEAST.spad" 1694047 1694056 1694316 1694321) (-1011 "RDIV.spad" 1693698 1693723 1694037 1694042) (-1010 "RDIST.spad" 1693261 1693272 1693688 1693693) (-1009 "RDETRS.spad" 1692057 1692075 1693251 1693256) (-1008 "RDETR.spad" 1690164 1690182 1692047 1692052) (-1007 "RDEEFS.spad" 1689237 1689254 1690154 1690159) (-1006 "RDEEF.spad" 1688233 1688250 1689227 1689232) (-1005 "RCFIELD.spad" 1685419 1685428 1688135 1688228) (-1004 "RCFIELD.spad" 1682691 1682702 1685409 1685414) (-1003 "RCAGG.spad" 1680603 1680614 1682681 1682686) (-1002 "RCAGG.spad" 1678442 1678455 1680522 1680527) (-1001 "RATRET.spad" 1677802 1677813 1678432 1678437) (-1000 "RATFACT.spad" 1677494 1677506 1677792 1677797) (-999 "RANDSRC.spad" 1676814 1676822 1677484 1677489) (-998 "RADUTIL.spad" 1676569 1676577 1676804 1676809) (-997 "RADIX.spad" 1673471 1673484 1675036 1675129) (-996 "RADFF.spad" 1671885 1671921 1672003 1672159) (-995 "RADCAT.spad" 1671479 1671487 1671875 1671880) (-994 "RADCAT.spad" 1671071 1671081 1671469 1671474) (-993 "QUEUE.spad" 1670414 1670424 1670678 1670705) (-992 "QUAT.spad" 1668996 1669006 1669338 1669403) (-991 "QUATCT2.spad" 1668615 1668633 1668986 1668991) (-990 "QUATCAT.spad" 1666780 1666790 1668545 1668610) (-989 "QUATCAT.spad" 1664696 1664708 1666463 1666468) (-988 "QUAGG.spad" 1663522 1663532 1664664 1664691) (-987 "QQUTAST.spad" 1663291 1663299 1663512 1663517) (-986 "QFORM.spad" 1662754 1662768 1663281 1663286) (-985 "QFCAT.spad" 1661457 1661467 1662656 1662749) (-984 "QFCAT.spad" 1659751 1659763 1660952 1660957) (-983 "QFCAT2.spad" 1659442 1659458 1659741 1659746) (-982 "QEQUAT.spad" 1658999 1659007 1659432 1659437) (-981 "QCMPACK.spad" 1653746 1653765 1658989 1658994) (-980 "QALGSET.spad" 1649821 1649853 1653660 1653665) (-979 "QALGSET2.spad" 1647817 1647835 1649811 1649816) (-978 "PWFFINTB.spad" 1645127 1645148 1647807 1647812) (-977 "PUSHVAR.spad" 1644456 1644475 1645117 1645122) (-976 "PTRANFN.spad" 1640582 1640592 1644446 1644451) (-975 "PTPACK.spad" 1637670 1637680 1640572 1640577) (-974 "PTFUNC2.spad" 1637491 1637505 1637660 1637665) (-973 "PTCAT.spad" 1636740 1636750 1637459 1637486) (-972 "PSQFR.spad" 1636047 1636071 1636730 1636735) (-971 "PSEUDLIN.spad" 1634905 1634915 1636037 1636042) (-970 "PSETPK.spad" 1620338 1620354 1634783 1634788) (-969 "PSETCAT.spad" 1614258 1614281 1620318 1620333) (-968 "PSETCAT.spad" 1608152 1608177 1614214 1614219) (-967 "PSCURVE.spad" 1607135 1607143 1608142 1608147) (-966 "PSCAT.spad" 1605902 1605931 1607033 1607130) (-965 "PSCAT.spad" 1604759 1604790 1605892 1605897) (-964 "PRTITION.spad" 1603704 1603712 1604749 1604754) (-963 "PRTDAST.spad" 1603423 1603431 1603694 1603699) (-962 "PRS.spad" 1592985 1593002 1603379 1603384) (-961 "PRQAGG.spad" 1592416 1592426 1592953 1592980) (-960 "PROPLOG.spad" 1591819 1591827 1592406 1592411) (-959 "PROPFRML.spad" 1589737 1589748 1591809 1591814) (-958 "PROPERTY.spad" 1589231 1589239 1589727 1589732) (-957 "PRODUCT.spad" 1586911 1586923 1587197 1587252) (-956 "PR.spad" 1585297 1585309 1586002 1586129) (-955 "PRINT.spad" 1585049 1585057 1585287 1585292) (-954 "PRIMES.spad" 1583300 1583310 1585039 1585044) (-953 "PRIMELT.spad" 1581281 1581295 1583290 1583295) (-952 "PRIMCAT.spad" 1580904 1580912 1581271 1581276) (-951 "PRIMARR.spad" 1579909 1579919 1580087 1580114) (-950 "PRIMARR2.spad" 1578632 1578644 1579899 1579904) (-949 "PREASSOC.spad" 1578004 1578016 1578622 1578627) (-948 "PPCURVE.spad" 1577141 1577149 1577994 1577999) (-947 "PORTNUM.spad" 1576916 1576924 1577131 1577136) (-946 "POLYROOT.spad" 1575745 1575767 1576872 1576877) (-945 "POLY.spad" 1573042 1573052 1573559 1573686) (-944 "POLYLIFT.spad" 1572303 1572326 1573032 1573037) (-943 "POLYCATQ.spad" 1570405 1570427 1572293 1572298) (-942 "POLYCAT.spad" 1563811 1563832 1570273 1570400) (-941 "POLYCAT.spad" 1556519 1556542 1562983 1562988) (-940 "POLY2UP.spad" 1555967 1555981 1556509 1556514) (-939 "POLY2.spad" 1555562 1555574 1555957 1555962) (-938 "POLUTIL.spad" 1554503 1554532 1555518 1555523) (-937 "POLTOPOL.spad" 1553251 1553266 1554493 1554498) (-936 "POINT.spad" 1552090 1552100 1552177 1552204) (-935 "PNTHEORY.spad" 1548756 1548764 1552080 1552085) (-934 "PMTOOLS.spad" 1547513 1547527 1548746 1548751) (-933 "PMSYM.spad" 1547058 1547068 1547503 1547508) (-932 "PMQFCAT.spad" 1546645 1546659 1547048 1547053) (-931 "PMPRED.spad" 1546114 1546128 1546635 1546640) (-930 "PMPREDFS.spad" 1545558 1545580 1546104 1546109) (-929 "PMPLCAT.spad" 1544628 1544646 1545490 1545495) (-928 "PMLSAGG.spad" 1544209 1544223 1544618 1544623) (-927 "PMKERNEL.spad" 1543776 1543788 1544199 1544204) (-926 "PMINS.spad" 1543352 1543362 1543766 1543771) (-925 "PMFS.spad" 1542925 1542943 1543342 1543347) (-924 "PMDOWN.spad" 1542211 1542225 1542915 1542920) (-923 "PMASS.spad" 1541223 1541231 1542201 1542206) (-922 "PMASSFS.spad" 1540192 1540208 1541213 1541218) (-921 "PLOTTOOL.spad" 1539972 1539980 1540182 1540187) (-920 "PLOT.spad" 1534803 1534811 1539962 1539967) (-919 "PLOT3D.spad" 1531223 1531231 1534793 1534798) (-918 "PLOT1.spad" 1530364 1530374 1531213 1531218) (-917 "PLEQN.spad" 1517580 1517607 1530354 1530359) (-916 "PINTERP.spad" 1517196 1517215 1517570 1517575) (-915 "PINTERPA.spad" 1516978 1516994 1517186 1517191) (-914 "PI.spad" 1516585 1516593 1516952 1516973) (-913 "PID.spad" 1515541 1515549 1516511 1516580) (-912 "PICOERCE.spad" 1515198 1515208 1515531 1515536) (-911 "PGROEB.spad" 1513795 1513809 1515188 1515193) (-910 "PGE.spad" 1505048 1505056 1513785 1513790) (-909 "PGCD.spad" 1503930 1503947 1505038 1505043) (-908 "PFRPAC.spad" 1503073 1503083 1503920 1503925) (-907 "PFR.spad" 1499730 1499740 1502975 1503068) (-906 "PFOTOOLS.spad" 1498988 1499004 1499720 1499725) (-905 "PFOQ.spad" 1498358 1498376 1498978 1498983) (-904 "PFO.spad" 1497777 1497804 1498348 1498353) (-903 "PF.spad" 1497351 1497363 1497582 1497675) (-902 "PFECAT.spad" 1495017 1495025 1497277 1497346) (-901 "PFECAT.spad" 1492711 1492721 1494973 1494978) (-900 "PFBRU.spad" 1490581 1490593 1492701 1492706) (-899 "PFBR.spad" 1488119 1488142 1490571 1490576) (-898 "PERM.spad" 1483800 1483810 1487949 1487964) (-897 "PERMGRP.spad" 1478536 1478546 1483790 1483795) (-896 "PERMCAT.spad" 1477088 1477098 1478516 1478531) (-895 "PERMAN.spad" 1475620 1475634 1477078 1477083) (-894 "PENDTREE.spad" 1474959 1474969 1475249 1475254) (-893 "PDRING.spad" 1473450 1473460 1474939 1474954) (-892 "PDRING.spad" 1471949 1471961 1473440 1473445) (-891 "PDEPROB.spad" 1470964 1470972 1471939 1471944) (-890 "PDEPACK.spad" 1464966 1464974 1470954 1470959) (-889 "PDECOMP.spad" 1464428 1464445 1464956 1464961) (-888 "PDECAT.spad" 1462782 1462790 1464418 1464423) (-887 "PCOMP.spad" 1462633 1462646 1462772 1462777) (-886 "PBWLB.spad" 1461215 1461232 1462623 1462628) (-885 "PATTERN.spad" 1455646 1455656 1461205 1461210) (-884 "PATTERN2.spad" 1455382 1455394 1455636 1455641) (-883 "PATTERN1.spad" 1453684 1453700 1455372 1455377) (-882 "PATRES.spad" 1451231 1451243 1453674 1453679) (-881 "PATRES2.spad" 1450893 1450907 1451221 1451226) (-880 "PATMATCH.spad" 1449050 1449081 1450601 1450606) (-879 "PATMAB.spad" 1448475 1448485 1449040 1449045) (-878 "PATLRES.spad" 1447559 1447573 1448465 1448470) (-877 "PATAB.spad" 1447323 1447333 1447549 1447554) (-876 "PARTPERM.spad" 1444685 1444693 1447313 1447318) (-875 "PARSURF.spad" 1444113 1444141 1444675 1444680) (-874 "PARSU2.spad" 1443908 1443924 1444103 1444108) (-873 "script-parser.spad" 1443428 1443436 1443898 1443903) (-872 "PARSCURV.spad" 1442856 1442884 1443418 1443423) (-871 "PARSC2.spad" 1442645 1442661 1442846 1442851) (-870 "PARPCURV.spad" 1442103 1442131 1442635 1442640) (-869 "PARPC2.spad" 1441892 1441908 1442093 1442098) (-868 "PAN2EXPR.spad" 1441304 1441312 1441882 1441887) (-867 "PALETTE.spad" 1440274 1440282 1441294 1441299) (-866 "PAIR.spad" 1439257 1439270 1439862 1439867) (-865 "PADICRC.spad" 1436587 1436605 1437762 1437855) (-864 "PADICRAT.spad" 1434602 1434614 1434823 1434916) (-863 "PADIC.spad" 1434297 1434309 1434528 1434597) (-862 "PADICCT.spad" 1432838 1432850 1434223 1434292) (-861 "PADEPAC.spad" 1431517 1431536 1432828 1432833) (-860 "PADE.spad" 1430257 1430273 1431507 1431512) (-859 "OWP.spad" 1429497 1429527 1430115 1430182) (-858 "OVAR.spad" 1429278 1429301 1429487 1429492) (-857 "OUT.spad" 1428362 1428370 1429268 1429273) (-856 "OUTFORM.spad" 1417658 1417666 1428352 1428357) (-855 "OUTBFILE.spad" 1417076 1417084 1417648 1417653) (-854 "OUTBCON.spad" 1416074 1416082 1417066 1417071) (-853 "OUTBCON.spad" 1415070 1415080 1416064 1416069) (-852 "OSI.spad" 1414545 1414553 1415060 1415065) (-851 "OSGROUP.spad" 1414463 1414471 1414535 1414540) (-850 "ORTHPOL.spad" 1412924 1412934 1414380 1414385) (-849 "OREUP.spad" 1412377 1412405 1412604 1412643) (-848 "ORESUP.spad" 1411676 1411700 1412057 1412096) (-847 "OREPCTO.spad" 1409495 1409507 1411596 1411601) (-846 "OREPCAT.spad" 1403552 1403562 1409451 1409490) (-845 "OREPCAT.spad" 1397499 1397511 1403400 1403405) (-844 "ORDSET.spad" 1396665 1396673 1397489 1397494) (-843 "ORDSET.spad" 1395829 1395839 1396655 1396660) (-842 "ORDRING.spad" 1395219 1395227 1395809 1395824) (-841 "ORDRING.spad" 1394617 1394627 1395209 1395214) (-840 "ORDMON.spad" 1394472 1394480 1394607 1394612) (-839 "ORDFUNS.spad" 1393598 1393614 1394462 1394467) (-838 "ORDFIN.spad" 1393418 1393426 1393588 1393593) (-837 "ORDCOMP.spad" 1391883 1391893 1392965 1392994) (-836 "ORDCOMP2.spad" 1391168 1391180 1391873 1391878) (-835 "OPTPROB.spad" 1389806 1389814 1391158 1391163) (-834 "OPTPACK.spad" 1382191 1382199 1389796 1389801) (-833 "OPTCAT.spad" 1379866 1379874 1382181 1382186) (-832 "OPSIG.spad" 1379518 1379526 1379856 1379861) (-831 "OPQUERY.spad" 1379067 1379075 1379508 1379513) (-830 "OP.spad" 1378809 1378819 1378889 1378956) (-829 "OPERCAT.spad" 1378397 1378407 1378799 1378804) (-828 "OPERCAT.spad" 1377983 1377995 1378387 1378392) (-827 "ONECOMP.spad" 1376728 1376738 1377530 1377559) (-826 "ONECOMP2.spad" 1376146 1376158 1376718 1376723) (-825 "OMSERVER.spad" 1375148 1375156 1376136 1376141) (-824 "OMSAGG.spad" 1374936 1374946 1375104 1375143) (-823 "OMPKG.spad" 1373548 1373556 1374926 1374931) (-822 "OM.spad" 1372513 1372521 1373538 1373543) (-821 "OMLO.spad" 1371938 1371950 1372399 1372438) (-820 "OMEXPR.spad" 1371772 1371782 1371928 1371933) (-819 "OMERR.spad" 1371315 1371323 1371762 1371767) (-818 "OMERRK.spad" 1370349 1370357 1371305 1371310) (-817 "OMENC.spad" 1369693 1369701 1370339 1370344) (-816 "OMDEV.spad" 1363982 1363990 1369683 1369688) (-815 "OMCONN.spad" 1363391 1363399 1363972 1363977) (-814 "OINTDOM.spad" 1363154 1363162 1363317 1363386) (-813 "OFMONOID.spad" 1359341 1359351 1363144 1363149) (-812 "ODVAR.spad" 1358602 1358612 1359331 1359336) (-811 "ODR.spad" 1358246 1358272 1358414 1358563) (-810 "ODPOL.spad" 1355592 1355602 1355932 1356059) (-809 "ODP.spad" 1345439 1345459 1345812 1345943) (-808 "ODETOOLS.spad" 1344022 1344041 1345429 1345434) (-807 "ODESYS.spad" 1341672 1341689 1344012 1344017) (-806 "ODERTRIC.spad" 1337613 1337630 1341629 1341634) (-805 "ODERED.spad" 1337000 1337024 1337603 1337608) (-804 "ODERAT.spad" 1334551 1334568 1336990 1336995) (-803 "ODEPRRIC.spad" 1331442 1331464 1334541 1334546) (-802 "ODEPROB.spad" 1330699 1330707 1331432 1331437) (-801 "ODEPRIM.spad" 1327973 1327995 1330689 1330694) (-800 "ODEPAL.spad" 1327349 1327373 1327963 1327968) (-799 "ODEPACK.spad" 1313951 1313959 1327339 1327344) (-798 "ODEINT.spad" 1313382 1313398 1313941 1313946) (-797 "ODEIFTBL.spad" 1310777 1310785 1313372 1313377) (-796 "ODEEF.spad" 1306144 1306160 1310767 1310772) (-795 "ODECONST.spad" 1305663 1305681 1306134 1306139) (-794 "ODECAT.spad" 1304259 1304267 1305653 1305658) (-793 "OCT.spad" 1302397 1302407 1303113 1303152) (-792 "OCTCT2.spad" 1302041 1302062 1302387 1302392) (-791 "OC.spad" 1299815 1299825 1301997 1302036) (-790 "OC.spad" 1297314 1297326 1299498 1299503) (-789 "OCAMON.spad" 1297162 1297170 1297304 1297309) (-788 "OASGP.spad" 1296977 1296985 1297152 1297157) (-787 "OAMONS.spad" 1296497 1296505 1296967 1296972) (-786 "OAMON.spad" 1296358 1296366 1296487 1296492) (-785 "OAGROUP.spad" 1296220 1296228 1296348 1296353) (-784 "NUMTUBE.spad" 1295807 1295823 1296210 1296215) (-783 "NUMQUAD.spad" 1283669 1283677 1295797 1295802) (-782 "NUMODE.spad" 1274805 1274813 1283659 1283664) (-781 "NUMINT.spad" 1272363 1272371 1274795 1274800) (-780 "NUMFMT.spad" 1271203 1271211 1272353 1272358) (-779 "NUMERIC.spad" 1263275 1263285 1271008 1271013) (-778 "NTSCAT.spad" 1261777 1261793 1263243 1263270) (-777 "NTPOLFN.spad" 1261322 1261332 1261694 1261699) (-776 "NSUP.spad" 1254332 1254342 1258872 1259025) (-775 "NSUP2.spad" 1253724 1253736 1254322 1254327) (-774 "NSMP.spad" 1249919 1249938 1250227 1250354) (-773 "NREP.spad" 1248291 1248305 1249909 1249914) (-772 "NPCOEF.spad" 1247537 1247557 1248281 1248286) (-771 "NORMRETR.spad" 1247135 1247174 1247527 1247532) (-770 "NORMPK.spad" 1245037 1245056 1247125 1247130) (-769 "NORMMA.spad" 1244725 1244751 1245027 1245032) (-768 "NONE.spad" 1244466 1244474 1244715 1244720) (-767 "NONE1.spad" 1244142 1244152 1244456 1244461) (-766 "NODE1.spad" 1243611 1243627 1244132 1244137) (-765 "NNI.spad" 1242498 1242506 1243585 1243606) (-764 "NLINSOL.spad" 1241120 1241130 1242488 1242493) (-763 "NIPROB.spad" 1239661 1239669 1241110 1241115) (-762 "NFINTBAS.spad" 1237121 1237138 1239651 1239656) (-761 "NETCLT.spad" 1237095 1237106 1237111 1237116) (-760 "NCODIV.spad" 1235293 1235309 1237085 1237090) (-759 "NCNTFRAC.spad" 1234935 1234949 1235283 1235288) (-758 "NCEP.spad" 1233095 1233109 1234925 1234930) (-757 "NASRING.spad" 1232691 1232699 1233085 1233090) (-756 "NASRING.spad" 1232285 1232295 1232681 1232686) (-755 "NARNG.spad" 1231629 1231637 1232275 1232280) (-754 "NARNG.spad" 1230971 1230981 1231619 1231624) (-753 "NAGSP.spad" 1230044 1230052 1230961 1230966) (-752 "NAGS.spad" 1219569 1219577 1230034 1230039) (-751 "NAGF07.spad" 1217962 1217970 1219559 1219564) (-750 "NAGF04.spad" 1212194 1212202 1217952 1217957) (-749 "NAGF02.spad" 1206003 1206011 1212184 1212189) (-748 "NAGF01.spad" 1201606 1201614 1205993 1205998) (-747 "NAGE04.spad" 1195066 1195074 1201596 1201601) (-746 "NAGE02.spad" 1185408 1185416 1195056 1195061) (-745 "NAGE01.spad" 1181292 1181300 1185398 1185403) (-744 "NAGD03.spad" 1179212 1179220 1181282 1181287) (-743 "NAGD02.spad" 1171743 1171751 1179202 1179207) (-742 "NAGD01.spad" 1165856 1165864 1171733 1171738) (-741 "NAGC06.spad" 1161643 1161651 1165846 1165851) (-740 "NAGC05.spad" 1160112 1160120 1161633 1161638) (-739 "NAGC02.spad" 1159367 1159375 1160102 1160107) (-738 "NAALG.spad" 1158902 1158912 1159335 1159362) (-737 "NAALG.spad" 1158457 1158469 1158892 1158897) (-736 "MULTSQFR.spad" 1155415 1155432 1158447 1158452) (-735 "MULTFACT.spad" 1154798 1154815 1155405 1155410) (-734 "MTSCAT.spad" 1152832 1152853 1154696 1154793) (-733 "MTHING.spad" 1152489 1152499 1152822 1152827) (-732 "MSYSCMD.spad" 1151923 1151931 1152479 1152484) (-731 "MSET.spad" 1149865 1149875 1151629 1151668) (-730 "MSETAGG.spad" 1149710 1149720 1149833 1149860) (-729 "MRING.spad" 1146681 1146693 1149418 1149485) (-728 "MRF2.spad" 1146249 1146263 1146671 1146676) (-727 "MRATFAC.spad" 1145795 1145812 1146239 1146244) (-726 "MPRFF.spad" 1143825 1143844 1145785 1145790) (-725 "MPOLY.spad" 1141260 1141275 1141619 1141746) (-724 "MPCPF.spad" 1140524 1140543 1141250 1141255) (-723 "MPC3.spad" 1140339 1140379 1140514 1140519) (-722 "MPC2.spad" 1139981 1140014 1140329 1140334) (-721 "MONOTOOL.spad" 1138316 1138333 1139971 1139976) (-720 "MONOID.spad" 1137635 1137643 1138306 1138311) (-719 "MONOID.spad" 1136952 1136962 1137625 1137630) (-718 "MONOGEN.spad" 1135698 1135711 1136812 1136947) (-717 "MONOGEN.spad" 1134466 1134481 1135582 1135587) (-716 "MONADWU.spad" 1132480 1132488 1134456 1134461) (-715 "MONADWU.spad" 1130492 1130502 1132470 1132475) (-714 "MONAD.spad" 1129636 1129644 1130482 1130487) (-713 "MONAD.spad" 1128778 1128788 1129626 1129631) (-712 "MOEBIUS.spad" 1127464 1127478 1128758 1128773) (-711 "MODULE.spad" 1127334 1127344 1127432 1127459) (-710 "MODULE.spad" 1127224 1127236 1127324 1127329) (-709 "MODRING.spad" 1126555 1126594 1127204 1127219) (-708 "MODOP.spad" 1125214 1125226 1126377 1126444) (-707 "MODMONOM.spad" 1124943 1124961 1125204 1125209) (-706 "MODMON.spad" 1121702 1121718 1122421 1122574) (-705 "MODFIELD.spad" 1121060 1121099 1121604 1121697) (-704 "MMLFORM.spad" 1119920 1119928 1121050 1121055) (-703 "MMAP.spad" 1119660 1119694 1119910 1119915) (-702 "MLO.spad" 1118087 1118097 1119616 1119655) (-701 "MLIFT.spad" 1116659 1116676 1118077 1118082) (-700 "MKUCFUNC.spad" 1116192 1116210 1116649 1116654) (-699 "MKRECORD.spad" 1115794 1115807 1116182 1116187) (-698 "MKFUNC.spad" 1115175 1115185 1115784 1115789) (-697 "MKFLCFN.spad" 1114131 1114141 1115165 1115170) (-696 "MKCHSET.spad" 1113996 1114006 1114121 1114126) (-695 "MKBCFUNC.spad" 1113481 1113499 1113986 1113991) (-694 "MINT.spad" 1112920 1112928 1113383 1113476) (-693 "MHROWRED.spad" 1111421 1111431 1112910 1112915) (-692 "MFLOAT.spad" 1109937 1109945 1111311 1111416) (-691 "MFINFACT.spad" 1109337 1109359 1109927 1109932) (-690 "MESH.spad" 1107069 1107077 1109327 1109332) (-689 "MDDFACT.spad" 1105262 1105272 1107059 1107064) (-688 "MDAGG.spad" 1104549 1104559 1105242 1105257) (-687 "MCMPLX.spad" 1100535 1100543 1101149 1101338) (-686 "MCDEN.spad" 1099743 1099755 1100525 1100530) (-685 "MCALCFN.spad" 1096845 1096871 1099733 1099738) (-684 "MAYBE.spad" 1096129 1096140 1096835 1096840) (-683 "MATSTOR.spad" 1093405 1093415 1096119 1096124) (-682 "MATRIX.spad" 1092109 1092119 1092593 1092620) (-681 "MATLIN.spad" 1089435 1089459 1091993 1091998) (-680 "MATCAT.spad" 1081020 1081042 1089403 1089430) (-679 "MATCAT.spad" 1072477 1072501 1080862 1080867) (-678 "MATCAT2.spad" 1071745 1071793 1072467 1072472) (-677 "MAPPKG3.spad" 1070644 1070658 1071735 1071740) (-676 "MAPPKG2.spad" 1069978 1069990 1070634 1070639) (-675 "MAPPKG1.spad" 1068796 1068806 1069968 1069973) (-674 "MAPPAST.spad" 1068109 1068117 1068786 1068791) (-673 "MAPHACK3.spad" 1067917 1067931 1068099 1068104) (-672 "MAPHACK2.spad" 1067682 1067694 1067907 1067912) (-671 "MAPHACK1.spad" 1067312 1067322 1067672 1067677) (-670 "MAGMA.spad" 1065102 1065119 1067302 1067307) (-669 "MACROAST.spad" 1064681 1064689 1065092 1065097) (-668 "M3D.spad" 1062377 1062387 1064059 1064064) (-667 "LZSTAGG.spad" 1059605 1059615 1062367 1062372) (-666 "LZSTAGG.spad" 1056831 1056843 1059595 1059600) (-665 "LWORD.spad" 1053536 1053553 1056821 1056826) (-664 "LSTAST.spad" 1053320 1053328 1053526 1053531) (-663 "LSQM.spad" 1051546 1051560 1051944 1051995) (-662 "LSPP.spad" 1051079 1051096 1051536 1051541) (-661 "LSMP.spad" 1049919 1049947 1051069 1051074) (-660 "LSMP1.spad" 1047723 1047737 1049909 1049914) (-659 "LSAGG.spad" 1047392 1047402 1047691 1047718) (-658 "LSAGG.spad" 1047081 1047093 1047382 1047387) (-657 "LPOLY.spad" 1046035 1046054 1046937 1047006) (-656 "LPEFRAC.spad" 1045292 1045302 1046025 1046030) (-655 "LO.spad" 1044693 1044707 1045226 1045253) (-654 "LOGIC.spad" 1044295 1044303 1044683 1044688) (-653 "LOGIC.spad" 1043895 1043905 1044285 1044290) (-652 "LODOOPS.spad" 1042813 1042825 1043885 1043890) (-651 "LODO.spad" 1042197 1042213 1042493 1042532) (-650 "LODOF.spad" 1041241 1041258 1042154 1042159) (-649 "LODOCAT.spad" 1039899 1039909 1041197 1041236) (-648 "LODOCAT.spad" 1038555 1038567 1039855 1039860) (-647 "LODO2.spad" 1037828 1037840 1038235 1038274) (-646 "LODO1.spad" 1037228 1037238 1037508 1037547) (-645 "LODEEF.spad" 1036000 1036018 1037218 1037223) (-644 "LNAGG.spad" 1031802 1031812 1035990 1035995) (-643 "LNAGG.spad" 1027568 1027580 1031758 1031763) (-642 "LMOPS.spad" 1024304 1024321 1027558 1027563) (-641 "LMODULE.spad" 1023946 1023956 1024294 1024299) (-640 "LMDICT.spad" 1023229 1023239 1023497 1023524) (-639 "LITERAL.spad" 1023135 1023146 1023219 1023224) (-638 "LIST.spad" 1020853 1020863 1022282 1022309) (-637 "LIST3.spad" 1020144 1020158 1020843 1020848) (-636 "LIST2.spad" 1018784 1018796 1020134 1020139) (-635 "LIST2MAP.spad" 1015661 1015673 1018774 1018779) (-634 "LINEXP.spad" 1015093 1015103 1015641 1015656) (-633 "LINDEP.spad" 1013870 1013882 1015005 1015010) (-632 "LIMITRF.spad" 1011784 1011794 1013860 1013865) (-631 "LIMITPS.spad" 1010667 1010680 1011774 1011779) (-630 "LIE.spad" 1008681 1008693 1009957 1010102) (-629 "LIECAT.spad" 1008157 1008167 1008607 1008676) (-628 "LIECAT.spad" 1007661 1007673 1008113 1008118) (-627 "LIB.spad" 1005709 1005717 1006320 1006335) (-626 "LGROBP.spad" 1003062 1003081 1005699 1005704) (-625 "LF.spad" 1001981 1001997 1003052 1003057) (-624 "LFCAT.spad" 1001000 1001008 1001971 1001976) (-623 "LEXTRIPK.spad" 996503 996518 1000990 1000995) (-622 "LEXP.spad" 994506 994533 996483 996498) (-621 "LETAST.spad" 994205 994213 994496 994501) (-620 "LEADCDET.spad" 992589 992606 994195 994200) (-619 "LAZM3PK.spad" 991293 991315 992579 992584) (-618 "LAUPOL.spad" 989982 989995 990886 990955) (-617 "LAPLACE.spad" 989555 989571 989972 989977) (-616 "LA.spad" 988995 989009 989477 989516) (-615 "LALG.spad" 988771 988781 988975 988990) (-614 "LALG.spad" 988555 988567 988761 988766) (-613 "KVTFROM.spad" 988290 988300 988545 988550) (-612 "KTVLOGIC.spad" 987713 987721 988280 988285) (-611 "KRCFROM.spad" 987451 987461 987703 987708) (-610 "KOVACIC.spad" 986164 986181 987441 987446) (-609 "KONVERT.spad" 985886 985896 986154 986159) (-608 "KOERCE.spad" 985623 985633 985876 985881) (-607 "KERNEL.spad" 984158 984168 985407 985412) (-606 "KERNEL2.spad" 983861 983873 984148 984153) (-605 "KDAGG.spad" 982964 982986 983841 983856) (-604 "KDAGG.spad" 982075 982099 982954 982959) (-603 "KAFILE.spad" 981038 981054 981273 981300) (-602 "JORDAN.spad" 978865 978877 980328 980473) (-601 "JOINAST.spad" 978559 978567 978855 978860) (-600 "JAVACODE.spad" 978425 978433 978549 978554) (-599 "IXAGG.spad" 976548 976572 978415 978420) (-598 "IXAGG.spad" 974526 974552 976395 976400) (-597 "IVECTOR.spad" 973297 973312 973452 973479) (-596 "ITUPLE.spad" 972442 972452 973287 973292) (-595 "ITRIGMNP.spad" 971253 971272 972432 972437) (-594 "ITFUN3.spad" 970747 970761 971243 971248) (-593 "ITFUN2.spad" 970477 970489 970737 970742) (-592 "ITAYLOR.spad" 968269 968284 970313 970438) (-591 "ISUPS.spad" 960680 960695 967243 967340) (-590 "ISUMP.spad" 960177 960193 960670 960675) (-589 "ISTRING.spad" 959180 959193 959346 959373) (-588 "ISAST.spad" 958899 958907 959170 959175) (-587 "IRURPK.spad" 957612 957631 958889 958894) (-586 "IRSN.spad" 955572 955580 957602 957607) (-585 "IRRF2F.spad" 954047 954057 955528 955533) (-584 "IRREDFFX.spad" 953648 953659 954037 954042) (-583 "IROOT.spad" 951979 951989 953638 953643) (-582 "IR.spad" 949768 949782 951834 951861) (-581 "IR2.spad" 948788 948804 949758 949763) (-580 "IR2F.spad" 947988 948004 948778 948783) (-579 "IPRNTPK.spad" 947748 947756 947978 947983) (-578 "IPF.spad" 947313 947325 947553 947646) (-577 "IPADIC.spad" 947074 947100 947239 947308) (-576 "IP4ADDR.spad" 946631 946639 947064 947069) (-575 "IOMODE.spad" 946252 946260 946621 946626) (-574 "IOBFILE.spad" 945613 945621 946242 946247) (-573 "IOBCON.spad" 945478 945486 945603 945608) (-572 "INVLAPLA.spad" 945123 945139 945468 945473) (-571 "INTTR.spad" 938369 938386 945113 945118) (-570 "INTTOOLS.spad" 936080 936096 937943 937948) (-569 "INTSLPE.spad" 935386 935394 936070 936075) (-568 "INTRVL.spad" 934952 934962 935300 935381) (-567 "INTRF.spad" 933316 933330 934942 934947) (-566 "INTRET.spad" 932748 932758 933306 933311) (-565 "INTRAT.spad" 931423 931440 932738 932743) (-564 "INTPM.spad" 929786 929802 931066 931071) (-563 "INTPAF.spad" 927554 927572 929718 929723) (-562 "INTPACK.spad" 917864 917872 927544 927549) (-561 "INT.spad" 917225 917233 917718 917859) (-560 "INTHERTR.spad" 916491 916508 917215 917220) (-559 "INTHERAL.spad" 916157 916181 916481 916486) (-558 "INTHEORY.spad" 912570 912578 916147 916152) (-557 "INTG0.spad" 906033 906051 912502 912507) (-556 "INTFTBL.spad" 900062 900070 906023 906028) (-555 "INTFACT.spad" 899121 899131 900052 900057) (-554 "INTEF.spad" 897436 897452 899111 899116) (-553 "INTDOM.spad" 896051 896059 897362 897431) (-552 "INTDOM.spad" 894728 894738 896041 896046) (-551 "INTCAT.spad" 892981 892991 894642 894723) (-550 "INTBIT.spad" 892484 892492 892971 892976) (-549 "INTALG.spad" 891666 891693 892474 892479) (-548 "INTAF.spad" 891158 891174 891656 891661) (-547 "INTABL.spad" 889676 889707 889839 889866) (-546 "INT8.spad" 889556 889564 889666 889671) (-545 "INT32.spad" 889435 889443 889546 889551) (-544 "INT16.spad" 889314 889322 889425 889430) (-543 "INS.spad" 886781 886789 889216 889309) (-542 "INS.spad" 884334 884344 886771 886776) (-541 "INPSIGN.spad" 883768 883781 884324 884329) (-540 "INPRODPF.spad" 882834 882853 883758 883763) (-539 "INPRODFF.spad" 881892 881916 882824 882829) (-538 "INNMFACT.spad" 880863 880880 881882 881887) (-537 "INMODGCD.spad" 880347 880377 880853 880858) (-536 "INFSP.spad" 878632 878654 880337 880342) (-535 "INFPROD0.spad" 877682 877701 878622 878627) (-534 "INFORM.spad" 874843 874851 877672 877677) (-533 "INFORM1.spad" 874468 874478 874833 874838) (-532 "INFINITY.spad" 874020 874028 874458 874463) (-531 "INETCLTS.spad" 873997 874005 874010 874015) (-530 "INEP.spad" 872529 872551 873987 873992) (-529 "INDE.spad" 872258 872275 872519 872524) (-528 "INCRMAPS.spad" 871679 871689 872248 872253) (-527 "INBFILE.spad" 870751 870759 871669 871674) (-526 "INBFF.spad" 866521 866532 870741 870746) (-525 "INBCON.spad" 864809 864817 866511 866516) (-524 "INBCON.spad" 863095 863105 864799 864804) (-523 "INAST.spad" 862760 862768 863085 863090) (-522 "IMPTAST.spad" 862468 862476 862750 862755) (-521 "IMATRIX.spad" 861413 861439 861925 861952) (-520 "IMATQF.spad" 860507 860551 861369 861374) (-519 "IMATLIN.spad" 859112 859136 860463 860468) (-518 "ILIST.spad" 857768 857783 858295 858322) (-517 "IIARRAY2.spad" 857156 857194 857375 857402) (-516 "IFF.spad" 856566 856582 856837 856930) (-515 "IFAST.spad" 856180 856188 856556 856561) (-514 "IFARRAY.spad" 853667 853682 855363 855390) (-513 "IFAMON.spad" 853529 853546 853623 853628) (-512 "IEVALAB.spad" 852918 852930 853519 853524) (-511 "IEVALAB.spad" 852305 852319 852908 852913) (-510 "IDPO.spad" 852103 852115 852295 852300) (-509 "IDPOAMS.spad" 851859 851871 852093 852098) (-508 "IDPOAM.spad" 851579 851591 851849 851854) (-507 "IDPC.spad" 850513 850525 851569 851574) (-506 "IDPAM.spad" 850258 850270 850503 850508) (-505 "IDPAG.spad" 850005 850017 850248 850253) (-504 "IDENT.spad" 849777 849785 849995 850000) (-503 "IDECOMP.spad" 847014 847032 849767 849772) (-502 "IDEAL.spad" 841937 841976 846949 846954) (-501 "ICDEN.spad" 841088 841104 841927 841932) (-500 "ICARD.spad" 840277 840285 841078 841083) (-499 "IBPTOOLS.spad" 838870 838887 840267 840272) (-498 "IBITS.spad" 838069 838082 838506 838533) (-497 "IBATOOL.spad" 834944 834963 838059 838064) (-496 "IBACHIN.spad" 833431 833446 834934 834939) (-495 "IARRAY2.spad" 832419 832445 833038 833065) (-494 "IARRAY1.spad" 831464 831479 831602 831629) (-493 "IAN.spad" 829677 829685 831280 831373) (-492 "IALGFACT.spad" 829278 829311 829667 829672) (-491 "HYPCAT.spad" 828702 828710 829268 829273) (-490 "HYPCAT.spad" 828124 828134 828692 828697) (-489 "HOSTNAME.spad" 827932 827940 828114 828119) (-488 "HOMOTOP.spad" 827675 827685 827922 827927) (-487 "HOAGG.spad" 824943 824953 827665 827670) (-486 "HOAGG.spad" 821986 821998 824710 824715) (-485 "HEXADEC.spad" 820088 820096 820453 820546) (-484 "HEUGCD.spad" 819103 819114 820078 820083) (-483 "HELLFDIV.spad" 818693 818717 819093 819098) (-482 "HEAP.spad" 818085 818095 818300 818327) (-481 "HEADAST.spad" 817616 817624 818075 818080) (-480 "HDP.spad" 807459 807475 807836 807967) (-479 "HDMP.spad" 804635 804650 805253 805380) (-478 "HB.spad" 802872 802880 804625 804630) (-477 "HASHTBL.spad" 801342 801373 801553 801580) (-476 "HASAST.spad" 801058 801066 801332 801337) (-475 "HACKPI.spad" 800541 800549 800960 801053) (-474 "GTSET.spad" 799480 799496 800187 800214) (-473 "GSTBL.spad" 797999 798034 798173 798188) (-472 "GSERIES.spad" 795166 795193 796131 796280) (-471 "GROUP.spad" 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T) (($) -4050 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902)))) +((($) -4050 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((($) -4050 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) ((|#2|) -4050 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1042)))) ((((-856)) . T)) ((((-856)) . T)) ((((-856)) . T)) @@ -217,17 +217,17 @@ ((((-168 (-224))) |has| |#1| (-1015)) (((-168 (-378))) |has| |#1| (-1015)) (((-534)) |has| |#1| (-609 (-534))) (((-1162 |#1|)) . T) (((-885 (-561))) |has| |#1| (-609 (-885 (-561)))) (((-885 (-378))) |has| |#1| (-609 (-885 (-378))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#1|) . 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T)) (|has| |#1| (-553)) (|has| |#1| (-553)) @@ -254,21 +254,21 @@ (((|#2|) . T) (($) . T) (((-406 (-561))) . T)) (-12 (|has| |#1| (-1090)) (|has| |#2| (-1090))) ((($) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((|#1|) . T)) -((((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) . T)) +((((-406 (-561))) -4050 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (((-1164 |#1| |#2| |#3|)) |has| |#1| (-362)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-406 (-561))) -4050 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) . T)) (((|#1|) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) (($) . 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T)) ((((-406 $) (-406 $)) |has| |#2| (-553)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-902)) ((((-1148) (-52)) . T)) ((((-561)) |has| #0=(-406 |#2|) (-634 (-561))) ((#0#) . T)) ((((-534)) . T) (((-224)) . T) (((-378)) . T) (((-885 (-378))) . T)) ((((-856)) . T)) -(-4007 (|has| |#1| (-21)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) +(-4050 (|has| |#1| (-21)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) (((|#1|) |has| |#1| (-171))) (((|#1| $) |has| |#1| (-285 |#1| |#1|))) ((((-856)) . T)) @@ -295,15 +295,15 @@ (((|#2|) . T) (((-561)) . T) (((-813 |#1|)) . T)) (|has| |#1| (-1090)) (((|#1|) . 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T)) (((|#1|) . T) (((-406 (-561))) . T) (((-561)) . T) (($) . T)) @@ -472,10 +472,10 @@ ((((-561) |#4|) . T)) ((((-561) |#3|) . T)) (((|#1|) . T) (((-561)) |has| |#1| (-634 (-561)))) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) -((((-1239 |#1| |#2| |#3| |#4|)) . T)) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +((((-1240 |#1| |#2| |#3| |#4|)) . T)) ((((-406 (-561))) . T) (((-561)) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) @@ -486,7 +486,7 @@ ((((-561)) . T)) ((($) . T) (((-561)) . T) (((-406 (-561))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-406 (-561)) #0#) . 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T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) (|has| |#1| (-38 (-406 (-561)))) -((((-387) (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) +((((-387) (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#2| (-1141)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) ((((-856)) . T) (((-1171)) . T)) ((((-856)) . T) (((-1171)) . T)) ((((-856)) . T) (((-1171)) . T)) @@ -784,7 +784,7 @@ ((((-387) (-1148)) . T)) (|has| |#1| (-553)) ((((-561) |#1|) . T)) -(-4007 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) (((|#2|) . T)) @@ -800,7 +800,7 @@ ((((-638 |#1|)) . T)) ((((-856)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -(-4007 (|has| |#1| (-844)) (|has| |#1| (-1090))) +(-4050 (|has| |#1| (-844)) (|has| |#1| (-1090))) (((|#2|) |has| |#2| (-308 |#2|))) (((#0=(-561) #0#) . T) ((#1=(-406 (-561)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -810,7 +810,7 @@ (((#0=(-561) #0#) . T) ((#1=(-406 (-561)) #1#) . T) (($ $) . T)) ((($) . T) (((-561)) . T) (((-406 (-561))) . T)) (|has| |#2| (-367)) -(-4007 (|has| |#1| (-844)) (|has| |#1| (-1090))) +(-4050 (|has| |#1| (-844)) (|has| |#1| (-1090))) (((|#1|) . T) (((-406 (-561))) . T) (($) . T)) (((|#1|) . T) (((-406 (-561))) . T) (($) . T)) (((|#1|) . T) (((-406 (-561))) . T) (($) . T)) @@ -824,23 +824,23 @@ ((((-856)) . T)) ((((-856)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) -((($) . T) (((-406 (-561))) -4007 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . 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T)) ((((-561) (-143)) . T)) ((($) . T)) -(-4007 (|has| |#4| (-171)) (|has| |#4| (-842)) (|has| |#4| (-1042))) -(-4007 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) +(-4050 (|has| |#4| (-171)) (|has| |#4| (-842)) (|has| |#4| (-1042))) +(-4050 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((((-1171)) . T) (((-856)) . T)) ((((-1171)) . T)) ((((-856)) . T)) @@ -876,14 +876,14 @@ (((|#1| (-964)) . T)) (((|#1| |#1|) . T)) ((($) . 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T)) ((((-406 (-561))) . #0=(|has| |#2| (-362))) (($) . #0#) ((|#2|) . T) (((-561)) . T)) (((|#1| |#2| |#3|) . T)) -(-4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-553)) (|has| |#1| (-1042))) +(-4050 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-553)) (|has| |#1| (-1042))) (|has| $ (-146)) (|has| $ (-146)) ((((-1171)) . T)) @@ -942,14 +942,14 @@ ((((-856)) . T)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-553)) (|has| |#1| (-1042)) (|has| |#1| (-1102))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-553)) (|has| |#1| (-1042)) (|has| |#1| (-1102))) ((($ $) |has| |#1| (-285 $ $)) ((|#1| $) |has| |#1| (-285 |#1| |#1|))) (((|#1| (-406 (-561))) . T)) (((|#1|) . T)) ((((-1166)) . T)) (|has| |#1| (-553)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) (|has| |#1| (-553)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) @@ -960,7 +960,7 @@ (|has| |#1| (-146)) (|has| |#1| (-144)) (|has| |#4| (-842)) -(((|#2| (-239 (-3498 |#1|) (-765)) (-858 |#1|)) . T)) +(((|#2| (-239 (-3548 |#1|) (-765)) (-858 |#1|)) . T)) (|has| |#3| (-842)) (((|#1| (-529 |#3|) |#3|) . T)) (|has| |#1| (-146)) @@ -975,20 +975,20 @@ (|has| |#1| (-144)) ((((-406 (-561))) |has| |#2| (-362)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) -(-4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) -(-4007 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) +(-4050 (|has| |#1| (-348)) (|has| |#1| (-367))) ((((-1132 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-171)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-232)) (|has| |#2| (-1042))) -(((|#2|) . T) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) -(-4007 (|has| |#3| (-787)) (|has| |#3| (-842))) -(-4007 (|has| |#3| (-787)) (|has| |#3| (-842))) +(((|#2|) . T) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) +(-4050 (|has| |#3| (-787)) (|has| |#3| (-842))) +(-4050 (|has| |#3| (-787)) (|has| |#3| (-842))) ((((-856)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-692)) . T)) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) (|has| |#1| (-553)) (((|#1|) . T)) (((|#1|) . T)) @@ -1012,11 +1012,11 @@ (((|#1| (-406 (-561))) . T)) (((|#3|) . T) (((-607 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-308 |#1|))) @@ -1127,11 +1127,11 @@ (|has| |#1| (-367)) ((((-1166) $) |has| |#1| (-512 (-1166) $)) (($ $) |has| |#1| (-308 $)) ((|#1| |#1|) |has| |#1| (-308 |#1|)) (((-1166) |#1|) |has| |#1| (-512 (-1166) |#1|))) ((((-1166)) |has| |#1| (-893 (-1166)))) -(-4007 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) +(-4050 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-387) |#1|) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-1090)) (((|#2|) . T) (((-856)) . T)) ((((-856)) . T)) @@ -1139,8 +1139,8 @@ ((((-903 |#1|)) . T)) ((((-856)) . T) (((-1171)) . T)) ((((-1171)) . T)) -((((-406 (-561))) |has| |#2| (-38 (-406 (-561)))) ((|#2|) |has| |#2| (-171)) (($) -4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902)))) -((((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((|#1|) |has| |#1| (-171)) (($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902)))) +((((-406 (-561))) |has| |#2| (-38 (-406 (-561)))) ((|#2|) |has| |#2| (-171)) (($) -4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902)))) +((((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((|#1|) |has| |#1| (-171)) (($) -4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) @@ -1149,16 +1149,16 @@ (((|#1|) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) (((|#1| |#1|) . T)) (((#0=(-863 |#1|)) |has| #0# (-308 #0#))) -((((-561)) . 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T)) (|has| |#1| (-1190)) (((#0=(-561) #0#) . T) ((#1=(-406 (-561)) #1#) . T) (($ $) . T)) ((((-406 (-561))) . T) (($) . T)) @@ -1169,8 +1169,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-406 (-561)) #0#) . T)) (|has| |#1| (-362)) ((((-561)) . T) (((-406 (-561))) . T) (($) . T)) -((($ $) . T) ((#0=(-406 (-561)) #0#) -4007 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((($ $) . T) ((#0=(-406 (-561)) #0#) -4050 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (((|#1|) . T) (($) . T) (((-406 (-561))) . T)) ((((-856)) . T)) ((((-856)) . T)) @@ -1185,14 +1185,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-842)) (|has| |#1| (-842)) -((($) . T) (((-406 (-561))) -4007 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) -(-4007 (|has| |#1| (-171)) (|has| |#1| (-553))) +((($) . 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T)) +((((-856)) -4050 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-608 (-856))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) (((-1254 |#2|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) ((((-1148) (-52)) . T)) @@ -1201,10 +1201,10 @@ ((((-561)) |has| #0=(-406 |#2|) (-634 (-561))) ((#0#) . T)) ((($) . T) (((-561)) . T)) ((((-561) (-143)) . T)) -((((-561) (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T) ((|#1| |#2|) . T)) +((((-561) (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T) ((|#1| |#2|) . T)) ((((-406 (-561))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-856)) . T)) ((((-903 |#1|)) . T)) (|has| |#1| (-362)) @@ -1219,7 +1219,7 @@ ((((-1166)) |has| |#1| (-893 (-1166)))) ((((-504)) . T)) (((|#1| (-1166)) . T)) -(((|#1| (-1253 |#1|) (-1253 |#1|)) . T)) +(((|#1| (-1254 |#1|) (-1254 |#1|)) . T)) ((((-856)) . T) (((-1171)) . T)) (((|#1| |#2|) . T)) ((($ $) . T)) @@ -1231,21 +1231,21 @@ ((((-856)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-561) (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T) ((|#1| |#2|) . T)) +((((-561) (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-553)) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-171))) -((((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((|#1|) |has| |#1| (-171)) (($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902)))) -((($) -4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) -((($) -4007 (|has| |#1| (-362)) (|has| |#1| (-553))) (((-561)) . 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T)) +((((-856)) -4050 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-608 (-856))) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-720)) (|has| |#3| (-787)) (|has| |#3| (-842)) (|has| |#3| (-1042)) (|has| |#3| (-1090))) (((-1254 |#3|)) . T)) ((((-561) |#2|) . T)) -(-4007 (|has| |#1| (-844)) (|has| |#1| (-1090))) -(((|#2| |#2|) -4007 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1042))) (($ $) |has| |#2| (-171))) +(-4050 (|has| |#1| (-844)) (|has| |#1| (-1090))) +(((|#2| |#2|) -4050 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1042))) (($ $) |has| |#2| (-171))) (((|#2|) . T) (((-561)) . T)) ((((-856)) . T)) ((((-856)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T) ((|#2|) . T)) ((((-856)) . T)) ((((-856)) . T)) ((((-1148) (-1166) (-561) (-224) (-856)) . T)) @@ -1320,8 +1320,8 @@ (|has| |#1| (-38 (-406 (-561)))) ((((-856)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) -(((|#2|) -4007 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1042))) (($) |has| |#2| (-171))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +(((|#2|) -4050 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1042))) (($) |has| |#2| (-171))) (|has| $ (-146)) ((((-406 |#2|)) . T)) ((((-886 |#1|)) . T) ((|#2|) . T) (((-561)) . T) (((-813 |#1|)) . T)) @@ -1333,11 +1333,11 @@ (((|#3|) |has| |#3| (-171))) (|has| |#1| (-146)) (|has| |#1| (-144)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) (((|#1|) . T)) (|has| |#2| (-232)) @@ -1374,7 +1374,7 @@ ((((-992 |#1|)) . T) ((|#1|) . T)) ((((-856)) . T)) ((((-856)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-406 (-561))) . T) (((-406 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1162 |#1|)) . T)) ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) @@ -1382,28 +1382,28 @@ (|has| |#1| (-844)) (((|#2|) . T)) ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) ((((-561) |#2|) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (((|#2|) . T)) ((((-561) |#3|) . T)) (((|#2|) . T)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -((((-1245 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-856)) . T)) -(|has| |#1| (-1090)) +((((-1246 |#1| |#2| |#3|)) |has| |#1| (-362))) (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1090)))) (((|#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1090)))) +(|has| |#1| (-1090)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(|has| |#1| (-38 (-406 (-561)))) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((#0=(-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) #0#) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((#0=(-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) #0#) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))))) (((|#2| |#2|) . T)) +(|has| |#1| (-38 (-406 (-561)))) (((|#2|) . T)) -(((|#1|) . T)) (|has| |#2| (-362)) (((|#2|) . T) (((-561)) |has| |#2| (-1031 (-561))) (((-406 (-561))) |has| |#2| (-1031 (-406 (-561))))) +(((|#1|) . T)) (((|#2|) . T)) ((((-1148) (-52)) . T)) (((|#2|) |has| |#2| (-171))) @@ -1432,19 +1432,19 @@ (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#2|) . T)) ((((-561) (-143)) . T)) -(((#0=(-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) #0#) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) -((($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +(((#0=(-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) #0#) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) +((($) -4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) (|has| |#1| (-844)) (((|#2| (-765) (-1072)) . T)) (((|#1| |#2|) . T)) -(-4007 (|has| |#1| (-171)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-171)) (|has| |#1| (-553))) (|has| |#1| (-785)) (((|#1|) |has| |#1| (-171))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4007 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) -(-4007 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) +(-4050 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) +(-4050 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) (((|#4|) . T)) (|has| |#1| (-144)) ((((-1148) |#1|) . T)) @@ -1456,12 +1456,12 @@ ((((-856)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#3|) . T)) -((((-1245 |#1| |#2| |#3|)) |has| |#1| (-362))) +((((-1246 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-856)) . T)) -(-4007 (|has| |#1| (-844)) (|has| |#1| (-1090))) +(-4050 (|has| |#1| (-844)) (|has| |#1| (-1090))) (((|#1|) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090))) (((-951 |#1|)) . T)) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090))) (((-951 |#1|)) . T)) (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) @@ -1475,8 +1475,8 @@ ((($) . T)) ((((-387) (-1148)) . T)) ((($) |has| |#1| (-553)) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) -((((-856)) -4007 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-608 (-856))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) (((-1253 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2252 (-1148)) (|:| -2654 #0#))) . T)) +((((-856)) -4050 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-608 (-856))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) (((-1254 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2285 (-1148)) (|:| -2677 #0#))) . T)) (((|#1|) . T)) ((((-856)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) @@ -1484,7 +1484,7 @@ (|has| |#2| (-144)) (|has| |#2| (-146)) (|has| |#1| (-471)) -(-4007 (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) +(-4050 (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) (|has| |#1| (-362)) ((((-856)) . T)) (|has| |#1| (-38 (-406 (-561)))) @@ -1495,8 +1495,8 @@ (|has| |#1| (-842)) ((((-856)) . T)) (((|#2|) . T)) -((((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) -4007 (|has| |#1| (-362)) (|has| |#1| (-553))) (((-1245 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) -(((|#1|) |has| |#1| (-171)) (((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) -4007 (|has| |#1| (-362)) (|has| |#1| (-553)))) +((((-406 (-561))) -4050 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) -4050 (|has| |#1| (-362)) (|has| |#1| (-553))) (((-1246 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) +(((|#1|) |has| |#1| (-171)) (((-406 (-561))) -4050 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-362))) (($) -4050 (|has| |#1| (-362)) (|has| |#1| (-553)))) ((($) |has| |#1| (-553)) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) (((|#2|) . T) (((-561)) . T) (((-813 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1505,7 +1505,7 @@ ((((-856)) . T)) ((((-856)) . T)) (|has| |#1| (-1090)) -(((|#2| (-480 (-3498 |#1|) (-765)) (-858 |#1|)) . T)) +(((|#2| (-480 (-3548 |#1|) (-765)) (-858 |#1|)) . T)) ((((-406 (-561))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1| (-529 (-1166)) (-1166)) . T)) (((|#1|) . T)) @@ -1525,22 +1525,22 @@ (|has| |#1| (-146)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-1166) (-52)) . T)) ((($ $) . T)) (((|#1| (-561)) . T)) ((((-903 |#1|)) . T)) -(((|#1|) -4007 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1042))) (($) -4007 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)))) +(((|#1|) -4050 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1042))) (($) -4050 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)))) (((|#1|) . T) (((-561)) |has| |#1| (-1031 (-561))) (((-406 (-561))) |has| |#1| (-1031 (-406 (-561))))) (|has| |#1| (-844)) (|has| |#1| (-844)) ((((-561) |#2|) . T)) ((((-561)) . T)) -((((-1245 |#1| |#2| |#3|)) -12 (|has| (-1245 |#1| |#2| |#3|) (-308 (-1245 |#1| |#2| |#3|))) (|has| |#1| (-362)))) +((((-1246 |#1| |#2| |#3|)) -12 (|has| (-1246 |#1| |#2| |#3|) (-308 (-1246 |#1| |#2| |#3|))) (|has| |#1| (-362)))) (|has| |#1| (-844)) ((((-682 |#2|)) . T) (((-856)) . T)) ((((-406 (-561))) . T) (((-561)) . T) (($) . T)) @@ -1552,11 +1552,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1090)))) (|has| |#2| (-844)) (|has| |#1| (-844)) -(((|#3|) -4007 (|has| |#3| (-171)) (|has| |#3| (-362)))) -(-4007 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-902))) +(((|#3|) -4050 (|has| |#3| (-171)) (|has| |#3| (-362)))) +(-4050 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-902))) ((($ $) . T) ((#0=(-406 (-561)) #0#) . T)) ((((-561) |#2|) . T)) -(((|#2|) -4007 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -4050 (|has| |#2| (-171)) (|has| |#2| (-362)))) (|has| |#1| (-348)) (((|#3| |#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1090)))) (((|#2|) . T) (((-561)) . T)) @@ -1565,7 +1565,7 @@ (|has| |#1| (-814)) (|has| |#1| (-814)) (((|#1|) . T)) -(-4007 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-842)) (|has| |#1| (-842)) (|has| |#1| (-842)) @@ -1574,13 +1574,13 @@ ((((-561)) . T) (($) . T) (((-406 (-561))) . T)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-561)))) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-1166)) |has| |#1| (-893 (-1166))) (((-1072)) . T)) (((|#1|) . T)) (|has| |#1| (-842)) -(((#0=(-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) #0#) |has| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (-308 (-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))))) +(((#0=(-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) #0#) |has| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (-308 (-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (|has| |#1| (-1090)) ((((-856)) . T) (((-1171)) . T)) @@ -1599,11 +1599,11 @@ (((|#1| (-765) (-1072)) . T)) (((|#3|) . T)) ((((-143)) . T)) -((((-406 (-561))) |has| |#1| (-1031 (-406 (-561)))) (((-561)) -4007 (|has| |#1| (-842)) (|has| |#1| (-1031 (-561)))) ((|#1|) . T)) +((((-406 (-561))) |has| |#1| (-1031 (-406 (-561)))) (((-561)) -4050 (|has| |#1| (-842)) (|has| |#1| (-1031 (-561)))) ((|#1|) . T)) (((|#1|) . T)) ((((-143)) . T)) (((|#2|) |has| |#2| (-171))) -(-4007 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) +(-4050 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) (((|#1|) . T)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -1626,32 +1626,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +(((|#1| (-1218 |#1| |#2| |#3|)) . T)) (((|#1| (-765)) . T)) (((|#1|) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-856)) . T)) (|has| |#1| (-1090)) ((((-1148) |#1|) . T)) @@ -1756,8 +1757,8 @@ (|has| |#2| (-144)) (((|#1| (-529 (-812 (-1166))) (-812 (-1166))) . T)) ((((-856)) . T)) -((((-1239 |#1| |#2| |#3| |#4|)) . T)) -((((-1239 |#1| |#2| |#3| |#4|)) . T)) +((((-1240 |#1| |#2| |#3| |#4|)) . T)) +((((-1240 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) |has| |#1| (-1042))) ((((-561) (-112)) . T)) ((((-856)) |has| |#1| (-1090))) @@ -1767,26 +1768,26 @@ (((|#1|) . T)) ((((-561)) . T)) ((((-856)) . T)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-856)) . T)) (((|#3|) . T)) -(-4007 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) +(-4050 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((((-856)) . 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T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))))) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-553)) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) @@ -1794,8 +1795,8 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1090))) ((((-903 |#1|)) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) -(((|#2|) -4007 (|has| |#2| (-171)) (|has| |#2| (-362)))) -((((-1238 |#2| |#3| |#4|)) . T)) +(((|#2|) -4050 (|has| |#2| (-171)) (|has| |#2| (-362)))) +((((-1239 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-814)) (|has| |#1| (-814)) @@ -1804,8 +1805,8 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1| (-561) (-1072)) . T)) -(-4007 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +(-4050 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042))) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#1| (-406 (-561)) (-1072)) . T)) (((|#1| (-765) (-1072)) . T)) (|has| |#1| (-844)) @@ -1818,33 +1819,33 @@ (|has| |#1| (-1090)) ((((-903 |#1|)) . T) (($) . T) (((-406 (-561))) . T)) (|has| |#1| (-1090)) -((((-561)) -4007 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)))) +((((-561)) -4050 (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)))) (((|#1|) . 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T)) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) |has| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (-308 (-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))))) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-902))) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) |has| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (-308 (-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-902))) (((|#2|) . T) (((-561)) |has| |#2| (-634 (-561)))) ((((-856)) . T)) ((((-856)) . T)) @@ -1875,25 +1876,25 @@ (|has| |#1| (-144)) ((((-561)) . T) ((|#1|) . T) (($) . T) (((-406 (-561))) . T) (((-1166)) |has| |#1| (-1031 (-1166)))) (((|#1| |#2|) . T)) -((((-406 (-561))) |has| |#1| (-1031 (-406 (-561)))) (((-561)) -4007 (|has| |#1| (-842)) (|has| |#1| (-1031 (-561)))) ((|#1|) . T)) +((((-406 (-561))) |has| |#1| (-1031 (-406 (-561)))) (((-561)) -4050 (|has| |#1| (-842)) (|has| |#1| (-1031 (-561)))) ((|#1|) . T)) ((((-143)) . T)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) (((|#1|) . T)) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-842)) (|has| |#2| (-1042))) (((|#1| |#1|) . T) ((#0=(-406 (-561)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-561)) . T)) ((((-856)) . T)) (((|#1|) . T) (((-406 (-561))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| (-406 |#2|) (-232)) ((((-638 |#1|)) . T)) (|has| |#1| (-902)) (((|#2|) |has| |#2| (-1042))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))))) (|has| |#1| (-362)) (((|#1|) |has| |#1| (-171))) (((|#1| |#1|) . T)) @@ -1920,7 +1921,7 @@ (((|#1| (-406 (-561)) (-1072)) . T)) (((|#1| (-765) (-1072)) . T)) (((#0=(-406 |#2|) #0#) . T) ((#1=(-406 (-561)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-561)) -4007 (|has| (-406 (-561)) (-1031 (-561))) (|has| |#1| (-1031 (-561)))) (((-406 (-561))) . T)) +(((|#1|) . T) (((-561)) -4050 (|has| (-406 (-561)) (-1031 (-561))) (|has| |#1| (-1031 (-561)))) (((-406 (-561))) . T)) (((|#1| (-597 |#1| |#3|) (-597 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -1941,25 +1942,25 @@ (((|#2|) |has| |#2| (-171))) (|has| |#2| (-842)) ((((-561)) . T) ((|#2|) . T) (((-406 (-561))) |has| |#2| (-1031 (-406 (-561))))) -((((-112)) |has| |#1| (-1090)) (((-856)) -4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)) (|has| |#1| (-1102)) (|has| |#1| (-1090)))) +((((-112)) |has| |#1| (-1090)) (((-856)) -4050 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)) (|has| |#1| (-1102)) (|has| |#1| (-1090)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))) . T)) ((((-856)) . T)) ((((-561) |#1|) . T)) ((((-856)) . T)) ((((-692)) . T) (((-406 (-561))) . T) (((-561)) . T)) (((|#1| |#1|) |has| |#1| (-171))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|))))) ((((-378)) . T)) ((((-692)) . T)) ((((-406 (-561))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1|) |has| |#1| (-171))) ((((-406 (-945 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-844)) @@ -1970,14 +1971,14 @@ (((|#3|) |has| |#3| (-1042))) ((((-1166)) |has| |#2| (-893 (-1166)))) ((((-856)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-406 (-561))) . T) (($) . T)) (|has| |#1| (-471)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-362)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-553)) (|has| |#1| (-1042)) (|has| |#1| (-1102))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-553)) (|has| |#1| (-1042)) (|has| |#1| (-1102))) (|has| |#1| (-38 (-406 (-561)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1998,11 +1999,11 @@ (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-844)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) |has| (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)) (-308 (-2 (|:| -2252 |#1|) (|:| -2654 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) |has| (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)) (-308 (-2 (|:| -2285 |#1|) (|:| -2677 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2020,11 +2021,11 @@ ((((-534)) |has| |#1| (-609 (-534))) (((-885 (-561))) |has| |#1| (-609 (-885 (-561)))) (((-885 (-378))) |has| |#1| (-609 (-885 (-378)))) (((-378)) . #0=(|has| |#1| (-1015))) (((-224)) . #0#)) (((|#1|) |has| |#1| (-362))) ((((-856)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((($ $) . T) (((-607 $) $) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -((($) . T) (((-1239 |#1| |#2| |#3| |#4|)) . T) (((-406 (-561))) . T)) -((($) -4007 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-553)) (|has| |#1| (-1042))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +((($) . T) (((-1240 |#1| |#2| |#3| |#4|)) . T) (((-406 (-561))) . T)) +((($) -4050 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-553)) (|has| |#1| (-1042))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-553))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-362)) @@ -2035,11 +2036,11 @@ ((((-378)) . T)) (((|#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1090)))) ((((-856)) . T)) -(-4007 (|has| |#2| (-450)) (|has| |#2| (-902))) +(-4050 (|has| |#2| (-450)) (|has| |#2| (-902))) (((|#1|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) ((((-534)) |has| |#1| (-609 (-534)))) (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) ((((-765)) . T)) @@ -2050,13 +2051,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((((-561)) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(((#0=(-1238 |#2| |#3| |#4|)) . T) (((-406 (-561))) |has| #0# (-38 (-406 (-561)))) (($) . T)) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(((#0=(-1239 |#2| |#3| |#4|)) . T) (((-406 (-561))) |has| #0# (-38 (-406 (-561)))) (($) . T)) ((((-561)) . T)) (|has| |#1| (-362)) -(-4007 (-12 (|has| (-1245 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-4007 (-12 (|has| (-1245 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-4050 (-12 (|has| (-1246 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-4050 (-12 (|has| (-1246 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-362)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -2071,23 +2072,23 @@ (((|#2|) . T)) (|has| |#1| (-1090)) (((|#1| |#2|) . T)) -((((-561)) . T) ((|#1|) . T) (((-406 (-561))) -4007 (|has| |#1| (-362)) (|has| |#1| (-1031 (-406 (-561)))))) +((((-561)) . T) ((|#1|) . T) (((-406 (-561))) -4050 (|has| |#1| (-362)) (|has| |#1| (-1031 (-406 (-561)))))) (((|#1|) . T) (((-561)) |has| |#1| (-634 (-561)))) (((|#3|) |has| |#3| (-171))) -(-4007 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) +(-4050 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-720)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042)) (|has| |#2| (-1090))) ((((-856)) . T)) ((((-561)) . T)) (((|#1| $) |has| |#1| (-285 |#1| |#1|))) ((((-406 (-561))) . T) (($) . T) (((-406 |#1|)) . T) ((|#1|) . T)) ((((-945 |#1|)) . T) (((-856)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4007 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-561)) #0#) |has| |#1| (-362))) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -4050 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-561)) #0#) |has| |#1| (-362))) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) . T)) ((((-945 |#1|)) . T)) ((($) . T)) ((((-561) |#1|) . T)) ((((-1166)) |has| (-406 |#2|) (-893 (-1166)))) -(((|#1|) . T) (($) -4007 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-561))) |has| |#1| (-362))) +(((|#1|) . T) (($) -4050 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-561))) |has| |#1| (-362))) ((((-534)) |has| |#2| (-609 (-534)))) ((((-682 |#2|)) . T) (((-856)) . T)) (((|#1|) . T)) @@ -2095,8 +2096,8 @@ (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1090)))) ((((-863 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) -(-4007 (|has| |#4| (-787)) (|has| |#4| (-842))) -(-4007 (|has| |#3| (-787)) (|has| |#3| (-842))) +(-4050 (|has| |#4| (-787)) (|has| |#4| (-842))) +(-4050 (|has| |#3| (-787)) (|has| |#3| (-842))) ((((-856)) . T)) ((((-856)) . T)) (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1090)))) @@ -2112,17 +2113,17 @@ ((((-406 (-561))) . T) (($) . T)) ((((-406 (-561))) . T) (($) . T)) ((((-406 (-561))) . T) (($) . T)) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-1209))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-1209))) ((($) . T)) ((((-406 (-561))) |has| #0=(-406 |#2|) (-1031 (-406 (-561)))) (((-561)) |has| #0# (-1031 (-561))) ((#0#) . T)) (((|#2|) . T) (((-561)) |has| |#2| (-634 (-561)))) (((|#1| (-765)) . T)) (|has| |#1| (-844)) (((|#1|) . T) (((-561)) |has| |#1| (-634 (-561)))) -((($) -4007 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-561))) -4007 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -4050 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-561))) -4050 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-561)) . T)) (|has| |#1| (-38 (-406 (-561)))) -((((-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))) |has| (-2 (|:| -2252 (-1148)) (|:| -2654 (-52))) (-308 (-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))))) +((((-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))) |has| (-2 (|:| -2285 (-1148)) (|:| -2677 (-52))) (-308 (-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (|has| |#1| (-842)) (|has| |#1| (-38 (-406 (-561)))) @@ -2145,29 +2146,29 @@ (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) ((((-1148)) . T) (((-1166)) . T) (((-224)) . T) (((-561)) . T)) -(((|#2|) . T) (((-561)) . T) (($) -4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((-1072)) . T) ((|#1|) . T) (((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-1031 (-406 (-561)))))) +(((|#2|) . T) (((-561)) . T) (($) -4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((-1072)) . T) ((|#1|) . 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T) ((#0=(-406 (-561)) #0#) |has| |#1| (-38 (-406 (-561))))) +((($ $) -4050 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1| |#1|) . T) ((#0=(-406 (-561)) #0#) |has| |#1| (-38 (-406 (-561))))) ((((-903 |#1|)) . T)) ((($) . T)) ((((-406 (-945 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) -((($) -4007 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((($) -4050 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) ((((-534)) |has| |#4| (-609 (-534)))) ((((-856)) . T) (((-638 |#4|)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-842)) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) |has| (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|)) (-308 (-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090))) (((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) |has| (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|)) (-308 (-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))))) (|has| |#1| (-1090)) (|has| |#1| (-362)) (|has| |#1| (-844)) @@ -2176,17 +2177,17 @@ (((|#1|) . T)) ((((-665 |#1|)) . T)) ((($) . T) (((-406 (-561))) . 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T)) (((|#1|) . T) (((-561)) |has| |#1| (-634 (-561)))) @@ -2209,9 +2210,9 @@ ((((-856)) . T)) ((((-856)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-1166) |#1|) |has| |#1| (-512 (-1166) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -(((|#1|) -4007 (|has| |#1| (-171)) (|has| |#1| (-362)))) +(((|#1|) -4050 (|has| |#1| (-171)) (|has| |#1| (-362)))) ((((-315 |#1|)) . T)) (((|#2|) |has| |#2| (-362))) (((|#2|) . T)) @@ -2233,13 +2234,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((($ $) . 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T)) (((|#1| $) |has| |#1| (-285 |#1| |#1|))) -((((-1239 |#1| |#2| |#3| |#4|)) . T) (((-406 (-561))) . T) (($) . T)) +((((-1240 |#1| |#2| |#3| |#4|)) . T) (((-406 (-561))) . T) (($) . T)) (((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-553)) (($) |has| |#1| (-553))) (|has| |#1| (-362)) (|has| |#1| (-144)) @@ -2289,34 +2290,34 @@ (((|#3|) |has| |#3| (-362))) (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) ((((-1166)) . T)) -((($) . T) (((-1238 |#2| |#3| |#4|)) . T) (((-406 (-561))) |has| (-1238 |#2| |#3| |#4|) (-38 (-406 (-561)))) (((-561)) . T)) +((($) . T) (((-1239 |#2| |#3| |#4|)) . T) (((-406 (-561))) |has| (-1239 |#2| |#3| |#4|) (-38 (-406 (-561)))) (((-561)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090)))) (((|#2| |#3|) . 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T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))) . T)) (((|#1|) . T)) ((((-856)) . T)) (((|#1| |#2|) . T)) (((|#1| (-406 (-561))) . T)) (((|#1|) . T)) -(-4007 (|has| |#1| (-289)) (|has| |#1| (-362))) +(-4050 (|has| |#1| (-289)) (|has| |#1| (-362))) ((((-143)) . T)) ((((-406 |#2|)) . T) (((-406 (-561))) . T) (($) . T)) (|has| |#1| (-842)) @@ -2385,7 +2386,7 @@ ((((-856)) . T)) ((((-856)) . T)) ((((-186)) . T) (((-856)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-856)) . T)) ((((-856)) . T)) @@ -2398,7 +2399,7 @@ ((((-856)) . T)) ((((-1148)) . T)) ((((-1166) |#1|) |has| |#1| (-512 (-1166) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -((((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) (|has| |#1| (-844)) ((((-856)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) @@ -2410,16 +2411,16 @@ (((|#2|) . T)) ((((-903 |#1|)) . T) (((-406 (-561))) . T) (($) . T)) ((($) . T) (((-561)) . T) (((-406 (-561))) . T) (((-607 $)) . T)) -(-4007 (|has| |#4| (-171)) (|has| |#4| (-720)) (|has| |#4| (-842)) (|has| |#4| (-1042))) -(-4007 (|has| |#3| (-171)) (|has| |#3| (-720)) (|has| |#3| (-842)) (|has| |#3| (-1042))) +(-4050 (|has| |#4| (-171)) (|has| |#4| (-720)) (|has| |#4| (-842)) (|has| |#4| (-1042))) +(-4050 (|has| |#3| (-171)) (|has| |#3| (-720)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((((-1166) (-52)) . T)) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4007 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-842)) (|has| |#2| (-1042))) (|has| |#1| (-902)) ((((-903 |#1|)) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) (|has| |#1| (-902)) @@ -2436,12 +2437,12 @@ (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (|has| |#1| (-814)) (((#0=(-903 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-561)) #1#) . T)) ((((-406 |#2|)) . T)) (|has| |#1| (-842)) -((((-1191 |#1|)) . T) (((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-1191 |#1|)) . T) (((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (((|#1| |#1|) . T) ((#0=(-406 (-561)) #0#) . T) ((#1=(-561) #1#) . T) (($ $) . T)) ((((-903 |#1|)) . T) (($) . T) (((-406 (-561))) . T)) (((|#2|) |has| |#2| (-1042)) (((-561)) -12 (|has| |#2| (-634 (-561))) (|has| |#2| (-1042)))) @@ -2452,26 +2453,26 @@ (((|#2|) . T)) ((((-856)) . T)) ((((-406 (-561))) . T) (((-692)) . T) (($) . T) (((-561)) . T)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2252 (-1166)) (|:| -2654 #0#))) . T)) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2285 (-1166)) (|:| -2677 #0#))) . T)) (|has| |#1| (-348)) ((((-561)) . T)) ((((-856)) . T)) (((|#1|) . T)) -(((#0=(-1239 |#1| |#2| |#3| |#4|) $) |has| #0# (-285 #0# #0#))) +(((#0=(-1240 |#1| |#2| |#3| |#4|) $) |has| #0# (-285 #0# #0#))) (|has| |#1| (-362)) (((#0=(-1072) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) (((#0=(-406 (-561)) #0#) . T) ((#1=(-692) #1#) . T) (($ $) . T)) ((((-315 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-406 (-561))) |has| |#1| (-362))) (|has| |#1| (-1090)) (((|#1|) . T)) -(((|#1|) -4007 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) -(((|#1|) -4007 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -4050 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -4050 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) (((|#2|) . T)) ((((-406 (-561))) . T) (((-692)) . T) (($) . T)) ((((-576)) . T)) @@ -2494,7 +2495,7 @@ (((|#1|) . T)) ((((-561)) . T)) (((|#2|) . T) (((-406 (-561))) |has| |#1| (-1031 (-406 (-561)))) ((|#1|) . T) (($) . T) (((-561)) . T)) -(-4007 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((|#2|) . T) (((-561)) |has| |#2| (-634 (-561)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2502,7 +2503,7 @@ ((($) . T) (((-406 (-561))) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T) (($) . T)) -(((|#1| (-1253 |#1|) (-1253 |#1|)) . T)) +(((|#1| (-1254 |#1|) (-1254 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) ((((-856)) . T)) ((((-856)) . T)) @@ -2532,7 +2533,7 @@ (|has| |#2| (-1015)) ((($) . T)) (|has| |#1| (-902)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2540,9 +2541,9 @@ ((($) . T)) (|has| |#1| (-362)) ((((-903 |#1|)) . T)) -((($) -4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((($) -4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) ((($ $) . T) ((#0=(-406 (-561)) #0#) . T)) -(-4007 (|has| |#1| (-367)) (|has| |#1| (-844))) +(-4050 (|has| |#1| (-367)) (|has| |#1| (-844))) (((|#1|) . T)) ((((-765)) . T)) ((((-856)) . T)) @@ -2553,16 +2554,16 @@ ((((-561)) . T) (($) . T)) ((((-561)) . T) (($) . T)) ((((-765) |#1|) . T)) -(((|#2| (-239 (-3498 |#1|) (-765))) . T)) +(((|#2| (-239 (-3548 |#1|) (-765))) . T)) (((|#1| (-529 |#3|)) . T)) ((((-406 (-561))) . T)) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((((-1148)) . T) (((-856)) . T)) -(((#0=(-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) #0#) |has| (-2 (|:| -2252 (-1166)) (|:| -2654 (-52))) (-308 (-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))))) +(((#0=(-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) #0#) |has| (-2 (|:| -2285 (-1166)) (|:| -2677 (-52))) (-308 (-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))))) ((((-1148)) . T)) (|has| |#1| (-902)) (|has| |#2| (-362)) -(-4007 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-856)) . T)) (((|#1|) . T)) @@ -2579,11 +2580,11 @@ (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-561)))) (-12 (|has| |#1| (-543)) (|has| |#1| (-822))) ((((-856)) . T)) -((((-1166)) -4007 (-12 (|has| |#1| (-15 * (|#1| (-561) |#1|))) (|has| |#1| (-893 (-1166)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-893 (-1166)))))) +((((-1166)) -4050 (-12 (|has| |#1| (-15 * (|#1| (-561) |#1|))) (|has| |#1| (-893 (-1166)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-893 (-1166)))))) (|has| |#1| (-362)) ((((-1166)) -12 (|has| |#1| (-15 * (|#1| (-406 (-561)) |#1|))) (|has| |#1| (-893 (-1166))))) (|has| |#1| (-362)) @@ -2594,13 +2595,13 @@ (((|#2|) |has| |#1| (-362))) (((|#2|) |has| |#1| (-362))) ((((-561)) . T) (($) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#2|) . T) (((-1166)) -12 (|has| |#1| (-362)) (|has| |#2| (-1031 (-1166)))) (((-561)) -12 (|has| |#1| (-362)) (|has| |#2| (-1031 (-561)))) (((-406 (-561))) -12 (|has| |#1| (-362)) (|has| |#2| (-1031 (-561))))) (((|#2|) . T)) -((((-1166) #0=(-1239 |#1| |#2| |#3| |#4|)) |has| #0# (-512 (-1166) #0#)) ((#0# #0#) |has| #0# (-308 #0#))) +((((-1166) #0=(-1240 |#1| |#2| |#3| |#4|)) |has| #0# (-512 (-1166) #0#)) ((#0# #0#) |has| #0# (-308 #0#))) ((((-607 $) $) . T) (($ $) . T)) ((((-168 (-224))) . T) (((-168 (-378))) . T) (((-1162 (-692))) . T) (((-885 (-378))) . T)) ((((-856)) . T)) @@ -2619,9 +2620,9 @@ ((((-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-879 (-378)))) (((-561)) -12 (|has| |#1| (-362)) (|has| |#2| (-879 (-561))))) (|has| |#1| (-362)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) (|has| |#1| (-362)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) (|has| |#1| (-362)) (|has| |#1| (-553)) (((|#1|) . T)) @@ -2630,22 +2631,22 @@ ((((-1148)) . T) (((-1166)) . T) (((-224)) . T) (((-561)) . T)) (((|#1|) . T)) ((((-406 |#2|)) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) -(-4007 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) (((|#2|) . T)) (((|#2|) . T)) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-720)) (|has| |#2| (-842)) (|has| |#2| (-1042))) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 |#1|))) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-720)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 |#1|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (|has| |#1| (-38 (-406 (-561)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-1148) |#1|) . T)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-578 |#1|)) . T)) ((($) . T)) @@ -2653,7 +2654,7 @@ (|has| |#1| (-553)) (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561)))) -(-4007 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-856)) . T)) ((($) . T)) @@ -2680,13 +2681,13 @@ ((((-856)) . T)) ((((-903 |#1|)) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-844)) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-844)) (|has| |#1| (-1090)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-224)) . T) (((-378)) . T) (((-885 (-378))) . T)) ((((-856)) . T)) -((((-1239 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-406 (-561))) . T)) +((((-1240 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-406 (-561))) . T)) (((|#1|) |has| |#1| (-171)) (($) |has| |#1| (-553)) (((-406 (-561))) |has| |#1| (-553))) ((((-856)) . T)) ((((-856)) . T)) @@ -2702,7 +2703,7 @@ ((((-561)) . T)) ((((-856)) . T)) ((((-561)) . T)) -(-4007 (|has| |#2| (-787)) (|has| |#2| (-842))) +(-4050 (|has| |#2| (-787)) (|has| |#2| (-842))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-856)) . T)) ((((-856)) . T)) @@ -2710,13 +2711,13 @@ ((((-856)) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((($) . T) ((#0=(-1238 |#2| |#3| |#4|)) |has| #0# (-171)) (((-406 (-561))) |has| #0# (-38 (-406 (-561))))) +((($) . T) ((#0=(-1239 |#2| |#3| |#4|)) |has| #0# (-171)) (((-406 (-561))) |has| #0# (-38 (-406 (-561))))) (((|#1|) . T) (($) . T) (((-406 (-561))) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) -(-4007 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +(-4050 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-720)) (|has| |#1| (-893 (-1166))) (|has| |#1| (-1042)) (|has| |#1| (-1102)) (|has| |#1| (-1090))) (|has| |#1| (-1141)) ((((-561) |#1|) . T)) (((|#1|) . T)) @@ -2736,8 +2737,8 @@ (((|#1|) . T)) (|has| |#1| (-553)) ((((-406 |#2|)) . T) (((-406 (-561))) . T) (($) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) ((((-378)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2746,7 +2747,7 @@ (|has| |#1| (-553)) (|has| |#1| (-1090)) ((((-774 |#1| (-858 |#2|))) |has| (-774 |#1| (-858 |#2|)) (-308 (-774 |#1| (-858 |#2|))))) -(-4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) +(-4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2758,13 +2759,13 @@ (|has| |#2| (-362)) ((((-578 |#1|)) . T) (((-406 (-561))) . T) (($) . T) (((-561)) . T)) ((((-561)) . T) (((-406 (-561))) . T) (($) . T)) -((((-2 (|:| -2252 (-1148)) (|:| -2654 (-52)))) . T)) +((((-2 (|:| -2285 (-1148)) (|:| -2677 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-561)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) ((((-856)) . T)) ((((-856)) . T)) -(-4007 (|has| |#3| (-787)) (|has| |#3| (-842))) +(-4050 (|has| |#3| (-787)) (|has| |#3| (-842))) ((((-856)) . T)) ((((-1110)) . T) (((-856)) . T)) ((((-534)) . T) (((-856)) . T)) @@ -2775,26 +2776,26 @@ ((((-561)) . T)) (((|#3|) . T)) ((((-856)) . T)) -(-4007 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) -((((-561)) . T) (((-406 (-561))) -4007 (|has| |#2| (-38 (-406 (-561)))) (|has| |#2| (-1031 (-406 (-561))))) ((|#2|) . T) (($) -4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) (((-858 |#1|)) . T)) -((((-1115 |#1| |#2|)) . T) ((|#2|) . T) (($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) . T) (((-406 (-561))) -4007 (|has| |#1| (-38 (-406 (-561)))) (|has| |#1| (-1031 (-406 (-561))))) (((-561)) . T)) -((((-1162 |#1|)) . T) (((-561)) . T) (($) -4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) (((-1072)) . T) ((|#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-406 (-561)) #0#) . T) (($ $) . T)) ((((-561)) . T)) @@ -3233,7 +3234,7 @@ ((((-561) |#1|) . T)) ((((-856)) . T)) ((($ $) . T) (((-1166) $) . T)) -((((-1245 |#1| |#2| |#3|)) . T)) +((((-1246 |#1| |#2| |#3|)) . T)) ((((-534)) |has| |#2| (-609 (-534))) (((-885 (-378))) |has| |#2| (-609 (-885 (-378)))) (((-885 (-561))) |has| |#2| (-609 (-885 (-561))))) ((((-856)) . T)) ((((-856)) . T)) @@ -3250,19 +3251,19 @@ (((|#1| |#2| (-239 |#1| |#2|) (-239 |#1| |#2|)) . T)) ((((-129)) . T)) ((((-856)) . T)) -((((-1245 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-406 (-561))) |has| |#2| (-38 (-406 (-561)))) ((|#2|) |has| |#2| (-171)) (($) -4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902)))) +((((-1246 |#1| |#2| |#3|)) |has| |#1| (-362))) +((((-406 (-561))) |has| |#2| (-38 (-406 (-561)))) ((|#2|) |has| |#2| (-171)) (($) -4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-406 (-561))) |has| |#2| (-38 (-406 (-561)))) ((|#2|) . T)) (|has| |#1| (-362)) -((($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((($) -4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) ((((-1094)) . T)) ((((-856)) . T)) -((($) -4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((($) -4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) ((($) . T) (((-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((|#1|) . T)) ((($) . T)) -((($) -4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) -((((-1245 |#1| |#2| |#3|)) . T) (((-1217 |#1| |#2| |#3|)) . T)) +((($) -4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((|#1|) |has| |#1| (-171)) (((-406 (-561))) |has| |#1| (-38 (-406 (-561))))) +((((-1246 |#1| |#2| |#3|)) . T) (((-1218 |#1| |#2| |#3|)) . T)) ((((-1166)) . T) (((-856)) . T)) (|has| |#2| (-902)) (((|#1|) . T)) @@ -3271,7 +3272,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-171))) ((((-692)) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) ((((-1171)) . T)) (((|#1|) |has| |#1| (-171))) ((((-1171)) . T)) @@ -3283,13 +3284,13 @@ ((((-1171)) . T)) ((((-1171)) . T)) ((((-1171)) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1171)) . T)) ((((-1171)) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -(-4007 (|has| |#1| (-171)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-171)) (|has| |#1| (-553))) (((|#1| (-561)) . T)) (((|#1| (-406 (-561))) . T)) (((|#1| (-765)) . T)) @@ -3304,16 +3305,16 @@ ((((-885 (-378))) . T) (((-885 (-561))) . T) (((-1166)) . T) (((-534)) . T)) (((|#1|) . T)) ((((-856)) . T)) -(-4007 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) -(-4007 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-787)) (|has| |#2| (-787)))) +(-4050 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-787)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-130)) (|has| |#2| (-130))) (-12 (|has| |#1| (-787)) (|has| |#2| (-787)))) ((((-561)) . T)) ((((-561)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-4007 (|has| |#2| (-171)) (|has| |#2| (-720)) (|has| |#2| (-842)) (|has| |#2| (-1042))) +(-4050 (|has| |#2| (-171)) (|has| |#2| (-720)) (|has| |#2| (-842)) (|has| |#2| (-1042))) ((((-1166)) -12 (|has| |#2| (-893 (-1166))) (|has| |#2| (-1042)))) -(-4007 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-720)) (|has| |#2| (-720)))) +(-4050 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-720)) (|has| |#2| (-720)))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-362)) @@ -3339,7 +3340,7 @@ (((|#1| |#2|) . T)) ((((-561)) . T) ((|#2|) |has| |#2| (-171))) ((((-114)) . T) ((|#1|) . T) (((-561)) . T)) -(-4007 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-4050 (|has| |#1| (-348)) (|has| |#1| (-367))) (((|#1| |#2|) . T)) ((((-224)) . T)) ((((-406 (-561))) . T) (($) . T) (((-561)) . T)) @@ -3351,7 +3352,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-534)) |has| |#1| (-609 (-534)))) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-844)) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-844)) (|has| |#1| (-1090)))) ((($) . T) (((-406 (-561))) . T)) (|has| |#1| (-902)) (|has| |#1| (-902)) @@ -3362,14 +3363,14 @@ (((|#1| |#1|) |has| |#1| (-171))) (((|#1|) . T) (((-561)) . T)) ((((-1171)) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-553))) -(-4007 (|has| |#1| (-21)) (|has| |#1| (-842))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-553))) +(-4050 (|has| |#1| (-21)) (|has| |#1| (-842))) (((|#2|) . T)) -(-4007 (|has| |#1| (-21)) (|has| |#1| (-842))) +(-4050 (|has| |#1| (-21)) (|has| |#1| (-842))) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#1|) . T)) -((((-856)) -4007 (-12 (|has| |#1| (-608 (-856))) (|has| |#2| (-608 (-856)))) (-12 (|has| |#1| (-1090)) (|has| |#2| (-1090))))) +((((-856)) -4050 (-12 (|has| |#1| (-608 (-856))) (|has| |#2| (-608 (-856)))) (-12 (|has| |#1| (-1090)) (|has| |#2| (-1090))))) ((((-406 |#2|) |#3|) . T)) ((((-406 (-561))) . T) (($) . T)) (|has| |#1| (-38 (-406 (-561)))) @@ -3381,19 +3382,19 @@ (((|#1|) . T) (((-406 (-561))) . T) (((-561)) . T) (($) . T)) (((#0=(-561) #0#) . T)) ((($) . T) (((-406 (-561))) . T)) -(-4007 (|has| |#4| (-171)) (|has| |#4| (-720)) (|has| |#4| (-842)) (|has| |#4| (-1042))) -(-4007 (|has| |#3| (-171)) (|has| |#3| (-720)) (|has| |#3| (-842)) (|has| |#3| (-1042))) +(-4050 (|has| |#4| (-171)) (|has| |#4| (-720)) (|has| |#4| (-842)) (|has| |#4| (-1042))) +(-4050 (|has| |#3| (-171)) (|has| |#3| (-720)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((((-856)) . T) (((-1171)) . T)) (|has| |#4| (-787)) -(-4007 (|has| |#4| (-787)) (|has| |#4| (-842))) +(-4050 (|has| |#4| (-787)) (|has| |#4| (-842))) (|has| |#4| (-842)) (|has| |#3| (-787)) ((((-1171)) . T)) -(-4007 (|has| |#3| (-787)) (|has| |#3| (-842))) +(-4050 (|has| |#3| (-787)) (|has| |#3| (-842))) (|has| |#3| (-842)) ((((-561)) . T)) (((|#2|) . T)) -((((-1166)) -4007 (-12 (|has| (-1164 |#1| |#2| |#3|) (-893 (-1166))) (|has| |#1| (-362))) (-12 (|has| |#1| (-15 * (|#1| (-561) |#1|))) (|has| |#1| (-893 (-1166)))))) +((((-1166)) -4050 (-12 (|has| (-1164 |#1| |#2| |#3|) (-893 (-1166))) (|has| |#1| (-362))) (-12 (|has| |#1| (-15 * (|#1| (-561) |#1|))) (|has| |#1| (-893 (-1166)))))) ((((-1166)) -12 (|has| |#1| (-15 * (|#1| (-406 (-561)) |#1|))) (|has| |#1| (-893 (-1166))))) ((((-1166)) -12 (|has| |#1| (-15 * (|#1| (-765) |#1|))) (|has| |#1| (-893 (-1166))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3408,11 +3409,11 @@ ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-1130 |#1| |#2|)) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-362))) -(((|#2|) . T) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1015)) -(((|#2|) . T) (((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) ((((-856)) . T)) ((((-534)) |has| |#2| (-609 (-534))) (((-885 (-561))) |has| |#2| (-609 (-885 (-561)))) (((-885 (-378))) |has| |#2| (-609 (-885 (-378)))) (((-378)) . #0=(|has| |#2| (-1015))) (((-224)) . #0#)) ((((-293 |#3|)) . T)) @@ -3428,15 +3429,15 @@ ((((-1164 |#1| |#2| |#3|)) . T)) ((((-1164 |#1| |#2| |#3|)) . T) (((-1157 |#1| |#2| |#3|)) . T)) ((((-856)) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) ((((-561) |#1|) . T)) ((((-1164 |#1| |#2| |#3|)) |has| |#1| (-362))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-362)) -(((|#3|) . T) ((|#2|) . T) (($) -4007 (|has| |#4| (-171)) (|has| |#4| (-842)) (|has| |#4| (-1042))) ((|#4|) -4007 (|has| |#4| (-171)) (|has| |#4| (-362)) (|has| |#4| (-1042)))) -(((|#2|) . T) (($) -4007 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((|#3|) -4007 (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-1042)))) +(((|#3|) . T) ((|#2|) . T) (($) -4050 (|has| |#4| (-171)) (|has| |#4| (-842)) (|has| |#4| (-1042))) ((|#4|) -4050 (|has| |#4| (-171)) (|has| |#4| (-362)) (|has| |#4| (-1042)))) +(((|#2|) . T) (($) -4050 (|has| |#3| (-171)) (|has| |#3| (-842)) (|has| |#3| (-1042))) ((|#3|) -4050 (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-1042)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-362)) @@ -3451,7 +3452,7 @@ ((((-186)) . T) (((-856)) . T)) ((((-856)) . T)) (((|#1|) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) ((((-129)) . T) (((-856)) . T)) ((((-561) |#1|) . T)) ((((-129)) . T)) @@ -3460,13 +3461,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-362)) (|has| |#2| (-285 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-902))) -(-4007 (|has| |#1| (-844)) (|has| |#1| (-1090))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-902))) +(-4050 (|has| |#1| (-844)) (|has| |#1| (-1090))) ((((-856)) . T)) ((((-856)) . T)) ((((-856)) . T)) (((|#1| (-529 |#2|)) . T)) -((((-2 (|:| -2252 (-1166)) (|:| -2654 (-52)))) . T)) +((((-2 (|:| -2285 (-1166)) (|:| -2677 (-52)))) . T)) ((((-561) (-129)) . T)) (((|#1| (-561)) . T)) (((|#1| (-406 (-561))) . T)) @@ -3480,8 +3481,8 @@ ((((-1171)) . T)) ((((-856)) . T) (((-1171)) . T)) ((((-856)) . T) (((-1171)) . T)) -(-4007 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) -(-4007 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) +(-4050 (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) +(-4050 (|has| |#1| (-450)) (|has| |#1| (-553)) (|has| |#1| (-902))) ((($) . T)) (((|#2| (-529 (-858 |#1|))) . T)) ((((-1171)) . T)) @@ -3496,13 +3497,13 @@ ((((-1171)) . T)) ((((-856)) . T) (((-1171)) . T)) ((((-1171)) . T)) -((((-856)) -4007 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) +((((-856)) -4050 (|has| |#1| (-608 (-856))) (|has| |#1| (-1090)))) (((|#1|) . T)) (((|#2| (-765)) . T)) (((|#1| |#2|) . T)) ((((-1148) |#1|) . T)) ((((-406 |#2|)) . T)) -((((-2 (|:| -2252 |#1|) (|:| -2654 |#2|))) . T)) +((((-2 (|:| -2285 |#1|) (|:| -2677 |#2|))) . T)) (|has| |#1| (-553)) (|has| |#1| (-553)) ((($) . T) ((|#2|) . T)) @@ -3511,14 +3512,14 @@ ((((-561)) . T) (($) . T)) (((|#2| $) |has| |#2| (-285 |#2| |#2|))) (((|#1| (-638 |#1|)) |has| |#1| (-842))) -(-4007 (|has| |#1| (-232)) (|has| |#1| (-348))) -(-4007 (|has| |#1| (-362)) (|has| |#1| (-348))) -((((-1249 |#1|)) . T) (((-561)) . T) ((|#2|) . T) (((-406 (-561))) |has| |#2| (-1031 (-406 (-561))))) +(-4050 (|has| |#1| (-232)) (|has| |#1| (-348))) +(-4050 (|has| |#1| (-362)) (|has| |#1| (-348))) +((((-1250 |#1|)) . T) (((-561)) . T) ((|#2|) . T) (((-406 (-561))) |has| |#2| (-1031 (-406 (-561))))) (|has| |#1| (-1090)) (((|#1|) . T)) -((((-1249 |#1|)) . T) (((-561)) . T) (($) -4007 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) (((-1072)) . T) ((|#2|) . T) (((-406 (-561))) -4007 (|has| |#2| (-38 (-406 (-561)))) (|has| |#2| (-1031 (-406 (-561)))))) +((((-1250 |#1|)) . T) (((-561)) . T) (($) -4050 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-553)) (|has| |#2| (-902))) (((-1072)) . T) ((|#2|) . T) (((-406 (-561))) -4050 (|has| |#2| (-38 (-406 (-561)))) (|has| |#2| (-1031 (-406 (-561)))))) ((((-406 (-561))) . T) (($) . T)) -((((-992 |#1|)) . T) ((|#1|) . T) (((-561)) -4007 (|has| (-992 |#1|) (-1031 (-561))) (|has| |#1| (-1031 (-561)))) (((-406 (-561))) -4007 (|has| (-992 |#1|) (-1031 (-406 (-561)))) (|has| |#1| (-1031 (-406 (-561)))))) +((((-992 |#1|)) . T) ((|#1|) . T) (((-561)) -4050 (|has| (-992 |#1|) (-1031 (-561))) (|has| |#1| (-1031 (-561)))) (((-406 (-561))) -4050 (|has| (-992 |#1|) (-1031 (-406 (-561)))) (|has| |#1| (-1031 (-406 (-561)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1090)))) @@ -3530,10 +3531,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1130 |#1| |#2|) #0#) |has| (-1130 |#1| |#2|) (-308 (-1130 |#1| |#2|)))) (((|#1|) . 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. -720) T) ((-1245 . -893) 146966) ((-1238 . -893) 146872) ((-1237 . -1048) 146707) ((-1217 . -893) 146540) ((-1216 . -1048) 146348) ((-1199 . -289) 146327) ((-1173 . -367) T) ((-1172 . -367) T) ((-1136 . -150) 146311) ((-1110 . -102) T) ((-1108 . -1090) T) ((-1070 . -23) T) ((-1065 . -102) T) ((-920 . -948) T) ((-731 . -308) 146249) ((-75 . -1205) T) ((-30 . -948) T) ((-168 . -902) 146202) ((-657 . -381) 146174) ((-112 . -838) T) ((-1 . -608) 146156) ((-1070 . -1102) T) ((-128 . -644) 146138) ((-50 . -615) 146122) ((-996 . -408) 146094) ((-591 . -893) 146007) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 145989) ((-865 . -1042) T) ((-827 . -844) 145968) ((-81 . -1205) T) ((-705 . -289) T) ((-40 . -1049) T) ((-578 . -171) T) ((-516 . -171) T) ((-509 . -608) 145950) ((-168 . -641) 145860) ((-505 . -608) 145842) ((-350 . -146) 145824) ((-350 . -144) T) ((-358 . -1102) T) ((-352 . -1102) T) ((-344 . -1102) T) ((-997 . -306) T) ((-907 . -306) T) ((-865 . -242) T) ((-108 . -1102) T) 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143894) ((-863 . -1049) T) ((-222 . -615) 143871) ((-326 . -285) 143848) ((-472 . -111) 143669) ((-1237 . -1042) T) ((-1216 . -1042) T) ((-810 . -376) 143653) ((-168 . -720) T) ((-647 . -102) T) ((-1237 . -242) 143632) ((-1237 . -232) 143584) ((-1216 . -232) 143489) ((-1216 . -242) 143468) ((-996 . -401) NIL) ((-663 . -634) 143416) ((-315 . -38) 143326) ((-312 . -38) 143255) ((-69 . -608) 143237) ((-318 . -491) 143203) ((-1178 . -287) 143182) ((-1103 . -1102) 143092) ((-83 . -1205) T) ((-61 . -608) 143074) ((-477 . -287) 143053) ((-1268 . -1031) 143030) ((-1154 . -1090) T) ((-1103 . -23) 142900) ((-810 . -893) 142836) ((-1226 . -720) T) ((-1092 . -1205) T) ((-472 . -611) 142662) ((-1077 . -289) 142593) ((-959 . -1090) T) ((-886 . -102) T) ((-776 . -289) 142504) ((-326 . -19) 142488) ((-59 . -287) 142465) ((-774 . -289) 142396) ((-849 . -720) T) ((-117 . -842) NIL) ((-514 . -287) 142373) ((-326 . -599) 142350) ((-494 . -287) 142327) ((-452 . -289) 142258) ((-1028 . -308) 142109) ((-674 . -488) 142090) ((-568 . -720) T) ((-669 . -488) 142071) ((-674 . -608) 142021) ((-669 . -608) 141987) ((-655 . -608) 141969) ((-476 . -488) 141950) ((-476 . -608) 141916) ((-244 . -609) 141877) ((-244 . -488) 141854) ((-137 . -488) 141835) ((-136 . -488) 141816) ((-132 . -488) 141797) ((-244 . -608) 141689) ((-212 . -102) T) ((-137 . -608) 141655) ((-136 . -608) 141621) ((-132 . -608) 141587) ((-1137 . -34) T) ((-936 . -1205) T) ((-342 . -711) 141532) ((-663 . -25) T) ((-663 . -21) T) ((-1166 . -611) 141513) ((-472 . -1042) T) ((-630 . -416) 141478) ((-602 . -416) 141443) ((-1110 . -1141) T) ((-578 . -289) T) ((-516 . -289) T) ((-1238 . -306) 141422) ((-472 . -232) 141374) ((-472 . -242) 141353) ((-1217 . -306) 141332) ((-1217 . -1015) NIL) ((-1070 . -130) T) ((-865 . -789) 141311) ((-143 . -102) T) ((-40 . -1090) T) ((-865 . -786) 141290) ((-638 . -1003) 141274) ((-577 . -1049) T) ((-561 . -1049) T) ((-493 . -1049) T) ((-406 . -450) T) ((-358 . -130) T) ((-315 . -399) 141258) ((-312 . -399) 141219) ((-352 . -130) T) ((-344 . -130) T) ((-1171 . -1090) T) ((-1110 . -38) 141206) ((-1084 . -608) 141173) ((-108 . -130) T) ((-947 . -1090) T) ((-914 . -1090) T) ((-765 . -1090) T) ((-665 . -1090) T) ((-694 . -146) T) ((-116 . -146) T) ((-1275 . -21) T) ((-1275 . -25) T) ((-1273 . -21) T) ((-1273 . -25) T) ((-657 . -1048) 141157) ((-529 . -844) T) ((-498 . -844) T) ((-354 . -1048) 141109) ((-351 . -1048) 141061) ((-343 . -1048) 141013) ((-250 . -1205) T) ((-249 . -1205) T) ((-263 . -1048) 140856) ((-246 . -1048) 140699) ((-657 . -111) 140678) ((-545 . -838) T) ((-354 . -111) 140616) ((-351 . -111) 140554) ((-343 . -111) 140492) ((-263 . -111) 140321) ((-246 . -111) 140150) ((-811 . -1209) 140129) ((-618 . -410) 140113) ((-44 . -21) T) ((-44 . -25) T) ((-809 . -634) 140019) ((-811 . -553) 139998) ((-250 . -1031) 139825) ((-249 . -1031) 139652) ((-126 . -119) 139636) ((-903 . -1048) 139601) ((-706 . -102) T) ((-692 . -1049) T) ((-534 . -613) 139504) ((-342 . -171) T) ((-151 . -25) T) ((-88 . -608) 139486) ((-151 . -21) T) ((-903 . -111) 139442) ((-40 . -711) 139387) ((-863 . -1090) T) ((-657 . -611) 139364) ((-639 . -611) 139345) ((-354 . -611) 139282) ((-351 . -611) 139219) ((-545 . -1090) T) ((-343 . -611) 139156) ((-326 . -609) 139117) ((-326 . -608) 139029) ((-263 . -611) 138782) ((-246 . -611) 138567) ((-1216 . -786) 138520) ((-1216 . -789) 138473) ((-250 . -376) 138442) ((-249 . -376) 138411) ((-647 . -38) 138381) ((-603 . -34) T) ((-480 . -1102) 138291) ((-473 . -34) T) ((-1103 . -130) 138161) ((-957 . -25) 137972) ((-903 . -611) 137922) ((-867 . -608) 137904) ((-957 . -21) 137859) ((-809 . -21) 137769) ((-809 . -25) 137620) ((-1211 . -367) T) ((-618 . -1049) T) ((-1168 . -553) 137599) ((-1162 . -47) 137576) ((-354 . -1042) T) ((-351 . -1042) T) ((-480 . -23) 137446) ((-343 . -1042) T) ((-246 . -1042) T) ((-263 . -1042) T) ((-1115 . -47) 137418) ((-117 . -1049) T) ((-1027 . -641) 137392) ((-951 . -34) T) ((-354 . -232) 137371) ((-354 . -242) T) 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. -1031) 136402) ((-1115 . -1031) 136285) ((-182 . -608) 136267) ((-848 . -1031) 136163) ((-776 . -285) 136090) ((-811 . -1102) T) ((-1027 . -720) T) ((-597 . -644) 136074) ((-1039 . -969) 136003) ((-992 . -102) T) ((-811 . -23) T) ((-706 . -1141) 135981) ((-687 . -1049) T) ((-597 . -372) 135965) ((-350 . -450) T) ((-342 . -289) T) ((-1254 . -1090) T) ((-247 . -1090) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -720) T) ((-704 . -1090) T) ((-692 . -1090) T) ((-360 . -471) T) ((-1199 . -608) 135947) ((-1162 . -376) 135931) ((-1115 . -376) 135915) ((-1017 . -410) 135877) ((-140 . -228) 135859) ((-378 . -788) T) ((-378 . -785) T) ((-863 . -171) T) ((-378 . -720) T) ((-705 . -608) 135841) ((-706 . -38) 135670) ((-1253 . -1251) 135654) ((-350 . -401) T) ((-1253 . -1090) 135604) ((-577 . -711) 135591) ((-561 . -711) 135578) ((-493 . -711) 135543) ((-315 . -624) 135522) ((-830 . -720) T) ((-821 . -720) T) ((-638 . -1205) T) ((-1070 . -634) 135470) ((-1162 . -893) 135413) 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-34) T) ((-811 . -130) T) ((-642 . -608) 133246) ((-575 . -102) T) ((-354 . -1272) 133230) ((-351 . -1272) 133214) ((-343 . -1272) 133198) ((-127 . -512) 133131) ((-121 . -512) 133064) ((-509 . -786) T) ((-509 . -789) T) ((-508 . -788) T) ((-103 . -308) 133002) ((-221 . -102) 132980) ((-687 . -1090) T) ((-692 . -171) T) ((-865 . -641) 132932) ((-65 . -383) T) ((-274 . -608) 132914) ((-65 . -394) T) ((-945 . -376) 132898) ((-863 . -289) T) ((-50 . -608) 132880) ((-992 . -38) 132828) ((-578 . -608) 132810) ((-479 . -376) 132794) ((-578 . -609) 132776) ((-516 . -608) 132758) ((-903 . -1272) 132745) ((-864 . -1205) T) ((-694 . -450) T) ((-493 . -512) 132711) ((-485 . -362) T) ((-354 . -367) 132690) ((-351 . -367) 132669) ((-343 . -367) 132648) ((-708 . -720) T) ((-216 . -362) T) ((-116 . -450) T) ((-1276 . -1267) 132632) ((-864 . -877) 132609) ((-864 . -879) NIL) ((-957 . -844) 132508) ((-809 . -844) 132459) ((-647 . -649) 132443) ((-1191 . -34) T) ((-170 . -608) 132425) ((-1103 . -21) 132335) ((-1103 . -25) 132186) ((-864 . -1031) 132163) ((-945 . -893) 132144) ((-1226 . -47) 132121) ((-903 . -367) T) ((-59 . -644) 132105) ((-514 . -644) 132089) ((-479 . -893) 132066) ((-71 . -439) T) ((-71 . -394) T) ((-494 . -644) 132050) ((-59 . -372) 132034) ((-618 . -171) T) ((-514 . -372) 132018) ((-494 . -372) 132002) ((-821 . -702) 131986) ((-1162 . -306) 131965) ((-1168 . -130) T) ((-117 . -171) T) ((-1136 . -308) 131903) ((-168 . -1205) T) ((-630 . -738) 131887) ((-602 . -738) 131871) ((-1265 . -130) T) ((-1238 . -913) 131850) ((-1217 . -913) 131829) ((-1217 . -814) NIL) ((-687 . -711) 131779) ((-1216 . -902) 131732) ((-1017 . -1090) T) ((-864 . -376) 131709) ((-864 . -337) 131686) ((-898 . -1102) T) ((-168 . -877) 131670) ((-168 . -879) 131595) ((-485 . -1102) T) ((-353 . -1090) T) ((-216 . -1102) T) ((-76 . -439) T) ((-76 . -394) T) ((-168 . -1031) 131491) ((-318 . -844) T) ((-1253 . -512) 131424) ((-1237 . -641) 131321) ((-1216 . -641) 131191) ((-865 . -788) 131170) 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T) ((-1053 . -543) T) ((-504 . -102) T) ((-500 . -102) T) ((-353 . -171) T) ((-342 . -608) 128918) ((-393 . -608) 128900) ((-472 . -720) T) ((-1110 . -842) T) ((-885 . -1031) 128868) ((-108 . -844) T) ((-651 . -1048) 128852) ((-485 . -130) T) ((-1239 . -1049) T) ((-216 . -130) T) ((-1146 . -102) 128830) ((-99 . -1090) T) ((-244 . -659) 128814) ((-244 . -644) 128798) ((-651 . -111) 128777) ((-582 . -611) 128761) ((-315 . -410) 128745) ((-244 . -372) 128729) ((-1149 . -234) 128676) ((-992 . -230) 128660) ((-74 . -1205) T) ((-48 . -171) T) ((-694 . -386) T) ((-694 . -142) T) ((-1276 . -102) T) ((-1185 . -611) 128642) ((-1077 . -1048) 128485) ((-263 . -902) 128464) ((-246 . -902) 128443) ((-776 . -1048) 128266) ((-774 . -1048) 128109) ((-603 . -1205) T) ((-1154 . -608) 128091) ((-1077 . -111) 127920) ((-1039 . -102) T) ((-473 . -1205) T) ((-459 . -1048) 127891) ((-452 . -1048) 127734) ((-657 . -641) 127718) ((-864 . -306) T) ((-776 . -111) 127527) ((-774 . -111) 127356) ((-354 . -641) 127308) ((-351 . -641) 127260) ((-343 . -641) 127212) ((-263 . -641) 127137) ((-246 . -641) 127062) ((-1148 . -844) T) ((-1078 . -1031) 127046) ((-459 . -111) 127007) ((-452 . -111) 126836) ((-1066 . -1031) 126813) ((-993 . -34) T) ((-959 . -608) 126795) ((-951 . -1205) T) ((-126 . -1003) 126779) ((-956 . -1102) T) ((-864 . -1015) NIL) ((-729 . -1102) T) ((-709 . -1102) T) ((-651 . -611) 126697) ((-1253 . -487) 126681) ((-1132 . -38) 126641) ((-956 . -23) T) ((-837 . -102) T) ((-811 . -21) T) ((-811 . -25) T) ((-729 . -23) T) ((-709 . -23) T) ((-110 . -654) T) ((-903 . -641) 126606) ((-578 . -1048) 126571) ((-516 . -1048) 126516) ((-226 . -57) 126474) ((-451 . -23) T) ((-406 . -102) T) ((-262 . -102) T) ((-687 . -289) T) ((-859 . -38) 126444) ((-578 . -111) 126400) ((-516 . -111) 126329) ((-1077 . -611) 126065) ((-417 . -1102) T) ((-315 . -1049) 125955) ((-312 . -1049) T) ((-128 . -1205) T) ((-776 . -611) 125703) ((-774 . -611) 125469) ((-651 . -1042) T) ((-1281 . -1090) T) ((-452 . 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-34) T) ((-996 . -1141) NIL) ((-725 . -553) 124323) ((-630 . -102) T) ((-602 . -102) T) ((-354 . -720) T) ((-351 . -720) T) ((-343 . -720) T) ((-263 . -720) T) ((-246 . -720) T) ((-1039 . -308) 124231) ((-894 . -1090) 124209) ((-50 . -1042) T) ((-1265 . -21) T) ((-1265 . -25) T) ((-1164 . -553) 124188) ((-1163 . -1209) 124167) ((-578 . -1042) T) ((-516 . -1042) T) ((-1157 . -1209) 124146) ((-360 . -1031) 124130) ((-321 . -1031) 124114) ((-1017 . -289) T) ((-378 . -879) 124096) ((-1163 . -553) 124047) ((-1157 . -553) 123998) ((-996 . -38) 123943) ((-793 . -1102) T) ((-903 . -720) T) ((-578 . -242) T) ((-578 . -232) T) ((-516 . -232) T) ((-516 . -242) T) ((-1116 . -553) 123922) ((-353 . -289) T) ((-640 . -688) 123906) ((-378 . -1031) 123866) ((-1110 . -1049) T) ((-103 . -125) 123850) ((-793 . -23) T) ((-1275 . -1270) 123826) ((-1253 . -285) 123803) ((-406 . -308) 123768) ((-1273 . -1270) 123747) ((-1239 . -1090) T) ((-863 . -608) 123729) ((-830 . -1031) 123698) ((-202 . -781) T) ((-201 . -781) T) ((-200 . -781) T) ((-199 . -781) T) ((-198 . -781) T) ((-197 . -781) T) ((-196 . -781) T) ((-195 . -781) T) ((-194 . -781) T) ((-193 . -781) T) ((-545 . -608) 123680) ((-493 . -995) T) ((-273 . -833) T) ((-272 . -833) T) ((-271 . -833) T) ((-270 . -833) T) ((-48 . -289) T) ((-269 . -833) T) ((-268 . -833) T) ((-267 . -833) T) ((-192 . -781) T) ((-607 . -844) T) ((-647 . -410) 123664) ((-222 . -611) 123626) ((-110 . -844) T) ((-646 . -21) T) ((-646 . -25) T) ((-1276 . -38) 123596) ((-117 . -285) 123547) ((-1253 . -19) 123531) ((-1253 . -599) 123508) ((-1266 . -1090) T) ((-1067 . -1090) T) ((-980 . -1090) T) ((-956 . -130) T) ((-731 . -1090) T) ((-729 . -130) T) ((-709 . -130) T) ((-509 . -787) T) ((-406 . -1141) 123486) ((-451 . -130) T) ((-509 . -788) T) ((-222 . -1042) T) ((-293 . -102) 123268) ((-140 . -1090) T) ((-692 . -995) T) ((-91 . -1205) T) ((-127 . -608) 123200) ((-121 . -608) 123132) ((-1281 . -171) T) ((-1163 . -362) 123111) ((-1157 . -362) 123090) ((-315 . -1090) T) ((-417 . -130) T) ((-312 . -1090) T) ((-406 . -38) 123042) ((-1123 . -102) T) ((-1239 . -711) 122934) ((-647 . -1049) T) ((-1125 . -1248) T) ((-318 . -144) 122913) ((-318 . -146) 122892) ((-138 . -1090) T) ((-135 . -1090) T) ((-114 . -1090) T) ((-852 . -102) T) ((-577 . -608) 122874) ((-561 . -609) 122773) ((-561 . -608) 122755) ((-493 . -608) 122737) ((-493 . -609) 122682) ((-483 . -23) T) ((-480 . -844) 122633) ((-485 . -634) 122615) ((-958 . -608) 122597) ((-216 . -634) 122579) ((-224 . -403) T) ((-655 . -641) 122563) ((-55 . -608) 122545) ((-1162 . -913) 122524) ((-725 . -1102) T) ((-350 . -102) T) ((-1204 . -1073) T) ((-1110 . -838) T) ((-812 . -844) T) ((-725 . -23) T) ((-342 . -1048) 122469) ((-1148 . -1147) T) ((-1137 . -107) 122453) ((-1164 . -1102) T) ((-1163 . -1102) T) ((-513 . -1031) 122437) ((-1157 . -1102) T) ((-1116 . -1102) T) ((-342 . -111) 122366) ((-997 . -1209) T) ((-126 . -1205) T) ((-907 . -1209) T) ((-687 . -285) NIL) ((-1254 . -608) 122348) ((-1164 . -23) T) 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120407) ((-647 . -1090) T) ((-603 . -107) 120354) ((-483 . -130) T) ((-473 . -107) 120304) ((-239 . -1102) 120214) ((-865 . -376) 120198) ((-865 . -337) 120182) ((-239 . -23) 120052) ((-40 . -611) 119982) ((-1053 . -913) T) ((-1053 . -814) T) ((-578 . -367) T) ((-516 . -367) T) ((-350 . -1141) T) ((-326 . -34) T) ((-44 . -416) 119966) ((-1171 . -611) 119901) ((-866 . -1205) T) ((-389 . -738) 119885) ((-1266 . -512) 119818) ((-725 . -130) T) ((-665 . -611) 119802) ((-1245 . -553) 119781) ((-1238 . -1209) 119760) ((-1238 . -553) 119711) ((-1217 . -1209) 119690) ((-310 . -1073) T) ((-1217 . -553) 119641) ((-731 . -512) 119574) ((-1216 . -1205) 119553) ((-1216 . -879) 119426) ((-886 . -1090) T) ((-143 . -838) T) ((-1216 . -877) 119396) ((-684 . -608) 119378) ((-1164 . -130) T) ((-521 . -308) 119316) ((-1163 . -130) T) ((-140 . -512) NIL) ((-1157 . -130) T) ((-1116 . -130) T) ((-1017 . -995) T) ((-997 . -23) T) ((-350 . -38) 119281) ((-997 . -1102) T) ((-907 . -1102) T) ((-82 . -608) 119263) ((-40 . -1042) T) ((-863 . -1048) 119250) ((-996 . -348) NIL) ((-865 . -893) 119209) ((-694 . -102) T) ((-964 . -23) T) ((-597 . -1205) T) ((-907 . -23) T) ((-863 . -111) 119194) ((-426 . -1102) T) ((-212 . -1090) T) ((-472 . -47) 119164) ((-133 . -102) T) ((-40 . -232) 119136) ((-40 . -242) T) ((-116 . -102) T) ((-592 . -553) 119115) ((-591 . -553) 119094) ((-687 . -608) 119076) ((-687 . -609) 118984) ((-315 . -512) 118950) ((-312 . -512) 118842) ((-1237 . -1031) 118826) ((-1216 . -1031) 118612) ((-992 . -410) 118596) ((-426 . -23) T) ((-1110 . -171) T) ((-1239 . -289) T) ((-647 . -711) 118566) ((-143 . -1090) T) ((-48 . -995) T) ((-406 . -230) 118550) ((-294 . -234) 118500) ((-864 . -913) T) ((-864 . -814) NIL) ((-863 . -611) 118472) ((-858 . -844) T) ((-1216 . -337) 118442) ((-1216 . -376) 118412) ((-221 . -1111) 118396) ((-1253 . -287) 118373) ((-1199 . -641) 118298) ((-956 . -21) T) ((-956 . -25) T) ((-729 . -21) T) ((-729 . -25) T) ((-709 . -21) T) ((-709 . -25) T) ((-705 . -641) 118263) ((-451 . -21) T) ((-451 . -25) T) ((-338 . -102) T) ((-173 . -102) T) ((-992 . -1049) T) ((-863 . -1042) T) ((-768 . -102) T) ((-1238 . -362) 118242) ((-1237 . -893) 118148) ((-1217 . -362) 118127) ((-1216 . -893) 117978) ((-1017 . -608) 117960) ((-406 . -822) 117913) ((-1164 . -491) 117879) ((-168 . -913) 117810) ((-1163 . -491) 117776) ((-1157 . -491) 117742) ((-706 . -1090) T) ((-1116 . -491) 117708) ((-577 . -1048) 117695) ((-561 . -1048) 117682) ((-493 . -1048) 117647) ((-315 . -289) 117626) ((-312 . -289) T) ((-353 . -608) 117608) ((-417 . -25) T) ((-417 . -21) T) ((-99 . -285) 117587) ((-577 . -111) 117572) ((-561 . -111) 117557) ((-493 . -111) 117513) ((-1166 . -879) 117480) ((-894 . -487) 117464) ((-48 . -608) 117446) ((-48 . -609) 117391) ((-239 . -130) 117261) ((-1226 . -913) 117240) ((-810 . -1209) 117219) ((-387 . -488) 117200) ((-1028 . -512) 117044) ((-387 . -608) 117010) ((-810 . -553) 116941) ((-582 . -641) 116916) ((-263 . -47) 116888) ((-246 . -47) 116845) ((-529 . -507) 116822) ((-577 . -611) 116794) ((-561 . -611) 116766) ((-493 . -611) 116699) ((-993 . -1205) T) ((-692 . -1048) 116664) ((-1245 . -23) T) ((-1245 . -1102) T) ((-1238 . -1102) T) ((-1217 . -1102) T) ((-996 . -369) 116636) ((-112 . -367) T) ((-472 . -893) 116542) ((-1238 . -23) T) ((-897 . -608) 116524) ((-55 . -611) 116506) ((-91 . -107) 116490) ((-1199 . -720) T) ((-898 . -844) 116441) ((-694 . -1141) T) ((-692 . -111) 116397) ((-1217 . -23) T) ((-592 . -1102) T) ((-591 . -1102) T) ((-706 . -711) 116226) ((-705 . -720) T) ((-1110 . -289) T) ((-997 . -130) T) ((-485 . -844) T) ((-964 . -130) T) ((-907 . -130) T) ((-793 . -25) T) ((-216 . -844) T) ((-793 . -21) T) ((-577 . -1042) T) ((-561 . -1042) T) ((-493 . -1042) T) ((-592 . -23) T) ((-342 . -1272) 116203) ((-318 . -450) 116182) ((-338 . -308) 116169) ((-591 . -23) T) ((-426 . -130) T) ((-651 . -641) 116143) ((-244 . -1003) 116127) ((-865 . -306) T) ((-1277 . -1267) 116111) ((-765 . -786) T) ((-765 . -789) T) 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-608) 114821) ((-433 . -608) 114803) ((-3 . -102) T) ((-1020 . -1198) 114772) ((-827 . -102) T) ((-682 . -57) 114730) ((-692 . -1042) T) ((-50 . -641) 114704) ((-288 . -450) T) ((-474 . -1198) 114673) ((0 . -102) T) ((-578 . -641) 114638) ((-516 . -641) 114583) ((-49 . -102) T) ((-903 . -1031) 114570) ((-692 . -242) T) ((-1070 . -408) 114549) ((-725 . -634) 114497) ((-992 . -1090) T) ((-706 . -171) 114388) ((-618 . -611) 114283) ((-485 . -985) 114265) ((-263 . -376) 114249) ((-246 . -376) 114233) ((-398 . -1090) T) ((-1019 . -102) 114211) ((-338 . -38) 114195) ((-216 . -985) 114177) ((-117 . -611) 114107) ((-173 . -38) 114039) ((-1237 . -306) 114018) ((-1216 . -306) 113997) ((-651 . -720) T) ((-99 . -608) 113979) ((-1157 . -634) 113931) ((-483 . -25) T) ((-483 . -21) T) ((-1216 . -1015) 113883) ((-618 . -1042) T) ((-378 . -403) T) ((-389 . -102) T) ((-1095 . -613) 113798) ((-263 . -893) 113744) ((-246 . -893) 113721) ((-117 . -1042) T) ((-810 . -1102) T) ((-1077 . -720) T) ((-618 . -232) 113700) ((-616 . -102) T) ((-776 . -720) T) ((-774 . -720) T) ((-412 . -1102) T) ((-117 . -242) T) ((-40 . -367) NIL) ((-117 . -232) NIL) ((-1210 . -844) T) ((-452 . -720) T) ((-810 . -23) T) ((-725 . -25) T) ((-725 . -21) T) ((-696 . -844) T) ((-1067 . -285) 113679) ((-78 . -395) T) ((-78 . -394) T) ((-531 . -761) 113661) ((-687 . -1048) 113611) ((-1245 . -130) T) ((-1238 . -130) T) ((-1217 . -130) T) ((-1132 . -410) 113595) ((-630 . -366) 113527) ((-602 . -366) 113459) ((-1146 . -1139) 113443) ((-103 . -1090) 113421) ((-1164 . -25) T) ((-1164 . -21) T) ((-1163 . -21) T) ((-992 . -711) 113369) ((-222 . -641) 113336) ((-687 . -111) 113270) ((-50 . -720) T) ((-1163 . -25) T) ((-350 . -348) T) ((-1157 . -21) T) ((-1070 . -450) 113221) ((-1157 . -25) T) ((-706 . -512) 113168) ((-578 . -720) T) ((-516 . -720) T) ((-1116 . -21) T) ((-1116 . -25) T) ((-592 . -130) T) ((-591 . -130) T) ((-358 . -450) T) ((-352 . -450) T) ((-344 . -450) T) ((-472 . -306) 113147) ((-312 . -285) 113082) ((-108 . -450) T) ((-79 . -439) T) ((-79 . -394) T) ((-475 . -102) T) ((-684 . -611) 113066) ((-1281 . -608) 113048) ((-1281 . -609) 113030) ((-1070 . -401) 113009) ((-1028 . -487) 112940) ((-561 . -789) T) ((-561 . -786) T) ((-1054 . -234) 112886) ((-358 . -401) 112837) ((-352 . -401) 112788) ((-344 . -401) 112739) ((-1268 . -1102) T) ((-687 . -611) 112674) ((-1268 . -23) T) ((-1255 . -102) T) ((-174 . -608) 112656) ((-1132 . -1049) T) ((-545 . -367) T) ((-663 . -738) 112640) ((-1168 . -144) 112619) ((-1168 . -146) 112598) ((-1136 . -1090) T) ((-1136 . -1062) 112567) ((-69 . -1205) T) ((-1017 . -1048) 112504) ((-859 . -1049) T) ((-239 . -634) 112410) ((-687 . -1042) T) ((-353 . -1048) 112355) ((-61 . -1205) T) ((-1017 . -111) 112271) ((-894 . -608) 112182) ((-687 . -242) T) ((-687 . -232) NIL) ((-837 . -842) 112161) ((-692 . -789) T) ((-692 . -786) T) ((-996 . -410) 112138) ((-353 . -111) 112067) ((-378 . -913) T) ((-406 . -842) 112046) ((-706 . -289) 111957) ((-222 . -720) T) ((-1245 . -491) 111923) ((-1238 . -491) 111889) ((-1217 . -491) 111855) ((-575 . -1090) T) ((-315 . -995) 111834) ((-221 . -1090) 111812) ((-318 . -966) 111774) ((-105 . -102) T) ((-48 . -1048) 111739) ((-1277 . -102) T) ((-380 . -102) T) ((-48 . -111) 111695) ((-997 . -634) 111677) ((-1239 . -608) 111659) ((-529 . -102) T) ((-498 . -102) T) ((-1123 . -1124) 111643) ((-151 . -1260) 111627) ((-244 . -1205) T) ((-1204 . -102) T) ((-1017 . -611) 111564) ((-1162 . -1209) 111543) ((-353 . -611) 111473) ((-1115 . -1209) 111452) ((-239 . -21) 111362) ((-239 . -25) 111213) ((-127 . -119) 111197) ((-121 . -119) 111181) ((-44 . -738) 111165) ((-1162 . -553) 111076) ((-1115 . -553) 111007) ((-1028 . -285) 110982) ((-1156 . -1073) T) ((-987 . -1073) T) ((-810 . -130) T) ((-117 . -789) NIL) ((-117 . -786) NIL) ((-354 . -306) T) ((-351 . -306) T) ((-343 . -306) T) ((-250 . -1102) 110892) ((-249 . -1102) 110802) ((-1017 . -1042) T) ((-996 . -1049) T) ((-48 . -611) 110735) ((-342 . -641) 110680) ((-616 . -38) 110664) ((-1266 . -608) 110626) ((-1266 . -609) 110587) ((-1067 . -608) 110569) ((-1017 . -242) T) ((-353 . -1042) T) ((-809 . -1260) 110539) ((-250 . -23) T) ((-249 . -23) T) ((-980 . -608) 110521) ((-731 . -609) 110482) ((-731 . -608) 110464) ((-793 . -844) 110443) ((-1149 . -150) 110390) ((-992 . -512) 110302) ((-353 . -232) T) ((-353 . -242) T) ((-387 . -611) 110283) ((-997 . -25) T) ((-140 . -608) 110265) ((-140 . -609) 110224) ((-903 . -306) T) ((-997 . -21) T) ((-964 . -25) T) ((-907 . -21) T) ((-907 . -25) T) ((-426 . -21) T) ((-426 . -25) T) ((-837 . -410) 110208) ((-48 . -1042) T) ((-1275 . -1267) 110192) ((-1273 . -1267) 110176) ((-1028 . -599) 110151) ((-315 . -609) 110012) ((-315 . -608) 109994) ((-312 . -609) NIL) ((-312 . -608) 109976) ((-48 . -242) T) ((-48 . -232) T) ((-647 . -285) 109937) ((-547 . -234) 109887) ((-138 . -608) 109854) ((-135 . -608) 109836) ((-114 . -608) 109818) ((-475 . -38) 109783) ((-1277 . -1274) 109762) ((-1268 . -130) T) ((-1276 . -1049) T) ((-1072 . -102) T) ((-88 . -1205) T) ((-498 . -308) NIL) ((-993 . -107) 109746) ((-882 . -1090) T) ((-878 . -1090) T) ((-1253 . -644) 109730) ((-1253 . -372) 109714) ((-326 . -1205) T) ((-589 . -844) T) ((-1132 . -1090) T) ((-1132 . -1045) 109654) ((-103 . -512) 109587) ((-920 . -608) 109569) ((-342 . -720) T) ((-30 . -608) 109551) ((-859 . -1090) T) ((-837 . -1049) 109530) ((-40 . -641) 109475) ((-224 . -1209) T) ((-406 . -1049) T) ((-1148 . -150) 109457) ((-992 . -289) 109408) ((-612 . -1090) T) ((-224 . -553) T) ((-318 . -1234) 109392) ((-318 . -1231) 109362) ((-1178 . -1181) 109341) ((-1065 . -608) 109323) ((-640 . -150) 109307) ((-627 . -150) 109253) ((-1178 . -107) 109203) ((-477 . -1181) 109182) ((-485 . -146) T) ((-485 . -144) NIL) ((-1110 . -609) 109097) ((-437 . -608) 109079) ((-216 . -146) T) ((-216 . -144) NIL) ((-1110 . -608) 109061) ((-129 . -102) T) ((-52 . -102) T) ((-1217 . -634) 109013) ((-477 . -107) 108963) ((-986 . -23) T) ((-1277 . -38) 108933) ((-1162 . -1102) T) ((-1115 . -1102) T) ((-1053 . -1209) T) ((-310 . -102) T) ((-848 . -1102) T) ((-945 . -1209) 108912) ((-479 . -1209) 108891) ((-725 . -844) 108870) ((-1053 . -553) T) ((-945 . -553) 108801) ((-1162 . -23) T) ((-1115 . -23) T) ((-848 . -23) T) ((-479 . -553) 108732) ((-1132 . -711) 108664) ((-1136 . -512) 108597) ((-1028 . -609) NIL) ((-1028 . -608) 108579) ((-96 . -1073) T) ((-859 . -711) 108549) ((-1199 . -47) 108518) ((-250 . -130) T) ((-249 . -130) T) ((-1094 . -1090) T) ((-996 . -1090) T) ((-62 . -608) 108500) ((-1157 . -844) NIL) ((-1017 . -786) T) ((-1017 . -789) T) ((-1281 . -1048) 108487) ((-1281 . -111) 108472) ((-863 . -641) 108459) ((-1245 . -25) T) ((-1245 . -21) T) ((-1238 . -21) T) ((-1238 . -25) T) ((-1217 . -21) T) ((-1217 . -25) T) ((-1020 . -150) 108443) ((-865 . -814) 108422) ((-865 . -913) T) ((-706 . -285) 108349) ((-592 . -21) T) ((-592 . -25) T) ((-591 . -21) T) ((-40 . -720) T) ((-221 . -512) 108282) ((-591 . -25) T) ((-474 . -150) 108266) ((-461 . -150) 108250) 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107308) ((-577 . -641) 107295) ((-561 . -641) 107282) ((-406 . -1090) T) ((-262 . -1090) T) ((-212 . -608) 107264) ((-493 . -641) 107229) ((-224 . -23) T) ((-1216 . -814) 107182) ((-1275 . -102) T) ((-353 . -1272) 107159) ((-1273 . -102) T) ((-1239 . -111) 107051) ((-143 . -608) 107033) ((-986 . -130) T) ((-44 . -102) T) ((-239 . -844) 106984) ((-1226 . -1209) 106963) ((-103 . -487) 106947) ((-1276 . -711) 106917) ((-1077 . -47) 106878) ((-1053 . -1102) T) ((-945 . -1102) T) ((-127 . -34) T) ((-121 . -34) T) ((-776 . -47) 106855) ((-774 . -47) 106827) ((-1226 . -553) 106738) ((-353 . -367) T) ((-479 . -1102) T) ((-1162 . -130) T) ((-1115 . -130) T) ((-452 . -47) 106717) ((-864 . -362) T) ((-848 . -130) T) ((-151 . -102) T) ((-1053 . -23) T) ((-945 . -23) T) ((-568 . -553) T) ((-810 . -25) T) ((-810 . -21) T) ((-1132 . -512) 106650) ((-588 . -1073) T) ((-582 . -1031) 106634) ((-1239 . -611) 106508) ((-479 . -23) T) ((-350 . -1049) T) ((-1199 . -893) 106489) ((-663 . -308) 106427) 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. -144) 103126) ((-250 . -634) 103032) ((-249 . -634) 102938) ((-318 . -283) 102904) ((-1146 . -512) 102837) ((-1123 . -1090) T) ((-224 . -1051) T) ((-809 . -308) 102775) ((-1077 . -893) 102710) ((-776 . -893) 102653) ((-774 . -893) 102637) ((-1275 . -38) 102607) ((-1273 . -38) 102577) ((-1226 . -1102) T) ((-849 . -1102) T) ((-452 . -893) 102554) ((-852 . -1090) T) ((-1226 . -23) T) ((-1110 . -611) 102526) ((-568 . -1102) T) ((-849 . -23) T) ((-618 . -720) T) ((-354 . -913) T) ((-351 . -913) T) ((-288 . -102) T) ((-343 . -913) T) ((-1053 . -130) T) ((-963 . -1073) T) ((-945 . -130) T) ((-117 . -788) NIL) ((-117 . -785) NIL) ((-117 . -720) T) ((-687 . -902) NIL) ((-1039 . -512) 102427) ((-479 . -130) T) ((-568 . -23) T) ((-668 . -308) 102365) ((-630 . -755) T) ((-602 . -755) T) ((-1217 . -844) NIL) ((-996 . -289) T) ((-250 . -21) T) ((-687 . -641) 102315) ((-350 . -1090) T) ((-250 . -25) T) ((-249 . -21) T) ((-249 . -25) T) ((-151 . -38) 102299) ((-2 . -102) T) ((-903 . -913) T) ((-480 . -1260) 102269) ((-222 . -1031) 102246) ((-1110 . -1042) T) ((-705 . -306) T) ((-293 . -711) 102188) ((-694 . -1049) T) ((-485 . -450) T) ((-406 . -512) 102100) ((-216 . -450) T) ((-1110 . -232) T) ((-294 . -150) 102050) ((-992 . -609) 102011) ((-992 . -608) 101993) ((-982 . -608) 101975) ((-116 . -1049) T) ((-647 . -1048) 101959) ((-224 . -491) T) ((-398 . -608) 101941) ((-398 . -609) 101918) ((-1046 . -1260) 101888) ((-647 . -111) 101867) ((-1132 . -487) 101851) ((-809 . -38) 101821) ((-63 . -439) T) ((-63 . -394) T) ((-1149 . -102) T) ((-864 . -130) T) ((-482 . -102) 101799) ((-1281 . -367) T) ((-1070 . -102) T) ((-1052 . -102) T) ((-350 . -711) 101744) ((-725 . -146) 101723) ((-725 . -144) 101702) ((-647 . -611) 101620) ((-1017 . -641) 101557) ((-521 . -1090) 101535) ((-358 . -102) T) ((-352 . -102) T) ((-344 . -102) T) ((-108 . -102) T) ((-502 . -1090) T) ((-353 . -641) 101480) ((-1162 . -634) 101428) ((-1115 . -634) 101376) ((-384 . -507) 101355) ((-827 . -842) 101334) ((-378 . 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-608) 100247) ((-1136 . -609) 100208) ((-1017 . -785) T) ((-1017 . -788) T) ((-1017 . -720) T) ((-706 . -1048) 100031) ((-482 . -308) 99969) ((-451 . -416) 99939) ((-350 . -171) T) ((-288 . -38) 99926) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-268 . -102) T) ((-342 . -1031) 99903) ((-267 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-205 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-192 . -102) T) ((-353 . -720) T) ((-706 . -111) 99712) ((-663 . -230) 99696) ((-578 . -306) T) ((-516 . -306) T) ((-293 . -512) 99645) ((-108 . -308) NIL) ((-72 . -394) T) ((-1103 . -102) 99435) ((-827 . -410) 99419) ((-1110 . -789) T) ((-1110 . -786) T) ((-694 . -1090) T) ((-575 . -608) 99401) ((-378 . -362) T) ((-168 . -491) 99379) ((-221 . -608) 99311) 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97866) ((-997 . -146) T) ((-997 . -144) NIL) ((-378 . -1102) T) ((-323 . -25) T) ((-321 . -23) T) ((-936 . -844) 97845) ((-706 . -325) 97822) ((-479 . -634) 97770) ((-40 . -1031) 97658) ((-706 . -232) T) ((-694 . -711) 97645) ((-338 . -1090) T) ((-173 . -1090) T) ((-330 . -844) T) ((-417 . -450) 97595) ((-378 . -23) T) ((-358 . -38) 97560) ((-352 . -38) 97525) ((-344 . -38) 97490) ((-80 . -439) T) ((-80 . -394) T) ((-224 . -25) T) ((-224 . -21) T) ((-830 . -1102) T) ((-108 . -38) 97440) ((-821 . -1102) T) ((-768 . -1090) T) ((-116 . -711) 97427) ((-665 . -1031) 97411) ((-607 . -102) T) ((-830 . -23) T) ((-821 . -23) T) ((-1146 . -285) 97388) ((-1103 . -308) 97326) ((-1092 . -234) 97310) ((-64 . -395) T) ((-64 . -394) T) ((-110 . -102) T) ((-40 . -376) 97287) ((-96 . -102) T) ((-646 . -846) 97271) ((-1125 . -1073) T) ((-1053 . -21) T) ((-1053 . -25) T) ((-809 . -230) 97240) ((-945 . -25) T) ((-945 . -21) T) ((-616 . -1049) T) ((-1110 . -367) T) ((-479 . -25) T) ((-479 . -21) T) ((-1020 . -308) 97178) ((-882 . -608) 97160) ((-878 . -608) 97142) ((-250 . -844) 97093) ((-249 . -844) 97044) ((-521 . -512) 96977) ((-864 . -634) 96954) ((-474 . -308) 96892) ((-461 . -308) 96830) ((-350 . -289) T) ((-1146 . -1241) 96814) ((-1132 . -608) 96776) ((-1132 . -609) 96737) ((-1130 . -102) T) ((-992 . -1048) 96633) ((-40 . -893) 96585) ((-1146 . -599) 96562) ((-1281 . -641) 96549) ((-859 . -488) 96526) ((-1054 . -150) 96472) ((-865 . -1209) T) ((-992 . -111) 96354) ((-338 . -711) 96338) ((-859 . -608) 96300) ((-173 . -711) 96232) ((-406 . -285) 96190) ((-865 . -553) T) ((-108 . -399) 96172) ((-84 . -383) T) ((-84 . -394) T) ((-694 . -171) T) ((-612 . -608) 96154) ((-99 . -720) T) ((-480 . -102) 95944) ((-99 . -471) T) ((-116 . -171) T) ((-1103 . -38) 95914) ((-168 . -634) 95862) ((-1046 . -102) T) ((-992 . -611) 95752) ((-864 . -25) T) ((-809 . -237) 95731) ((-864 . -21) T) ((-812 . -102) T) ((-413 . -102) T) ((-384 . -102) T) ((-110 . -308) NIL) ((-226 . -102) 95709) ((-127 . -1205) T) ((-121 . -1205) T) ((-1027 . -130) T) ((-663 . -366) 95693) ((-992 . -1042) T) ((-1226 . -634) 95641) ((-1094 . -608) 95623) ((-996 . -608) 95605) ((-513 . -23) T) ((-508 . -23) T) ((-342 . -306) T) ((-506 . -23) T) ((-321 . -130) T) ((-3 . -1090) T) ((-996 . -609) 95589) ((-992 . -242) 95568) ((-992 . -232) 95547) ((-1281 . -720) T) ((-1245 . -144) 95526) ((-827 . -1090) T) ((-1245 . -146) 95505) ((-1238 . -146) 95484) ((-1238 . -144) 95463) ((-1237 . -1209) 95442) ((-1217 . -144) 95349) ((-1217 . -146) 95256) ((-1216 . -1209) 95235) ((-378 . -130) T) ((-561 . -879) 95217) ((0 . -1090) T) ((-173 . -171) T) ((-168 . -21) T) ((-168 . -25) T) ((-49 . -1090) T) ((-1239 . -641) 95122) ((-1237 . -553) 95073) ((-708 . -1102) T) ((-1216 . -553) 95024) ((-561 . -1031) 95006) ((-591 . -146) 94985) ((-591 . -144) 94964) ((-493 . -1031) 94907) ((-1125 . -1127) T) ((-87 . -383) T) ((-87 . -394) T) ((-865 . -362) T) ((-830 . -130) T) ((-821 . -130) T) ((-708 . -23) T) ((-504 . -608) 94873) ((-500 . -608) 94855) ((-1277 . -1049) T) ((-378 . -1051) T) ((-1019 . -1090) 94833) ((-55 . -1031) 94815) ((-894 . -34) T) ((-480 . -308) 94753) ((-588 . -102) T) ((-1146 . -609) 94714) ((-1146 . -608) 94646) ((-1162 . -844) 94625) ((-45 . -102) T) ((-1115 . -844) 94604) ((-811 . -102) T) ((-1226 . -25) T) ((-1226 . -21) T) ((-849 . -25) T) ((-44 . -366) 94588) ((-849 . -21) T) ((-725 . -450) 94539) ((-1276 . -608) 94521) ((-1046 . -308) 94459) ((-664 . -1073) T) ((-601 . -1073) T) ((-389 . -1090) T) ((-568 . -25) T) ((-568 . -21) T) ((-179 . -1073) T) ((-160 . -1073) T) ((-155 . -1073) T) ((-153 . -1073) T) ((-616 . -1090) T) ((-692 . -879) 94441) ((-1253 . -1205) T) ((-226 . -308) 94379) ((-143 . -367) T) ((-1039 . -609) 94321) ((-1039 . -608) 94264) ((-312 . -902) NIL) ((-692 . -1031) 94209) ((-705 . -913) T) ((-472 . -1209) 94188) ((-1163 . -450) 94167) ((-1157 . -450) 94146) ((-329 . -102) T) ((-865 . -1102) T) ((-315 . -641) 93967) ((-312 . -641) 93896) ((-472 . -553) 93847) ((-338 . -512) 93813) ((-547 . -150) 93763) ((-40 . -306) T) ((-837 . -608) 93745) ((-694 . -289) T) ((-865 . -23) T) ((-378 . -491) T) ((-1070 . -230) 93715) ((-510 . -102) T) ((-406 . -609) 93522) ((-406 . -608) 93504) ((-262 . -608) 93486) ((-116 . -289) T) ((-1239 . -720) T) ((-1237 . -362) 93465) ((-1216 . -362) 93444) ((-1266 . -34) T) ((-117 . -1205) T) ((-108 . -230) 93426) ((-1168 . -102) T) ((-475 . -1090) T) ((-521 . -487) 93410) ((-731 . -34) T) ((-480 . -38) 93380) ((-140 . -34) T) ((-117 . -877) 93357) ((-117 . -879) NIL) ((-618 . -1031) 93240) ((-638 . -844) 93219) ((-1265 . -102) T) ((-294 . -102) T) ((-706 . -367) 93198) ((-117 . -1031) 93175) ((-389 . -711) 93159) ((-616 . -711) 93143) ((-45 . -308) 92947) ((-810 . -144) 92926) ((-810 . -146) 92905) ((-1276 . -381) 92884) ((-813 . -844) T) ((-1255 . -1090) T) ((-1149 . -228) 92831) ((-385 . -844) 92810) ((-1245 . -1193) 92776) ((-1245 . -1190) 92742) ((-1238 . -1190) 92708) ((-513 . -130) T) ((-1238 . -1193) 92674) ((-1217 . -1190) 92640) ((-1217 . -1193) 92606) ((-1245 . -35) 92572) ((-1245 . -95) 92538) ((-630 . -608) 92507) ((-602 . -608) 92476) ((-224 . -844) T) ((-1238 . -95) 92442) ((-1238 . -35) 92408) ((-1237 . -1102) T) ((-1110 . -641) 92395) ((-1217 . -95) 92361) ((-1216 . -1102) T) ((-589 . -150) 92343) ((-1070 . -348) 92322) ((-173 . -289) T) ((-117 . -376) 92299) ((-117 . -337) 92276) ((-1217 . -35) 92242) ((-863 . -306) T) ((-312 . -788) NIL) ((-312 . -785) NIL) ((-315 . -720) 92091) ((-312 . -720) T) ((-472 . -362) 92070) ((-358 . -348) 92049) ((-352 . -348) 92028) ((-344 . -348) 92007) ((-315 . -471) 91986) ((-1237 . -23) T) ((-1216 . -23) T) ((-712 . -1102) T) ((-708 . -130) T) ((-646 . -102) T) ((-475 . -711) 91951) ((-45 . -281) 91901) ((-105 . -1090) T) ((-68 . -608) 91883) ((-963 . -102) T) ((-858 . -102) T) ((-618 . -893) 91842) ((-1277 . -1090) T) ((-380 . -1090) T) ((-1204 . -1090) T) ((-1103 . -230) 91811) ((-82 . -1205) T) ((-1053 . -844) T) ((-945 . -844) 91790) 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87955) ((-1162 . -144) 87934) ((-1162 . -146) 87913) ((-1115 . -146) 87892) ((-1115 . -144) 87871) ((-630 . -1048) 87855) ((-602 . -1048) 87839) ((-663 . -1090) T) ((-663 . -1045) 87779) ((-1164 . -1244) 87763) ((-1164 . -1231) 87740) ((-485 . -1141) T) ((-1163 . -1236) 87701) ((-1163 . -1231) 87671) ((-1163 . -1234) 87655) ((-216 . -1141) T) ((-342 . -913) T) ((-812 . -265) 87639) ((-630 . -111) 87618) ((-602 . -111) 87597) ((-1157 . -1215) 87558) ((-837 . -1042) 87537) ((-1157 . -1231) 87514) ((-513 . -25) T) ((-493 . -301) T) ((-509 . -23) T) ((-508 . -25) T) ((-506 . -25) T) ((-505 . -23) T) ((-1157 . -1213) 87498) ((-406 . -1042) T) ((-318 . -1049) T) ((-687 . -306) T) ((-108 . -842) T) ((-706 . -720) T) ((-406 . -242) T) ((-406 . -232) 87477) ((-485 . -38) 87427) ((-216 . -38) 87377) ((-472 . -491) 87343) ((-1148 . -1134) T) ((-1091 . -102) T) ((-694 . -608) 87325) ((-694 . -609) 87240) ((-708 . -21) T) ((-708 . -25) T) ((-1125 . -102) T) ((-133 . -608) 87222) ((-116 . -608) 87204) ((-156 . -25) T) ((-1275 . -1090) T) ((-865 . -634) 87152) ((-1273 . -1090) T) ((-956 . -102) T) ((-729 . -102) T) ((-709 . -102) T) ((-451 . -102) T) ((-810 . -450) 87103) ((-44 . -1090) T) ((-1078 . -844) T) ((-657 . -130) T) ((-1054 . -308) 86954) ((-663 . -711) 86938) ((-288 . -1049) T) ((-354 . -130) T) ((-351 . -130) T) ((-343 . -130) T) ((-263 . -130) T) ((-246 . -130) T) ((-417 . -102) T) ((-151 . -1090) T) ((-45 . -228) 86888) ((-951 . -844) 86867) ((-992 . -641) 86805) ((-239 . -1260) 86775) ((-1017 . -306) T) ((-293 . -1048) 86696) ((-903 . -130) T) ((-40 . -913) T) ((-485 . -399) 86678) ((-353 . -306) T) ((-216 . -399) 86660) ((-1070 . -410) 86644) ((-293 . -111) 86560) ((-1173 . -844) T) ((-1172 . -844) T) ((-865 . -25) T) ((-865 . -21) T) ((-338 . -608) 86542) ((-1239 . -47) 86486) ((-224 . -146) T) ((-173 . -608) 86468) ((-1103 . -842) 86447) ((-768 . -608) 86429) ((-128 . -844) T) ((-603 . -234) 86376) ((-473 . -234) 86326) ((-1275 . -711) 86296) ((-48 . -306) T) 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85153) ((-318 . -1090) T) ((-406 . -789) 85132) ((-406 . -786) 85111) ((-498 . -487) 85093) ((-1239 . -1031) 85059) ((-1237 . -21) T) ((-1237 . -25) T) ((-1216 . -21) T) ((-1216 . -25) T) ((-809 . -711) 85001) ((-350 . -611) 84931) ((-692 . -403) T) ((-1266 . -1205) T) ((-601 . -102) T) ((-1103 . -410) 84900) ((-996 . -367) NIL) ((-664 . -102) T) ((-179 . -102) T) ((-160 . -102) T) ((-155 . -102) T) ((-153 . -102) T) ((-103 . -34) T) ((-731 . -1205) T) ((-44 . -755) T) ((-589 . -102) T) ((-77 . -395) T) ((-77 . -394) T) ((-646 . -649) 84884) ((-140 . -1205) T) ((-864 . -146) T) ((-864 . -144) NIL) ((-1204 . -93) T) ((-350 . -1042) T) ((-70 . -382) T) ((-70 . -394) T) ((-1155 . -102) T) ((-663 . -512) 84817) ((-682 . -308) 84755) ((-956 . -38) 84652) ((-729 . -38) 84622) ((-547 . -308) 84426) ((-315 . -1205) T) ((-350 . -232) T) ((-350 . -242) T) ((-312 . -1205) T) ((-288 . -1090) T) ((-1170 . -608) 84408) ((-705 . -1209) T) ((-1146 . -644) 84392) ((-1199 . -553) 84371) ((-705 . -553) T) ((-315 . -877) 84355) ((-315 . -879) 84280) ((-312 . -877) 84241) ((-312 . -879) NIL) ((-793 . -308) 84206) ((-318 . -711) 84047) ((-323 . -322) 84024) ((-483 . -102) T) ((-472 . -25) T) ((-472 . -21) T) ((-417 . -38) 83998) ((-315 . -1031) 83661) ((-224 . -1190) T) ((-224 . -1193) T) ((-3 . -608) 83643) ((-312 . -1031) 83573) ((-2 . -1090) T) ((-2 . |RecordCategory|) T) ((-827 . -608) 83555) ((-1103 . -1049) 83485) ((-577 . -913) T) ((-561 . -814) T) ((-561 . -913) T) ((-493 . -913) T) ((-135 . -1031) 83469) ((-224 . -95) T) ((-75 . -439) T) ((-75 . -394) T) ((0 . -608) 83451) ((-168 . -146) 83430) ((-168 . -144) 83381) ((-224 . -35) T) ((-49 . -608) 83363) ((-475 . -1049) T) ((-485 . -230) 83345) ((-482 . -961) 83329) ((-480 . -842) 83308) ((-216 . -230) 83290) ((-81 . -439) T) ((-81 . -394) T) ((-1136 . -34) T) ((-809 . -171) 83269) ((-725 . -102) T) ((-1019 . -608) 83236) ((-498 . -285) 83211) ((-315 . -376) 83180) ((-312 . -376) 83141) ((-312 . -337) 83102) ((-1075 . -608) 83084) ((-810 . -942) 83031) ((-655 . -130) T) ((-1226 . -144) 83010) ((-1226 . -146) 82989) ((-1164 . -102) T) ((-1163 . -102) T) ((-1157 . -102) T) ((-1149 . -1090) T) ((-1116 . -102) T) ((-221 . -34) T) ((-288 . -711) 82976) ((-1149 . -605) 82952) ((-589 . -308) NIL) ((-482 . -1090) 82930) ((-389 . -608) 82912) ((-508 . -844) T) ((-1140 . -228) 82862) ((-1245 . -1244) 82846) ((-1245 . -1231) 82823) ((-1238 . -1236) 82784) ((-1238 . -1231) 82754) ((-1238 . -1234) 82738) ((-1217 . -1215) 82699) ((-1217 . -1231) 82676) ((-616 . -608) 82658) ((-1217 . -1213) 82642) ((-692 . -913) T) ((-1164 . -283) 82608) ((-1163 . -283) 82574) ((-1157 . -283) 82540) ((-1070 . -1090) T) ((-1052 . -1090) T) ((-48 . -301) T) ((-315 . -893) 82506) ((-312 . -893) NIL) ((-1052 . -1059) 82485) ((-1110 . -879) 82467) ((-793 . -38) 82451) ((-263 . -634) 82399) ((-246 . -634) 82347) ((-694 . -1048) 82334) ((-591 . -1231) 82311) ((-1116 . -283) 82277) ((-318 . -171) 82208) ((-358 . -1090) T) ((-352 . -1090) T) 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NIL) ((-351 . -25) T) ((-351 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-263 . -25) T) ((-263 . -21) T) ((-246 . -25) T) ((-246 . -21) T) ((-83 . -383) T) ((-83 . -394) T) ((-133 . -611) 81059) ((-116 . -611) 81031) ((-1255 . -608) 81013) ((-1211 . -844) T) ((-1199 . -1102) T) ((-1199 . -23) T) ((-1157 . -308) 80898) ((-1116 . -308) 80885) ((-1070 . -711) 80753) ((-859 . -641) 80713) ((-936 . -973) 80697) ((-903 . -21) T) ((-288 . -171) T) ((-903 . -25) T) ((-310 . -93) T) ((-865 . -844) 80648) ((-705 . -1102) T) ((-705 . -23) T) ((-694 . -1042) T) ((-640 . -1090) 80626) ((-627 . -1090) T) ((-578 . -1209) T) ((-516 . -1209) T) ((-694 . -232) T) ((-627 . -605) 80601) ((-578 . -553) T) ((-516 . -553) T) ((-358 . -711) 80553) ((-338 . -1048) 80537) ((-352 . -711) 80489) ((-344 . -711) 80441) ((-173 . -1048) 80373) ((-173 . -111) 80284) ((-108 . -711) 80234) ((-338 . -111) 80213) ((-273 . -1090) T) ((-272 . -1090) T) ((-271 . -1090) T) ((-270 . -1090) T) ((-269 . -1090) T) ((-268 . -1090) T) ((-267 . -1090) T) ((-211 . -1090) T) ((-210 . -1090) T) ((-168 . -1193) 80191) ((-168 . -1190) 80169) ((-208 . -1090) T) ((-207 . -1090) T) ((-116 . -1042) T) ((-206 . -1090) T) ((-205 . -1090) T) ((-202 . -1090) T) ((-201 . -1090) T) ((-200 . -1090) T) ((-199 . -1090) T) ((-198 . -1090) T) ((-197 . -1090) T) ((-196 . -1090) T) ((-195 . -1090) T) ((-194 . -1090) T) ((-193 . -1090) T) ((-192 . -1090) T) ((-239 . -102) 79959) ((-168 . -35) 79937) ((-168 . -95) 79915) ((-647 . -1031) 79811) ((-480 . -1049) 79741) ((-1103 . -1090) 79531) ((-1132 . -34) T) ((-663 . -487) 79515) ((-73 . -1205) T) ((-105 . -608) 79497) ((-1277 . -608) 79479) ((-380 . -608) 79461) ((-338 . -611) 79413) ((-173 . -611) 79330) ((-1204 . -488) 79311) ((-725 . -38) 79160) ((-568 . -1193) T) ((-568 . -1190) T) ((-529 . -608) 79142) ((-518 . -308) 79080) ((-498 . -608) 79062) ((-498 . -609) 79044) ((-1204 . -608) 79010) ((-1157 . -1141) NIL) ((-1020 . -1062) 78979) ((-1020 . -1090) T) ((-997 . -102) T) 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-23) T) ((-103 . -1003) 77806) ((-45 . -36) 77785) ((-607 . -1090) T) ((-350 . -367) T) ((-522 . -102) T) ((-493 . -27) T) ((-239 . -308) 77723) ((-1077 . -1102) T) ((-1276 . -641) 77697) ((-776 . -1102) T) ((-774 . -1102) T) ((-452 . -1102) T) ((-1053 . -450) T) ((-945 . -450) 77648) ((-1105 . -1073) T) ((-110 . -1090) T) ((-1077 . -23) T) ((-811 . -1049) T) ((-776 . -23) T) ((-774 . -23) T) ((-479 . -450) 77599) ((-1149 . -512) 77382) ((-380 . -381) 77361) ((-1168 . -410) 77345) ((-459 . -23) T) ((-452 . -23) T) ((-96 . -1090) T) ((-482 . -512) 77278) ((-288 . -289) T) ((-1072 . -608) 77260) ((-1072 . -609) 77241) ((-406 . -902) 77220) ((-50 . -1102) T) ((-1017 . -913) T) ((-996 . -720) T) ((-706 . -879) NIL) ((-578 . -1102) T) ((-516 . -1102) T) ((-837 . -641) 77193) ((-1199 . -130) T) ((-1157 . -399) 77145) ((-997 . -308) NIL) ((-809 . -487) 77129) ((-353 . -913) T) ((-1146 . -34) T) ((-406 . -641) 77081) ((-50 . -23) T) ((-705 . -130) T) ((-706 . -1031) 76961) ((-578 . -23) T) 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76105) ((-221 . -253) 76089) ((-1217 . -102) T) ((-1046 . -1090) T) ((-997 . -1141) T) ((-1046 . -1045) 76029) ((-812 . -1090) T) ((-342 . -1209) T) ((-630 . -641) 76013) ((-616 . -111) 75992) ((-602 . -641) 75976) ((-592 . -102) T) ((-310 . -488) 75957) ((-582 . -130) T) ((-591 . -102) T) ((-413 . -1090) T) ((-384 . -1090) T) ((-310 . -608) 75923) ((-226 . -1090) 75901) ((-640 . -512) 75834) ((-627 . -512) 75678) ((-827 . -1042) 75657) ((-638 . -150) 75641) ((-342 . -553) T) ((-706 . -893) 75584) ((-547 . -228) 75534) ((-1245 . -283) 75500) ((-1070 . -289) 75451) ((-485 . -842) T) ((-222 . -1102) T) ((-1238 . -283) 75417) ((-1217 . -283) 75383) ((-997 . -38) 75333) ((-216 . -842) T) ((-1199 . -491) 75299) ((-907 . -38) 75251) ((-837 . -788) 75230) ((-837 . -785) 75209) ((-837 . -720) 75188) ((-358 . -289) T) ((-352 . -289) T) ((-344 . -289) T) ((-168 . -450) 75119) ((-426 . -38) 75103) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -788) 75082) ((-406 . -785) 75061) ((-406 . -720) T) 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. -599) 63233) ((-353 . -553) T) ((-216 . -512) NIL) ((-865 . -450) T) ((-417 . -1090) T) ((-406 . -1031) 63097) ((-318 . -111) 62918) ((-687 . -362) T) ((-224 . -283) T) ((-1202 . -611) 62895) ((-48 . -1209) T) ((-809 . -1042) 62825) ((-577 . -130) T) ((-561 . -130) T) ((-493 . -130) T) ((-1162 . -1141) 62803) ((-48 . -553) T) ((-1149 . -287) 62779) ((-1053 . -102) T) ((-945 . -102) T) ((-315 . -27) 62758) ((-809 . -232) 62710) ((-248 . -829) 62692) ((-239 . -842) 62671) ((-186 . -829) 62653) ((-707 . -102) T) ((-294 . -487) 62590) ((-479 . -102) T) ((-725 . -1049) T) ((-607 . -608) 62572) ((-607 . -609) 62433) ((-406 . -376) 62417) ((-406 . -337) 62401) ((-318 . -611) 62227) ((-1162 . -38) 62056) ((-1115 . -38) 61905) ((-848 . -38) 61875) ((-389 . -641) 61859) ((-638 . -308) 61797) ((-956 . -711) 61694) ((-729 . -711) 61664) ((-221 . -107) 61648) ((-45 . -285) 61573) ((-616 . -641) 61547) ((-311 . -1090) T) ((-288 . -1048) 61534) ((-110 . -608) 61516) ((-110 . -609) 61498) ((-451 . 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. -34) T) ((-776 . -102) T) ((-774 . -102) T) ((-1245 . -611) 21039) ((-1238 . -611) 20782) ((-459 . -102) T) ((-452 . -102) T) ((-1217 . -611) 20577) ((-239 . -789) 20528) ((-239 . -786) 20479) ((-642 . -102) T) ((-592 . -611) 20437) ((-591 . -611) 20319) ((-1226 . -289) 20230) ((-657 . -629) 20214) ((-185 . -608) 20196) ((-638 . -285) 20173) ((-1027 . -711) 20157) ((-568 . -289) T) ((-956 . -641) 20082) ((-1276 . -130) T) ((-729 . -641) 20042) ((-709 . -641) 20029) ((-274 . -102) T) ((-451 . -641) 19959) ((-50 . -102) T) ((-578 . -102) T) ((-516 . -102) T) ((-1245 . -1042) T) ((-1238 . -1042) T) ((-1217 . -1042) T) ((-1245 . -232) 19918) ((-321 . -711) 19900) ((-1238 . -242) 19879) ((-1238 . -232) 19831) ((-1217 . -232) 19718) ((-1217 . -242) 19697) ((-1199 . -38) 19594) ((-997 . -789) T) ((-592 . -1042) T) ((-591 . -1042) T) ((-997 . -786) T) ((-964 . -789) T) ((-964 . -786) T) ((-865 . -1049) T) ((-863 . -862) 19578) ((-109 . -608) 19560) ((-687 . -450) T) ((-378 . -711) 19525) 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. -308) 147071) ((-479 . -720) T) ((-1246 . -893) 146984) ((-1239 . -893) 146890) ((-1238 . -1048) 146725) ((-1218 . -893) 146558) ((-1217 . -1048) 146366) ((-1199 . -289) 146345) ((-1173 . -367) T) ((-1172 . -367) T) ((-1136 . -150) 146329) ((-1110 . -102) T) ((-1108 . -1090) T) ((-1070 . -23) T) ((-1065 . -102) T) ((-920 . -948) T) ((-731 . -308) 146267) ((-75 . -1205) T) ((-30 . -948) T) ((-168 . -902) 146220) ((-657 . -381) 146192) ((-112 . -838) T) ((-1 . -608) 146174) ((-1070 . -1102) T) ((-128 . -644) 146156) ((-50 . -615) 146140) ((-996 . -408) 146112) ((-591 . -893) 146025) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 146007) ((-865 . -1042) T) ((-827 . -844) 145986) ((-81 . -1205) T) ((-705 . -289) T) ((-40 . -1049) T) ((-578 . -171) T) ((-516 . -171) T) ((-509 . -608) 145968) ((-168 . -641) 145878) ((-505 . -608) 145860) ((-350 . -146) 145842) ((-350 . -144) T) ((-358 . -1102) T) ((-352 . -1102) T) ((-344 . -1102) T) ((-997 . -306) T) ((-907 . -306) T) ((-865 . -242) 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133303) ((-865 . -902) 133282) ((-126 . -34) T) ((-811 . -130) T) ((-642 . -608) 133264) ((-575 . -102) T) ((-354 . -1273) 133248) ((-351 . -1273) 133232) ((-343 . -1273) 133216) ((-127 . -512) 133149) ((-121 . -512) 133082) ((-509 . -786) T) ((-509 . -789) T) ((-508 . -788) T) ((-103 . -308) 133020) ((-221 . -102) 132998) ((-687 . -1090) T) ((-692 . -171) T) ((-865 . -641) 132950) ((-65 . -383) T) ((-274 . -608) 132932) ((-65 . -394) T) ((-945 . -376) 132916) ((-863 . -289) T) ((-50 . -608) 132898) ((-992 . -38) 132846) ((-578 . -608) 132828) ((-479 . -376) 132812) ((-578 . -609) 132794) ((-516 . -608) 132776) ((-903 . -1273) 132763) ((-864 . -1205) T) ((-694 . -450) T) ((-493 . -512) 132729) ((-485 . -362) T) ((-354 . -367) 132708) ((-351 . -367) 132687) ((-343 . -367) 132666) ((-708 . -720) T) ((-216 . -362) T) ((-116 . -450) T) ((-1277 . -1268) 132650) ((-864 . -877) 132627) ((-864 . -879) NIL) ((-957 . -844) 132526) ((-809 . -844) 132477) ((-647 . -649) 132461) ((-1191 . -34) T) 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-641) 131209) ((-865 . -788) 131188) ((-865 . -785) 131167) ((-865 . -720) T) ((-485 . -23) T) ((-222 . -608) 131149) ((-173 . -450) T) ((-221 . -308) 131087) ((-86 . -439) T) ((-86 . -394) T) ((-216 . -23) T) ((-1278 . -1271) 131066) ((-577 . -289) T) ((-561 . -289) T) ((-670 . -1031) 131050) ((-493 . -289) T) ((-135 . -468) 131005) ((-48 . -1090) T) ((-706 . -230) 130989) ((-864 . -893) NIL) ((-1227 . -879) NIL) ((-882 . -102) T) ((-878 . -102) T) ((-387 . -1090) T) ((-168 . -376) 130973) ((-168 . -337) 130957) ((-1227 . -1031) 130837) ((-849 . -1031) 130733) ((-1132 . -102) T) ((-646 . -130) T) ((-117 . -512) 130641) ((-655 . -786) 130620) ((-655 . -789) 130599) ((-568 . -1031) 130581) ((-293 . -1261) 130551) ((-859 . -102) T) ((-956 . -553) 130530) ((-1199 . -1048) 130413) ((-480 . -634) 130319) ((-897 . -1090) T) ((-1017 . -711) 130256) ((-705 . -1048) 130221) ((-612 . -102) T) ((-597 . -34) T) ((-1137 . -1205) T) ((-1199 . -111) 130090) ((-472 . -641) 129987) ((-353 . -711) 129932) ((-168 . -893) 129891) ((-692 . -289) T) ((-687 . -171) T) ((-705 . -111) 129847) ((-1282 . -1049) T) ((-1227 . -376) 129831) ((-417 . -1209) 129809) ((-1108 . -608) 129791) ((-312 . -842) NIL) ((-417 . -553) T) ((-224 . -306) T) ((-1217 . -785) 129744) ((-1217 . -788) 129697) ((-1238 . -720) T) ((-1217 . -720) T) ((-48 . -711) 129662) ((-224 . -1015) T) ((-350 . -1261) 129639) ((-1240 . -410) 129605) ((-712 . -720) T) ((-1227 . -893) 129548) ((-1199 . -611) 129430) ((-112 . -608) 129412) ((-112 . -609) 129394) ((-712 . -471) T) ((-705 . -611) 129344) ((-480 . -21) 129254) ((-127 . -487) 129238) ((-121 . -487) 129222) ((-480 . -25) 129073) ((-618 . -289) T) ((-582 . -1048) 129048) ((-436 . -1090) T) ((-1053 . -306) T) ((-117 . -289) T) ((-1094 . -102) T) ((-996 . -102) T) ((-582 . -111) 129016) ((-1132 . -308) 128954) ((-1199 . -1042) T) ((-1053 . -1015) T) ((-66 . -1205) T) ((-1046 . -25) T) ((-1046 . -21) T) ((-705 . -1042) T) ((-384 . -21) T) ((-384 . -25) T) ((-687 . -512) NIL) ((-1017 . -171) T) ((-705 . -242) T) ((-1053 . -543) T) ((-504 . -102) T) ((-500 . -102) T) ((-353 . -171) T) ((-342 . -608) 128936) ((-393 . -608) 128918) ((-472 . -720) T) ((-1110 . -842) T) ((-885 . -1031) 128886) ((-108 . -844) T) ((-651 . -1048) 128870) ((-485 . -130) T) ((-1240 . -1049) T) ((-216 . -130) T) ((-1146 . -102) 128848) ((-99 . -1090) T) ((-244 . -659) 128832) ((-244 . -644) 128816) ((-651 . -111) 128795) ((-582 . -611) 128779) ((-315 . -410) 128763) ((-244 . -372) 128747) ((-1149 . -234) 128694) ((-992 . -230) 128678) ((-74 . -1205) T) ((-48 . -171) T) ((-694 . -386) T) ((-694 . -142) T) ((-1277 . -102) T) ((-1185 . -611) 128660) ((-1077 . -1048) 128503) ((-263 . -902) 128482) ((-246 . -902) 128461) ((-776 . -1048) 128284) ((-774 . -1048) 128127) ((-603 . -1205) T) ((-1154 . -608) 128109) ((-1077 . -111) 127938) ((-1039 . -102) T) ((-473 . -1205) T) ((-459 . -1048) 127909) ((-452 . -1048) 127752) ((-657 . -641) 127736) ((-864 . -306) T) ((-776 . -111) 127545) 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-1042) T) ((-1282 . -1090) T) ((-452 . -611) 125272) ((-168 . -306) 125203) ((-417 . -23) T) ((-40 . -608) 125185) ((-40 . -609) 125169) ((-108 . -985) 125151) ((-116 . -862) 125135) ((-642 . -611) 125119) ((-48 . -512) 125085) ((-1191 . -1003) 125069) ((-1171 . -608) 125036) ((-1178 . -34) T) ((-947 . -608) 125002) ((-914 . -608) 124984) ((-1103 . -844) 124935) ((-765 . -608) 124917) ((-665 . -608) 124899) ((-1146 . -308) 124837) ((-477 . -34) T) ((-1082 . -1205) T) ((-475 . -450) T) ((-1131 . -34) T) ((-1077 . -1042) T) ((-50 . -611) 124806) ((-776 . -1042) T) ((-774 . -1042) T) ((-640 . -234) 124790) ((-627 . -234) 124736) ((-578 . -611) 124686) ((-516 . -611) 124616) ((-1227 . -306) 124595) ((-1077 . -325) 124556) ((-452 . -1042) T) ((-1168 . -21) T) ((-1077 . -232) 124535) ((-776 . -325) 124512) ((-776 . -232) T) ((-774 . -325) 124484) ((-725 . -1209) 124463) ((-326 . -644) 124447) ((-1168 . -25) T) ((-59 . -34) T) ((-517 . -34) T) ((-514 . -34) T) ((-452 . -325) 124426) ((-326 . -372) 124410) ((-495 . -34) T) ((-494 . -34) T) ((-996 . -1141) NIL) ((-725 . -553) 124341) ((-630 . -102) T) ((-602 . -102) T) ((-354 . -720) T) ((-351 . -720) T) ((-343 . -720) T) ((-263 . -720) T) ((-246 . -720) T) ((-1039 . -308) 124249) ((-894 . -1090) 124227) ((-50 . -1042) T) ((-1266 . -21) T) ((-1266 . -25) T) ((-1164 . -553) 124206) ((-1163 . -1209) 124185) ((-578 . -1042) T) ((-516 . -1042) T) ((-1157 . -1209) 124164) ((-360 . -1031) 124148) ((-321 . -1031) 124132) ((-1017 . -289) T) ((-378 . -879) 124114) ((-1163 . -553) 124065) ((-1157 . -553) 124016) ((-996 . -38) 123961) ((-793 . -1102) T) ((-903 . -720) T) ((-578 . -242) T) ((-578 . -232) T) ((-516 . -232) T) ((-516 . -242) T) ((-1116 . -553) 123940) ((-353 . -289) T) ((-640 . -688) 123924) ((-378 . -1031) 123884) ((-1110 . -1049) T) ((-103 . -125) 123868) ((-793 . -23) T) ((-1276 . -1271) 123844) ((-1254 . -285) 123821) ((-406 . -308) 123786) ((-1274 . -1271) 123765) ((-1240 . -1090) T) ((-863 . -608) 123747) ((-830 . 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123129) ((-1157 . -362) 123108) ((-315 . -1090) T) ((-417 . -130) T) ((-312 . -1090) T) ((-406 . -38) 123060) ((-1123 . -102) T) ((-1240 . -711) 122952) ((-647 . -1049) T) ((-1125 . -1249) T) ((-318 . -144) 122931) ((-318 . -146) 122910) ((-138 . -1090) T) ((-135 . -1090) T) ((-114 . -1090) T) ((-852 . -102) T) ((-577 . -608) 122892) ((-561 . -609) 122791) ((-561 . -608) 122773) ((-493 . -608) 122755) ((-493 . -609) 122700) ((-483 . -23) T) ((-480 . -844) 122651) ((-485 . -634) 122633) ((-958 . -608) 122615) ((-216 . -634) 122597) ((-224 . -403) T) ((-655 . -641) 122581) ((-55 . -608) 122563) ((-1162 . -913) 122542) ((-725 . -1102) T) ((-350 . -102) T) ((-1204 . -1073) T) ((-1110 . -838) T) ((-812 . -844) T) ((-725 . -23) T) ((-342 . -1048) 122487) ((-1148 . -1147) T) ((-1137 . -107) 122471) ((-1164 . -1102) T) ((-1163 . -1102) T) ((-513 . -1031) 122455) ((-1157 . -1102) T) ((-1116 . -1102) T) ((-342 . -111) 122384) ((-997 . -1209) T) ((-126 . -1205) T) ((-907 . -1209) T) ((-687 . -285) NIL) ((-1255 . -608) 122366) ((-1164 . -23) T) ((-1163 . -23) T) ((-1157 . -23) T) ((-997 . -553) T) ((-1132 . -230) 122350) ((-907 . -553) T) ((-1116 . -23) T) ((-247 . -608) 122332) ((-1065 . -1090) T) ((-793 . -130) T) ((-704 . -608) 122314) ((-315 . -711) 122224) ((-312 . -711) 122153) ((-692 . -608) 122135) ((-692 . -609) 122080) ((-406 . -399) 122064) ((-437 . -1090) T) ((-485 . -25) T) ((-485 . -21) T) ((-1110 . -1090) T) ((-216 . -25) T) ((-216 . -21) T) ((-706 . -410) 122048) ((-708 . -1031) 122017) ((-1254 . -608) 121929) ((-1254 . -609) 121890) ((-1240 . -171) T) ((-244 . -34) T) ((-342 . -611) 121820) ((-393 . -611) 121802) ((-919 . -967) T) ((-1191 . -1205) T) ((-655 . -785) 121781) ((-655 . -788) 121760) ((-397 . -394) T) ((-521 . -102) 121738) ((-1028 . -1090) T) ((-221 . -988) 121722) ((-502 . -102) T) ((-618 . -608) 121704) ((-45 . -844) NIL) ((-618 . -609) 121681) ((-1028 . -605) 121656) ((-894 . -512) 121589) ((-342 . -1042) T) ((-117 . -609) NIL) ((-117 . -608) 121571) ((-865 . -1205) T) ((-663 . -416) 121555) ((-663 . -1113) 121500) ((-498 . -150) 121482) ((-342 . -232) T) ((-342 . -242) T) ((-40 . -1048) 121427) ((-865 . -877) 121411) ((-865 . -879) 121336) ((-706 . -1049) T) ((-687 . -995) NIL) ((-3 . |UnionCategory|) T) ((-1238 . -47) 121306) ((-1217 . -47) 121283) ((-1131 . -1003) 121254) ((-224 . -913) T) ((-40 . -111) 121183) ((-865 . -1031) 121047) ((-1110 . -711) 121034) ((-1095 . -608) 121016) ((-1070 . -146) 120995) ((-1070 . -144) 120946) ((-997 . -362) T) ((-318 . -1193) 120912) ((-378 . -306) T) ((-318 . -1190) 120878) ((-315 . -171) 120857) ((-312 . -171) T) ((-996 . -230) 120834) ((-907 . -362) T) ((-578 . -1273) 120821) ((-516 . -1273) 120798) ((-358 . -146) 120777) ((-358 . -144) 120728) ((-352 . -146) 120707) ((-352 . -144) 120658) ((-603 . -1181) 120634) ((-344 . -146) 120613) ((-344 . -144) 120564) ((-318 . -35) 120530) ((-473 . -1181) 120509) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120475) ((-378 . -1015) T) 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. -1102) T) ((-907 . -1102) T) ((-82 . -608) 119281) ((-40 . -1042) T) ((-863 . -1048) 119268) ((-996 . -348) NIL) ((-865 . -893) 119227) ((-694 . -102) T) ((-964 . -23) T) ((-597 . -1205) T) ((-907 . -23) T) ((-863 . -111) 119212) ((-426 . -1102) T) ((-212 . -1090) T) ((-472 . -47) 119182) ((-133 . -102) T) ((-40 . -232) 119154) ((-40 . -242) T) ((-116 . -102) T) ((-592 . -553) 119133) ((-591 . -553) 119112) ((-687 . -608) 119094) ((-687 . -609) 119002) ((-315 . -512) 118968) ((-312 . -512) 118860) ((-1238 . -1031) 118844) ((-1217 . -1031) 118630) ((-992 . -410) 118614) ((-426 . -23) T) ((-1110 . -171) T) ((-1240 . -289) T) ((-647 . -711) 118584) ((-143 . -1090) T) ((-48 . -995) T) ((-406 . -230) 118568) ((-294 . -234) 118518) ((-864 . -913) T) ((-864 . -814) NIL) ((-863 . -611) 118490) ((-858 . -844) T) ((-1217 . -337) 118460) ((-1217 . -376) 118430) ((-221 . -1111) 118414) ((-1254 . -287) 118391) ((-1199 . -641) 118316) ((-956 . -21) T) ((-956 . -25) T) ((-729 . -21) T) ((-729 . -25) T) ((-709 . -21) T) ((-709 . -25) T) ((-705 . -641) 118281) ((-451 . -21) T) ((-451 . -25) T) ((-338 . -102) T) ((-173 . -102) T) ((-992 . -1049) T) ((-863 . -1042) T) ((-768 . -102) T) ((-1239 . -362) 118260) ((-1238 . -893) 118166) ((-1218 . -362) 118145) ((-1217 . -893) 117996) ((-1017 . -608) 117978) ((-406 . -822) 117931) ((-1164 . -491) 117897) ((-168 . -913) 117828) ((-1163 . -491) 117794) ((-1157 . -491) 117760) ((-706 . -1090) T) ((-1116 . -491) 117726) ((-577 . -1048) 117713) ((-561 . -1048) 117700) ((-493 . -1048) 117665) ((-315 . -289) 117644) ((-312 . -289) T) ((-353 . -608) 117626) ((-417 . -25) T) ((-417 . -21) T) ((-99 . -285) 117605) ((-577 . -111) 117590) ((-561 . -111) 117575) ((-493 . -111) 117531) ((-1166 . -879) 117498) ((-894 . -487) 117482) ((-48 . -608) 117464) ((-48 . -609) 117409) ((-239 . -130) 117279) ((-1227 . -913) 117258) ((-810 . -1209) 117237) ((-387 . -488) 117218) ((-1028 . -512) 117062) ((-387 . -608) 117028) ((-810 . -553) 116959) ((-582 . 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-1268) 116129) ((-765 . -786) T) ((-765 . -789) T) ((-694 . -38) 116116) ((-561 . -232) T) ((-493 . -242) T) ((-493 . -232) T) ((-1140 . -234) 116066) ((-1077 . -902) 116045) ((-116 . -38) 116032) ((-208 . -794) T) ((-207 . -794) T) ((-206 . -794) T) ((-205 . -794) T) ((-865 . -1015) 116010) ((-1267 . -487) 115994) ((-776 . -902) 115973) ((-774 . -902) 115952) ((-1178 . -1205) T) ((-452 . -902) 115931) ((-731 . -487) 115915) ((-1077 . -641) 115840) ((-692 . -611) 115775) ((-776 . -641) 115700) ((-618 . -1048) 115687) ((-477 . -1205) T) ((-342 . -367) T) ((-140 . -487) 115669) ((-774 . -641) 115594) ((-1131 . -1205) T) ((-546 . -844) T) ((-459 . -641) 115565) ((-263 . -879) 115424) ((-246 . -879) NIL) ((-117 . -1048) 115369) ((-452 . -641) 115294) ((-657 . -1031) 115271) ((-618 . -111) 115256) ((-354 . -1031) 115240) ((-351 . -1031) 115224) ((-343 . -1031) 115208) ((-263 . -1031) 115052) ((-246 . -1031) 114928) ((-117 . -111) 114857) ((-59 . -1205) T) ((-517 . -1205) T) ((-514 . -1205) T) ((-495 . -1205) T) ((-494 . -1205) T) ((-436 . -608) 114839) ((-433 . -608) 114821) ((-3 . -102) T) ((-1020 . -1198) 114790) ((-827 . -102) T) ((-682 . -57) 114748) ((-692 . -1042) T) ((-50 . -641) 114722) ((-288 . -450) T) ((-474 . -1198) 114691) ((0 . -102) T) ((-578 . -641) 114656) ((-516 . -641) 114601) ((-49 . -102) T) ((-903 . -1031) 114588) ((-692 . -242) T) ((-1070 . -408) 114567) ((-725 . -634) 114515) ((-992 . -1090) T) ((-706 . -171) 114406) ((-618 . -611) 114301) ((-485 . -985) 114283) ((-263 . -376) 114267) ((-246 . -376) 114251) ((-398 . -1090) T) ((-1019 . -102) 114229) ((-338 . -38) 114213) ((-216 . -985) 114195) ((-117 . -611) 114125) ((-173 . -38) 114057) ((-1238 . -306) 114036) ((-1217 . -306) 114015) ((-651 . -720) T) ((-99 . -608) 113997) ((-1157 . -634) 113949) ((-483 . -25) T) ((-483 . -21) T) ((-1217 . -1015) 113901) ((-618 . -1042) T) ((-378 . -403) T) ((-389 . -102) T) ((-1095 . -613) 113816) ((-263 . -893) 113762) ((-246 . -893) 113739) ((-117 . -1042) T) 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. -842) 112064) ((-706 . -289) 111975) ((-222 . -720) T) ((-1246 . -491) 111941) ((-1239 . -491) 111907) ((-1218 . -491) 111873) ((-575 . -1090) T) ((-315 . -995) 111852) ((-221 . -1090) 111830) ((-318 . -966) 111792) ((-105 . -102) T) ((-48 . -1048) 111757) ((-1278 . -102) T) ((-380 . -102) T) ((-48 . -111) 111713) ((-997 . -634) 111695) ((-1240 . -608) 111677) ((-529 . -102) T) ((-498 . -102) T) ((-1123 . -1124) 111661) ((-151 . -1261) 111645) ((-244 . -1205) T) ((-1204 . -102) T) ((-1017 . -611) 111582) ((-1162 . -1209) 111561) ((-353 . -611) 111491) ((-1115 . -1209) 111470) ((-239 . -21) 111380) ((-239 . -25) 111231) ((-127 . -119) 111215) ((-121 . -119) 111199) ((-44 . -738) 111183) ((-1162 . -553) 111094) ((-1115 . -553) 111025) ((-1028 . -285) 111000) ((-1156 . -1073) T) ((-987 . -1073) T) ((-810 . -130) T) ((-117 . -789) NIL) ((-117 . -786) NIL) ((-354 . -306) T) ((-351 . -306) T) ((-343 . -306) T) ((-250 . -1102) 110910) ((-249 . -1102) 110820) ((-1017 . -1042) T) ((-996 . -1049) T) ((-48 . -611) 110753) ((-342 . -641) 110698) ((-616 . -38) 110682) ((-1267 . -608) 110644) ((-1267 . -609) 110605) ((-1067 . -608) 110587) ((-1017 . -242) T) ((-353 . -1042) T) ((-809 . -1261) 110557) ((-250 . -23) T) ((-249 . -23) T) ((-980 . -608) 110539) ((-731 . -609) 110500) ((-731 . -608) 110482) ((-793 . -844) 110461) ((-1149 . -150) 110408) ((-992 . -512) 110320) ((-353 . -232) T) ((-353 . -242) T) ((-387 . -611) 110301) ((-997 . -25) T) ((-140 . -608) 110283) ((-140 . -609) 110242) ((-903 . -306) T) ((-997 . -21) T) ((-964 . -25) T) ((-907 . -21) T) ((-907 . -25) T) ((-426 . -21) T) ((-426 . -25) T) ((-837 . -410) 110226) ((-48 . -1042) T) ((-1276 . -1268) 110210) ((-1274 . -1268) 110194) ((-1028 . -599) 110169) ((-315 . -609) 110030) ((-315 . -608) 110012) ((-312 . -609) NIL) ((-312 . -608) 109994) ((-48 . -242) T) ((-48 . -232) T) ((-647 . -285) 109955) ((-547 . -234) 109905) ((-138 . -608) 109872) ((-135 . -608) 109854) ((-114 . -608) 109836) ((-475 . -38) 109801) 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108981) ((-986 . -23) T) ((-1278 . -38) 108951) ((-1162 . -1102) T) ((-1115 . -1102) T) ((-1053 . -1209) T) ((-310 . -102) T) ((-848 . -1102) T) ((-945 . -1209) 108930) ((-479 . -1209) 108909) ((-725 . -844) 108888) ((-1053 . -553) T) ((-945 . -553) 108819) ((-1162 . -23) T) ((-1115 . -23) T) ((-848 . -23) T) ((-479 . -553) 108750) ((-1132 . -711) 108682) ((-1136 . -512) 108615) ((-1028 . -609) NIL) ((-1028 . -608) 108597) ((-96 . -1073) T) ((-859 . -711) 108567) ((-1199 . -47) 108536) ((-250 . -130) T) ((-249 . -130) T) ((-1094 . -1090) T) ((-996 . -1090) T) ((-62 . -608) 108518) ((-1157 . -844) NIL) ((-1017 . -786) T) ((-1017 . -789) T) ((-1282 . -1048) 108505) ((-1282 . -111) 108490) ((-863 . -641) 108477) ((-1246 . -25) T) ((-1246 . -21) T) ((-1239 . -21) T) ((-1239 . -25) T) ((-1218 . -21) T) ((-1218 . -25) T) ((-1020 . -150) 108461) ((-865 . -814) 108440) ((-865 . -913) T) ((-706 . -285) 108367) ((-592 . -21) T) ((-592 . -25) T) ((-591 . -21) T) ((-40 . -720) T) ((-221 . -512) 108300) ((-591 . -25) T) ((-474 . -150) 108284) ((-461 . -150) 108268) ((-914 . -788) T) ((-914 . -720) T) ((-765 . -787) T) ((-765 . -788) T) ((-504 . -1090) T) ((-500 . -1090) T) ((-765 . -720) T) ((-224 . -362) T) ((-1146 . -1090) 108246) ((-864 . -1209) T) ((-647 . -608) 108228) ((-864 . -553) T) ((-687 . -367) NIL) ((-1282 . -611) 108210) ((-358 . -1261) 108194) ((-663 . -102) T) ((-352 . -1261) 108178) ((-344 . -1261) 108162) ((-1277 . -1090) T) ((-518 . -844) 108141) ((-811 . -450) 108120) ((-1039 . -1090) T) ((-1039 . -1062) 108049) ((-1020 . -969) 108018) ((-813 . -1102) T) ((-996 . -711) 107963) ((-385 . -1102) T) ((-474 . -969) 107932) ((-461 . -969) 107901) ((-110 . -150) 107883) ((-73 . -608) 107865) ((-886 . -608) 107847) ((-1070 . -718) 107826) ((-1282 . -1042) T) ((-810 . -634) 107774) ((-293 . -1049) 107716) ((-168 . -1209) 107621) ((-224 . -1102) T) ((-323 . -23) T) ((-1157 . -985) 107573) ((-837 . -1090) T) ((-1240 . -1048) 107478) ((-1116 . -734) 107457) ((-1238 . 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105147) ((-1096 . -394) T) ((-618 . -641) 105134) ((-452 . -879) NIL) ((-668 . -102) 105112) ((-1077 . -1031) 104939) ((-864 . -23) T) ((-776 . -1031) 104798) ((-774 . -1031) 104655) ((-117 . -641) 104600) ((-452 . -1031) 104476) ((-315 . -611) 104040) ((-312 . -611) 103923) ((-642 . -1031) 103907) ((-622 . -102) T) ((-221 . -487) 103891) ((-1254 . -34) T) ((-135 . -611) 103875) ((-630 . -711) 103859) ((-602 . -711) 103843) ((-663 . -38) 103803) ((-318 . -102) T) ((-85 . -608) 103785) ((-50 . -1031) 103769) ((-1110 . -1048) 103756) ((-1077 . -376) 103740) ((-776 . -376) 103724) ((-60 . -57) 103686) ((-692 . -788) T) ((-692 . -785) T) ((-578 . -1031) 103673) ((-516 . -1031) 103650) ((-692 . -720) T) ((-323 . -130) T) ((-315 . -1042) 103540) ((-312 . -1042) T) ((-168 . -1102) T) ((-774 . -376) 103524) ((-45 . -150) 103474) ((-997 . -985) 103456) ((-452 . -376) 103440) ((-406 . -171) T) ((-315 . -242) 103419) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1090) 103201) ((-224 . -130) T) 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-25) T) ((-151 . -38) 102317) ((-2 . -102) T) ((-903 . -913) T) ((-480 . -1261) 102287) ((-222 . -1031) 102264) ((-1110 . -1042) T) ((-705 . -306) T) ((-293 . -711) 102206) ((-694 . -1049) T) ((-485 . -450) T) ((-406 . -512) 102118) ((-216 . -450) T) ((-1110 . -232) T) ((-294 . -150) 102068) ((-992 . -609) 102029) ((-992 . -608) 102011) ((-982 . -608) 101993) ((-116 . -1049) T) ((-647 . -1048) 101977) ((-224 . -491) T) ((-398 . -608) 101959) ((-398 . -609) 101936) ((-1046 . -1261) 101906) ((-647 . -111) 101885) ((-1132 . -487) 101869) ((-809 . -38) 101839) ((-63 . -439) T) ((-63 . -394) T) ((-1149 . -102) T) ((-864 . -130) T) ((-482 . -102) 101817) ((-1282 . -367) T) ((-1070 . -102) T) ((-1052 . -102) T) ((-350 . -711) 101762) ((-725 . -146) 101741) ((-725 . -144) 101720) ((-647 . -611) 101638) ((-1017 . -641) 101575) ((-521 . -1090) 101553) ((-358 . -102) T) ((-352 . -102) T) ((-344 . -102) T) ((-108 . -102) T) ((-502 . -1090) T) ((-353 . -641) 101498) ((-1162 . -634) 101446) ((-1115 . -634) 101394) ((-384 . -507) 101373) ((-827 . -842) 101352) ((-378 . -1209) T) ((-687 . -720) T) ((-338 . -1049) T) ((-1218 . -985) 101304) ((-173 . -1049) T) ((-103 . -608) 101236) ((-1164 . -144) 101215) ((-1164 . -146) 101194) ((-378 . -553) T) ((-1163 . -146) 101173) ((-1163 . -144) 101152) ((-1157 . -144) 101059) ((-406 . -289) T) ((-1157 . -146) 100966) ((-1116 . -146) 100945) ((-1116 . -144) 100924) ((-318 . -38) 100765) ((-168 . -130) T) ((-312 . -789) NIL) ((-312 . -786) NIL) ((-647 . -1042) T) ((-48 . -641) 100730) ((-886 . -611) 100707) ((-1156 . -102) T) ((-987 . -102) T) ((-986 . -21) T) ((-127 . -1003) 100691) ((-121 . -1003) 100675) ((-986 . -25) T) ((-894 . -119) 100659) ((-1148 . -102) T) ((-810 . -844) 100638) ((-1227 . -130) T) ((-1162 . -25) T) ((-1162 . -21) T) ((-849 . -130) T) ((-1115 . -25) T) ((-1115 . -21) T) ((-848 . -25) T) ((-848 . -21) T) ((-776 . -306) 100617) ((-640 . -102) 100595) ((-627 . -102) T) ((-1149 . -308) 100390) ((-568 . -130) T) ((-616 . -842) 100369) ((-1146 . -487) 100353) ((-1140 . -150) 100303) ((-1136 . -608) 100265) ((-1136 . -609) 100226) ((-1017 . -785) T) ((-1017 . -788) T) ((-1017 . -720) T) ((-706 . -1048) 100049) ((-482 . -308) 99987) ((-451 . -416) 99957) ((-350 . -171) T) ((-288 . -38) 99944) ((-273 . -102) T) ((-272 . -102) T) ((-271 . -102) T) ((-270 . -102) T) ((-269 . -102) T) ((-268 . -102) T) ((-342 . -1031) 99921) ((-267 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-208 . -102) T) ((-207 . -102) T) ((-206 . -102) T) ((-205 . -102) T) ((-202 . -102) T) ((-201 . -102) T) ((-200 . -102) T) ((-199 . -102) T) ((-198 . -102) T) ((-197 . -102) T) ((-196 . -102) T) ((-195 . -102) T) ((-194 . -102) T) ((-193 . -102) T) ((-192 . -102) T) ((-353 . -720) T) ((-706 . -111) 99730) ((-663 . -230) 99714) ((-578 . -306) T) ((-516 . -306) T) ((-293 . -512) 99663) ((-108 . -308) NIL) ((-72 . -394) T) ((-1103 . -102) 99453) ((-827 . -410) 99437) ((-1110 . -789) T) ((-1110 . -786) T) ((-694 . -1090) T) ((-575 . -608) 99419) ((-378 . -362) T) ((-168 . -491) 99397) ((-221 . -608) 99329) ((-133 . -1090) T) ((-116 . -1090) T) ((-48 . -720) T) ((-1039 . -487) 99294) ((-140 . -424) 99276) ((-140 . -367) T) ((-1020 . -102) T) ((-510 . -507) 99255) ((-706 . -611) 99011) ((-474 . -102) T) ((-461 . -102) T) ((-1027 . -1102) T) ((-1171 . -1031) 98946) ((-1164 . -35) 98912) ((-1164 . -95) 98878) ((-1164 . -1193) 98844) ((-1164 . -1190) 98810) ((-1148 . -308) NIL) ((-89 . -395) T) ((-89 . -394) T) ((-1070 . -1141) 98789) ((-1163 . -1190) 98755) ((-1163 . -1193) 98721) ((-1027 . -23) T) ((-1163 . -95) 98687) ((-568 . -491) T) ((-1163 . -35) 98653) ((-1157 . -1190) 98619) ((-1157 . -1193) 98585) ((-1157 . -95) 98551) ((-360 . -1102) T) ((-358 . -1141) 98530) ((-352 . -1141) 98509) ((-344 . -1141) 98488) ((-1157 . -35) 98454) ((-1116 . -35) 98420) ((-1116 . -95) 98386) ((-108 . -1141) T) ((-1116 . -1193) 98352) ((-827 . -1049) 98331) ((-640 . -308) 98269) ((-627 . -308) 98120) ((-1116 . -1190) 98086) ((-706 . -1042) T) ((-1053 . -634) 98068) ((-1070 . -38) 97936) ((-945 . -634) 97884) ((-997 . -146) T) ((-997 . -144) NIL) ((-378 . -1102) T) ((-323 . -25) T) ((-321 . -23) T) ((-936 . -844) 97863) ((-706 . -325) 97840) ((-479 . -634) 97788) ((-40 . -1031) 97676) ((-706 . -232) T) ((-694 . -711) 97663) ((-338 . -1090) T) ((-173 . -1090) T) ((-330 . -844) T) ((-417 . -450) 97613) ((-378 . -23) T) ((-358 . -38) 97578) ((-352 . -38) 97543) ((-344 . -38) 97508) ((-80 . -439) T) ((-80 . -394) T) ((-224 . -25) T) ((-224 . -21) T) ((-830 . -1102) T) ((-108 . -38) 97458) ((-821 . -1102) T) ((-768 . -1090) T) ((-116 . -711) 97445) ((-665 . -1031) 97429) ((-607 . -102) T) ((-830 . -23) T) ((-821 . -23) T) ((-1146 . -285) 97406) ((-1103 . -308) 97344) ((-1092 . -234) 97328) ((-64 . -395) T) ((-64 . -394) T) ((-110 . -102) T) ((-40 . -376) 97305) ((-96 . -102) T) ((-646 . -846) 97289) ((-1125 . -1073) T) ((-1053 . -21) T) ((-1053 . -25) T) ((-809 . -230) 97258) ((-945 . -25) T) ((-945 . -21) T) ((-616 . 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-1090) T) ((-1204 . -1090) T) ((-1103 . -230) 91829) ((-82 . -1205) T) ((-1053 . -844) T) ((-945 . -844) 91808) ((-117 . -893) NIL) ((-776 . -913) 91787) ((-707 . -844) T) ((-529 . -1090) T) ((-498 . -1090) T) ((-354 . -1209) T) ((-351 . -1209) T) ((-343 . -1209) T) ((-263 . -1209) 91766) ((-246 . -1209) 91745) ((-531 . -854) T) ((-479 . -844) 91724) ((-1148 . -822) T) ((-1132 . -1048) 91708) ((-389 . -755) T) ((-687 . -1205) T) ((-684 . -1031) 91692) ((-354 . -553) T) ((-351 . -553) T) ((-343 . -553) T) ((-263 . -553) 91623) ((-246 . -553) 91554) ((-523 . -1073) T) ((-1132 . -111) 91533) ((-451 . -738) 91503) ((-859 . -1048) 91473) ((-811 . -38) 91415) ((-687 . -877) 91397) ((-687 . -879) 91379) ((-294 . -308) 91183) ((-903 . -1209) T) ((-663 . -410) 91167) ((-859 . -111) 91132) ((-687 . -1031) 91077) ((-997 . -450) T) ((-903 . -553) T) ((-531 . -608) 91059) ((-578 . -913) T) ((-472 . -1102) T) ((-516 . -913) T) ((-1146 . -287) 91036) ((-907 . -450) T) ((-65 . -608) 91018) ((-627 . -228) 90964) ((-472 . -23) T) ((-1110 . -788) T) ((-865 . -130) T) ((-1110 . -785) T) ((-1269 . -1271) 90943) ((-1110 . -720) T) ((-647 . -641) 90917) ((-293 . -608) 90658) ((-1132 . -611) 90576) ((-1028 . -34) T) ((-809 . -842) 90555) ((-577 . -306) T) ((-561 . -306) T) ((-493 . -306) T) ((-1278 . -711) 90525) ((-687 . -376) 90507) ((-687 . -337) 90489) ((-475 . -171) T) ((-380 . -711) 90459) ((-859 . -611) 90394) ((-864 . -844) NIL) ((-561 . -1015) T) ((-493 . -1015) T) ((-1123 . -608) 90376) ((-1103 . -237) 90355) ((-213 . -102) T) ((-1140 . -102) T) ((-71 . -608) 90337) ((-1132 . -1042) T) ((-1168 . -38) 90234) ((-852 . -608) 90216) ((-561 . -543) T) ((-663 . -1049) T) ((-725 . -942) 90169) ((-1132 . -232) 90148) ((-1072 . -1090) T) ((-1027 . -25) T) ((-1027 . -21) T) ((-996 . -1048) 90093) ((-898 . -102) T) ((-859 . -1042) T) ((-687 . -893) NIL) ((-354 . -328) 90077) ((-354 . -362) T) ((-351 . -328) 90061) ((-351 . -362) T) ((-343 . -328) 90045) ((-343 . -362) T) ((-485 . -102) T) 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-609) 87258) ((-708 . -21) T) ((-708 . -25) T) ((-1125 . -102) T) ((-133 . -608) 87240) ((-116 . -608) 87222) ((-156 . -25) T) ((-1276 . -1090) T) ((-865 . -634) 87170) ((-1274 . -1090) T) ((-956 . -102) T) ((-729 . -102) T) ((-709 . -102) T) ((-451 . -102) T) ((-810 . -450) 87121) ((-44 . -1090) T) ((-1078 . -844) T) ((-657 . -130) T) ((-1054 . -308) 86972) ((-663 . -711) 86956) ((-288 . -1049) T) ((-354 . -130) T) ((-351 . -130) T) ((-343 . -130) T) ((-263 . -130) T) ((-246 . -130) T) ((-417 . -102) T) ((-151 . -1090) T) ((-45 . -228) 86906) ((-951 . -844) 86885) ((-992 . -641) 86823) ((-239 . -1261) 86793) ((-1017 . -306) T) ((-293 . -1048) 86714) ((-903 . -130) T) ((-40 . -913) T) ((-485 . -399) 86696) ((-353 . -306) T) ((-216 . -399) 86678) ((-1070 . -410) 86662) ((-293 . -111) 86578) ((-1173 . -844) T) ((-1172 . -844) T) ((-865 . -25) T) ((-865 . -21) T) ((-338 . -608) 86560) ((-1240 . -47) 86504) ((-224 . -146) T) ((-173 . -608) 86486) ((-1103 . -842) 86465) ((-768 . -608) 86447) ((-128 . -844) T) ((-603 . -234) 86394) ((-473 . -234) 86344) ((-1276 . -711) 86314) ((-48 . -306) T) ((-1274 . -711) 86284) ((-65 . -611) 86213) ((-957 . -1090) T) ((-809 . -1090) 86003) ((-311 . -102) T) ((-894 . -1205) T) ((-48 . -1015) T) ((-1217 . -634) 85911) ((-682 . -102) 85889) ((-44 . -711) 85873) ((-547 . -102) T) ((-293 . -611) 85804) ((-67 . -382) T) ((-67 . -394) T) ((-655 . -23) T) ((-663 . -755) T) ((-1202 . -1090) 85782) ((-350 . -1048) 85727) ((-668 . -1090) 85705) ((-1053 . -146) T) ((-945 . -146) 85684) ((-945 . -144) 85663) ((-793 . -102) T) ((-151 . -711) 85647) ((-479 . -146) 85626) ((-479 . -144) 85605) ((-350 . -111) 85534) ((-1070 . -1049) T) ((-321 . -844) 85513) ((-1246 . -966) 85482) ((-622 . -1090) T) ((-1239 . -966) 85444) ((-509 . -130) T) ((-505 . -130) T) ((-294 . -228) 85394) ((-358 . -1049) T) ((-352 . -1049) T) ((-344 . -1049) T) ((-293 . -1042) 85336) ((-1218 . -966) 85305) ((-378 . -844) T) ((-108 . -1049) T) ((-992 . -720) T) ((-863 . -913) T) ((-837 . -789) 85284) ((-837 . -786) 85263) ((-417 . -308) 85202) ((-466 . -102) T) ((-591 . -966) 85171) ((-318 . -1090) T) ((-406 . -789) 85150) ((-406 . -786) 85129) ((-498 . -487) 85111) ((-1240 . -1031) 85077) ((-1238 . -21) T) ((-1238 . -25) T) ((-1217 . -21) T) ((-1217 . -25) T) ((-809 . -711) 85019) ((-350 . -611) 84949) ((-692 . -403) T) ((-1267 . -1205) T) ((-601 . -102) T) ((-1103 . -410) 84918) ((-996 . -367) NIL) ((-664 . -102) T) ((-179 . -102) T) ((-160 . -102) T) ((-155 . -102) T) ((-153 . -102) T) ((-103 . -34) T) ((-731 . -1205) T) ((-44 . -755) T) ((-589 . -102) T) ((-77 . -395) T) ((-77 . -394) T) ((-646 . -649) 84902) ((-140 . -1205) T) ((-864 . -146) T) ((-864 . -144) NIL) ((-1204 . -93) T) ((-350 . -1042) T) ((-70 . -382) T) ((-70 . -394) T) ((-1155 . -102) T) ((-663 . -512) 84835) ((-682 . -308) 84773) ((-956 . -38) 84670) ((-729 . -38) 84640) ((-547 . -308) 84444) ((-315 . -1205) T) ((-350 . -232) T) ((-350 . -242) T) ((-312 . -1205) T) ((-288 . -1090) 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. -609) 79044) ((-1204 . -608) 79010) ((-1157 . -1141) NIL) ((-1020 . -1062) 78979) ((-1020 . -1090) T) ((-997 . -102) T) ((-964 . -102) T) ((-907 . -102) T) ((-886 . -1031) 78956) ((-1132 . -720) T) ((-996 . -641) 78901) ((-474 . -1090) T) ((-461 . -1090) T) ((-582 . -23) T) ((-568 . -35) T) ((-568 . -95) T) ((-426 . -102) T) ((-1054 . -228) 78847) ((-1164 . -38) 78744) ((-859 . -720) T) ((-687 . -913) T) ((-509 . -25) T) ((-505 . -21) T) ((-505 . -25) T) ((-1163 . -38) 78585) ((-338 . -1042) T) ((-1157 . -38) 78381) ((-1070 . -171) T) ((-173 . -1042) T) ((-1116 . -38) 78278) ((-706 . -47) 78255) ((-358 . -171) T) ((-352 . -171) T) ((-517 . -57) 78229) ((-495 . -57) 78179) ((-350 . -1273) 78156) ((-224 . -450) T) ((-318 . -289) 78107) ((-344 . -171) T) ((-173 . -242) T) ((-1217 . -844) 78006) ((-108 . -171) T) ((-865 . -985) 77990) ((-651 . -1102) T) ((-578 . -362) T) ((-578 . -328) 77977) ((-516 . -328) 77954) ((-516 . -362) T) ((-315 . -306) 77933) ((-312 . -306) T) ((-597 . -844) 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. -38) 75103) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -788) 75082) ((-406 . -785) 75061) ((-406 . -720) T) ((-498 . -287) 75036) ((-475 . -1048) 75001) ((-651 . -130) T) ((-616 . -611) 74970) ((-1103 . -512) 74903) ((-335 . -130) T) ((-168 . -401) 74882) ((-480 . -711) 74824) ((-809 . -285) 74801) ((-475 . -111) 74757) ((-646 . -1049) T) ((-1227 . -450) 74688) ((-1265 . -1073) T) ((-1264 . -1073) T) ((-1077 . -130) T) ((-1046 . -711) 74630) ((-263 . -844) 74609) ((-246 . -844) 74588) ((-776 . -130) T) ((-774 . -130) T) ((-568 . -450) T) ((-1020 . -512) 74521) ((-616 . -1042) T) ((-588 . -1090) T) ((-531 . -172) T) ((-459 . -130) T) ((-452 . -130) T) ((-45 . -1090) T) ((-384 . -711) 74491) ((-811 . -1090) T) ((-474 . -512) 74424) ((-461 . -512) 74357) ((-451 . -366) 74327) ((-45 . -605) 74306) ((-315 . -301) T) ((-475 . -611) 74256) ((-663 . -608) 74218) ((-59 . -844) 74197) ((-1218 . -308) 74082) ((-997 . -399) 74064) ((-809 . -599) 74041) ((-514 . -844) 74020) ((-494 . -844) 73999) ((-40 . -1209) T) ((-992 . -1031) 73895) ((-50 . -130) T) ((-578 . -130) T) ((-516 . -130) T) ((-293 . -641) 73755) ((-342 . -328) 73732) ((-342 . -362) T) ((-321 . -322) 73709) ((-318 . -285) 73694) ((-40 . -553) T) ((-378 . -1190) T) ((-378 . -1193) T) ((-1028 . -1181) 73669) ((-1178 . -234) 73619) ((-1157 . -230) 73571) ((-329 . -1090) T) ((-378 . -95) T) ((-378 . -35) T) ((-1028 . -107) 73517) ((-475 . -1042) T) ((-477 . -234) 73467) ((-1149 . -487) 73401) ((-1278 . -1048) 73385) ((-380 . -1048) 73369) ((-475 . -242) T) ((-810 . -102) T) ((-708 . -146) 73348) ((-708 . -144) 73327) ((-482 . -487) 73311) ((-483 . -334) 73280) ((-1278 . -111) 73259) ((-510 . -1090) T) ((-480 . -171) 73238) ((-992 . -376) 73222) ((-412 . -102) T) ((-380 . -111) 73201) ((-992 . -337) 73185) ((-278 . -976) 73169) ((-277 . -976) 73153) ((-1276 . -608) 73135) ((-1274 . -608) 73117) ((-110 . -512) NIL) ((-1162 . -1230) 73101) ((-848 . -846) 73085) ((-1168 . -1090) T) ((-103 . -1205) T) ((-945 . -942) 73046) ((-811 . -711) 72988) ((-1218 . -1141) NIL) ((-479 . -942) 72933) ((-1053 . -142) T) ((-60 . -102) 72911) ((-44 . -608) 72893) ((-78 . -608) 72875) ((-350 . -641) 72820) ((-1266 . -1090) T) ((-509 . -844) T) ((-342 . -1102) T) ((-294 . -1090) T) ((-992 . -893) 72779) ((-294 . -605) 72758) ((-1278 . -611) 72707) ((-1246 . -38) 72604) ((-1239 . -38) 72445) ((-1218 . -38) 72241) ((-485 . -1049) T) ((-380 . -611) 72225) ((-216 . -1049) T) ((-342 . -23) T) ((-151 . -608) 72207) ((-827 . -789) 72186) ((-827 . -786) 72165) ((-1204 . -611) 72146) ((-592 . -38) 72119) ((-591 . -38) 72016) ((-863 . -553) T) ((-222 . -130) T) ((-318 . -995) 71982) ((-79 . -608) 71964) ((-706 . -306) 71943) ((-293 . -720) 71845) ((-818 . -102) T) ((-858 . -838) T) ((-293 . -471) 71824) ((-1269 . -102) T) ((-40 . -362) T) ((-865 . -146) 71803) ((-865 . -144) 71782) ((-1148 . -487) 71764) ((-1278 . -1042) T) ((-480 . -512) 71697) ((-1136 . -1205) T) ((-957 . -608) 71679) ((-640 . -487) 71663) ((-627 . -487) 71594) ((-809 . -608) 71325) ((-48 . -27) T) ((-1168 . -711) 71222) ((-646 . -1090) T) ((-855 . -854) T) ((-435 . -363) 71196) ((-1092 . -102) T) ((-963 . -1090) T) ((-858 . -1090) T) ((-810 . -308) 71183) ((-531 . -525) T) ((-531 . -573) T) ((-1274 . -381) 71155) ((-1046 . -512) 71088) ((-1149 . -285) 71064) ((-239 . -230) 71033) ((-1266 . -711) 71003) ((-1156 . -93) T) ((-987 . -93) T) ((-811 . -171) 70982) ((-1202 . -488) 70959) ((-226 . -512) 70892) ((-616 . -789) 70871) ((-616 . -786) 70850) ((-1202 . -608) 70762) ((-221 . -1205) T) ((-668 . -608) 70694) ((-1146 . -1003) 70678) ((-936 . -102) 70628) ((-350 . -720) T) ((-855 . -608) 70610) ((-1218 . -399) 70562) ((-1103 . -487) 70546) ((-60 . -308) 70484) ((-330 . -102) T) ((-1199 . -21) T) ((-1199 . -25) T) ((-40 . -1102) T) ((-705 . -21) T) ((-622 . -608) 70466) ((-513 . -322) 70445) ((-705 . -25) T) ((-108 . -285) NIL) ((-914 . -1102) T) ((-40 . -23) T) ((-765 . -1102) T) ((-561 . -1209) T) ((-493 . -1209) T) ((-318 . -608) 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. -102) T) ((-638 . -609) 15497) ((-638 . -608) 15409) ((-578 . -1141) T) ((-516 . -1141) T) ((-1137 . -487) 15393) ((-1191 . -1090) 15371) ((-1132 . -25) T) ((-1132 . -21) T) ((-1269 . -611) 15320) ((-472 . -1049) T) ((-1211 . -1090) T) ((-1218 . -786) NIL) ((-1218 . -789) NIL) ((-992 . -844) 15299) ((-832 . -1090) T) ((-813 . -608) 15281) ((-859 . -21) T) ((-859 . -25) T) ((-793 . -720) T) ((-173 . -1209) T) ((-578 . -38) 15246) ((-516 . -38) 15211) ((-385 . -608) 15193) ((-323 . -608) 15175) ((-168 . -285) 15133) ((-63 . -1205) T) ((-112 . -102) T) ((-865 . -1090) T) ((-173 . -553) T) ((-708 . -711) 15103) ((-293 . -130) 14986) ((-224 . -608) 14968) ((-224 . -609) 14898) ((-996 . -634) 14837) ((-1269 . -1042) T) ((-1110 . -146) T) ((-627 . -1181) 14812) ((-725 . -902) 14791) ((-589 . -34) T) ((-640 . -107) 14775) ((-627 . -107) 14721) ((-1227 . -285) 14648) ((-725 . -641) 14573) ((-294 . -1205) T) ((-1168 . -1031) 14469) ((-936 . -613) 14446) ((-574 . -573) T) ((-574 . -525) T) 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11370) ((-472 . -1090) T) ((-338 . -1102) T) ((-173 . -1102) T) ((-318 . -913) 11349) ((-1238 . -711) 11190) ((-865 . -171) T) ((-1217 . -711) 11004) ((-837 . -21) 10956) ((-837 . -25) 10908) ((-244 . -1139) 10892) ((-126 . -512) 10825) ((-406 . -25) T) ((-406 . -21) T) ((-338 . -23) T) ((-168 . -609) 10591) ((-168 . -608) 10573) ((-173 . -23) T) ((-638 . -287) 10550) ((-518 . -34) T) ((-891 . -608) 10532) ((-89 . -1205) T) ((-835 . -608) 10514) ((-802 . -608) 10496) ((-763 . -608) 10478) ((-670 . -608) 10460) ((-239 . -641) 10308) ((-1166 . -1090) T) ((-1162 . -1048) 10131) ((-1140 . -1205) T) ((-1115 . -1048) 9974) ((-848 . -1048) 9958) ((-1221 . -613) 9942) ((-1162 . -111) 9751) ((-1115 . -111) 9580) ((-848 . -111) 9559) ((-1227 . -609) NIL) ((-1227 . -608) 9541) ((-342 . -1141) T) ((-849 . -608) 9523) ((-1066 . -285) 9502) ((-80 . -1205) T) ((-997 . -902) NIL) ((-603 . -285) 9478) ((-1191 . -512) 9411) ((-485 . -1205) T) ((-568 . -608) 9393) ((-473 . -285) 9372) ((-515 . -93) T) 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-1042) T) ((-239 . -785) 7753) ((-239 . -788) 7704) ((-239 . -787) 7683) ((-1162 . -325) 7660) ((-239 . -720) 7570) ((-951 . -19) 7554) ((-485 . -376) 7536) ((-485 . -337) 7518) ((-1115 . -325) 7490) ((-353 . -1261) 7467) ((-216 . -376) 7449) ((-216 . -337) 7431) ((-951 . -599) 7408) ((-1162 . -232) T) ((-657 . -1090) T) ((-639 . -1090) T) ((-1250 . -1090) T) ((-1178 . -1090) T) ((-1077 . -252) 7345) ((-354 . -1090) T) ((-351 . -1090) T) ((-343 . -1090) T) ((-263 . -1090) T) ((-246 . -1090) T) ((-84 . -1205) T) ((-127 . -102) 7323) ((-121 . -102) 7301) ((-1178 . -605) 7280) ((-477 . -1090) T) ((-1131 . -1090) T) ((-477 . -605) 7259) ((-250 . -789) 7210) ((-250 . -786) 7161) ((-249 . -789) 7112) ((-40 . -1141) NIL) ((-249 . -786) 7063) ((-1105 . -611) 7044) ((-128 . -19) 7026) ((-1070 . -913) 6977) ((-997 . -788) T) ((-997 . -785) T) ((-997 . -720) T) ((-964 . -788) T) ((-128 . -599) 6952) ((-907 . -720) T) ((-91 . -487) 6936) ((-485 . -893) NIL) ((-903 . -1090) T) ((-224 . -1048) 6901) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index a2c44b20..96c0e49f 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3440472335) -(4393 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3440812766) +(4402 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -441,7 +441,7 @@ |TriangularSetCategory| |TaylorSeries| |TubePlot| |TubePlotTools| |Tuple| |TwoFactorize| |TypeAst| |Type| |UserDefinedPartialOrdering| |UserDefinedVariableOrdering| |UniqueFactorizationDomain&| - |UniqueFactorizationDomain| |UInt16| |UInt32| + |UniqueFactorizationDomain| |UInt16| |UInt32| |UInt8| |UnivariateLaurentSeriesFunctions2| |UnivariateLaurentSeriesCategory| |UnivariateLaurentSeriesConstructorCategory&| |UnivariateLaurentSeriesConstructorCategory| @@ -476,659 +476,664 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |moebiusMu| |factorset| |powmod| |sort| |deref| - |extendedResultant| |gcdPrimitive| |tubePlot| |rotate| - |brillhartIrreducible?| |zeroSetSplitIntoTriangularSystems| |freeOf?| - |rowEchelon| |complementaryBasis| |evenInfiniteProduct| |separate| - |lagrange| |setMinPoints| |fortran| |members| |mapUnivariate| - |quotient| |generalizedContinuumHypothesisAssumed| |poisson| |cAcoth| - |cyclePartition| |rightUnits| |sub| |palginfieldint| |asinhIfCan| - |setPredicates| |startStats!| |makeGraphImage| |sequence| - |safeCeiling| |bat| |LazardQuotient2| |initTable!| - |topFortranOutputStack| |showArrayValues| |cos2sec| |dot| |null?| - |stoseInvertible?| |find| |signAround| |random| |radPoly| - |OMputEndAtp| |e04fdf| |e02dff| |getMeasure| |OMgetApp| - |viewWriteAvailable| |complexEigenvectors| |rectangularMatrix| |critT| - |setIntersection| |cyclicSubmodule| |iiabs| |lazyPquo| |finite?| - |perfectNthRoot| |removeSuperfluousQuasiComponents| |rootNormalize| - |presub| |presuper| |setrest!| |leftRegularRepresentation| |setUnion| - |rightMult| |const| |mainVariable| |ideal| |setnext!| |roughBase?| - |extractProperty| |reciprocalPolynomial| |power| |copyInto!| - |bivariateSLPEBR| |apply| |digits| |mapdiv| |datalist| - |patternMatchTimes| |currentEnv| |s17aef| |OMgetVariable| |green| - |createNormalPoly| |pushdown| |nil| |virtualDegree| |wholeRadix| - |rightDiscriminant| |diagonalProduct| |bit?| |leadingIdeal| - |symmetricProduct| |OMsetEncoding| |monomial| |floor| |df2ef| |index?| - |integralBasisAtInfinity| |coth2trigh| |size| |derivative| - |quotientByP| |call| |palgint| |capacity| |c05nbf| |satisfy?| - |multivariate| |removeCoshSq| |preprocess| |depth| |quasiComponent| - |limitedIntegrate| |merge| |e02zaf| |interReduce| |imagj| - |monicDecomposeIfCan| |variables| |leftQuotient| |RittWuCompare| - |setProperties| |extend| |approximate| |function| |reduceLODE| - |characteristicSerie| |curryLeft| |float?| |scopes| |repeatUntilLoop| - |makingStats?| |makeUnit| |roughBasicSet| |linSolve| |id| |complex| - |factorByRecursion| |qroot| |first| |rk4a| |rationalFunction| - |besselI| |byte| |monicRightDivide| |argscript| |coerceImages| - |stoseInvertibleSetreg| |predicates| |squareFreeFactors| |eval| |rest| - |jordanAdmissible?| |OMunhandledSymbol| |list?| |computeCycleEntry| - |script| |formula| |numericIfCan| |hasoln| |screenResolution| |delay| - |table| |problemPoints| |iflist2Result| |substitute| |f04atf| |close| - |numberOfCycles| |rk4f| |exponentialOrder| |groebnerIdeal| |f07fdf| - |qinterval| |e01bff| |closedCurve?| |new| |obj| |removeDuplicates| - |romberg| |selectFiniteRoutines| |clearFortranOutputStack| - |chebyshevT| |charpol| |dihedralGroup| |zeroVector| |c06gcf| - |cosIfCan| |taylor| |getOperator| |generalPosition| |search| - |arrayStack| |genericLeftNorm| |ParCondList| |remove| - |sturmVariationsOf| |display| |wordsForStrongGenerators| |printTypes| - |cache| |sinh2csch| |tex| BY |tab1| |laurent| |monicLeftDivide| - |cycleRagits| |leftFactor| |fintegrate| |setErrorBound| |checkForZero| - |operation| |OMgetAtp| |orbit| |monic?| |tower| |heap| |and?| |nrows| - |constant| |puiseux| |fractRagits| |setref| |froot| |stopTableGcd!| - |last| |cyclicCopy| |fixedPointExquo| |mesh| |stripCommentsAndBlanks| - |addPointLast| |ncols| |roman| |totalDifferential| |internal?| - |frobenius| |indicialEquationAtInfinity| |assoc| |someBasis| |Si| - |intcompBasis| |oddlambert| |mkcomm| |bezoutMatrix| - |leftCharacteristicPolynomial| |inv| |stFuncN| |e02ahf| |evenlambert| - |genericRightTrace| |squareMatrix| |s17dcf| |listRepresentation| - |vertConcat| |tubePoints| |leftRemainder| |ground?| |rdregime| - |noLinearFactor?| |OMgetEndObject| |input| |showScalarValues| - |vectorise| |diff| |yCoord| |lazyPrem| |ground| |cRationalPower| - |subResultantsChain| |graphs| |OMputEndBVar| |nextPartition| - |computeInt| |clip| |rank| |coth2tanh| |library| |outputForm| |curry| - |oneDimensionalArray| |primeFrobenius| |s17aff| |complexNumeric| - |leadingMonomial| |getCurve| |listLoops| |cartesian| |lcm| |e01saf| - |distribute| |epilogue| |d01ajf| |option?| |factorsOfDegree| - |OMputString| |leadingCoefficient| |squareFreePart| - |setScreenResolution3D| |rules| |idealiser| |univariate?| |mapDown!| - |euler| |algebraicDecompose| |bezoutDiscriminant| |kernels| |plus!| - |primitiveMonomials| |parametersOf| |region| |left| |exactQuotient| - |pack!| |append| |modifyPoint| |selectPolynomials| |powern| - |bipolarCylindrical| |coerceP| |sayLength| |dAndcExp| |frst| - |viewZoomDefault| |semicolonSeparate| |reductum| |univariate| |right| - |exprToXXP| |gcd| |cycleLength| |integralBasis| |headAst| |set| - |zeroDimensional?| |removeRoughlyRedundantFactorsInContents| |size?| - |lastSubResultant| |partition| |possiblyNewVariety?| |prefixRagits| - |factorFraction| |palgRDE0| |cAtan| |false| |iiacos| |primextintfrac| - |polyRDE| |returnType!| |insertRoot!| |iiasinh| |appendPoint| - |primextendedint| |sum| |f02agf| |pureLex| |pushdterm| - |currentSubProgram| |nextNormalPoly| |ratPoly| |complexIntegrate| - |evaluate| |integral?| |factor| |binaryTree| - |rightCharacteristicPolynomial| |putColorInfo| |var1Steps| |randomLC| - |nextItem| |isPlus| |sqrt| |OMputError| |startPolynomial| |gderiv| - |string?| |shanksDiscLogAlgorithm| |sizeLess?| |norm| |real| |htrigs| - |aQuartic| |prinb| |geometric| |lp| |swapRows!| |internalIntegrate0| - |backOldPos| |lexGroebner| |semiDegreeSubResultantEuclidean| |imag| - |s18def| |ptree| |equality| |changeMeasure| |c05adf| |directProduct| - |topPredicate| |idealSimplify| |remainder| |OMopenFile| |superscript| - |showSummary| |insertBottom!| |numberOfFractionalTerms| |coleman| - |probablyZeroDim?| |radicalEigenvectors| |interpretString| |midpoints| - |integralLastSubResultant| |iiacsc| |leftLcm| - |internalLastSubResultant| |binary| |maxColIndex| |brace| - |binomThmExpt| |inconsistent?| |point?| |hash| |showAttributes| - |f02aef| |ScanFloatIgnoreSpacesIfCan| |rubiksGroup| |operators| - |OMencodingBinary| |destruct| |edf2fi| |show| |count| |smith| - |setlast!| |clikeUniv| |reducedContinuedFraction| |e02aef| |symbol| - |solid?| |midpoint| = |slex| |makeViewport3D| |constDsolve| - |viewport3D| |palgLODE| |expression| |setPrologue!| |pquo| - |singleFactorBound| |listOfMonoms| |trace| |lo| |laplace| |asinIfCan| - |realSolve| |fortranLinkerArgs| |integer| |algebraic?| |edf2ef| - |gbasis| < |collectUpper| |exquo| |incr| |associatorDependence| - |cycle| |charthRoot| |antiCommutator| > |div| |latex| |cot2trig| - |build| |iterationVar| |diophantineSystem| |unitNormal| - |pushNewContour| |makeSketch| |drawComplex| <= |quo| - |quasiMonicPolynomials| |changeThreshhold| |OMlistSymbols| - |incrementKthElement| |bat1| |viewDefaults| |mkAnswer| >= - |scanOneDimSubspaces| |label| |llprop| |purelyAlgebraic?| |adaptive| - |limitPlus| |sdf2lst| |linearlyDependentOverZ?| |drawToScale| - |inGroundField?| |rem| |partialFraction| |newTypeLists| - |createPrimitiveElement| |updatD| |realEigenvectors| |fill!| - |fixedDivisor| |ip4Address| |expandPower| |primitive?| |measure| - |listConjugateBases| |LyndonCoordinates| |eisensteinIrreducible?| - |prevPrime| |skewSFunction| |symmetric?| |branchPoint?| |compBound| + - |equiv?| |d01akf| |sPol| |f01rdf| |upperCase!| |credPol| |transpose| - |SFunction| |zeroSquareMatrix| |groebSolve| - - |rewriteIdealWithRemainder| |outputArgs| |mapUnivariateIfCan| |isList| - |initiallyReduce| |critBonD| |setAdaptive3D| |numericalIntegration| / - |ode2| |plotPolar| |points| |e02daf| |f04jgf| |setProperty!| |imagE| - |partitions| |integrate| |leftExtendedGcd| |basisOfLeftNucleus| - |infLex?| |expIfCan| |nor| |rCoord| |constructor| |s17ahf| - |monomRDEsys| |rquo| |divideExponents| |symmetricRemainder| |trim| - |element?| |findCycle| |f04faf| |pdct| - |createLowComplexityNormalBasis| |nextPrimitiveNormalPoly| |option| - |signatureAst| |mergeFactors| |critMonD1| |low| |elliptic| |e02bdf| - |errorInfo| |rootSimp| |color| |argument| |f02ajf| |blankSeparate| - |symmetricGroup| |nothing| |createRandomElement| |addBadValue| - |listYoungTableaus| |FormatRoman| |polyRicDE| |setStatus| |refine| - |exprHasWeightCosWXorSinWX| |d01bbf| |diagonal| |airyAi| |f04mbf| - |mainValue| |paren| |zoom| |graphImage| |univcase| |leftZero| - |divisor| |charClass| |complete| |hexDigit| |OMputBind| - |representationType| |s20adf| |binaryTournament| |testDim| - |goodnessOfFit| |addMatch| |cothIfCan| |kovacic| |acscIfCan| - |pascalTriangle| |wordInGenerators| |objectOf| |basisOfCentroid| - |discreteLog| |permanent| |cardinality| |lfextlimint| |UnVectorise| - |schema| |nullary| |outputList| |rightTrim| |powerAssociative?| - |coerceListOfPairs| |invertible?| |debug3D| |quadratic| - |leftExactQuotient| |empty?| |factorOfDegree| |OMencodingUnknown| - |leftTrim| |myDegree| |hexDigit?| |resultantReduit| |gcdcofactprim| - |nextColeman| |qPot| |po| |simpleBounds?| |nodes| |rightFactorIfCan| - |mainMonomial| |karatsubaOnce| UP2UTS |Hausdorff| - |factorSquareFreeByRecursion| |setScreenResolution| |bipolar| |s17akf| - |enumerate| |roughSubIdeal?| |allRootsOf| |yellow| |elem?| |multiple?| - |nlde| |rarrow| |axesColorDefault| |randnum| |exteriorDifferential| - |squareTop| |hMonic| |resultantEuclidean| |s18adf| |sample| |s21bbf| - |collect| |BumInSepFFE| |setvalue!| |orthonormalBasis| |divide| |li| - |ran| |setright!| |drawCurves| |monomialIntPoly| |degreeSubResultant| - |trivialIdeal?| |fTable| |stoseSquareFreePart| |initials| |e01sff| - |setleft!| |choosemon| |zeroDimPrime?| |addiag| |quadraticForm| - |applyRules| |s14aaf| |reflect| |minimumExponent| |optional?| - |composite| |tubeRadius| |acschIfCan| |module| |testModulus| - |selectsecond| |lazyPremWithDefault| |generalInfiniteProduct| |light| - |roughUnitIdeal?| |seed| |distance| |rroot| |coord| |getPickedPoints| - |lieAlgebra?| |selectMultiDimensionalRoutines| |OMputEndObject| - |hasPredicate?| |mainKernel| |bsolve| |c02agf| |comparison| |back| - |keys| |positiveSolve| |hi| |sortConstraints| |relationsIdeal| - |primitiveElement| |iExquo| |autoReduced?| |e02gaf| |eulerE| - |composites| |expenseOfEvaluation| |outputGeneral| |e02akf| |root?| - |s21baf| |irreducibleFactors| |OMbindTCP| |scalarTypeOf| |acoshIfCan| - |constantLeft| |maxint| |denomRicDE| |iteratedInitials| |intChoose| - |removeRedundantFactorsInPols| |binarySearchTree| |totalGroebner| - |unprotectedRemoveRedundantFactors| |yRange| |alphabetic| |repeating| - |fibonacci| |OMgetSymbol| |uncouplingMatrices| |normalElement| - |constantIfCan| |digamma| |extractPoint| |zRange| |BasicMethod| - |areEquivalent?| |jacobi| |tRange| |cAsech| |e04dgf| - |fullPartialFraction| |gcdPolynomial| |map!| |intPatternMatch| - |numberOfMonomials| |rationalPower| |stopTableInvSet!| |ode| - |fixPredicate| |numberOfImproperPartitions| |qsetelt!| - |collectQuasiMonic| |explicitlyEmpty?| |atanhIfCan| |B1solve| - |irreducibleRepresentation| |complement| |checkRur| |OMputApp| - |overbar| |test| |e02bef| |showFortranOutputStack| - |internalSubQuasiComponent?| |indicialEquations| |tubePointsDefault| - |factorList| |sup| |decompose| |monomial?| |minordet| |tanh2coth| - |reduced?| |airyBi| |generate| |iiexp| |getConstant| |symFunc| - |factorial| |insertMatch| |pomopo!| |rightUnit| |bytes| |arbitrary| - |prefix| |df2st| |lazyPseudoQuotient| |negative?| - |createNormalElement| |simplifyExp| |rk4| |delete!| |equiv| - |OMreceive| |particularSolution| |expressIdealMember| |tan2cot| - |c06fpf| |f01bsf| |raisePolynomial| |every?| |integralMatrix| |acsch| - |double?| |compose| |semiSubResultantGcdEuclidean1| |karatsuba| - |getBadValues| |generalTwoFactor| |nary?| |associatedSystem| - |rightOne| |limit| |resultantReduitEuclidean| |rootsOf| |algintegrate| - |d02raf| |pointColorDefault| |subscriptedVariables| |OMconnOutDevice| - |generic?| |byteBuffer| |bfEntry| |cTanh| |null| |uniform01| |or?| - |clearTable!| |f04mcf| |extendedIntegrate| |initiallyReduced?| - |innerint| |getCode| |singularAtInfinity?| |useEisensteinCriterion?| - |extendedint| |not| |stoseInternalLastSubResultant| |f04adf| - |overset?| |acothIfCan| |dim| |simplifyLog| |extractTop!| |implies| - |d02gbf| |wordInStrongGenerators| |and| |se2rfi| |Is| |mathieu11| - |untab| |eigenvalues| |rotatez| |commaSeparate| |getGoodPrime| - |anfactor| |or| |exprHasAlgebraicWeight| |diagonal?| |c06ebf| - |halfExtendedSubResultantGcd1| |conjug| |diagonals| |outputFloating| - |nextsousResultant2| |stopTable!| |xor| |nextPrime| |integerBound| - |Nul| |overlabel| |userOrdered?| |front| |parametric?| |setLength!| - |elseBranch| |indicialEquation| |case| |monomRDE| |multiEuclideanTree| - |cCot| |isobaric?| |prepareSubResAlgo| |graphCurves| |quatern| - |mainVariables| |round| |Zero| |symbolTable| |OMParseError?| |term?| - |iiatanh| |associative?| |readLineIfCan!| |wholeRagits| - |basisOfMiddleNucleus| |certainlySubVariety?| |viewDeltaYDefault| - |One| |baseRDE| |startTableInvSet!| |/\\| |SturmHabichtCoefficients| - |permutation| |rightTrace| |OMputAttr| |less?| - |semiResultantEuclideannaif| |asecIfCan| |ode1| |localUnquote| - |useNagFunctions| |\\/| |buildSyntax| |edf2df| |shiftLeft| - |var2StepsDefault| |OMsupportsCD?| |primPartElseUnitCanonical| - |arguments| |elementary| |bandedJacobian| |ratpart| - |definingEquations| |s20acf| |subtractIfCan| |thetaCoord| - |getOperands| |key| |connect| |csubst| |prod| |divideIfCan| - |represents| |lazy?| |e01sef| |conjugate| |c06ekf| |center| - |increment| |resetAttributeButtons| |upperCase| |quadratic?| |cCsc| - |whitePoint| |inverseIntegralMatrixAtInfinity| |filename| |palglimint| - |mapGen| |root| |splitNodeOf!| |rk4qc| |outputAsTex| |elt| |csc2sin| - |multiplyCoefficients| |log2| |primintegrate| |npcoef| |crest| |not?| - |second| |selectOptimizationRoutines| |vspace| |cycles| - |oddInfiniteProduct| |range| |mainCoefficients| |palgLODE0| - |irreducibleFactor| |parse| |third| |mainContent| |cyclicEqual?| - |style| |tensorProduct| |linearAssociatedOrder| - |pushFortranOutputStack| |coefChoose| |createIrreduciblePoly| - |factorAndSplit| |f02bjf| |setelt!| |cross| |computeBasis| |modTree| - |orOperands| |popFortranOutputStack| |leftDivide| |lazyPseudoDivide| - |univariatePolynomials| |clearTheFTable| |limitedint| - |sizePascalTriangle| |balancedBinaryTree| |inR?| |diag| |split| |cup| - |removeSinSq| |cylindrical| |errorKind| |queue| |createThreeSpace| - |lyndon| |maxrow| |normalDenom| |lazyVariations| |setprevious!| - |setProperties!| |splitSquarefree| |factorials| |outputFixed| - |expintfldpoly| |getlo| |shuffle| |innerSolve1| |numberOfComposites| - 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|varselect| |ricDsolve| |basisOfRightNucloid| |recoverAfterFail| - |Aleph| |setDifference| |antisymmetricTensors| - |removeSuperfluousCases| |more?| |curryRight| |mathieu23| |arg2| - |completeEchelonBasis| |abs| |fortranDouble| |rightRemainder| - |divisors| |Ci| |aspFilename| |accuracyIF| |d03eef| |stopMusserTrials| - |Gamma| |nthRootIfCan| |push!| |solveLinear| |nthCoef| - |genericLeftTraceForm| |iicosh| |f02abf| |conditions| |optional| - |directSum| |term| |largest| LODO2FUN |isPower| |c06gsf| - |flexibleArray| |cSinh| |removeDuplicates!| |mindegTerm| |match| - |tanQ| |sizeMultiplication| |mergeDifference| |over| |result| - |shiftRight| |tanIfCan| |mapBivariate| |d02kef| |s17def| |oddintegers| - |delta| |substring?| |relativeApprox| |resetVariableOrder| - |decreasePrecision| |compound?| |properties| |wronskianMatrix| - |rational?| |clearDenominator| |commutator| |OMputVariable| - |OMconnInDevice| |zerosOf| |useSingleFactorBound?| |wreath| - |pseudoDivide| |translate| |OMgetError| |d03edf| |minset| |conical| - |stiffnessAndStabilityOfODEIF| |getMultiplicationTable| |suffix?| - |generic| |ksec| |symmetricPower| |calcRanges| |morphism| |iicos| - |viewSizeDefault| |writable?| |curve?| |logGamma| |pattern| |hspace| - |tryFunctionalDecomposition?| |subscript| |quasiRegular| |rotate!| - |lquo| |nextPrimitivePoly| |f01maf| |prefix?| |iilog| |rightQuotient| - |triangulate| |revert| |s17ajf| |sn| |fractionPart| |iipow| - |pmintegrate| |elRow1!| |row| |upperCase?| |leftNorm| SEGMENT - |cyclic?| |getIdentifier| |curve| |homogeneous?| |Lazard2| - |numberOfFactors| |unexpand| |strongGenerators| |subQuasiComponent?| - |completeHermite| |semiResultantEuclidean2| |HenselLift| |setfirst!| - |OMgetType| |infRittWu?| |lambda| |message| |wrregime| |solve| - |gramschmidt| |closed?| |iidsum| |purelyTranscendental?| |lfunc| - |maxPoints| |weights| |evaluateInverse| |createMultiplicationTable| - |aromberg| |f02akf| |s17dhf| |neglist| |torsionIfCan| |Beta| - |semiResultantReduitEuclidean| |leaves| |f2df| |shallowExpand| - 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|splitDenominator| |degreePartition| |redpps| |basisOfLeftAnnihilator| - |viewThetaDefault| |leastMonomial| |modifyPointData| |mr| - |coordinates| |sumOfDivisors| |listOfLists| |divideIfCan!| |optpair| - |write!| |minIndex| |badValues| |lprop| |printInfo!| |d02cjf| - |listBranches| |sturmSequence| |changeBase| |getProperty| |sh| - |movedPoints| |quasiRegular?| |computeCycleLength| |linearMatrix| - |source| |removeSquaresIfCan| |enqueue!| |erf| |complexEigenvalues| - |dec| NOT |OMclose| |symbol?| |toseLastSubResultant| |remove!| - |d02bhf| |qfactor| |mightHaveRoots| |fglmIfCan| |UpTriBddDenomInv| - |iiperm| |categories| OR |e01bgf| |extractSplittingLeaf| - |complexElementary| ~= |bandedHessian| |arity| |typeList| - |tracePowMod| |df2fi| |retractIfCan| |constantKernel| AND |Vectorise| - |invertibleElseSplit?| |coerce| |check| |mapCoef| |dilog| |jacobian| - |isConnected?| |reverseLex| |basisOfNucleus| |numer| |construct| - |expandLog| |headReduced?| |pseudoQuotient| |whileLoop| - |showClipRegion| |basisOfCommutingElements| |countable?| |redmat| - 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|completeHensel| |s15aef| |ldf2lst| |phiCoord| |create| - |numberOfDivisors| |reshape| |f01brf| |atan| |setFieldInfo| - |monicModulo| |exportedOperators| |explimitedint| |gethi| - |stosePrepareSubResAlgo| |sincos| |nextSublist| |dmpToP| |acot| - |equivOperands| |setOfMinN| |regularRepresentation| |clipParametric| - |deriv| |selectPDERoutines| |asec| |extensionDegree| |char| - |identityMatrix| |setsubMatrix!| |validExponential| - |doubleFloatFormat| |mathieu22| |has?| |pol| |OMgetAttr| |acsc| - |coHeight| |f04qaf| |order| |stiffnessAndStabilityFactor| |resetNew| - |makeObject| |setelt| |isAbsolutelyIrreducible?| |eof?| |pointData| - |iroot| |sinh| |concat!| |convert| |readable?| |lazyEvaluate| |hue| - |red| |rootSplit| |multinomial| |setVariableOrder| |update| - |leastPower| |s19adf| |relerror| |squareFreePrim| |copy| |coef| - |removeRoughlyRedundantFactorsInPols| |scaleRoots| |f02aaf| |ridHack1| - |subCase?| |reduceBasisAtInfinity| |OMputAtp| |exponent| |rightLcm| - |part?| |genus| |superHeight| |getStream| |rur| |hconcat| |rdHack1| - |float| |digit| |tableForDiscreteLogarithm| |push| |insertTop!| - |logIfCan| |lllip| |deepCopy| |expintegrate| |d01aqf| |expt| - |monicRightFactorIfCan| |autoCoerce| |df2mf| |unparse| |s19abf| - |discriminantEuclidean| |inverse| |failed| |pdf2df| |OMmakeConn| - |lazyPseudoRemainder| |univariatePolynomial| |selectfirst| - |leadingExponent| |groebner| |lyndon?| |f01rcf| |prime| |match?| - |position| |assign| |commonDenominator| |LyndonWordsList| RF2UTS - |padecf| |cExp| |e02baf| |addMatchRestricted| |multMonom| - |countRealRoots| |innerEigenvectors| |antisymmetric?| |setLabelValue| - |aCubic| |mainPrimitivePart| |clipWithRanges| |extendedEuclidean| - |plot| |rischNormalize| |split!| |youngGroup| |children| |iifact| - |characteristic| |monomialIntegrate| |position!| |complexZeros| - |fortranCarriageReturn| |shiftRoots| |setTopPredicate| |coerceS| - |lazyIrreducibleFactors| |sorted?| |printHeader| |triangSolve| - |typeLists| |bitLength| |matrixConcat3D| |algint| |aLinear| - |numberOfIrreduciblePoly| |imagk| |normalForm| |radicalRoots| - |approximants| |approxNthRoot| |factors| |monicCompleteDecompose| - |makeEq| |Frobenius| |comp| |rischDE| |setEmpty!| GE |quadraticNorm| - |rightScalarTimes!| |normalDeriv| |lhs| |difference| |rationalPoint?| - |simpsono| |ord| |OMgetBVar| |explicitEntries?| |opeval| |makeprod| GT - |critpOrder| |hermiteH| |invmod| |rhs| |addPoint| |repSq| - |eyeDistance| |completeEval| |weighted| |next| |lighting| |randomR| - |routines| LE |leftScalarTimes!| |headRemainder| |reducedDiscriminant| - |lllp| |setButtonValue| |defineProperty| |doublyTransitive?| - |endOfFile?| |mapUp!| |alternative?| LT |summation| - |normalizeAtInfinity| |swap| |sparsityIF| |spherical| |removeSinhSq| - |modularGcd| |pade| |isMult| |bubbleSort!| |lyndonIfCan| |powers| - |updateStatus!| |elliptic?| |stFunc1| |leadingTerm| |qelt| - |trapezoidal| |legendreP| |symbolIfCan| |log| |e01bhf| |normFactors| - |generalizedEigenvectors| |nil?| |eigenvector| |qsetelt| - |cyclicParents| |e01sbf| |selectAndPolynomials| |imagi| - |halfExtendedSubResultantGcd2| |singRicDE| |vconcat| - |stoseInvertible?reg| |loopPoints| |cycleSplit!| |unknown| |pastel| - |jordanAlgebra?| |deepestInitial| |f02wef| |xRange| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |f04faf| |quotedOperators| |quickSort| + |algebraicVariables| |create| |bindings| |hasHi| |s18aef| |surface| + |useEisensteinCriterion?| |halfExtendedResultant2| + |genericLeftTraceForm| |permutations| |enterPointData| |isOpen?| + |over| |balancedFactorisation| |semiSubResultantGcdEuclidean1| + |explicitlyEmpty?| |prevPrime| |An| |d02raf| |resetNew| |shufflein| + |cosh2sech| |critT| |firstUncouplingMatrix| |rootNormalize| |cCos| + |setColumn!| |separateDegrees| |sort| |diag| |tubeRadius| + |sizeMultiplication| |factorials| |showAll?| |lfextlimint| + |generalSqFr| |leftOne| |karatsubaOnce| |exprToXXP| |FormatArabic| + |univariateSolve| |radicalRoots| |LiePolyIfCan| |pile| |fortran| + |lookup| |leftFactor| |continuedFraction| |intersect| |subst| + |setIntersection| |deleteProperty!| |freeOf?| + |cyclotomicDecomposition| |s17dcf| |Ei| |cyclicCopy| |chvar| |e04jaf| + |identityMatrix| |aQuadratic| |setUnion| |nthCoef| |fracPart| + |coerceL| |minColIndex| |iicos| |powers| |leastAffineMultiple| + |leftExactQuotient| |mappingAst| |viewport2D| |random| |apply| + |leftUnits| |d01alf| |overlabel| |randomR| |mapExponents| + |coerceListOfPairs| |currentEnv| |seriesSolve| |nthFlag| |generators| + |nil| |cothIfCan| |e02ahf| |ellipticCylindrical| |showAllElements| + |complexSolve| |makeprod| |monomial| |linearAssociatedLog| + |fortranDoubleComplex| |vspace| |rotate!| |size| |extract!| + |createThreeSpace| |call| |e02daf| |ignore?| |univcase| |multivariate| + |BasicMethod| |subCase?| |nextPrimitivePoly| |lazyPrem| |binaryTree| + |selectOrPolynomials| |quasiMonic?| |startTableGcd!| |printHeader| + |sup| |saturate| |variables| |andOperands| |atanhIfCan| |approximate| + |probablyZeroDim?| |objects| |function| |deleteRoutine!| + |lastSubResultantElseSplit| |extractIndex| |selectIntegrationRoutines| + |drawStyle| |complex| |id| |selectAndPolynomials| |tab| |divide| + |orthonormalBasis| |base| |first| |twist| |someBasis| |rightMult| + |fortranLiteralLine| |readByte!| |d01ajf| |complex?| |nthRootIfCan| + |depth| |quadratic?| |mapBivariate| |eval| |rest| |vconcat| + |multinomial| |solid?| |insertTop!| |lyndonIfCan| |leftRemainder| + |clipPointsDefault| |logIfCan| |table| |normalizeAtInfinity| |modulus| + |substitute| |close| RF2UTS |rationalApproximation| + |halfExtendedSubResultantGcd1| |bumprow| |bumptab| |iidsum| + |deepExpand| |new| |fTable| |presuper| |removeDuplicates| |obj| + |magnitude| |c06eaf| |invertibleSet| |rootsOf| |setPrologue!| |search| + |taylor| |tubeRadiusDefault| |Frobenius| |repSq| |getVariableOrder| + |dualSignature| |remove| |iterationVar| |cache| |tanNa| |display| + |constant?| |LagrangeInterpolation| |script| BY |laurent| |palgextint| + |nullity| |pointColorPalette| |dmp2rfi| |generalizedEigenvector| + |makingStats?| |cycleEntry| |intermediateResultsIF| |unmakeSUP| + |constant| |tower| |puiseux| |nextPartition| |cosSinInfo| + |tableForDiscreteLogarithm| |lazyVariations| |last| |pascalTriangle| + |computeCycleEntry| |restorePrecision| |dioSolve| |leadingIndex| + |point| |iitan| |selectODEIVPRoutines| |compactFraction| |chiSquare| + |assoc| |swap| |infinityNorm| |fortranLiteral| |leftGcd| |f01rdf| + |tex| |inv| |rubiksGroup| |seed| |minimumDegree| |Lazard| + |readUInt32!| |viewpoint| |squareTop| |setTex!| |factorAndSplit| + |d01akf| |ground?| |s17ajf| |strongGenerators| |difference| + |makeViewport2D| |readUInt16!| |input| |possiblyNewVariety?| + |harmonic| |coth2tanh| |expenseOfEvaluation| |symbol?| |ground| + |series| |iisin| |listexp| |curveColor| |xCoord| |readInt32!| + |library| |Beta| |showTypeInOutput| |limitedint| |f02agf| |mapmult| + |setleft!| |maxIndex| |leadingMonomial| |index?| |complexNumeric| + |e02baf| |region| |previous| |lcm| |readInt16!| |c06gqf| |connect| + |sh| |unparse| |viewPosDefault| |updatD| |positiveRemainder| + |leadingCoefficient| |selectOptimizationRoutines| |rules| |minus!| + |factorFraction| |roughBase?| |minPoly| |character?| + |resetAttributeButtons| UP2UTS |eq?| |kernels| |primitiveMonomials| + |uniform01| |left| |expPot| |minimalPolynomial| |append| |replace| + |setErrorBound| |viewPhiDefault| |rootProduct| |cyclicEntries| + |atanIfCan| |univariate| |min| |reductum| |right| |startStats!| + |postfix| |untab| |gcd| |neglist| |set| |reflect| |makeVariable| + |dimensionOfIrreducibleRepresentation| |mainMonomials| |prem| + |splitNodeOf!| |jacobi| |mainSquareFreePart| |false| |exponential1| + |skewSFunction| |insert!| |rotatey| |rightLcm| |normalise| |sum| + |LowTriBddDenomInv| |makeSeries| |complexEigenvalues| + |resultantEuclideannaif| |contract| |squareFreePrim| + |symmetricTensors| |ref| |internalSubPolSet?| |zeroVector| + |expextendedint| |factor| |changeThreshhold| |newSubProgram| |imagI| + |debug3D| |getBadValues| |noKaratsuba| |integralBasisAtInfinity| + |monicRightFactorIfCan| |arguments| |sqrt| |roman| |exactQuotient!| + |innerint| |trim| |maximumExponent| |LazardQuotient| |cyclic?| + |LyndonBasis| |s17dlf| |basisOfRightAnnihilator| |gcdcofactprim| + |real| |e02zaf| |maxrank| |imaginary| |sign| |explogs2trigs| |lp| + |nullary| |removeSinhSq| |interReduce| |imag| |pseudoRemainder| + |numericalIntegration| |semiSubResultantGcdEuclidean2| |ptree| |cAcos| + |rotatex| |LyndonWordsList| |numericalOptimization| |cycle| + |directProduct| |singular?| |completeHermite| |noLinearFactor?| + |s18aff| |sort!| |setFieldInfo| |baseRDEsys| |getProperty| |integral| + |showSummary| |factorsOfDegree| |c05adf| |branchPointAtInfinity?| + |zoom| |clearTheSymbolTable| |iibinom| |whileLoop| |jacobian| + |closed?| |rotatez| |number?| |brace| |iiacot| |lfinfieldint| |df2mf| + |hash| |leftExtendedGcd| |isPower| |hdmpToDmp| |printStats!| + |showAttributes| |destruct| |tableau| |makeSUP| |factorGroebnerBasis| + |square?| |createNormalPoly| |show| |count| |acothIfCan| |decimal| + |fi2df| |f04adf| |paren| |symbol| |objectOf| |LiePoly| = |lagrange| + |decreasePrecision| |s19aaf| |sPol| |OMputEndObject| |algDsolve| + |OMsupportsCD?| |expression| |bombieriNorm| |leastPower| |diff| + |conical| |trace| |lo| |realZeros| |clearTheFTable| + |numberOfImproperPartitions| |integer| |subSet| |infiniteProduct| + |remainder| |unrankImproperPartitions0| < |internalAugment| |exquo| + |sylvesterMatrix| |monomial?| |incr| |normal01| |doubleComplex?| + |gderiv| |space| |powern| |outputSpacing| > |div| |extendedint| + |limitedIntegrate| |OMgetEndObject| |rightUnit| |plotPolar| |integer?| + |nextColeman| |goto| |collectQuasiMonic| |read!| <= |quo| |OMgetType| + |operator| |crushedSet| |purelyAlgebraicLeadingMonomial?| |OMsend| + |radicalEigenvalues| |iroot| |typeLists| |groebSolve| >= |label| + |rootOfIrreduciblePoly| |positive?| |getRef| |internal?| |addiag| + |readLine!| |fortranDouble| |eigenMatrix| |yCoordinates| |rem| |cSech| + |root?| |numberOfIrreduciblePoly| |factorByRecursion| |limit| |trigs| + |sumOfDivisors| |flexible?| |getDatabase| |setStatus| + |rightFactorIfCan| |check| |resize| |upperCase!| |tanSum| |operation| + |exprex| + |cCoth| |definingInequation| |algintegrate| |traverse| + |generalizedContinuumHypothesisAssumed| |setEpilogue!| |overlap| + |stronglyReduced?| - |parent| |getCode| |besselJ| |finiteBasis| + |besselY| |integralCoordinates| |f01ref| |style| / |maxint| + |preprocess| |lexico| |wholeRagits| |moebius| |satisfy?| + |createLowComplexityNormalBasis| |showTheFTable| |principal?| + |shiftRoots| |splitConstant| |push| |redPo| |OMputSymbol| + |constructor| |unitNormal| |mathieu12| |swap!| |listLoops| + |beauzamyBound| |component| |resultantReduit| |c06gbf| |c06gsf| + |isAbsolutelyIrreducible?| |perfectNthPower?| |OMputString| |s14aaf| + |removeZeroes| |option| |monomials| |element?| |totalLex| |Si| + |closedCurve?| |fortranLinkerArgs| |OMgetEndAttr| + |internalLastSubResultant| |primintegrate| |coefficients| |f02fjf| + |indicialEquations| |jacobiIdentity?| |nothing| |singRicDE| + |createMultiplicationTable| |subNodeOf?| |packageCall| |ratDsolve| + |OMgetString| |lfunc| |listConjugateBases| |UP2ifCan| |rightRemainder| + |latex| |subspace| |inverse| |tracePowMod| |iiacsch| |padicallyExpand| + |screenResolution3D| |realElementary| |besselI| |normal?| |mapSolve| + |kroneckerDelta| |nthExpon| |janko2| |highCommonTerms| |updateStatus!| + |lyndon?| |removeCosSq| |cPower| |quoted?| |bag| |quadratic| + |euclideanSize| |hitherPlane| |groebner| |pointSizeDefault| + |prolateSpheroidal| |divergence| |outputList| |monicLeftDivide| + |getMeasure| |rightTrim| |reverseLex| |numberOfDivisors| + |boundOfCauchy| |asechIfCan| |trailingCoefficient| |e02gaf| + |monomialIntPoly| |meshFun2Var| |e01daf| |mix| |euler| |leftTrim| + |bivariatePolynomials| |aQuartic| |complexLimit| |commonDenominator| + |distFact| |hspace| |rootSplit| |createIrreduciblePoly| |elliptic| + |unvectorise| |subNode?| |partialNumerators| |newLine| |coordinate| + |semiResultantEuclidean2| |readIfCan!| |singularAtInfinity?| + |numberOfComputedEntries| |null?| |normalElement| |expandPower| + |interval| |c06ecf| |socf2socdf| |shuffle| |leftTrace| + |numberOfFractionalTerms| |select!| |generalizedEigenvectors| + |OMopenString| |OMputEndAtp| |bat1| |acosIfCan| |quasiRegular| + |sqfrFactor| |Lazard2| |solveLinearPolynomialEquation| + |transcendentalDecompose| |delta| |OMreadFile| |internalZeroSetSplit| + |ramifiedAtInfinity?| |denominator| |mapUnivariate| |callForm?| + |choosemon| |quasiComponent| |move| |qelt| |genericRightDiscriminant| + |li| |linear| |inR?| |areEquivalent?| |prepareDecompose| |fintegrate| + |wordInStrongGenerators| |qsetelt| |torsion?| |term?| + |makeYoungTableau| |submod| |makeResult| |f01qdf| |truncate| + |pleskenSplit| |supersub| |mvar| |identity| |s17agf| |or?| |xRange| + |antiCommutative?| |makeTerm| |polynomial| |gcdPolynomial| |basicSet| + |arity| |bat| |binaryFunction| |axesColorDefault| |measure| + |BumInSepFFE| |yRange| |lazyPquo| |curve?| |consnewpol| |graphState| + |basisOfRightNucleus| |complexRoots| |blankSeparate| |linearMatrix| + |iprint| |OMconnInDevice| |zRange| |recolor| |createRandomElement| + |mapUp!| |besselK| |exists?| |frobenius| |leftScalarTimes!| |map!| + |chineseRemainder| |Hausdorff| |bivariateSLPEBR| |largest| |realSolve| + |hi| |cAcsch| |e02bdf| |has?| |maxPoints3D| |d03faf| |qsetelt!| + |rootBound| |solve1| |numberOfMonomials| |fibonacci| |errorInfo| + |lambda| |cycles| |collectUnder| |cycleElt| |tanhIfCan| |e01bhf| |po| + |c05nbf| |scanOneDimSubspaces| |factorList| |quasiAlgebraicSet| + |even?| |univariatePolynomials| |functionIsFracPolynomial?| |float?| + |column| |upperCase?| |functionIsContinuousAtEndPoints| |cardinality| + |keys| |outputForm| |tubePointsDefault| |f2df| |OMsetEncoding| + |psolve| |norm| |tanh2trigh| |term| |exQuo| |conjugate| + |principalAncestors| |prologue| |bipolar| |generalInfiniteProduct| + |OMread| |quasiMonicPolynomials| |curve| |factorial| + |rewriteIdealWithQuasiMonicGenerators| |deepestTail| |qfactor| + |perspective| |quadraticNorm| |cAtan| |rischDE| |mainExpression| + |iiacoth| |integralLastSubResultant| |useSingleFactorBound?| + |tanh2coth| |sorted?| |pastel| |test| |diagonal?| |purelyAlgebraic?| + |createPrimitiveElement| |clearTheIFTable| |lllp| |acscIfCan| + |primextendedint| |insertMatch| |f04atf| |elements| |odd?| + |setVariableOrder| |variationOfParameters| |diagonals| |moduloP| + |OMputAttr| |simplifyExp| |polyred| |cycleLength| |outlineRender| + |generate| |biRank| |clearTable!| |operators| |monomRDE| |content| + |yellow| |fortranComplex| |squareFreePolynomial| |node?| |prefix| + |semiResultantEuclideannaif| |multiEuclideanTree| |irreducible?| + |reorder| |plus!| |antiAssociative?| |rightDiscriminant| + |cRationalPower| |list?| |hexDigit?| |d02ejf| + |inverseIntegralMatrixAtInfinity| |leftPower| |c06fqf| |OMgetEndAtp| + |numFunEvals3D| |cAcsc| |s18def| |polyRicDE| |compiledFunction| + |split!| |selectSumOfSquaresRoutines| |zeroOf| |rightExactQuotient| + |polyPart| |genericLeftMinimalPolynomial| |stripCommentsAndBlanks| + |groebner?| |f01qef| |retractable?| |npcoef| |nthFractionalTerm| + |commaSeparate| |ScanFloatIgnoreSpaces| |abs| |polCase| |sech2cosh| + |just| |sincos| |OMgetSymbol| |halfExtendedSubResultantGcd2| + |numberOfHues| |primextintfrac| |null| |polygon?| + |transcendenceDegree| |denomRicDE| |pair?| |quote| |f04jgf| + |chebyshevT| |cyclicEqual?| |divisorCascade| |prepareSubResAlgo| + |range| |not| |toseSquareFreePart| |alphanumeric?| |OMputVariable| + |pack!| |rewriteIdealWithHeadRemainder| |dim| |OMserve| + |monicDecomposeIfCan| |palginfieldint| |gradient| |ran| |and| + |patternMatch| |quadraticForm| |oddintegers| |weakBiRank| + |noncommutativeJordanAlgebra?| |OMreadStr| |roughBasicSet| + |rischDEsys| |purelyTranscendental?| |or| |lazyPseudoDivide| + |diagonal| |weight| |mainDefiningPolynomial| + |semiDiscriminantEuclidean| |lifting1| |dmpToP| |subresultantSequence| + |pop!| |extendedResultant| |branchIfCan| |tanQ| |expintegrate| |xor| + |rk4| |currentCategoryFrame| |insertionSort!| |leviCivitaSymbol| + |jordanAdmissible?| |trueEqual| |fortranCompilerName| |split| + |signatureAst| |absolutelyIrreducible?| |f04mcf| |case| + |rationalPower| |whitePoint| |slex| |extractIfCan| |bringDown| + |d01anf| |separate| |insertBottom!| |e02ddf| |identitySquareMatrix| + |hyperelliptic| |Zero| |mainVariable?| |toseInvertibleSet| + |nextsubResultant2| |oddInfiniteProduct| |idealiserMatrix| |one?| + |subTriSet?| |write!| |relativeApprox| |zeroDimensional?| |One| + |degreeSubResultant| |fixPredicate| |graphStates| |/\\| |argscript| + |startTable!| |algebraicOf| |hostPlatform| |firstSubsetGray| + |dAndcExp| |elementary| |dimensionsOf| |rightOne| |swapColumns!| + |basisOfRightNucloid| |\\/| |unitVector| |aLinear| |axes| + |extractTop!| |mainCoefficients| |geometric| |composite| |maxPoints| + |reduced?| |algebraicCoefficients?| |colorFunction| |key| + |multiEuclidean| |f02abf| |zeroSquareMatrix| |merge!| |iiasec| |vark| + |distdfact| |setProperty!| |mkPrim| |alphabetic?| |predicates| + |logical?| |center| |iiatanh| |viewport3D| |backOldPos| + |replaceKthElement| |mapCoef| |intPatternMatch| |lazyPremWithDefault| + |brillhartTrials| |leadingBasisTerm| |filename| |numeric| + |reduceByQuasiMonic| |zerosOf| |degreePartition| + |linearAssociatedOrder| |complexIntegrate| |elt| |palgRDE0| + |controlPanel| |selectPolynomials| |startPolynomial| + |lazyPseudoQuotient| |not?| |second| |radical| |resultantEuclidean| + |euclideanNormalForm| |rarrow| |symmetricDifference| |enumerate| + |moduleSum| |matrixConcat3D| |quatern| |parse| |third| |cyclicGroup| + |refine| |extendIfCan| |setfirst!| |iicosh| |lquo| |physicalLength| + |duplicates| |compose| |equivOperands| |critBonD| |genericRightNorm| + |att2Result| |selectsecond| |subscriptedVariables| |sn| + |changeWeightLevel| |nullSpace| |pquo| |redPol| |mapUnivariateIfCan| + |indices| |directSum| |power!| |pmComplexintegrate| |OMbindTCP| + |indicialEquationAtInfinity| |firstDenom| |userOrdered?| |allRootsOf| + |paraboloidal| |duplicates?| |radicalOfLeftTraceForm| + |stoseLastSubResultant| |parts| |normalized?| |exponential| |trunc| + |cSinh| |mainKernel| |f04mbf| |outputGeneral| |palglimint| + |hasTopPredicate?| |isobaric?| |fractionFreeGauss!| |decomposeFunc| + |setLabelValue| |expr| |stirling2| |maxdeg| |unit| |qualifier| + |drawToScale| |coerceP| |mathieu22| |dimension| |explicitlyFinite?| + |rischNormalize| |ScanArabic| |readInt8!| |resultant| + |symmetricProduct| |functionIsOscillatory| |returns| |systemCommand| + |generalTwoFactor| |kind| |lastSubResultantEuclidean| |iFTable| + |monicModulo| |regularRepresentation| |equality| |bandedHessian| + |iteratedInitials| |op| |gramschmidt| |entries| |mapdiv| + |computeCycleLength| |Vectorise| |implies| |stack| |cCosh| + |OMunhandledSymbol| |sturmSequence| |squareFreeLexTriangular| + |variable| |minGbasis| |curry| |anticoord| |prime| |orbits| |multiset| + |schema| |triangulate| |normal| |complexEigenvectors| |iterators| + |selectfirst| |algebraicSort| |middle| |nextItem| |tanIfCan| |low| + |insertRoot!| FG2F |raisePolynomial| |index| |fortranLogical| + |triangular?| |setRealSteps| |f01bsf| |setMaxPoints3D| |concat!| + |ceiling| |modTree| |internalSubQuasiComponent?| + |clearFortranOutputStack| |cscIfCan| |fortranCarriageReturn| + |coercePreimagesImages| |stopTableGcd!| |SturmHabicht| |OMgetBind| + |finiteBound| |removeConstantTerm| |f01rcf| |loadNativeModule| + |evaluateInverse| |constantIfCan| |increase| |medialSet| |child| + |union| |prinshINFO| |pair| |removeZero| |transcendent?| + |showIntensityFunctions| |binaryTournament| |maxRowIndex| + |createNormalPrimitivePoly| |rightMinimalPolynomial| |updatF| + |rdregime| |radix| |autoReduced?| |drawCurves| |cylindrical| |s15adf| + |s18dcf| |makeEq| |zeroDimPrime?| |ptFunc| |genericRightTrace| + |curryLeft| |e01sff| |key?| |computeInt| |ScanFloatIgnoreSpacesIfCan| + |gethi| |rootOf| |systemSizeIF| |inconsistent?| |c02agf| + |showTheIFTable| |lowerCase| |double| |optAttributes| |mathieu24| + |groebnerIdeal| |value| |setMaxPoints| |empty?| |critMonD1| |e04dgf| + |Aleph| |qPot| |leadingIdeal| |edf2ef| |perfectNthRoot| |OMgetEndBVar| + |indicialEquation| |d03edf| |f07aef| |partitions| |setLength!| + |toseInvertible?| |coshIfCan| |leftZero| |shiftRight| |checkForZero| + |taylorIfCan| |integers| |external?| |s20acf| |binary| |baseRDE| + |cAsin| |rightZero| |stopMusserTrials| |normInvertible?| |uniform| + |primitivePart!| |linearlyDependent?| |isPlus| |associatorDependence| + |palgint| |sequences| |spherical| |viewSizeDefault| |readable?| + |leadingExponent| |evenInfiniteProduct| |OMmakeConn| + |OMencodingBinary| |fractRagits| |child?| |d01gbf| |LyndonCoordinates| + |shallowCopy| |generalPosition| |squareFreePart| |shallowExpand| + |mainValue| |rule| |graphs| |nativeModuleExtension| |integrate| |say| + |completeEval| |pseudoDivide| |intcompBasis| |hconcat| |fractionPart| + |modifyPoint| |halfExtendedResultant1| |d01amf| |rational| + |zeroMatrix| |radicalSolve| |declare!| |monomialIntegrate| |e01baf| + |e04naf| |lazyIrreducibleFactors| |aromberg| |adaptive3D?| + |gcdPrimitive| |subResultantsChain| |stoseInvertibleSetreg| + |modularGcdPrimitive| |copy!| |wordsForStrongGenerators| |iisqrt3| + |laguerre| |charpol| |SturmHabichtMultiple| |blue| |ocf2ocdf| |mulmod| + |movedPoints| |mainVariables| |monicRightDivide| + |nextNormalPrimitivePoly| |simpsono| |binarySearchTree| |solveLinear| + |completeSmith| |Ci| |midpoints| |tablePow| |findBinding| + |bezoutDiscriminant| |rootPoly| |startTableInvSet!| |permanent| + |univariatePolynomial| |shiftLeft| |testModulus| |basis| + |clipWithRanges| |rowEchelon| |groebnerFactorize| |commutative?| + |argumentListOf| |d02bbf| |getOrder| |deepCopy| |torsionIfCan| + |SturmHabichtCoefficients| |lfextendedint| |oddlambert| |s20adf| + |quartic| |void| |ridHack1| |reset| |isOp| |createGenericMatrix| + |direction| |setPosition| |componentUpperBound| |basisOfMiddleNucleus| + |viewDeltaXDefault| |smith| |zeroDimPrimary?| |maxrow| |scale| + |subPolSet?| |heapSort| |jordanAlgebra?| |cos2sec| |pointLists| + |listOfMonoms| |segment| |convergents| |matrixGcd| |PDESolve| |write| + |parseString| |equiv| |shellSort| |credPol| |reverse| |setOrder| + |removeRedundantFactors| |characteristicSerie| |save| |directory| + |tanintegrate| |atoms| |setEmpty!| |numberOfCycles| |numberOfChildren| + |makeUnit| |normalDeriv| |constDsolve| |KrullNumber| |sample| |exp1| + |outputBinaryFile| |entry| |complexElementary| |internalIntegrate| + |setMinPoints3D| |printCode| |extendedEuclidean| |OMUnknownSymbol?| + |size?| |s14baf| |B1solve| |outputArgs| |rightQuotient| |s21bcf| + |presub| |showArrayValues| |s14abf| |listYoungTableaus| |double?| + |unrankImproperPartitions1| |rightScalarTimes!| |separateFactors| + |acotIfCan| |leftUnit| |resetVariableOrder| |applyRules| |adaptive| + |comment| |kmax| |iipow| |atrapezoidal| |c06fpf| |ldf2lst| + |extractClosed| |sizePascalTriangle| |safeFloor| |checkPrecision| + |explimitedint| |weights| |setAdaptive3D| |denominators| |divideIfCan| + |coord| |OMputEndBind| |complexNormalize| |OMUnknownCD?| |froot| + |totalfract| |makeGraphImage| |prime?| F2FG |setsubMatrix!| + |possiblyInfinite?| |iiacsc| |externalList| |eigenvector| |cyclotomic| + |f02wef| |useNagFunctions| |squareFreeFactors| |s17aef| |changeBase| + |idealiser| |complementaryBasis| |cAsech| |setright!| |subscript| + |flatten| |nextPrime| |complexZeros| |imagj| |eigenvalues| + |associator| |copies| |universe| |setPoly| |f01brf| |discriminant| + |concat| |showClipRegion| |trigs2explogs| |minPoints3D| + |initializeGroupForWordProblem| |cfirst| |parents| |elem?| |factors| + |back| |interpolate| |top| |OMgetObject| |nand| |discreteLog| + |horizConcat| |escape| |var1Steps| |bandedJacobian| |cSin| |argument| + |multMonom| |rightDivide| |yCoord| |unitsColorDefault| |palgextint0| + |overbar| |phiCoord| |firstNumer| |solveLinearlyOverQ| + |fortranCharacter| |true| |closeComponent| |rowEch| |mergeDifference| + |vedf2vef| |linSolve| |asecIfCan| |iiatan| |topPredicate| + |extensionDegree| |badValues| |ord| |currentScope| |acoshIfCan| + |dominantTerm| |compdegd| |vertConcat| |readLineIfCan!| |binomThmExpt| + |definingEquations| |ffactor| |orOperands| |e04mbf| |pdct| |setvalue!| + |associatedSystem| |vectorise| |integralMatrix| |rightGcd| |zeroDim?| + |evenlambert| |polynomialZeros| |addMatch| |basisOfCenter| + |basisOfCentroid| |colorDef| |acsch| |coefChoose| + |removeRoughlyRedundantFactorsInPols| |aspFilename| |solveRetract| + |c05pbf| |OMclose| |exprHasWeightCosWXorSinWX| |makeFR| |mainVariable| + |edf2efi| |outerProduct| |basisOfLeftAnnihilator| + |rewriteSetByReducingWithParticularGenerators| |headAst| |nodeOf?| + |OMlistCDs| |signature| |equiv?| |OMputEndError| |antisymmetric?| + |integerIfCan| |leftMult| |varList| |infLex?| |f01mcf| |super| + |reopen!| |lexGroebner| |printInfo| |f07fdf| |cAcoth| + |rectangularMatrix| |bytes| |signAround| |setProperty| |lowerCase!| + |moebiusMu| |pointPlot| |bits| |meshPar1Var| |currentSubProgram| + |unaryFunction| |localReal?| |root| |ParCondList| + |reciprocalPolynomial| |perfectSqrt| |setMinPoints| |rombergo| + |headReduced?| |semiDegreeSubResultantEuclidean| |cyclicParents| + |btwFact| |normDeriv2| |euclideanGroebner| |nthr| |constantOperator| + |copyInto!| |algint| |conditionP| |getIdentifier| |delete| + |rowEchLocal| |linearPolynomials| |OMgetAtp| |matrix| |lexTriangular| + |indiceSubResultant| |symbolTableOf| |semiIndiceSubResultantEuclidean| + |triangSolve| |outputAsTex| |f04maf| |eyeDistance| |normalDenom| + |antiCommutator| |leftRank| |cyclePartition| |bitTruth| + |showTheRoutinesTable| |linear?| |headReduce| |trace2PowMod| + |cschIfCan| |makeSketch| |innerSolve1| |screenResolution| |augment| + |empty| |extendedSubResultantGcd| |fixedPointExquo| |parametersOf| + |lprop| |optimize| |nsqfree| UTS2UP |increasePrecision| |thenBranch| + |zero| |ratPoly| |HenselLift| |interpretString| |acschIfCan| + |removeRedundantFactorsInPols| |LazardQuotient2| |toroidal| + |fortranInteger| |mkcomm| |stiffnessAndStabilityFactor| |setleaves!| + |linearDependenceOverZ| |brillhartIrreducible?| |airyAi| |comparison| + |enqueue!| |outputFloating| |s13aaf| |printStatement| + |lastSubResultant| |And| |mat| |completeEchelonBasis| |lazyGintegrate| + |implies?| |numberOfNormalPoly| |setValue!| |charClass| + |powerAssociative?| |edf2fi| |addPoint2| |Or| |linearAssociatedExp| + |hMonic| |pToDmp| |setrest!| |decrease| |doublyTransitive?| |digit?| + |leftTraceMatrix| |discriminantEuclidean| |cond| |leadingTerm| |Not| + |removeSuperfluousCases| |pr2dmp| |intensity| |showRegion| + |expintfldpoly| |quotient| |block| |sinh2csch| |wreath| |top!| + |scaleRoots| |nonSingularModel| |useEisensteinCriterion| + |OMconnOutDevice| |subtractIfCan| |identification| |plus| + |setprevious!| |collect| |f01qcf| |resetBadValues| |cyclicSubmodule| + |frst| |invertIfCan| |factorSquareFree| |getConstant| |iiGamma| + |SFunction| |numberOfComposites| |internalDecompose| + |differentialVariables| |minimize| |musserTrials| |outputAsScript| + |color| |parametric?| |repeating| |cosh| |trapezoidalo| |OMputBind| + |simpson| |computePowers| |exactQuotient| + |stoseIntegralLastSubResultant| |log10| |genericPosition| + |setFormula!| |unitCanonical| |radicalSimplify| |tanh| |iiperm| + |extractPoint| |max| |lazyResidueClass| |iCompose| |constantLeft| + |imagi| |pseudoQuotient| |UnVectorise| |bitand| |notOperand| |coth| + |clearDenominator| |times| |problemPoints| |alternative?| + |repeatUntilLoop| |isQuotient| |iisqrt2| |bitior| |factorPolynomial| + |randomLC| |localAbs| |semiResultantReduitEuclidean| |sech| + |predicate| |central?| |OMputError| |popFortranOutputStack| + |stopTable!| |complexNumericIfCan| |prod| |commutator| + |radicalEigenvectors| |flagFactor| |cAsinh| |subQuasiComponent?| + |csch| |rationalPoint?| |alternatingGroup| |cubic| |fortranTypeOf| + |numberOfPrimitivePoly| 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|crest| + |byte| |parameters| |declare| |fglmIfCan| |multiple| |positiveSolve| + |e01bff| |high| |ipow| |f04arf| |debug| |expenseOfEvaluationIF| + |df2ef| |rightRankPolynomial| |monic?| |oneDimensionalArray| |head| + |applyQuote| |f04asf| |perfectSquare?| |expIfCan| D |reseed| |cAtanh| + |upDateBranches| |definingPolynomial| |changeVar| |option?| + |RittWuCompare| |iilog| |unit?| |tail| |complexForm| |pmintegrate| + |f07adf| |inGroundField?| |laurentRep| + |zeroSetSplitIntoTriangularSystems| |countRealRoots| + |rightAlternative?| |trapezoidal| |meshPar2Var| |s13acf| |reduce| + |open?| |midpoint| |chiSquare1| |doubleResultant| |recoverAfterFail| + |sequence| |computeBasis| |wordInGenerators| |ruleset| |bitCoef| + |rightPower| |algSplitSimple| |s17dhf| |birth| |c02aff| |f01maf| + |fill!| |generator| |numberOfFactors| |diophantineSystem| + |setImagSteps| |lowerPolynomial| |createPrimitiveNormalPoly| + |complexExpand| |cAcosh| |find| |bothWays| |rootSimp| |c06ebf| |critM| + |pushdterm| 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|associative?| |routines| |stoseInvertibleSetsqfreg| |minrank| + |digamma| |orbit| |splitSquarefree| |lfintegrate| |hermite| + |ricDsolve| |multiplyExponents| |monicCompleteDecompose| |d01gaf| + |unexpand| |removeRedundantFactorsInContents| |coHeight| |bit?| + |impliesOperands| |sqfree| |string?| |associatedEquations| |output| + |bumptab1| |compile| |scan| |power| |changeNameToObjf| + |LyndonWordsList1| |numFunEvals| |mkIntegral| |d01bbf| |code| |int| + |symmetricPower| |f07fef| |s17def| |e02dcf| |cup| + |toseLastSubResultant| |varselect| |s21bbf| |partialQuotients| + |realRoots| |setClosed| |findCycle| |iiacos| |uncouplingMatrices| + |setTopPredicate| |elliptic?| |fractRadix| |#| |isConnected?| |close!| + |critpOrder| |squareFree| |ksec| + |removeRoughlyRedundantFactorsInContents| |constantOpIfCan| + |prindINFO| |diagonalMatrix| |e04fdf| |divideExponents| |solid| + |partition| |bezoutResultant| |coleman| |bipolarCylindrical| |ranges| + |dom| |epilogue| |safetyMargin| |factorSquareFreeByRecursion| + |laurentIfCan| |incrementBy| |OMParseError?| |arbitrary| + |resultantReduitEuclidean| |xn| |OMcloseConn| |palgintegrate| + |palgLODE0| |rdHack1| |taylorRep| |buildSyntax| |expand| + |inverseIntegralMatrix| |approxNthRoot| |rCoord| |getOperator| |node| + |round| |initials| |pol| |lieAdmissible?| |filterWhile| |s17aff| + |OMputBVar| |ideal| |polyRDE| |cSec| |primeFrobenius| |e04gcf| |rst| + |quotientByP| |filterUntil| |basisOfNucleus| |rk4qc| |sumOfSquares| + |legendreP| |getButtonValue| |tanAn| |sec2cos| |numericIfCan| + |bracket| |select| |parabolicCylindrical| |bsolve| |rightTraceMatrix| + |imagJ| |createPrimitivePoly| |title| |ldf2vmf| |wronskianMatrix| + |linears| |cyclic| |options| |e02ajf| |structuralConstants| |logpart| + |integerBound| |fillPascalTriangle| |bernoulliB| |printInfo!| + |clipParametric| |alternating| |eigenvectors| |dot| |cot2trig| + |semicolonSeparate| |integralBasis| |product| |outputFixed| |hue| + |initiallyReduce| |reducedForm| |dictionary| |abelianGroup| |e| + |initial| |dflist| |primes| |e02adf| |var1StepsDefault| |string| + |iidprod| |expandTrigProducts| |iiasin| |minRowIndex| |fprindINFO| + |plusInfinity| |mirror| |leftDiscriminant| |nextsousResultant2| + |RemainderList| |eof?| |normalizedDivide| |romberg| |graeffe| + |charthRoot| |minusInfinity| |rename!| |makeRecord| + |semiLastSubResultantEuclidean| |measure2Result| |optpair| + |singleFactorBound| |prinpolINFO| |OMgetEndError| |f04axf| |mainForm| + |bezoutMatrix| |digits| |symmetricRemainder| |OMgetVariable| + |safeCeiling| |less?| |quasiRegular?| |reduceLODE| |initTable!| + |iicoth| |coerceImages| |variable?| |ode| |linkToFortran| + |stoseInvertibleSet| |getProperties| |karatsuba| |e02agf| + |drawComplexVectorField| |dequeue| |sizeLess?| |fullDisplay| |s18acf| + |ScanRoman| |extend| |branchPoint?| |selectPDERoutines| |Is| |critB| + |checkRur| |indiceSubResultantEuclidean| |inverseColeman| |airyBi| + |symmetric?| |OMencodingUnknown| |part?| |irreducibleFactor| |any?| + |physicalLength!| |numberOfVariables| |rightNorm| |UpTriBddDenomInv| + |reducedSystem| |inspect| |cCot| |equation| |type| |supRittWu?| + |nextSubsetGray| |f02adf| |exteriorDifferential| |bernoulli| + |getSyntaxFormsFromFile| |makeFloatFunction| |redpps| |roughSubIdeal?| + |c06gcf| |recip| |denomLODE| |hermiteH| |cross| |width| |OMgetEndApp| + |OMputInteger| |zeroSetSplit| |meatAxe| |setnext!| |iifact| + |characteristic| |simpleBounds?| |imagE| |particularSolution| + |normalForm| |toScale| |coordinates| |qqq| |inverseLaplace| |list| + |factorset| |setStatus!| |createLowComplexityTable| + |countRealRootsMultiple| |oblateSpheroidal| |palgRDE| |makeMulti| + |s01eaf| |entry?| |rightFactorCandidate| |car| |init| |degree| + |fortranReal| |children| |eulerE| |OMputObject| + |linearlyDependentOverZ?| |ip4Address| |digit| |leader| |cot2tan| + |cdr| |setClipValue| |f02akf| |solveid| |arg1| |taylorQuoByVar| + |permutation| |OMwrite| |transform| |lieAlgebra?| |exprToGenUPS| + |setDifference| |constantKernel| |internalInfRittWu?| |arg2| |f02aef| + |dihedralGroup| |makeSin| |addPointLast| |doubleFloatFormat| |lazy?| + |mapDown!| |cCsch| |asinhIfCan| |push!| |llprop| |parabolic| + |stopTableInvSet!| |clipBoolean| |modularFactor| |explicitEntries?| + |bounds| |hessian| |mainPrimitivePart| |conditions| |optional| + |unravel| |inf| |chebyshevU| |prinb| |setProperties| |laplacian| + |hclf| |setPredicates| |match| |getCurve| |showScalarValues| |result| + |mapMatrixIfCan| |totalDegree| |nextSublist| |eulerPhi| + |integralAtInfinity?| |lazyEvaluate| |approximants| + |selectFiniteRoutines| |substring?| |ratDenom| |properties| |s17dgf| + |maxColIndex| |ReduceOrder| |internalIntegrate0| |bivariate?| + |notelem| |getGoodPrime| |swapRows!| |messagePrint| |iisech| + |relerror| |numberOfComponents| |translate| |multisect| + |totalGroebner| |printingInfo?| |roughUnitIdeal?| |quoByVar| + |subHeight| |subset?| |suffix?| |nextLatticePermutation| |calcRanges| + |permutationRepresentation| |vector| |OMsupportsSymbol?| + |selectMultiDimensionalRoutines| |nextNormalPoly| |deriv| + |infieldIntegrate| |OMencodingXML| |pattern| |f04qaf| + |exprHasAlgebraicWeight| |expint| |getlo| |stoseInvertible?| + |nilFactor| |palgint0| |inrootof| |nonQsign| |prefix?| |rroot| + |scopes| |changeMeasure| |sinIfCan| |collectUpper| |rightRecip| + |derivationCoordinates| |sparsityIF| |totalDifferential| + |setProperties!| GF2FG SEGMENT |doubleDisc| |wholePart| + |primintfldpoly| |makeop| |bubbleSort!| |getMultiplicationTable| + |innerSolve| |OMgetAttr| |d01apf| |e01sef| |pdf2ef| |cLog| |s15aef| + |rootRadius| |showFortranOutputStack| |localUnquote| |minimumExponent| + |message| |scalarTypeOf| |slash| |loopPoints| |isMult| |rur| |d03eef| + |repeating?| |extractProperty| |rowEchelonLocal| |chainSubResultants| + |polar| |atom?| |linGenPos| |differentiate| |elRow2!| |principalIdeal| + |setAdaptive| |basisOfLeftNucloid| |getGraph| |infinite?| + |modifyPointData| |writeLine!| |d02kef| |coefficient| |powerSum| + |characteristicPolynomial| |basisOfCommutingElements| + |stoseInvertible?sqfreg| |mesh?| |exponents| |s21bdf| |datalist| + |infix?| |e02dff| |primitive?| |matrixDimensions| + |constantToUnaryFunction| |interpret| |log2| |leaves| |rootPower| + |minIndex| |contours| |returnType!| |mask| |fixedDivisor| + |cyclotomicFactorization| |listRepresentation| |OMputEndBVar| + |generalizedContinuumHypothesisAssumed?| |mathieu23| |fmecg| |poisson| + |tube| |stosePrepareSubResAlgo| |iiasech| |HermiteIntegrate| + |mantissa| |secIfCan| |appendPoint| |cons| |f02axf| |cycleRagits| + |unary?| |failed?| |OMreceive| |gcdprim| |incrementKthElement| + |every?| |goodPoint| |retract| |hdmpToP| |sinhcosh| |kovacic| + |closedCurve| |error| |primitiveElement| |invmod| |lineColorDefault| + |intChoose| |shanksDiscLogAlgorithm| |specialTrigs| |times!| + |viewWriteAvailable| |iisinh| |setScreenResolution| |assert| + |associates?| |optional?| |green| |status| |addBadValue| |bright| + |integralRepresents| |setLegalFortranSourceExtensions| |pade| + |completeHensel| |mainContent| |domainOf| |precision| |returnTypeOf| + |cap| |mr| |removeCoshSq| |companionBlocks| |monomRDEsys| + |simplifyLog| |sayLength| |imagK| |iicsch| |setRow!| |floor| |leftLcm| + |stFunc1| |binding| |algebraic?| |linearPart| |reverse!| |order| + |iisec| |nonLinearPart| |stFuncN| |OMconnectTCP| |pdf2df| + |solveLinearPolynomialEquationByFractions| |source| |erf| + |OMgetInteger| |splitLinear| |factorOfDegree| + |stiffnessAndStabilityOfODEIF| NOT |qinterval| |primeFactor| |s18adf| + |s17adf| |solveInField| |countable?| |reduction| |iitanh| |addmod| OR + |sncndn| |categories| ~= |d02gbf| |sinhIfCan| |badNum| |gcdcofact| + |d01aqf| |symFunc| |light| |retractIfCan| |argumentList!| AND |coerce| + |writeByte!| |cAcot| |SturmHabichtSequence| |e01bgf| |stirling1| + |mainCharacterization| |primlimitedint| |dilog| |reindex| |omError| + |arrayStack| |dec| |numer| |construct| |rational?| |point?| |ODESolve| + |dfRange| |shrinkable| |transpose| |sin| |bfEntry| |elseBranch| + |denom| |stronglyReduce| |red| |mindeg| |nodes| |nthExponent| + |innerEigenvectors| |target| |endOfFile?| |cos| |e01sbf| |s13adf| + |mainMonomial| |basisOfLeftNucleus| |getZechTable| |rightRank| + |laguerreL| |determinant| |tan| |limitPlus| |rightUnits| |s17ahf| + |c06ekf| |pi| |leftAlternative?| |mkAnswer| |listBranches| + |sortConstraints| |mergeFactors| |fixedPoints| |cot| + |reducedContinuedFraction| |csc2sin| |continue| |infinity| + |idealSimplify| |unitNormalize| |members| |dequeue!| + |combineFeatureCompatibility| |Gamma| |leftQuotient| |sec| + |extendedIntegrate| |d02bhf| |rk4f| |cAsec| |s19abf| |normFactors| + |integral?| |flexibleArray| |isList| |csc| |f02awf| |OMputAtp| + |wrregime| |increment| |pushdown| |youngGroup| |inc| + |inputOutputBinaryFile| |OMgetError| |asin| |invertible?| + |triangularSystems| |any| |kernel| |degreeSubResultantEuclidean| + |normalizedAssociate| |setOfMinN| |hasSolution?| |ravel| + |exportedOperators| |primaryDecomp| |acos| |rewriteSetWithReduction| + |solve| |map| * |draw| |deref| |lSpaceBasis| + |tryFunctionalDecomposition?| |homogeneous?| |reshape| |rspace| + |isTimes| |atan| |factorSFBRlcUnit| |primPartElseUnitCanonical| + |leftNorm| |generateIrredPoly| |multiple?| |exponent| |f02bbf| + |s17akf| |acot| |processTemplate| |generalizedInverse| |dark| |is?| + |splitDenominator| |factorsOfCyclicGroupSize| |minPol| |asec| + |cycleSplit!| |sts2stst| |char| |rightRegularRepresentation| |genus| + |relationsIdeal| |viewZoomDefault| |gbasis| |OMputApp| |acsc| + |morphism| |aCubic| |testDim| |makeObject| |setelt| + |leftRegularRepresentation| |asinIfCan| |coerceS| |complement| + |eisensteinIrreducible?| |sinh| |trivialIdeal?| |scripted?| |convert| + |prefixRagits| |rangeIsFinite| |weighted| |invertibleElseSplit?| + |update| |compBound| |palglimint0| |mindegTerm| |copy| |coef| + |OMgetBVar| |terms| |primitivePart| |writeUInt8!| |zCoord| |and?| + |sechIfCan| |antisymmetricTensors| |commutativeEquality| |se2rfi| + |front| |rightExtendedGcd| |nil?| |useSingleFactorBound| + |squareMatrix| |float| |rationalFunction| |regime| |mdeg| |setref| + |simplifyPower| |realEigenvectors| |putColorInfo| |pureLex| |mapGen| + |autoCoerce| |lyndon| |validExponential| |viewDefaults| |failed| + |usingTable?| |localIntegralBasis| |stoseInvertible?reg| + |setCondition!| |decompose| |infix| |newReduc| |position!| |match?| + |position| |writable?| |genericLeftNorm| |figureUnits| |rk4a| + |tan2cot| |randnum| |cTan| |OMputEndApp| |extractBottom!| + |hasPredicate?| |partialDenominators| |categoryFrame| |curryRight| + |whatInfinity| |iExquo| |zag| |iicot| |reify| |lambert| + |subresultantVector| |hex| |member?| |iiexp| + |constantCoefficientRicDE| |leftRankPolynomial| + |rightCharacteristicPolynomial| |distance| |f02aaf| |symmetricSquare| + |d01asf| |GospersMethod| |expt| |ListOfTerms| |leadingSupport| + |expandLog| |d01fcf| |primlimintfrac| |getOperands| |cCsc| |zero?| + |comp| |lhs| GE |length| |karatsubaDivide| |OMgetFloat| + |endSubProgram| |knownInfBasis| |writeInt8!| |supDimElseRittWu?| + |algebraicDecompose| |symbolTable| |iflist2Result| GT + |leftCharacteristicPolynomial| |rhs| |scripts| |real?| |f02aff| + |clipSurface| |next| |factorSquareFreePolynomial| |printTypes| + |sumSquares| |primPartElseUnitCanonical!| LE |anfactor| |separant| + |delete!| |s21baf| |OMopenFile| |roughEqualIdeals?| |generalLambert| + |exprHasLogarithmicWeights| |f02bjf| LT |nthRoot| |errorKind| + |infRittWu?| |stFunc2| |lighting| |distribute| |ef2edf| + |pushFortranOutputStack| |topFortranOutputStack| |generic| + |coth2trigh| |henselFact| |sumOfKthPowerDivisors| |weierstrass| + |e04ycf| |generic?| |edf2df| |divisor| + |removeSuperfluousQuasiComponents| |monicDivide| |getPickedPoints| + |log| |iicsc| |thetaCoord| |csch2sinh| |balancedBinaryTree| + |var2StepsDefault| |divideIfCan!| |ddFact| |pole?| + |reducedDiscriminant| |exponentialOrder| |unknown| |c06fuf| |lllip| + |mapExpon| |showTheSymbolTable| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-406 (-561))) -4050 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-38 |#1|) . T) ((-38 $) -4050 (|has| |#1| (-553)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-35) |has| |#1| (-1190)) ((-95) |has| |#1| (-1190)) ((-102) . T) ((-111 #0# #0#) -4050 (|has| |#1| (-348)) (|has| |#1| (-362))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-130) . T) ((-144) -4050 (|has| |#1| (-348)) (|has| |#1| (-144))) ((-146) |has| |#1| (-146)) ((-611 #0#) -4050 (|has| |#1| (-1031 (-406 (-561)))) (|has| |#1| (-348)) (|has| |#1| (-362))) ((-611 (-561)) . T) ((-611 |#1|) . T) ((-611 $) -4050 (|has| |#1| (-553)) (|has| |#1| (-348)) (|has| |#1| (-362)) (|has| |#1| (-306))) ((-608 (-856)) . T) ((-171) . T) ((-609 (-168 (-224))) |has| |#1| (-1015)) ((-609 (-168 (-378))) |has| |#1| (-1015)) ((-609 (-534)) |has| |#1| (-609 (-534))) ((-609 (-885 (-378))) |has| |#1| (-609 (-885 (-378)))) ((-609 (-885 (-561))) |has| |#1| (-609 (-885 (-561)))) ((-609 #1=(-1162 |#1|)) . 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -4007 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4007 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-611 #0=(-406 (-561))) -12 (|has| |#2| (-1031 (-406 (-561)))) (|has| |#2| (-1090))) ((-611 (-561)) -4007 (|has| |#2| (-1042)) (-12 (|has| |#2| (-1031 (-561))) (|has| |#2| (-1090))) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-611 |#2|) -4007 (|has| |#2| (-1090)) (|has| |#2| (-171))) ((-608 (-856)) -4007 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-608 (-856))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-608 (-1253 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1042)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1042))) ((-285 #1=(-561) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1042)) ((-410 |#2|) |has| |#2| (-1090)) ((-487 |#2|) . T) ((-599 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-641 |#2|) -4007 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-641 $) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-634 (-561)) -12 (|has| |#2| (-634 (-561))) (|has| |#2| (-1042))) ((-634 |#2|) |has| |#2| (-1042)) ((-711 |#2|) -4007 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-720) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-785) |has| |#2| (-842)) ((-786) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-787) |has| |#2| (-787)) ((-788) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-789) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-842) |has| |#2| (-842)) ((-844) -4007 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-893 (-1166)) -12 (|has| |#2| (-893 (-1166))) (|has| |#2| (-1042))) ((-1031 #0#) -12 (|has| |#2| (-1031 (-406 (-561)))) (|has| |#2| (-1090))) ((-1031 (-561)) -12 (|has| |#2| (-1031 (-561))) (|has| |#2| (-1090))) ((-1031 |#2|) |has| |#2| (-1090)) ((-1048 |#2|) -4007 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1048 $) |has| |#2| (-171)) ((-1042) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1049) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1102) -4007 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-1090) -4007 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1205) . T) ((-1260 |#2|) |has| |#2| (-362))) -((-3130 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-3185 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-4120 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) -(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -3130 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3185 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -4120 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-765) (-1205) (-1205)) (T -238)) -((-4120 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-765)) (-4 *6 (-1205)) (-4 *7 (-1205)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-3185 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-765)) (-4 *6 (-1205)) (-4 *2 (-1205)) (-5 *1 (-238 *5 *6 *2)))) (-3130 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-765)) (-4 *7 (-1205)) (-4 *5 (-1205)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) -(-10 -7 (-15 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -4050 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4050 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-611 #0=(-406 (-561))) -12 (|has| |#2| (-1031 (-406 (-561)))) (|has| |#2| (-1090))) ((-611 (-561)) -4050 (|has| |#2| (-1042)) (-12 (|has| |#2| (-1031 (-561))) (|has| |#2| (-1090))) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-611 |#2|) -4050 (|has| |#2| (-1090)) (|has| |#2| (-171))) ((-608 (-856)) -4050 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-608 (-856))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-608 (-1254 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1042)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1042))) ((-285 #1=(-561) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1042)) ((-410 |#2|) |has| |#2| (-1090)) ((-487 |#2|) . T) ((-599 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1090))) ((-641 |#2|) -4050 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-641 $) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-634 (-561)) -12 (|has| |#2| (-634 (-561))) (|has| |#2| (-1042))) ((-634 |#2|) |has| |#2| (-1042)) ((-711 |#2|) -4050 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-720) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-785) |has| |#2| (-842)) ((-786) -4050 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-787) |has| |#2| (-787)) ((-788) -4050 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-789) -4050 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-842) |has| |#2| (-842)) ((-844) -4050 (|has| |#2| (-842)) (|has| |#2| (-787))) ((-893 (-1166)) -12 (|has| |#2| (-893 (-1166))) (|has| |#2| (-1042))) ((-1031 #0#) -12 (|has| |#2| (-1031 (-406 (-561)))) (|has| |#2| (-1090))) ((-1031 (-561)) -12 (|has| |#2| (-1031 (-561))) (|has| |#2| (-1090))) ((-1031 |#2|) |has| |#2| (-1090)) ((-1048 |#2|) -4050 (|has| |#2| (-1042)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1048 $) |has| |#2| (-171)) ((-1042) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1049) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-171))) ((-1102) -4050 (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-720)) (|has| |#2| (-171))) ((-1090) -4050 (|has| |#2| (-1090)) (|has| |#2| (-1042)) (|has| |#2| (-842)) (|has| |#2| (-787)) (|has| |#2| (-720)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1205) . T) ((-1261 |#2|) |has| |#2| (-362))) +((-3522 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-3176 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-4165 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) +(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -3522 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3176 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -4165 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-765) (-1205) (-1205)) (T -238)) +((-4165 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-765)) (-4 *6 (-1205)) (-4 *7 (-1205)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-3176 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-765)) (-4 *6 (-1205)) (-4 *2 (-1205)) (-5 *1 (-238 *5 *6 *2)))) (-3522 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-765)) (-4 *7 (-1205)) (-4 *5 (-1205)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-406 (-561))) |has| |#1| (-38 (-406 (-561)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -4050 (|has| |#1| (-902)) (|has| |#1| (-553)) (|has| |#1| (-450))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-561)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4050 (|has| |#1| (-902)) (|has| |#1| (-553)) (|has| |#1| (-450)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-611 #0#) -4050 (|has| |#1| (-1031 (-406 (-561)))) (|has| |#1| (-38 (-406 (-561))))) ((-611 (-561)) . T) ((-611 |#1|) . T) ((-611 |#2|) . T) ((-611 |#3|) . T) ((-611 $) -4050 (|has| |#1| (-902)) (|has| |#1| (-553)) (|has| |#1| (-450))) ((-608 (-856)) . 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T) ((-893 (-1166)) -12 (|has| |#1| (-15 * (|#1| |#2| |#1|))) (|has| |#1| (-893 (-1166)))) ((-966 |#1| |#2| (-1072)) . T) ((-1048 #0#) |has| |#1| (-38 (-406 (-561)))) ((-1048 |#1|) . T) ((-1048 $) -4050 (|has| |#1| (-553)) (|has| |#1| (-171))) ((-1042) . T) ((-1049) . T) ((-1102) . T) ((-1090) . 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(-171) (-367) (-609 (-561)) (-1141)) NIL @@ -5279,4 +5284,4 @@ NIL NIL NIL NIL -((-3 3189391 3189396 3189401 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3189376 3189381 3189386 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3189361 3189366 3189371 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3189346 3189351 3189356 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1281 3188522 3189221 3189298 "ZMOD" 3189303 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1280 3187632 3187796 3188005 "ZLINDEP" 3188354 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1279 3176936 3178700 3180672 "ZDSOLVE" 3185762 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1278 3176182 3176323 3176512 "YSTREAM" 3176782 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1277 3173993 3175483 3175687 "XRPOLY" 3176025 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1276 3170581 3171864 3172439 "XPR" 3173465 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1275 3168337 3169912 3170116 "XPOLY" 3170412 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1274 3166128 3167462 3167517 "XPOLYC" 3167805 NIL XPOLYC (NIL T 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"WFFINTBS" 3140319 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1261 3137312 3137739 3138201 "WEIER" 3138980 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1260 3136459 3136883 3136925 "VSPACE" 3137061 NIL VSPACE (NIL T) -9 NIL 3137135 NIL) (-1259 3136297 3136324 3136415 "VSPACE-" 3136420 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1258 3136105 3136148 3136216 "VOID" 3136251 T VOID (NIL) -8 NIL NIL NIL) (-1257 3134241 3134600 3135006 "VIEW" 3135721 T VIEW (NIL) -7 NIL NIL NIL) (-1256 3130666 3131304 3132041 "VIEWDEF" 3133526 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1255 3120002 3122214 3124387 "VIEW3D" 3128515 T VIEW3D (NIL) -8 NIL NIL NIL) (-1254 3112284 3113913 3115492 "VIEW2D" 3118445 T VIEW2D (NIL) -8 NIL NIL NIL) (-1253 3107688 3112054 3112146 "VECTOR" 3112227 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1252 3106265 3106524 3106842 "VECTOR2" 3107418 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1251 3099792 3104049 3104092 "VECTCAT" 3105085 NIL VECTCAT (NIL T) -9 NIL 3105671 NIL) (-1250 3098806 3099060 3099450 "VECTCAT-" 3099455 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1249 3098287 3098457 3098577 "VARIABLE" 3098721 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1248 3098220 3098225 3098255 "UTYPE" 3098260 T UTYPE (NIL) -9 NIL NIL NIL) (-1247 3097050 3097204 3097466 "UTSODETL" 3098046 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1246 3094490 3094950 3095474 "UTSODE" 3096591 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1245 3086366 3092116 3092605 "UTS" 3094059 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1244 3077609 3082933 3082976 "UTSCAT" 3084088 NIL UTSCAT (NIL T) -9 NIL 3084845 NIL) (-1243 3074964 3075679 3076668 "UTSCAT-" 3076673 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1242 3074591 3074634 3074767 "UTS2" 3074915 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1241 3068864 3071429 3071472 "URAGG" 3073542 NIL URAGG (NIL T) -9 NIL 3074265 NIL) (-1240 3065803 3066666 3067789 "URAGG-" 3067794 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1239 3061527 3064417 3064889 "UPXSSING" 3065467 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1238 3053629 3060774 3061047 "UPXS" 3061312 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1237 3046742 3053533 3053605 "UPXSCONS" 3053610 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1236 3036987 3043737 3043799 "UPXSCCA" 3044373 NIL UPXSCCA (NIL T T) -9 NIL 3044606 NIL) (-1235 3036625 3036710 3036884 "UPXSCCA-" 3036889 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1234 3026723 3033246 3033289 "UPXSCAT" 3033937 NIL UPXSCAT (NIL T) -9 NIL 3034545 NIL) (-1233 3026153 3026232 3026411 "UPXS2" 3026638 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1232 3024807 3025060 3025411 "UPSQFREE" 3025896 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1231 3018595 3021609 3021664 "UPSCAT" 3022825 NIL UPSCAT (NIL T T) -9 NIL 3023599 NIL) (-1230 3017799 3018006 3018333 "UPSCAT-" 3018338 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1229 3003649 3011647 3011690 "UPOLYC" 3013791 NIL UPOLYC (NIL T) -9 NIL 3015012 NIL) (-1228 2994978 2997403 3000550 "UPOLYC-" 3000555 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) 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"TRIGCAT-" 2878913 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1191 2875585 2877546 2877827 "TREE" 2878442 NIL TREE (NIL T) -8 NIL NIL NIL) (-1190 2874859 2875387 2875417 "TRANFUN" 2875452 T TRANFUN (NIL) -9 NIL 2875518 NIL) (-1189 2874138 2874329 2874609 "TRANFUN-" 2874614 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1188 2873942 2873974 2874035 "TOPSP" 2874099 T TOPSP (NIL) -7 NIL NIL NIL) (-1187 2873290 2873405 2873559 "TOOLSIGN" 2873823 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1186 2871951 2872467 2872706 "TEXTFILE" 2873073 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1185 2869890 2870404 2870833 "TEX" 2871544 T TEX (NIL) -8 NIL NIL NIL) (-1184 2869671 2869702 2869774 "TEX1" 2869853 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1183 2869319 2869382 2869472 "TEMUTL" 2869603 T TEMUTL (NIL) -7 NIL NIL NIL) (-1182 2867473 2867753 2868078 "TBCMPPK" 2869042 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1181 2859361 2865633 2865689 "TBAGG" 2866089 NIL TBAGG (NIL T T) -9 NIL 2866300 NIL) (-1180 2854431 2855919 2857673 "TBAGG-" 2857678 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1179 2853815 2853922 2854067 "TANEXP" 2854320 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1178 2847316 2853672 2853765 "TABLE" 2853770 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1177 2846728 2846827 2846965 "TABLEAU" 2847213 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1176 2841336 2842556 2843804 "TABLBUMP" 2845514 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1175 2840764 2840864 2840992 "SYSTEM" 2841230 T SYSTEM (NIL) -7 NIL NIL NIL) (-1174 2837227 2837922 2838705 "SYSSOLP" 2840015 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1173 2836284 2836751 2836864 "SYSNNI" 2837050 NIL SYSNNI (NIL NIL) -8 NIL NIL 2837129) (-1172 2835737 2836142 2836184 "SYSINT" 2836189 NIL SYSINT (NIL NIL) -8 NIL NIL 2836197) (-1171 2832071 2832998 2833714 "SYNTAX" 2835043 T SYNTAX (NIL) -8 NIL NIL NIL) (-1170 2829229 2829831 2830463 "SYMTAB" 2831461 T SYMTAB (NIL) -8 NIL NIL NIL) (-1169 2824478 2825380 2826363 "SYMS" 2828268 T SYMS (NIL) -8 NIL NIL NIL) (-1168 2821750 2823936 2824166 "SYMPOLY" 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"SUCHTAST" 2768225 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1155 2767224 2767427 2767567 "SUCH" 2767810 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1154 2761118 2762130 2763089 "SUBSPACE" 2766312 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1153 2760548 2760638 2760802 "SUBRESP" 2761006 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1152 2753917 2755213 2756524 "STTF" 2759284 NIL STTF (NIL T) -7 NIL NIL NIL) (-1151 2748090 2749210 2750357 "STTFNC" 2752817 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1150 2739405 2741272 2743066 "STTAYLOR" 2746331 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1149 2732649 2739269 2739352 "STRTBL" 2739357 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1148 2728040 2732604 2732635 "STRING" 2732640 T STRING (NIL) -8 NIL NIL NIL) (-1147 2722928 2727413 2727443 "STRICAT" 2727502 T STRICAT (NIL) -9 NIL 2727564 NIL) (-1146 2715738 2720547 2721158 "STREAM" 2722352 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1145 2715248 2715325 2715469 "STREAM3" 2715655 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1144 2714230 2714413 2714648 "STREAM2" 2715061 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1143 2713918 2713970 2714063 "STREAM1" 2714172 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1142 2712934 2713115 2713346 "STINPROD" 2713734 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1141 2712512 2712696 2712726 "STEP" 2712806 T STEP (NIL) -9 NIL 2712884 NIL) (-1140 2706055 2712411 2712488 "STBL" 2712493 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1139 2701229 2705276 2705319 "STAGG" 2705472 NIL STAGG (NIL T) -9 NIL 2705561 NIL) (-1138 2698931 2699533 2700405 "STAGG-" 2700410 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1137 2697126 2698701 2698793 "STACK" 2698874 NIL STACK (NIL T) -8 NIL NIL NIL) (-1136 2689851 2695267 2695723 "SREGSET" 2696756 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1135 2682277 2683645 2685158 "SRDCMPK" 2688457 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1134 2675244 2679717 2679747 "SRAGG" 2681050 T SRAGG (NIL) -9 NIL 2681658 NIL) (-1133 2674261 2674516 2674895 "SRAGG-" 2674900 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1132 2668756 2673208 2673629 "SQMATRIX" 2673887 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1131 2662505 2665474 2666201 "SPLTREE" 2668101 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1130 2658495 2659161 2659807 "SPLNODE" 2661931 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1129 2657542 2657775 2657805 "SPFCAT" 2658249 T SPFCAT (NIL) -9 NIL NIL NIL) (-1128 2656279 2656489 2656753 "SPECOUT" 2657300 T SPECOUT (NIL) -7 NIL NIL NIL) (-1127 2647931 2649675 2649705 "SPADXPT" 2654097 T SPADXPT (NIL) -9 NIL 2656131 NIL) (-1126 2647692 2647732 2647801 "SPADPRSR" 2647884 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1125 2645875 2647647 2647678 "SPADAST" 2647683 T SPADAST (NIL) -8 NIL NIL NIL) (-1124 2637846 2639593 2639636 "SPACEC" 2644009 NIL SPACEC (NIL T) -9 NIL 2645825 NIL) (-1123 2636017 2637778 2637827 "SPACE3" 2637832 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1122 2634769 2634940 2635231 "SORTPAK" 2635822 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1121 2632819 2633122 2633541 "SOLVETRA" 2634433 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1120 2631830 2632052 2632326 "SOLVESER" 2632592 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1119 2627050 2627931 2628933 "SOLVERAD" 2630882 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1118 2622865 2623474 2624203 "SOLVEFOR" 2626417 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1117 2617162 2622214 2622311 "SNTSCAT" 2622316 NIL SNTSCAT (NIL T T T T) -9 NIL 2622386 NIL) (-1116 2611305 2615485 2615876 "SMTS" 2616852 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1115 2605756 2611193 2611270 "SMP" 2611275 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1114 2603915 2604216 2604614 "SMITH" 2605453 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1113 2596810 2600966 2601069 "SMATCAT" 2602420 NIL SMATCAT (NIL NIL T T T) -9 NIL 2602970 NIL) (-1112 2593750 2594573 2595751 "SMATCAT-" 2595756 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1111 2591463 2592986 2593029 "SKAGG" 2593290 NIL SKAGG (NIL T) -9 NIL 2593425 NIL) (-1110 2587805 2590879 2591074 "SINT" 2591261 T SINT (NIL) -8 NIL NIL 2591434) (-1109 2587577 2587615 2587681 "SIMPAN" 2587761 T SIMPAN (NIL) -7 NIL NIL NIL) (-1108 2586884 2587112 2587252 "SIG" 2587459 T SIG (NIL) -8 NIL NIL NIL) (-1107 2585722 2585943 2586218 "SIGNRF" 2586643 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1106 2584527 2584678 2584969 "SIGNEF" 2585551 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1105 2583860 2584110 2584234 "SIGAST" 2584425 T SIGAST (NIL) -8 NIL NIL NIL) (-1104 2581550 2582004 2582510 "SHP" 2583401 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1103 2575456 2581451 2581527 "SHDP" 2581532 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1102 2575055 2575221 2575251 "SGROUP" 2575344 T SGROUP (NIL) -9 NIL 2575406 NIL) (-1101 2574913 2574939 2575012 "SGROUP-" 2575017 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1100 2571749 2572446 2573169 "SGCF" 2574212 T SGCF (NIL) -7 NIL NIL NIL) (-1099 2566144 2571196 2571293 "SFRTCAT" 2571298 NIL SFRTCAT (NIL T T T T) -9 NIL 2571337 NIL) (-1098 2559568 2560583 2561719 "SFRGCD" 2565127 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1097 2552696 2553767 2554953 "SFQCMPK" 2558501 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1096 2552318 2552407 2552517 "SFORT" 2552637 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1095 2551463 2552158 2552279 "SEXOF" 2552284 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1094 2550597 2551344 2551412 "SEX" 2551417 T SEX (NIL) -8 NIL NIL NIL) (-1093 2546136 2546825 2546920 "SEXCAT" 2549857 NIL SEXCAT (NIL T T T T T) -9 NIL 2550435 NIL) (-1092 2543316 2546070 2546118 "SET" 2546123 NIL SET (NIL T) -8 NIL NIL NIL) (-1091 2541567 2542029 2542334 "SETMN" 2543057 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1090 2541173 2541299 2541329 "SETCAT" 2541446 T SETCAT (NIL) -9 NIL 2541531 NIL) (-1089 2540953 2541005 2541104 "SETCAT-" 2541109 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1088 2537340 2539414 2539457 "SETAGG" 2540327 NIL SETAGG (NIL T) -9 NIL 2540667 NIL) (-1087 2536798 2536914 2537151 "SETAGG-" 2537156 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1086 2536268 2536494 2536595 "SEQAST" 2536719 T SEQAST (NIL) -8 NIL NIL NIL) (-1085 2535467 2535761 2535822 "SEGXCAT" 2536108 NIL SEGXCAT (NIL T T) -9 NIL 2536228 NIL) (-1084 2534523 2535133 2535315 "SEG" 2535320 NIL SEG (NIL T) -8 NIL NIL NIL) (-1083 2533502 2533716 2533759 "SEGCAT" 2534281 NIL SEGCAT (NIL T) -9 NIL 2534502 NIL) (-1082 2532551 2532881 2533081 "SEGBIND" 2533337 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1081 2532172 2532231 2532344 "SEGBIND2" 2532486 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1080 2531773 2531973 2532050 "SEGAST" 2532117 T SEGAST (NIL) -8 NIL NIL NIL) (-1079 2530992 2531118 2531322 "SEG2" 2531617 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1078 2530429 2530927 2530974 "SDVAR" 2530979 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1077 2522719 2530199 2530329 "SDPOL" 2530334 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1076 2521312 2521578 2521897 "SCPKG" 2522434 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1075 2520448 2520628 2520828 "SCOPE" 2521134 T SCOPE (NIL) -8 NIL NIL NIL) (-1074 2519669 2519802 2519981 "SCACHE" 2520303 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1073 2519341 2519501 2519531 "SASTCAT" 2519536 T SASTCAT (NIL) -9 NIL 2519549 NIL) (-1072 2518855 2519176 2519252 "SAOS" 2519287 T SAOS (NIL) -8 NIL NIL NIL) (-1071 2518420 2518455 2518628 "SAERFFC" 2518814 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1070 2512394 2518317 2518397 "SAE" 2518402 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1069 2511987 2512022 2512181 "SAEFACT" 2512353 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1068 2510308 2510622 2511023 "RURPK" 2511653 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1067 2508944 2509223 2509535 "RULESET" 2510142 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1066 2506131 2506634 2507099 "RULE" 2508625 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1065 2505770 2505925 2506008 "RULECOLD" 2506083 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1064 2505268 2505487 2505581 "RSTRCAST" 2505698 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1063 2500117 2500911 2501831 "RSETGCD" 2504467 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1062 2489374 2494426 2494523 "RSETCAT" 2498642 NIL RSETCAT (NIL T T T T) -9 NIL 2499739 NIL) (-1061 2487301 2487840 2488664 "RSETCAT-" 2488669 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1060 2479688 2481063 2482583 "RSDCMPK" 2485900 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2477693 2478134 2478208 "RRCC" 2479294 NIL RRCC (NIL T T) -9 NIL 2479638 NIL) (-1058 2477044 2477218 2477497 "RRCC-" 2477502 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1057 2476514 2476740 2476841 "RPTAST" 2476965 T RPTAST (NIL) -8 NIL NIL NIL) (-1056 2450520 2460107 2460174 "RPOLCAT" 2470838 NIL RPOLCAT (NIL T T T) -9 NIL 2473997 NIL) (-1055 2442020 2444358 2447480 "RPOLCAT-" 2447485 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1054 2433067 2440231 2440713 "ROUTINE" 2441560 T ROUTINE (NIL) -8 NIL NIL NIL) (-1053 2429900 2432693 2432833 "ROMAN" 2432949 T ROMAN (NIL) -8 NIL NIL NIL) (-1052 2428175 2428760 2429020 "ROIRC" 2429705 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1051 2424568 2426811 2426841 "RNS" 2427145 T RNS (NIL) -9 NIL 2427418 NIL) (-1050 2423077 2423460 2423994 "RNS-" 2424069 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1049 2422526 2422908 2422938 "RNG" 2422943 T RNG (NIL) -9 NIL 2422964 NIL) (-1048 2421918 2422280 2422323 "RMODULE" 2422385 NIL RMODULE (NIL T) -9 NIL 2422427 NIL) (-1047 2420754 2420848 2421184 "RMCAT2" 2421819 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1046 2417631 2420100 2420397 "RMATRIX" 2420516 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1045 2410573 2412807 2412922 "RMATCAT" 2416281 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2417263 NIL) (-1044 2409948 2410095 2410402 "RMATCAT-" 2410407 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1043 2409515 2409590 2409718 "RINTERP" 2409867 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1042 2408648 2409168 2409198 "RING" 2409254 T RING (NIL) -9 NIL 2409340 NIL) (-1041 2408440 2408484 2408581 "RING-" 2408586 NIL RING- (NIL T) -8 NIL NIL NIL) (-1040 2407281 2407518 2407776 "RIDIST" 2408204 T RIDIST (NIL) -7 NIL NIL NIL) (-1039 2398597 2406749 2406955 "RGCHAIN" 2407129 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1038 2397973 2398353 2398394 "RGBCSPC" 2398452 NIL RGBCSPC (NIL T) -9 NIL 2398504 NIL) (-1037 2397157 2397512 2397553 "RGBCMDL" 2397785 NIL RGBCMDL (NIL T) -9 NIL 2397899 NIL) (-1036 2394151 2394765 2395435 "RF" 2396521 NIL RF (NIL T) -7 NIL NIL NIL) (-1035 2393797 2393860 2393963 "RFFACTOR" 2394082 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1034 2393522 2393557 2393654 "RFFACT" 2393756 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1033 2391639 2392003 2392385 "RFDIST" 2393162 T RFDIST (NIL) -7 NIL NIL NIL) (-1032 2391092 2391184 2391347 "RETSOL" 2391541 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1031 2390728 2390808 2390851 "RETRACT" 2390984 NIL RETRACT (NIL T) -9 NIL 2391071 NIL) (-1030 2390577 2390602 2390689 "RETRACT-" 2390694 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1029 2390206 2390399 2390469 "RETAST" 2390529 T RETAST (NIL) -8 NIL NIL NIL) (-1028 2383060 2389859 2389986 "RESULT" 2390101 T RESULT (NIL) -8 NIL NIL NIL) (-1027 2381686 2382329 2382528 "RESRING" 2382963 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1026 2381322 2381371 2381469 "RESLATC" 2381623 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1025 2381028 2381062 2381169 "REPSQ" 2381281 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1024 2378450 2379030 2379632 "REP" 2380448 T REP (NIL) -7 NIL NIL NIL) (-1023 2378148 2378182 2378293 "REPDB" 2378409 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1022 2372058 2373437 2374660 "REP2" 2376960 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1021 2368435 2369116 2369924 "REP1" 2371285 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1020 2361161 2366576 2367032 "REGSET" 2368065 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1019 2359974 2360309 2360559 "REF" 2360946 NIL REF (NIL T) -8 NIL NIL NIL) (-1018 2359351 2359454 2359621 "REDORDER" 2359858 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1017 2355356 2358564 2358791 "RECLOS" 2359179 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1016 2354408 2354589 2354804 "REALSOLV" 2355163 T REALSOLV (NIL) -7 NIL NIL NIL) (-1015 2354254 2354295 2354325 "REAL" 2354330 T REAL (NIL) -9 NIL 2354365 NIL) (-1014 2350737 2351539 2352423 "REAL0Q" 2353419 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1013 2346338 2347326 2348387 "REAL0" 2349718 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1012 2345836 2346055 2346149 "RDUCEAST" 2346266 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1011 2345241 2345313 2345520 "RDIV" 2345758 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1010 2344309 2344483 2344696 "RDIST" 2345063 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1009 2342906 2343193 2343565 "RDETRS" 2344017 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1008 2340718 2341172 2341710 "RDETR" 2342448 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1007 2339329 2339607 2340011 "RDEEFS" 2340434 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1006 2337824 2338130 2338562 "RDEEF" 2339017 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1005 2332085 2334960 2334990 "RCFIELD" 2336285 T RCFIELD (NIL) -9 NIL 2337015 NIL) (-1004 2330149 2330653 2331349 "RCFIELD-" 2331424 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1003 2326465 2328250 2328293 "RCAGG" 2329377 NIL RCAGG (NIL T) -9 NIL 2329842 NIL) (-1002 2326093 2326187 2326350 "RCAGG-" 2326355 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1001 2325428 2325540 2325705 "RATRET" 2325977 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1000 2324981 2325048 2325169 "RATFACT" 2325356 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-999 2324296 2324416 2324566 "RANDSRC" 2324851 T RANDSRC (NIL) -7 NIL NIL NIL) (-998 2324033 2324077 2324148 "RADUTIL" 2324245 T RADUTIL (NIL) -7 NIL NIL NIL) (-997 2317195 2322875 2323183 "RADIX" 2323757 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-996 2308852 2317039 2317167 "RADFF" 2317172 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-995 2308504 2308579 2308607 "RADCAT" 2308764 T RADCAT (NIL) -9 NIL NIL NIL) (-994 2308289 2308337 2308434 "RADCAT-" 2308439 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-993 2306440 2308064 2308153 "QUEUE" 2308233 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-992 2303016 2306377 2306422 "QUAT" 2306427 NIL QUAT (NIL T) -8 NIL NIL NIL) (-991 2302654 2302697 2302824 "QUATCT2" 2302967 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-990 2296401 2299703 2299743 "QUATCAT" 2300523 NIL QUATCAT (NIL T) -9 NIL 2301289 NIL) (-989 2292545 2293582 2294969 "QUATCAT-" 2295063 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-988 2290065 2291629 2291670 "QUAGG" 2292045 NIL QUAGG (NIL T) -9 NIL 2292220 NIL) (-987 2289697 2289890 2289958 "QQUTAST" 2290017 T QQUTAST (NIL) -8 NIL NIL NIL) (-986 2288622 2289095 2289267 "QFORM" 2289569 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-985 2279834 2285039 2285079 "QFCAT" 2285737 NIL QFCAT (NIL T) -9 NIL 2286738 NIL) (-984 2275406 2276607 2278198 "QFCAT-" 2278292 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-983 2275044 2275087 2275214 "QFCAT2" 2275357 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-982 2274504 2274614 2274744 "QEQUAT" 2274934 T QEQUAT (NIL) -8 NIL NIL NIL) (-981 2267652 2268723 2269907 "QCMPACK" 2273437 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-980 2265228 2265649 2266077 "QALGSET" 2267307 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-979 2264473 2264647 2264879 "QALGSET2" 2265048 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-978 2263164 2263387 2263704 "PWFFINTB" 2264246 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-977 2261346 2261514 2261868 "PUSHVAR" 2262978 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-976 2257264 2258318 2258359 "PTRANFN" 2260243 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-975 2255666 2255957 2256279 "PTPACK" 2256975 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-974 2255298 2255355 2255464 "PTFUNC2" 2255603 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-973 2249825 2254170 2254211 "PTCAT" 2254507 NIL PTCAT (NIL T) -9 NIL 2254660 NIL) (-972 2249483 2249518 2249642 "PSQFR" 2249784 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-971 2248078 2248376 2248710 "PSEUDLIN" 2249181 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-970 2234848 2237212 2239536 "PSETPK" 2245838 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-969 2227892 2230606 2230702 "PSETCAT" 2233723 NIL PSETCAT (NIL T T T T) -9 NIL 2234537 NIL) (-968 2225728 2226362 2227183 "PSETCAT-" 2227188 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-967 2225077 2225242 2225270 "PSCURVE" 2225538 T PSCURVE (NIL) -9 NIL 2225705 NIL) (-966 2221433 2222915 2222980 "PSCAT" 2223824 NIL PSCAT (NIL T T T) -9 NIL 2224064 NIL) (-965 2220496 2220712 2221112 "PSCAT-" 2221117 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2219228 2219861 2220066 "PRTITION" 2220311 T PRTITION (NIL) -8 NIL NIL NIL) (-963 2218730 2218949 2219041 "PRTDAST" 2219156 T PRTDAST (NIL) -8 NIL NIL NIL) (-962 2207828 2210034 2212222 "PRS" 2216592 NIL PRS (NIL T T) -7 NIL NIL NIL) (-961 2205686 2207178 2207218 "PRQAGG" 2207401 NIL PRQAGG (NIL T) -9 NIL 2207503 NIL) (-960 2205072 2205301 2205329 "PROPLOG" 2205514 T PROPLOG (NIL) -9 NIL 2205636 NIL) (-959 2202242 2202886 2203350 "PROPFRML" 2204640 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-958 2201702 2201812 2201942 "PROPERTY" 2202132 T PROPERTY (NIL) -8 NIL NIL NIL) (-957 2195787 2199868 2200688 "PRODUCT" 2200928 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-956 2193100 2195245 2195479 "PR" 2195598 NIL PR (NIL T T) -8 NIL NIL NIL) (-955 2192896 2192928 2192987 "PRINT" 2193061 T PRINT (NIL) -7 NIL NIL NIL) (-954 2192236 2192353 2192505 "PRIMES" 2192776 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-953 2190301 2190702 2191168 "PRIMELT" 2191815 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-952 2190030 2190079 2190107 "PRIMCAT" 2190231 T PRIMCAT (NIL) -9 NIL NIL NIL) (-951 2186191 2189968 2190013 "PRIMARR" 2190018 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-950 2185198 2185376 2185604 "PRIMARR2" 2186009 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-949 2184841 2184897 2185008 "PREASSOC" 2185136 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-948 2184316 2184449 2184477 "PPCURVE" 2184682 T PPCURVE (NIL) -9 NIL 2184818 NIL) (-947 2183938 2184111 2184194 "PORTNUM" 2184253 T PORTNUM (NIL) -8 NIL NIL NIL) (-946 2181297 2181696 2182288 "POLYROOT" 2183519 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-945 2175242 2180901 2181061 "POLY" 2181170 NIL POLY (NIL T) -8 NIL NIL NIL) (-944 2174625 2174683 2174917 "POLYLIFT" 2175178 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-943 2170900 2171349 2171978 "POLYCATQ" 2174170 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-942 2157717 2163075 2163140 "POLYCAT" 2166654 NIL POLYCAT (NIL T T T) -9 NIL 2168582 NIL) (-941 2151167 2153028 2155412 "POLYCAT-" 2155417 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-940 2150754 2150822 2150942 "POLY2UP" 2151093 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-939 2150386 2150443 2150552 "POLY2" 2150691 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-938 2149071 2149310 2149586 "POLUTIL" 2150160 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-937 2147426 2147703 2148034 "POLTOPOL" 2148793 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-936 2142944 2147362 2147408 "POINT" 2147413 NIL POINT (NIL T) -8 NIL NIL NIL) (-935 2141131 2141488 2141863 "PNTHEORY" 2142589 T PNTHEORY (NIL) -7 NIL NIL NIL) (-934 2139550 2139847 2140259 "PMTOOLS" 2140829 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-933 2139143 2139221 2139338 "PMSYM" 2139466 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-932 2138653 2138722 2138896 "PMQFCAT" 2139068 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-931 2138008 2138118 2138274 "PMPRED" 2138530 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-930 2137404 2137490 2137651 "PMPREDFS" 2137909 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-929 2136047 2136255 2136640 "PMPLCAT" 2137166 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-928 2135579 2135658 2135810 "PMLSAGG" 2135962 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-927 2135054 2135130 2135311 "PMKERNEL" 2135497 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-926 2134671 2134746 2134859 "PMINS" 2134973 NIL PMINS (NIL T) -7 NIL NIL NIL) (-925 2134099 2134168 2134384 "PMFS" 2134596 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-924 2133327 2133445 2133650 "PMDOWN" 2133976 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-923 2132490 2132649 2132831 "PMASS" 2133165 T PMASS (NIL) -7 NIL NIL NIL) (-922 2131764 2131875 2132038 "PMASSFS" 2132376 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-921 2131419 2131487 2131581 "PLOTTOOL" 2131690 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-920 2126041 2127230 2128378 "PLOT" 2130291 T PLOT (NIL) -8 NIL NIL NIL) (-919 2121855 2122889 2123810 "PLOT3D" 2125140 T PLOT3D (NIL) -8 NIL NIL NIL) (-918 2120767 2120944 2121179 "PLOT1" 2121659 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-917 2096161 2100833 2105684 "PLEQN" 2116033 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-916 2095479 2095601 2095781 "PINTERP" 2096026 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-915 2095172 2095219 2095322 "PINTERPA" 2095426 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-914 2094420 2094941 2095028 "PI" 2095068 T PI (NIL) -8 NIL NIL 2095135) (-913 2092817 2093758 2093786 "PID" 2093968 T PID (NIL) -9 NIL 2094102 NIL) (-912 2092542 2092579 2092667 "PICOERCE" 2092774 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-911 2091862 2092001 2092177 "PGROEB" 2092398 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-910 2087449 2088263 2089168 "PGE" 2090977 T PGE (NIL) -7 NIL NIL NIL) (-909 2085573 2085819 2086185 "PGCD" 2087166 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-908 2084911 2085014 2085175 "PFRPAC" 2085457 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-907 2081591 2083459 2083812 "PFR" 2084590 NIL PFR (NIL T) -8 NIL NIL NIL) (-906 2079980 2080224 2080549 "PFOTOOLS" 2081338 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-905 2078513 2078752 2079103 "PFOQ" 2079737 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-904 2076986 2077198 2077561 "PFO" 2078297 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-903 2073574 2076875 2076944 "PF" 2076949 NIL PF (NIL NIL) -8 NIL NIL NIL) (-902 2071008 2072245 2072273 "PFECAT" 2072858 T PFECAT (NIL) -9 NIL 2073242 NIL) (-901 2070453 2070607 2070821 "PFECAT-" 2070826 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-900 2069057 2069308 2069609 "PFBRU" 2070202 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-899 2066924 2067275 2067707 "PFBR" 2068708 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-898 2062840 2064300 2064976 "PERM" 2066281 NIL PERM (NIL T) -8 NIL NIL NIL) (-897 2058106 2059047 2059917 "PERMGRP" 2062003 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-896 2056238 2057169 2057210 "PERMCAT" 2057656 NIL PERMCAT (NIL T) -9 NIL 2057961 NIL) (-895 2055891 2055932 2056056 "PERMAN" 2056191 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-894 2053427 2055556 2055678 "PENDTREE" 2055802 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-893 2051520 2052254 2052295 "PDRING" 2052952 NIL PDRING (NIL T) -9 NIL 2053238 NIL) (-892 2050623 2050841 2051203 "PDRING-" 2051208 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-891 2047865 2048616 2049284 "PDEPROB" 2049975 T PDEPROB (NIL) -8 NIL NIL NIL) (-890 2045412 2045914 2046469 "PDEPACK" 2047330 T PDEPACK (NIL) -7 NIL NIL NIL) (-889 2044324 2044514 2044765 "PDECOMP" 2045211 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-888 2041929 2042746 2042774 "PDECAT" 2043561 T PDECAT (NIL) -9 NIL 2044274 NIL) (-887 2041680 2041713 2041803 "PCOMP" 2041890 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-886 2039885 2040481 2040778 "PBWLB" 2041409 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-885 2032390 2033958 2035296 "PATTERN" 2038568 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-884 2032022 2032079 2032188 "PATTERN2" 2032327 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-883 2029779 2030167 2030624 "PATTERN1" 2031611 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-882 2027174 2027728 2028209 "PATRES" 2029344 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-881 2026738 2026805 2026937 "PATRES2" 2027101 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-880 2024621 2025026 2025433 "PATMATCH" 2026405 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-879 2024157 2024340 2024381 "PATMAB" 2024488 NIL PATMAB (NIL T) -9 NIL 2024571 NIL) (-878 2022702 2023011 2023269 "PATLRES" 2023962 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-877 2022248 2022371 2022412 "PATAB" 2022417 NIL PATAB (NIL T) -9 NIL 2022589 NIL) (-876 2019729 2020261 2020834 "PARTPERM" 2021695 T PARTPERM (NIL) -7 NIL NIL NIL) (-875 2019350 2019413 2019515 "PARSURF" 2019660 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-874 2018982 2019039 2019148 "PARSU2" 2019287 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-873 2018746 2018786 2018853 "PARSER" 2018935 T PARSER (NIL) -7 NIL NIL NIL) (-872 2018367 2018430 2018532 "PARSCURV" 2018677 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-871 2017999 2018056 2018165 "PARSC2" 2018304 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-870 2017638 2017696 2017793 "PARPCURV" 2017935 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-869 2017270 2017327 2017436 "PARPC2" 2017575 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-868 2016790 2016876 2016995 "PAN2EXPR" 2017171 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-867 2015596 2015911 2016139 "PALETTE" 2016582 T PALETTE (NIL) -8 NIL NIL NIL) (-866 2014064 2014601 2014961 "PAIR" 2015282 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-865 2007970 2013323 2013517 "PADICRC" 2013919 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-864 2001234 2007316 2007500 "PADICRAT" 2007818 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-863 1999584 2001171 2001216 "PADIC" 2001221 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-862 1996794 1998324 1998364 "PADICCT" 1998945 NIL PADICCT (NIL NIL) -9 NIL 1999227 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(NIL) -9 NIL 1956209 NIL) (-837 1952241 1954235 1954644 "ORDCOMP" 1955273 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-836 1951507 1951634 1951820 "ORDCOMP2" 1952101 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-835 1948115 1948998 1949812 "OPTPROB" 1950713 T OPTPROB (NIL) -8 NIL NIL NIL) (-834 1944917 1945556 1946260 "OPTPACK" 1947431 T OPTPACK (NIL) -7 NIL NIL NIL) (-833 1942630 1943370 1943398 "OPTCAT" 1944217 T OPTCAT (NIL) -9 NIL 1944867 NIL) (-832 1942073 1942307 1942412 "OPSIG" 1942545 T OPSIG (NIL) -8 NIL NIL NIL) (-831 1941841 1941880 1941946 "OPQUERY" 1942027 T OPQUERY (NIL) -7 NIL NIL NIL) (-830 1939007 1940152 1940656 "OP" 1941370 NIL OP (NIL T) -8 NIL NIL NIL) (-829 1938542 1938713 1938754 "OPERCAT" 1938889 NIL OPERCAT (NIL T) -9 NIL 1938957 NIL) (-828 1938388 1938415 1938501 "OPERCAT-" 1938506 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-827 1935233 1937185 1937554 "ONECOMP" 1938052 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-826 1934538 1934653 1934827 "ONECOMP2" 1935105 NIL ONECOMP2 (NIL T 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"OFMONOID" 1915280 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-812 1911208 1911707 1911752 "ODVAR" 1911757 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-811 1908666 1910953 1911108 "ODR" 1911113 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-810 1901010 1908442 1908568 "ODPOL" 1908573 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-809 1894886 1900882 1900987 "ODP" 1900992 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-808 1893652 1893867 1894142 "ODETOOLS" 1894660 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-807 1890621 1891277 1891993 "ODESYS" 1892985 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-806 1885503 1886411 1887436 "ODERTRIC" 1889696 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-805 1884929 1885011 1885205 "ODERED" 1885415 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-804 1881817 1882365 1883042 "ODERAT" 1884352 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-803 1878777 1879241 1879838 "ODEPRRIC" 1881346 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-802 1876747 1877316 1877802 "ODEPROB" 1878311 T ODEPROB (NIL) -8 NIL NIL NIL) (-801 1873269 1873752 1874399 "ODEPRIM" 1876226 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-800 1872518 1872620 1872880 "ODEPAL" 1873161 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-799 1868680 1869471 1870335 "ODEPACK" 1871674 T ODEPACK (NIL) -7 NIL NIL NIL) (-798 1867713 1867820 1868049 "ODEINT" 1868569 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-797 1861814 1863239 1864686 "ODEIFTBL" 1866286 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-796 1857149 1857935 1858894 "ODEEF" 1860973 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-795 1856484 1856573 1856803 "ODECONST" 1857054 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-794 1854635 1855270 1855298 "ODECAT" 1855903 T ODECAT (NIL) -9 NIL 1856434 NIL) (-793 1851542 1854347 1854466 "OCT" 1854548 NIL OCT (NIL T) -8 NIL NIL NIL) (-792 1851180 1851223 1851350 "OCTCT2" 1851493 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-791 1845954 1848354 1848394 "OC" 1849491 NIL OC (NIL T) -9 NIL 1850349 NIL) (-790 1843181 1843929 1844919 "OC-" 1845013 NIL OC- (NIL T T) -8 NIL NIL NIL) (-789 1842559 1843001 1843029 "OCAMON" 1843034 T OCAMON (NIL) -9 NIL 1843055 NIL) (-788 1842116 1842431 1842459 "OASGP" 1842464 T OASGP (NIL) -9 NIL 1842484 NIL) (-787 1841403 1841866 1841894 "OAMONS" 1841934 T OAMONS (NIL) -9 NIL 1841977 NIL) (-786 1840843 1841250 1841278 "OAMON" 1841283 T OAMON (NIL) -9 NIL 1841303 NIL) (-785 1840147 1840639 1840667 "OAGROUP" 1840672 T OAGROUP (NIL) -9 NIL 1840692 NIL) (-784 1839837 1839887 1839975 "NUMTUBE" 1840091 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-783 1833410 1834928 1836464 "NUMQUAD" 1838321 T NUMQUAD (NIL) -7 NIL NIL NIL) (-782 1829166 1830154 1831179 "NUMODE" 1832405 T NUMODE (NIL) -7 NIL NIL NIL) (-781 1826547 1827401 1827429 "NUMINT" 1828352 T NUMINT (NIL) -9 NIL 1829116 NIL) (-780 1825495 1825692 1825910 "NUMFMT" 1826349 T NUMFMT (NIL) -7 NIL NIL NIL) (-779 1811854 1814799 1817331 "NUMERIC" 1823002 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-778 1806251 1811303 1811398 "NTSCAT" 1811403 NIL NTSCAT (NIL T T T T) -9 NIL 1811442 NIL) (-777 1805445 1805610 1805803 "NTPOLFN" 1806090 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-776 1793285 1802270 1803082 "NSUP" 1804666 NIL NSUP (NIL T) -8 NIL NIL NIL) (-775 1792917 1792974 1793083 "NSUP2" 1793222 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-774 1782914 1792691 1792824 "NSMP" 1792829 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-773 1781346 1781647 1782004 "NREP" 1782602 NIL NREP (NIL T) -7 NIL NIL NIL) (-772 1779937 1780189 1780547 "NPCOEF" 1781089 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-771 1779003 1779118 1779334 "NORMRETR" 1779818 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-770 1777044 1777334 1777743 "NORMPK" 1778711 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-769 1776729 1776757 1776881 "NORMMA" 1777010 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-768 1776556 1776686 1776715 "NONE" 1776720 T NONE (NIL) -8 NIL NIL NIL) (-767 1776345 1776374 1776443 "NONE1" 1776520 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-766 1775828 1775890 1776076 "NODE1" 1776277 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-765 1774099 1774922 1775177 "NNI" 1775524 T NNI (NIL) -8 NIL NIL 1775759) (-764 1772519 1772832 1773196 "NLINSOL" 1773767 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-763 1768787 1769755 1770654 "NIPROB" 1771640 T NIPROB (NIL) -8 NIL NIL NIL) (-762 1767544 1767778 1768080 "NFINTBAS" 1768549 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-761 1766984 1767194 1767235 "NETCLT" 1767407 NIL NETCLT (NIL T) -9 NIL 1767489 NIL) (-760 1765692 1765923 1766204 "NCODIV" 1766752 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-759 1765454 1765491 1765566 "NCNTFRAC" 1765649 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-758 1763634 1763998 1764418 "NCEP" 1765079 NIL NCEP (NIL T) -7 NIL NIL NIL) (-757 1762545 1763284 1763312 "NASRING" 1763422 T NASRING (NIL) -9 NIL 1763496 NIL) (-756 1762340 1762384 1762478 "NASRING-" 1762483 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-755 1761493 1761992 1762020 "NARNG" 1762137 T NARNG (NIL) -9 NIL 1762228 NIL) (-754 1761185 1761252 1761386 "NARNG-" 1761391 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-753 1760064 1760271 1760506 "NAGSP" 1760970 T NAGSP (NIL) -7 NIL NIL NIL) (-752 1751336 1753020 1754693 "NAGS" 1758411 T NAGS (NIL) -7 NIL NIL NIL) (-751 1749884 1750192 1750523 "NAGF07" 1751025 T NAGF07 (NIL) -7 NIL NIL NIL) (-750 1744422 1745713 1747020 "NAGF04" 1748597 T NAGF04 (NIL) -7 NIL NIL NIL) (-749 1737390 1739004 1740637 "NAGF02" 1742809 T NAGF02 (NIL) -7 NIL NIL NIL) (-748 1732614 1733714 1734831 "NAGF01" 1736293 T NAGF01 (NIL) -7 NIL NIL NIL) (-747 1726242 1727808 1729393 "NAGE04" 1731049 T NAGE04 (NIL) -7 NIL NIL NIL) (-746 1717411 1719532 1721662 "NAGE02" 1724132 T NAGE02 (NIL) -7 NIL NIL NIL) (-745 1713364 1714311 1715275 "NAGE01" 1716467 T NAGE01 (NIL) -7 NIL NIL NIL) (-744 1711159 1711693 1712251 "NAGD03" 1712826 T NAGD03 (NIL) -7 NIL NIL NIL) (-743 1702909 1704837 1706791 "NAGD02" 1709225 T NAGD02 (NIL) -7 NIL NIL NIL) (-742 1696720 1698145 1699585 "NAGD01" 1701489 T NAGD01 (NIL) -7 NIL NIL NIL) (-741 1692929 1693751 1694588 "NAGC06" 1695903 T NAGC06 (NIL) -7 NIL NIL NIL) (-740 1691394 1691726 1692082 "NAGC05" 1692593 T NAGC05 (NIL) -7 NIL NIL NIL) (-739 1690770 1690889 1691033 "NAGC02" 1691270 T NAGC02 (NIL) -7 NIL NIL NIL) (-738 1689830 1690387 1690427 "NAALG" 1690506 NIL NAALG (NIL T) -9 NIL 1690567 NIL) (-737 1689665 1689694 1689784 "NAALG-" 1689789 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-736 1683615 1684723 1685910 "MULTSQFR" 1688561 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-735 1682934 1683009 1683193 "MULTFACT" 1683527 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-734 1676027 1679897 1679950 "MTSCAT" 1681020 NIL MTSCAT (NIL T T) -9 NIL 1681534 NIL) (-733 1675739 1675793 1675885 "MTHING" 1675967 NIL MTHING (NIL T) -7 NIL NIL NIL) (-732 1675531 1675564 1675624 "MSYSCMD" 1675699 T MSYSCMD (NIL) -7 NIL NIL NIL) (-731 1671643 1674286 1674606 "MSET" 1675244 NIL MSET (NIL T) -8 NIL NIL NIL) (-730 1668738 1671204 1671245 "MSETAGG" 1671250 NIL MSETAGG (NIL T) -9 NIL 1671284 NIL) (-729 1664621 1666117 1666862 "MRING" 1668038 NIL MRING (NIL T T) -8 NIL NIL NIL) (-728 1664187 1664254 1664385 "MRF2" 1664548 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-727 1663805 1663840 1663984 "MRATFAC" 1664146 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-726 1661417 1661712 1662143 "MPRFF" 1663510 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-725 1655477 1661271 1661368 "MPOLY" 1661373 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-724 1654967 1655002 1655210 "MPCPF" 1655436 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-723 1654481 1654524 1654708 "MPC3" 1654918 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1653676 1653757 1653978 "MPC2" 1654396 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-721 1651977 1652314 1652704 "MONOTOOL" 1653336 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-720 1651228 1651519 1651547 "MONOID" 1651766 T MONOID (NIL) -9 NIL 1651913 NIL) (-719 1650774 1650893 1651074 "MONOID-" 1651079 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-718 1641633 1647541 1647600 "MONOGEN" 1648274 NIL MONOGEN (NIL T T) -9 NIL 1648730 NIL) (-717 1638851 1639586 1640586 "MONOGEN-" 1640705 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-716 1637710 1638130 1638158 "MONADWU" 1638550 T MONADWU (NIL) -9 NIL 1638788 NIL) (-715 1637082 1637241 1637489 "MONADWU-" 1637494 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-714 1636467 1636685 1636713 "MONAD" 1636920 T MONAD (NIL) -9 NIL 1637032 NIL) (-713 1636152 1636230 1636362 "MONAD-" 1636367 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-712 1634468 1635065 1635344 "MOEBIUS" 1635905 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-711 1633860 1634238 1634278 "MODULE" 1634283 NIL MODULE (NIL T) -9 NIL 1634309 NIL) (-710 1633428 1633524 1633714 "MODULE-" 1633719 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-709 1631143 1631792 1632119 "MODRING" 1633252 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1628129 1629248 1629769 "MODOP" 1630672 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-707 1626744 1627196 1627473 "MODMONOM" 1627992 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-706 1616551 1625035 1625449 "MODMON" 1626381 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-705 1613742 1615395 1615671 "MODFIELD" 1616426 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-704 1612746 1613023 1613213 "MMLFORM" 1613572 T MMLFORM (NIL) -8 NIL NIL NIL) (-703 1612272 1612315 1612494 "MMAP" 1612697 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-702 1610489 1611222 1611263 "MLO" 1611686 NIL MLO (NIL T) -9 NIL 1611928 NIL) (-701 1607856 1608371 1608973 "MLIFT" 1609970 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-700 1607247 1607331 1607485 "MKUCFUNC" 1607767 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-699 1606846 1606916 1607039 "MKRECORD" 1607170 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-698 1605894 1606055 1606283 "MKFUNC" 1606657 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-697 1605282 1605386 1605542 "MKFLCFN" 1605777 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-696 1604825 1605192 1605251 "MKCHSET" 1605256 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-695 1604102 1604204 1604389 "MKBCFUNC" 1604718 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-694 1600844 1603656 1603792 "MINT" 1603986 T MINT (NIL) -8 NIL NIL NIL) (-693 1599656 1599899 1600176 "MHROWRED" 1600599 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-692 1595082 1598191 1598596 "MFLOAT" 1599271 T MFLOAT (NIL) -8 NIL NIL NIL) (-691 1594439 1594515 1594686 "MFINFACT" 1594994 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-690 1590754 1591602 1592486 "MESH" 1593575 T MESH (NIL) -7 NIL NIL NIL) (-689 1589144 1589456 1589809 "MDDFACT" 1590441 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-688 1585986 1588303 1588344 "MDAGG" 1588599 NIL MDAGG (NIL T) -9 NIL 1588742 NIL) (-687 1575764 1585279 1585486 "MCMPLX" 1585799 T MCMPLX (NIL) -8 NIL NIL NIL) (-686 1574905 1575051 1575251 "MCDEN" 1575613 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-685 1572795 1573065 1573445 "MCALCFN" 1574635 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-684 1571720 1571960 1572193 "MAYBE" 1572601 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-683 1569332 1569855 1570417 "MATSTOR" 1571191 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-682 1565338 1568704 1568952 "MATRIX" 1569117 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-681 1561107 1561811 1562547 "MATLIN" 1564695 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-680 1551261 1554399 1554476 "MATCAT" 1559356 NIL MATCAT (NIL T T T) -9 NIL 1560773 NIL) (-679 1547625 1548638 1549994 "MATCAT-" 1549999 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-678 1546219 1546372 1546705 "MATCAT2" 1547460 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-677 1544331 1544655 1545039 "MAPPKG3" 1545894 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-676 1543312 1543485 1543707 "MAPPKG2" 1544155 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-675 1541811 1542095 1542422 "MAPPKG1" 1543018 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-674 1540917 1541217 1541394 "MAPPAST" 1541654 T MAPPAST (NIL) -8 NIL NIL NIL) (-673 1540528 1540586 1540709 "MAPHACK3" 1540853 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-672 1540120 1540181 1540295 "MAPHACK2" 1540460 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-671 1539558 1539661 1539803 "MAPHACK1" 1540011 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-670 1537664 1538258 1538562 "MAGMA" 1539286 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-669 1537170 1537388 1537479 "MACROAST" 1537593 T MACROAST (NIL) -8 NIL NIL NIL) (-668 1533637 1535409 1535870 "M3D" 1536742 NIL M3D (NIL T) -8 NIL NIL NIL) (-667 1527791 1532006 1532047 "LZSTAGG" 1532829 NIL LZSTAGG (NIL T) -9 NIL 1533124 NIL) (-666 1523765 1524922 1526379 "LZSTAGG-" 1526384 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-665 1520879 1521656 1522143 "LWORD" 1523310 NIL LWORD (NIL T) -8 NIL NIL NIL) (-664 1520482 1520683 1520758 "LSTAST" 1520824 T LSTAST (NIL) -8 NIL NIL NIL) (-663 1513683 1520253 1520387 "LSQM" 1520392 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-662 1512907 1513046 1513274 "LSPP" 1513538 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-661 1510719 1511020 1511476 "LSMP" 1512596 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-660 1507498 1508172 1508902 "LSMP1" 1510021 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-659 1501423 1506665 1506706 "LSAGG" 1506768 NIL LSAGG (NIL T) -9 NIL 1506846 NIL) (-658 1498118 1499042 1500255 "LSAGG-" 1500260 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-657 1495744 1497262 1497511 "LPOLY" 1497913 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-656 1495326 1495411 1495534 "LPEFRAC" 1495653 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-655 1493673 1494420 1494673 "LO" 1495158 NIL LO (NIL T T T) -8 NIL NIL NIL) (-654 1493325 1493437 1493465 "LOGIC" 1493576 T LOGIC (NIL) -9 NIL 1493657 NIL) (-653 1493187 1493210 1493281 "LOGIC-" 1493286 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-652 1492380 1492520 1492713 "LODOOPS" 1493043 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-651 1489838 1492296 1492362 "LODO" 1492367 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-650 1488376 1488611 1488964 "LODOF" 1489585 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-649 1484732 1487129 1487170 "LODOCAT" 1487608 NIL LODOCAT (NIL T) -9 NIL 1487819 NIL) (-648 1484465 1484523 1484650 "LODOCAT-" 1484655 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-647 1481820 1484306 1484424 "LODO2" 1484429 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-646 1479290 1481757 1481802 "LODO1" 1481807 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-645 1478150 1478315 1478627 "LODEEF" 1479113 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-644 1473436 1476280 1476321 "LNAGG" 1477268 NIL LNAGG (NIL T) -9 NIL 1477712 NIL) (-643 1472583 1472797 1473139 "LNAGG-" 1473144 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-642 1468746 1469508 1470147 "LMOPS" 1471998 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-641 1468141 1468503 1468544 "LMODULE" 1468605 NIL LMODULE (NIL T) -9 NIL 1468647 NIL) (-640 1465387 1467786 1467909 "LMDICT" 1468051 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-639 1465113 1465295 1465355 "LITERAL" 1465360 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-638 1458340 1464059 1464357 "LIST" 1464848 NIL LIST (NIL T) -8 NIL NIL NIL) (-637 1457865 1457939 1458078 "LIST3" 1458260 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-636 1456872 1457050 1457278 "LIST2" 1457683 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-635 1455006 1455318 1455717 "LIST2MAP" 1456519 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-634 1453736 1454372 1454413 "LINEXP" 1454668 NIL LINEXP (NIL T) -9 NIL 1454817 NIL) (-633 1452383 1452643 1452940 "LINDEP" 1453488 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-632 1449150 1449869 1450646 "LIMITRF" 1451638 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-631 1447426 1447721 1448137 "LIMITPS" 1448845 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-630 1441881 1446937 1447165 "LIE" 1447247 NIL LIE (NIL T T) -8 NIL NIL NIL) (-629 1440930 1441373 1441413 "LIECAT" 1441553 NIL LIECAT (NIL T) -9 NIL 1441704 NIL) (-628 1440771 1440798 1440886 "LIECAT-" 1440891 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-627 1433383 1440220 1440385 "LIB" 1440626 T LIB (NIL) -8 NIL NIL NIL) (-626 1429020 1429901 1430836 "LGROBP" 1432500 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-625 1426886 1427160 1427522 "LF" 1428741 NIL LF (NIL T T) -7 NIL NIL NIL) (-624 1425726 1426418 1426446 "LFCAT" 1426653 T LFCAT (NIL) -9 NIL 1426792 NIL) (-623 1422630 1423258 1423946 "LEXTRIPK" 1425090 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-622 1419401 1420200 1420703 "LEXP" 1422210 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-621 1418904 1419122 1419214 "LETAST" 1419329 T LETAST (NIL) -8 NIL NIL NIL) (-620 1417302 1417615 1418016 "LEADCDET" 1418586 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-619 1416492 1416566 1416795 "LAZM3PK" 1417223 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-618 1411447 1414569 1415107 "LAUPOL" 1416004 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-617 1411012 1411056 1411224 "LAPLACE" 1411397 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-616 1408986 1410113 1410364 "LA" 1410845 NIL LA (NIL T T T) -8 NIL NIL NIL) (-615 1408067 1408617 1408658 "LALG" 1408720 NIL LALG (NIL T) -9 NIL 1408779 NIL) (-614 1407781 1407840 1407976 "LALG-" 1407981 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-613 1407616 1407640 1407681 "KVTFROM" 1407743 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-612 1406419 1406833 1407062 "KTVLOGIC" 1407407 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-611 1406254 1406278 1406319 "KRCFROM" 1406381 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-610 1405158 1405345 1405644 "KOVACIC" 1406054 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-609 1404993 1405017 1405058 "KONVERT" 1405120 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-608 1404828 1404852 1404893 "KOERCE" 1404955 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-607 1402562 1403322 1403715 "KERNEL" 1404467 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-606 1402064 1402145 1402275 "KERNEL2" 1402476 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-605 1395915 1400603 1400657 "KDAGG" 1401034 NIL KDAGG (NIL T T) -9 NIL 1401240 NIL) (-604 1395444 1395568 1395773 "KDAGG-" 1395778 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1388619 1395105 1395260 "KAFILE" 1395322 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-602 1383074 1388130 1388358 "JORDAN" 1388440 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-601 1382480 1382723 1382844 "JOINAST" 1382973 T JOINAST (NIL) -8 NIL NIL NIL) (-600 1382326 1382385 1382440 "JAVACODE" 1382445 T JAVACODE (NIL) -8 NIL NIL NIL) (-599 1378625 1380531 1380585 "IXAGG" 1381514 NIL IXAGG (NIL T T) -9 NIL 1381973 NIL) (-598 1377544 1377850 1378269 "IXAGG-" 1378274 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-597 1373124 1377466 1377525 "IVECTOR" 1377530 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-596 1371890 1372127 1372393 "ITUPLE" 1372891 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-595 1370326 1370503 1370809 "ITRIGMNP" 1371712 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-594 1369071 1369275 1369558 "ITFUN3" 1370102 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-593 1368703 1368760 1368869 "ITFUN2" 1369008 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-592 1366540 1367565 1367864 "ITAYLOR" 1368437 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-591 1355523 1360677 1361840 "ISUPS" 1365410 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-590 1354627 1354767 1355003 "ISUMP" 1355370 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-589 1349891 1354428 1354507 "ISTRING" 1354580 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-588 1349394 1349612 1349704 "ISAST" 1349819 T ISAST (NIL) -8 NIL NIL NIL) (-587 1348604 1348685 1348901 "IRURPK" 1349308 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-586 1347540 1347741 1347981 "IRSN" 1348384 T IRSN (NIL) -7 NIL NIL NIL) (-585 1345569 1345924 1346360 "IRRF2F" 1347178 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-584 1345316 1345354 1345430 "IRREDFFX" 1345525 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-583 1343931 1344190 1344489 "IROOT" 1345049 NIL IROOT (NIL T) -7 NIL NIL NIL) (-582 1340563 1341615 1342307 "IR" 1343271 NIL IR (NIL T) -8 NIL NIL NIL) (-581 1338176 1338671 1339237 "IR2" 1340041 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-580 1337248 1337361 1337582 "IR2F" 1338059 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-579 1337039 1337073 1337133 "IPRNTPK" 1337208 T IPRNTPK (NIL) -7 NIL NIL NIL) (-578 1333658 1336928 1336997 "IPF" 1337002 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-577 1332021 1333583 1333640 "IPADIC" 1333645 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-576 1331361 1331581 1331711 "IP4ADDR" 1331911 T IP4ADDR (NIL) -8 NIL NIL NIL) (-575 1330861 1331065 1331175 "IOMODE" 1331271 T IOMODE (NIL) -8 NIL NIL NIL) (-574 1330209 1330458 1330585 "IOBFILE" 1330754 T IOBFILE (NIL) -8 NIL NIL NIL) (-573 1329963 1330113 1330141 "IOBCON" 1330146 T IOBCON (NIL) -9 NIL 1330167 NIL) (-572 1329460 1329518 1329708 "INVLAPLA" 1329899 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-571 1319109 1321462 1323848 "INTTR" 1327124 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-570 1315453 1316195 1317059 "INTTOOLS" 1318294 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-569 1315039 1315130 1315247 "INTSLPE" 1315356 T INTSLPE (NIL) -7 NIL NIL NIL) (-568 1313034 1314962 1315021 "INTRVL" 1315026 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-567 1310636 1311148 1311723 "INTRF" 1312519 NIL INTRF (NIL T) -7 NIL NIL NIL) (-566 1310047 1310144 1310286 "INTRET" 1310534 NIL INTRET (NIL T) -7 NIL NIL NIL) (-565 1308044 1308433 1308903 "INTRAT" 1309655 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-564 1305272 1305855 1306481 "INTPM" 1307529 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-563 1301975 1302574 1303319 "INTPAF" 1304658 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-562 1297154 1298116 1299167 "INTPACK" 1300944 T INTPACK (NIL) -7 NIL NIL NIL) (-561 1294066 1296883 1297010 "INT" 1297047 T INT (NIL) -8 NIL NIL NIL) (-560 1293318 1293470 1293678 "INTHERTR" 1293908 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-559 1292757 1292837 1293025 "INTHERAL" 1293232 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-558 1290603 1291046 1291503 "INTHEORY" 1292320 T INTHEORY (NIL) -7 NIL NIL NIL) (-557 1281911 1283532 1285311 "INTG0" 1288955 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-556 1262484 1267274 1272084 "INTFTBL" 1277121 T INTFTBL (NIL) -8 NIL NIL NIL) (-555 1261733 1261871 1262044 "INTFACT" 1262343 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-554 1259118 1259564 1260128 "INTEF" 1261287 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-553 1257585 1258290 1258318 "INTDOM" 1258619 T INTDOM (NIL) -9 NIL 1258826 NIL) (-552 1256954 1257128 1257370 "INTDOM-" 1257375 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-551 1253449 1255338 1255392 "INTCAT" 1256191 NIL INTCAT (NIL T) -9 NIL 1256511 NIL) (-550 1252922 1253024 1253152 "INTBIT" 1253341 T INTBIT (NIL) -7 NIL NIL NIL) (-549 1251593 1251747 1252061 "INTALG" 1252767 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-548 1251050 1251140 1251310 "INTAF" 1251497 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-547 1244504 1250860 1251000 "INTABL" 1251005 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-546 1243964 1244377 1244405 "INT8" 1244410 T INT8 (NIL) -8 NIL NIL 1244418) (-545 1243423 1243836 1243864 "INT32" 1243869 T INT32 (NIL) -8 NIL NIL 1243877) (-544 1242882 1243295 1243323 "INT16" 1243328 T INT16 (NIL) -8 NIL NIL 1243336) (-543 1237897 1240571 1240599 "INS" 1241533 T INS (NIL) -9 NIL 1242198 NIL) (-542 1235137 1235908 1236882 "INS-" 1236955 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233912 1234139 1234437 "INPSIGN" 1234890 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1233030 1233147 1233344 "INPRODPF" 1233792 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231924 1232041 1232278 "INPRODFF" 1232910 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230924 1231076 1231336 "INNMFACT" 1231760 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1230121 1230218 1230406 "INMODGCD" 1230823 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228630 1228874 1229198 "INFSP" 1229866 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227814 1227931 1228114 "INFPROD0" 1228510 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224696 1225879 1226394 "INFORM" 1227307 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224306 1224366 1224464 "INFORM1" 1224631 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223829 1223918 1224032 "INFINITY" 1224212 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223280 1223549 1223650 "INETCLTS" 1223748 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221897 1222146 1222467 "INEP" 1223028 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221173 1221794 1221859 "INDE" 1221864 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220737 1220805 1220922 "INCRMAPS" 1221100 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219750 1220006 1220212 "INBFILE" 1220551 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1215061 1215986 1216930 "INBFF" 1218838 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214715 1214796 1214824 "INBCON" 1214962 T INBCON (NIL) -9 NIL 1215045 NIL) (-524 1214558 1214592 1214667 "INBCON-" 1214672 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1214060 1214279 1214371 "INAST" 1214486 T INAST (NIL) -8 NIL NIL NIL) (-522 1213514 1213739 1213845 "IMPTAST" 1213974 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1210008 1213358 1213462 "IMATRIX" 1213467 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208720 1208843 1209158 "IMATQF" 1209864 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206940 1207167 1207504 "IMATLIN" 1208476 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201566 1206864 1206922 "ILIST" 1206927 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199519 1201426 1201539 "IIARRAY2" 1201544 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194952 1199430 1199494 "IFF" 1199499 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194326 1194569 1194685 "IFAST" 1194856 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189369 1193618 1193806 "IFARRAY" 1194183 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188576 1189273 1189346 "IFAMON" 1189351 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188160 1188225 1188279 "IEVALAB" 1188486 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187835 1187903 1188063 "IEVALAB-" 1188068 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187493 1187749 1187812 "IDPO" 1187817 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186770 1187382 1187457 "IDPOAMS" 1187462 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1186104 1186659 1186734 "IDPOAM" 1186739 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185189 1185439 1185492 "IDPC" 1185905 NIL IDPC (NIL T T) -9 NIL 1186054 NIL) (-506 1184685 1185081 1185154 "IDPAM" 1185159 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1184088 1184577 1184650 "IDPAG" 1184655 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183856 1184003 1184053 "IDENT" 1184058 T IDENT (NIL) -8 NIL NIL NIL) (-503 1180111 1180959 1181854 "IDECOMP" 1183013 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172985 1174034 1175081 "IDEAL" 1179147 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172149 1172261 1172460 "ICDEN" 1172869 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171248 1171629 1171776 "ICARD" 1172022 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169308 1169621 1170026 "IBPTOOLS" 1170925 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164942 1168928 1169041 "IBITS" 1169227 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161665 1162241 1162936 "IBATOOL" 1164359 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159445 1159906 1160439 "IBACHIN" 1161200 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157322 1159291 1159394 "IARRAY2" 1159399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153475 1157248 1157305 "IARRAY1" 1157310 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147469 1151887 1152368 "IAN" 1153014 T IAN (NIL) -8 NIL NIL NIL) (-492 1146980 1147037 1147210 "IALGFACT" 1147406 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146508 1146621 1146649 "HYPCAT" 1146856 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1146046 1146163 1146349 "HYPCAT-" 1146354 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145668 1145841 1145924 "HOSTNAME" 1145983 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145513 1145550 1145591 "HOMOTOP" 1145596 NIL HOMOTOP (NIL T) -9 NIL 1145629 NIL) (-487 1142192 1143523 1143564 "HOAGG" 1144545 NIL HOAGG (NIL T) -9 NIL 1145224 NIL) (-486 1140786 1141185 1141711 "HOAGG-" 1141716 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134828 1140383 1140531 "HEXADEC" 1140658 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133576 1133798 1134061 "HEUGCD" 1134605 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132679 1133413 1133543 "HELLFDIV" 1133548 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130907 1132456 1132544 "HEAP" 1132623 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130198 1130459 1130593 "HEADAST" 1130793 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1124118 1130113 1130175 "HDP" 1130180 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117869 1123753 1123905 "HDMP" 1124019 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117194 1117333 1117497 "HB" 1117725 T HB (NIL) -7 NIL NIL NIL) (-477 1110691 1117040 1117144 "HASHTBL" 1117149 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110194 1110412 1110504 "HASAST" 1110619 T HASAST (NIL) -8 NIL NIL NIL) (-475 1108006 1109816 1109998 "HACKPI" 1110032 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103701 1107859 1107972 "GTSET" 1107977 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097227 1103579 1103677 "GSTBL" 1103682 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089540 1096258 1096523 "GSERIES" 1097018 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088707 1089098 1089126 "GROUP" 1089329 T GROUP (NIL) -9 NIL 1089463 NIL) (-470 1088073 1088232 1088483 "GROUP-" 1088488 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086442 1086761 1087148 "GROEBSOL" 1087750 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085382 1085644 1085695 "GRMOD" 1086224 NIL GRMOD (NIL T T) -9 NIL 1086392 NIL) (-467 1085150 1085186 1085314 "GRMOD-" 1085319 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080476 1081504 1082504 "GRIMAGE" 1084170 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078943 1079203 1079527 "GRDEF" 1080172 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078387 1078503 1078644 "GRAY" 1078822 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077600 1077980 1078031 "GRALG" 1078184 NIL GRALG (NIL T T) -9 NIL 1078277 NIL) (-462 1077261 1077334 1077497 "GRALG-" 1077502 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1074065 1076846 1077024 "GPOLSET" 1077168 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073419 1073476 1073734 "GOSPER" 1074002 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069178 1069857 1070383 "GMODPOL" 1073118 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068183 1068367 1068605 "GHENSEL" 1068990 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062234 1063077 1064104 "GENUPS" 1067267 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061931 1061982 1062071 "GENUFACT" 1062177 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061343 1061420 1061585 "GENPGCD" 1061849 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060817 1060852 1061065 "GENMFACT" 1061302 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059385 1059640 1059947 "GENEEZ" 1060560 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053298 1058996 1059158 "GDMP" 1059308 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042675 1047069 1048175 "GCNAALG" 1052281 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1041102 1041930 1041958 "GCDDOM" 1042213 T GCDDOM (NIL) -9 NIL 1042370 NIL) (-449 1040572 1040699 1040914 "GCDDOM-" 1040919 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039244 1039429 1039733 "GB" 1040351 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027864 1030190 1032582 "GBINTERN" 1036935 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025701 1025993 1026414 "GBF" 1027539 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024482 1024647 1024914 "GBEUCLID" 1025517 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023831 1023956 1024105 "GAUSSFAC" 1024353 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022198 1022500 1022814 "GALUTIL" 1023550 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020506 1020780 1021104 "GALPOLYU" 1021925 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017871 1018161 1018568 "GALFACTU" 1020203 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009677 1011176 1012784 "GALFACT" 1016303 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1007065 1007723 1007751 "FVFUN" 1008907 T FVFUN (NIL) -9 NIL 1009627 NIL) (-438 1006331 1006513 1006541 "FVC" 1006832 T FVC (NIL) -9 NIL 1007015 NIL) (-437 1005973 1006128 1006209 "FUNCTION" 1006283 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003744 1004295 1004761 "FT" 1005527 T FT (NIL) -8 NIL NIL NIL) (-435 1002562 1003045 1003248 "FTEM" 1003561 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000818 1001107 1001511 "FSUPFACT" 1002253 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999215 999504 999836 "FST" 1000506 T FST (NIL) -8 NIL NIL NIL) (-432 998386 998492 998687 "FSRED" 999097 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997065 997320 997674 "FSPRMELT" 998101 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994150 994588 995087 "FSPECF" 996628 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976210 984653 984693 "FS" 988541 NIL FS (NIL T) -9 NIL 990830 NIL) (-428 964860 967850 971906 "FS-" 972203 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964374 964428 964605 "FSINT" 964801 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962701 963367 963670 "FSERIES" 964153 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961715 961831 962062 "FSCINT" 962581 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957949 960659 960700 "FSAGG" 961070 NIL FSAGG (NIL T) -9 NIL 961329 NIL) (-423 955711 956312 957108 "FSAGG-" 957203 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954753 954896 955123 "FSAGG2" 955564 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952408 952687 953241 "FS2UPS" 954471 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951990 952033 952188 "FS2" 952359 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950847 951018 951327 "FS2EXPXP" 951815 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950273 950388 950540 "FRUTIL" 950727 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941728 945768 947126 "FR" 948947 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936803 939446 939486 "FRNAALG" 940882 NIL FRNAALG (NIL T) -9 NIL 941489 NIL) (-415 932481 933552 934827 "FRNAALG-" 935577 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932119 932162 932289 "FRNAAF2" 932432 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930526 930973 931268 "FRMOD" 931931 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928305 928909 929226 "FRIDEAL" 930317 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927500 927587 927876 "FRIDEAL2" 928212 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926633 927047 927088 "FRETRCT" 927093 NIL FRETRCT (NIL T) -9 NIL 927269 NIL) (-409 925745 925976 926327 "FRETRCT-" 926332 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922957 924133 924192 "FRAMALG" 925074 NIL FRAMALG (NIL T T) -9 NIL 925366 NIL) (-407 921091 921546 922176 "FRAMALG-" 922399 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915049 920566 920842 "FRAC" 920847 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914685 914742 914849 "FRAC2" 914986 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914321 914378 914485 "FR2" 914622 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908994 911846 911874 "FPS" 912993 T FPS (NIL) -9 NIL 913550 NIL) (-402 908443 908552 908716 "FPS-" 908862 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905897 907532 907560 "FPC" 907785 T FPC (NIL) -9 NIL 907927 NIL) (-400 905690 905730 905827 "FPC-" 905832 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904568 905178 905219 "FPATMAB" 905224 NIL FPATMAB (NIL T) -9 NIL 905376 NIL) (-398 902268 902744 903170 "FPARFRAC" 904205 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897662 898160 898842 "FORTRAN" 901700 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895378 895878 896417 "FORT" 897143 T FORT (NIL) -7 NIL NIL NIL) (-395 893054 893616 893644 "FORTFN" 894704 T FORTFN (NIL) -9 NIL 895328 NIL) (-394 892818 892868 892896 "FORTCAT" 892955 T FORTCAT (NIL) -9 NIL 893017 NIL) (-393 890951 891434 891824 "FORMULA" 892448 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890739 890769 890838 "FORMULA1" 890915 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890262 890314 890487 "FORDER" 890681 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889358 889522 889715 "FOP" 890089 T FOP (NIL) -7 NIL NIL NIL) (-389 887966 888638 888812 "FNLA" 889240 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886721 887110 887138 "FNCAT" 887598 T FNCAT (NIL) -9 NIL 887858 NIL) (-387 886287 886680 886708 "FNAME" 886713 T FNAME (NIL) -8 NIL NIL NIL) (-386 884950 885879 885907 "FMTC" 885912 T FMTC (NIL) -9 NIL 885948 NIL) (-385 881312 882473 883102 "FMONOID" 884354 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880531 881054 881203 "FM" 881208 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877955 878601 878629 "FMFUN" 879773 T FMFUN (NIL) -9 NIL 880481 NIL) (-382 877224 877405 877433 "FMC" 877723 T FMC (NIL) -9 NIL 877905 NIL) (-381 874418 875252 875306 "FMCAT" 876501 NIL FMCAT (NIL T T) -9 NIL 876996 NIL) (-380 873311 874184 874284 "FM1" 874363 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871085 871501 871995 "FLOATRP" 872862 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864709 868814 869435 "FLOAT" 870484 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862147 862647 863225 "FLOATCP" 864176 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860956 861760 861801 "FLINEXP" 861806 NIL FLINEXP (NIL T) -9 NIL 861899 NIL) (-375 860110 860345 860673 "FLINEXP-" 860678 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859186 859330 859554 "FLASORT" 859962 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856403 857245 857297 "FLALG" 858524 NIL FLALG (NIL T T) -9 NIL 858991 NIL) (-372 850187 853889 853930 "FLAGG" 855192 NIL FLAGG (NIL T) -9 NIL 855844 NIL) (-371 848913 849252 849742 "FLAGG-" 849747 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847955 848098 848325 "FLAGG2" 848766 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844930 845904 845963 "FINRALG" 847091 NIL FINRALG (NIL T T) -9 NIL 847599 NIL) (-368 844090 844319 844658 "FINRALG-" 844663 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843496 843709 843737 "FINITE" 843933 T FINITE (NIL) -9 NIL 844040 NIL) (-366 835954 838115 838155 "FINAALG" 841822 NIL FINAALG (NIL T) -9 NIL 843275 NIL) (-365 831295 832336 833480 "FINAALG-" 834859 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830690 831050 831153 "FILE" 831225 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829374 829686 829740 "FILECAT" 830424 NIL FILECAT (NIL T T) -9 NIL 830640 NIL) (-362 827242 828736 828764 "FIELD" 828804 T FIELD (NIL) -9 NIL 828884 NIL) (-361 825862 826247 826758 "FIELD-" 826763 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823740 824497 824844 "FGROUP" 825548 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822830 822994 823214 "FGLMICPK" 823572 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818697 822755 822812 "FFX" 822817 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818298 818359 818494 "FFSLPE" 818630 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814291 815070 815866 "FFPOLY" 817534 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813795 813831 814040 "FFPOLY2" 814249 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809681 813714 813777 "FFP" 813782 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805114 809592 809656 "FF" 809661 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800275 804457 804647 "FFNBX" 804968 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795249 799410 799668 "FFNBP" 800129 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789917 794533 794744 "FFNB" 795082 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788749 788947 789262 "FFINTBAS" 789714 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784977 787156 787184 "FFIELDC" 787804 T FFIELDC (NIL) -9 NIL 788180 NIL) (-347 783640 784010 784507 "FFIELDC-" 784512 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783210 783255 783379 "FFHOM" 783582 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780908 781392 781909 "FFF" 782725 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776561 780650 780751 "FFCGX" 780851 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772228 776293 776400 "FFCGP" 776504 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767446 771955 772063 "FFCG" 772164 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749279 758317 758403 "FFCAT" 763568 NIL FFCAT (NIL T T T) -9 NIL 765019 NIL) (-340 744477 745524 746838 "FFCAT-" 748068 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743888 743931 744166 "FFCAT2" 744428 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733100 736860 738080 "FEXPR" 742740 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732100 732535 732576 "FEVALAB" 732660 NIL FEVALAB (NIL T) -9 NIL 732921 NIL) (-336 731259 731469 731807 "FEVALAB-" 731812 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729852 730642 730845 "FDIV" 731158 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726918 727633 727748 "FDIVCAT" 729316 NIL FDIVCAT (NIL T T T T) -9 NIL 729753 NIL) (-333 726680 726707 726877 "FDIVCAT-" 726882 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725900 725987 726264 "FDIV2" 726587 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724586 724845 725134 "FCPAK1" 725631 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723714 724086 724227 "FCOMP" 724477 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707451 710864 714402 "FC" 720196 T FC (NIL) -8 NIL NIL NIL) (-328 700030 704015 704055 "FAXF" 705857 NIL FAXF (NIL T) -9 NIL 706549 NIL) (-327 697309 697964 698789 "FAXF-" 699254 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692409 696685 696861 "FARRAY" 697166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687662 689694 689747 "FAMR" 690770 NIL FAMR (NIL T T) -9 NIL 691230 NIL) (-324 686552 686854 687289 "FAMR-" 687294 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685748 686474 686527 "FAMONOID" 686532 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683560 684244 684297 "FAMONC" 685238 NIL FAMONC (NIL T T) -9 NIL 685624 NIL) (-321 682252 683314 683451 "FAGROUP" 683456 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680047 680366 680769 "FACUTIL" 681933 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679146 679331 679553 "FACTFUNC" 679857 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671551 678397 678609 "EXPUPXS" 679002 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669034 669574 670160 "EXPRTUBE" 670985 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665228 665820 666557 "EXPRODE" 668373 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650602 663883 664311 "EXPR" 664832 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645009 645596 646409 "EXPR2UPS" 649900 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644645 644702 644809 "EXPR2" 644946 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636050 643777 644074 "EXPEXPAN" 644482 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635877 636007 636036 "EXIT" 636041 T EXIT (NIL) -8 NIL NIL NIL) (-310 635384 635601 635692 "EXITAST" 635806 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635011 635073 635186 "EVALCYC" 635316 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634552 634670 634711 "EVALAB" 634881 NIL EVALAB (NIL T) -9 NIL 634985 NIL) (-307 634033 634155 634376 "EVALAB-" 634381 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631501 632769 632797 "EUCDOM" 633352 T EUCDOM (NIL) -9 NIL 633702 NIL) (-305 629906 630348 630938 "EUCDOM-" 630943 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617446 620204 622954 "ESTOOLS" 627176 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617078 617135 617244 "ESTOOLS2" 617383 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616829 616871 616951 "ESTOOLS1" 617030 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610734 612462 612490 "ES" 615258 T ES (NIL) -9 NIL 616667 NIL) (-300 605682 606968 608785 "ES-" 608949 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602057 602817 603597 "ESCONT" 604922 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601802 601834 601916 "ESCONT1" 602019 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601477 601527 601627 "ES2" 601746 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601107 601165 601274 "ES1" 601413 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600323 600452 600628 "ERROR" 600951 T ERROR (NIL) -7 NIL NIL NIL) (-294 593826 600182 600273 "EQTBL" 600278 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586383 589140 590589 "EQ" 592410 NIL -3328 (NIL T) -8 NIL NIL NIL) (-292 586015 586072 586181 "EQ2" 586320 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581307 582353 583446 "EP" 584954 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579889 580190 580507 "ENV" 581010 T ENV (NIL) -8 NIL NIL NIL) (-289 579068 579588 579616 "ENTIRER" 579621 T ENTIRER (NIL) -9 NIL 579667 NIL) (-288 575570 577023 577393 "EMR" 578867 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574714 574899 574953 "ELTAGG" 575333 NIL ELTAGG (NIL T T) -9 NIL 575544 NIL) (-286 574433 574495 574636 "ELTAGG-" 574641 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574222 574251 574305 "ELTAB" 574389 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573348 573494 573693 "ELFUTS" 574073 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573090 573146 573174 "ELEMFUN" 573279 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572960 572981 573049 "ELEMFUN-" 573054 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567851 571060 571101 "ELAGG" 572041 NIL ELAGG (NIL T) -9 NIL 572504 NIL) (-280 566136 566570 567233 "ELAGG-" 567238 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564793 565073 565368 "ELABEXPR" 565861 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557659 559460 560287 "EFUPXS" 564069 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551109 552910 553720 "EFULS" 556935 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548531 548889 549368 "EFSTRUC" 550741 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537603 539168 540728 "EF" 547046 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536704 537088 537237 "EAB" 537474 T EAB (NIL) -8 NIL NIL NIL) (-273 535913 536663 536691 "E04UCFA" 536696 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535122 535872 535900 "E04NAFA" 535905 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534331 535081 535109 "E04MBFA" 535114 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533540 534290 534318 "E04JAFA" 534323 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532751 533499 533527 "E04GCFA" 533532 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531962 532710 532738 "E04FDFA" 532743 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531171 531921 531949 "E04DGFA" 531954 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525349 526696 528060 "E04AGNT" 529827 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524055 524535 524575 "DVARCAT" 525050 NIL DVARCAT (NIL T) -9 NIL 525249 NIL) (-264 523259 523471 523785 "DVARCAT-" 523790 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516159 523058 523187 "DSMP" 523192 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510969 512104 513172 "DROPT" 515111 T DROPT (NIL) -8 NIL NIL NIL) (-261 510634 510693 510791 "DROPT1" 510904 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505749 506875 508012 "DROPT0" 509517 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504094 504419 504805 "DRAWPT" 505383 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498681 499604 500683 "DRAW" 503068 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498314 498367 498485 "DRAWHACK" 498622 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497045 497314 497605 "DRAWCX" 498043 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496561 496629 496780 "DRAWCURV" 496971 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487032 488991 491106 "DRAWCFUN" 494466 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483845 485727 485768 "DQAGG" 486397 NIL DQAGG (NIL T) -9 NIL 486670 NIL) (-252 472124 478823 478906 "DPOLCAT" 480758 NIL DPOLCAT (NIL T T T T) -9 NIL 481303 NIL) (-251 466963 468309 470267 "DPOLCAT-" 470272 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460118 466824 466922 "DPMO" 466927 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453176 459898 460065 "DPMM" 460070 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452840 453095 453143 "DOMCTOR" 453148 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452135 452362 452499 "DOMAIN" 452723 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445886 451770 451922 "DMP" 452036 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445486 445542 445686 "DLP" 445824 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439356 444813 445003 "DLIST" 445328 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436200 438209 438250 "DLAGG" 438800 NIL DLAGG (NIL T) -9 NIL 439030 NIL) (-242 435013 435643 435671 "DIVRING" 435763 T DIVRING (NIL) -9 NIL 435846 NIL) (-241 434250 434440 434740 "DIVRING-" 434745 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432352 432709 433115 "DISPLAY" 433864 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426294 432266 432329 "DIRPROD" 432334 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425142 425345 425610 "DIRPROD2" 426087 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414405 420357 420410 "DIRPCAT" 420820 NIL DIRPCAT (NIL NIL T) -9 NIL 421660 NIL) (-236 411731 412373 413254 "DIRPCAT-" 413591 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411018 411178 411364 "DIOSP" 411565 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407720 409930 409971 "DIOPS" 410405 NIL DIOPS (NIL T) -9 NIL 410634 NIL) (-233 407269 407383 407574 "DIOPS-" 407579 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406161 406755 406783 "DIFRING" 406970 T DIFRING (NIL) -9 NIL 407080 NIL) (-231 405807 405884 406036 "DIFRING-" 406041 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403612 404850 404891 "DIFEXT" 405254 NIL DIFEXT (NIL T) -9 NIL 405548 NIL) (-229 401897 402325 402991 "DIFEXT-" 402996 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399219 401429 401470 "DIAGG" 401475 NIL DIAGG (NIL T) -9 NIL 401495 NIL) (-227 398603 398760 399012 "DIAGG-" 399017 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394068 397562 397839 "DHMATRIX" 398372 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389680 390589 391599 "DFSFUN" 393078 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384796 388611 388923 "DFLOAT" 389388 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383024 383305 383701 "DFINTTLS" 384504 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380089 381045 381445 "DERHAM" 382690 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377938 379864 379953 "DEQUEUE" 380033 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377153 377286 377482 "DEGRED" 377800 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373548 374293 375146 "DEFINTRF" 376381 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371075 371544 372143 "DEFINTEF" 373067 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370452 370695 370810 "DEFAST" 370980 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364494 370049 370197 "DECIMAL" 370324 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362006 362464 362970 "DDFACT" 364038 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361602 361645 361796 "DBLRESP" 361957 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359501 359835 360195 "DBASE" 361369 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358770 358981 359127 "DATAARY" 359400 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357903 358729 358757 "D03FAFA" 358762 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357037 357862 357890 "D03EEFA" 357895 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354987 355453 355942 "D03AGNT" 356568 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354303 354946 354974 "D02EJFA" 354979 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353619 354262 354290 "D02CJFA" 354295 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352935 353578 353606 "D02BHFA" 353611 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352251 352894 352922 "D02BBFA" 352927 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345449 347037 348643 "D02AGNT" 350665 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343218 343740 344286 "D01WGTS" 344923 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342313 343177 343205 "D01TRNS" 343210 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341408 342272 342300 "D01GBFA" 342305 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340503 341367 341395 "D01FCFA" 341400 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339598 340462 340490 "D01ASFA" 340495 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338693 339557 339585 "D01AQFA" 339590 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337788 338652 338680 "D01APFA" 338685 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336883 337747 337775 "D01ANFA" 337780 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335978 336842 336870 "D01AMFA" 336875 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335073 335937 335965 "D01ALFA" 335970 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334168 335032 335060 "D01AKFA" 335065 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333263 334127 334155 "D01AJFA" 334160 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326560 328111 329672 "D01AGNT" 331722 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325897 326025 326177 "CYCLOTOM" 326428 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322632 323345 324072 "CYCLES" 325190 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321944 322078 322249 "CVMP" 322493 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319715 319973 320349 "CTRIGMNP" 321672 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319438 319674 319702 "CTOR" 319707 T CTOR (NIL) -8 NIL NIL NIL) (-185 318974 319169 319270 "CTORKIND" 319357 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318445 318673 318701 "CTORCAT" 318821 T CTORCAT (NIL) -9 NIL 318904 NIL) (-183 318140 318220 318346 "CTORCAT-" 318351 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317656 317843 317941 "CTORCALL" 318062 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 317030 317129 317282 "CSTTOOLS" 317553 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312829 313486 314244 "CRFP" 316342 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312331 312550 312642 "CRCEAST" 312757 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311378 311563 311791 "CRAPACK" 312135 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310762 310863 311067 "CPMATCH" 311254 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310487 310515 310621 "CPIMA" 310728 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306851 307523 308241 "COORDSYS" 309822 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306235 306364 306514 "CONTOUR" 306721 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302161 304238 304730 "CONTFRAC" 305775 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 302041 302062 302090 "CONDUIT" 302127 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301214 301734 301762 "COMRING" 301767 T COMRING (NIL) -9 NIL 301819 NIL) (-170 300295 300572 300756 "COMPPROP" 301050 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299956 299991 300119 "COMPLPAT" 300254 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 290013 299765 299874 "COMPLEX" 299879 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289649 289706 289813 "COMPLEX2" 289950 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289367 289402 289500 "COMPFACT" 289608 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273540 283760 283800 "COMPCAT" 284804 NIL COMPCAT (NIL T) -9 NIL 286189 NIL) (-164 263056 265979 269606 "COMPCAT-" 269962 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262785 262813 262916 "COMMUPC" 263022 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262580 262613 262672 "COMMONOP" 262746 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262163 262331 262418 "COMM" 262513 T COMM (NIL) -8 NIL NIL NIL) (-160 261767 261967 262042 "COMMAAST" 262108 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 261016 261210 261238 "COMBOPC" 261576 T COMBOPC (NIL) -9 NIL 261751 NIL) (-158 259912 260122 260364 "COMBINAT" 260806 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 256110 256683 257323 "COMBF" 259334 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254896 255226 255461 "COLOR" 255895 T COLOR (NIL) -8 NIL NIL NIL) (-155 254399 254617 254709 "COLONAST" 254824 T COLONAST (NIL) -8 NIL NIL NIL) (-154 254039 254086 254211 "CMPLXRT" 254346 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253514 253739 253838 "CLLCTAST" 253960 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 249016 250044 251124 "CLIP" 252454 T CLIP (NIL) -7 NIL NIL NIL) (-151 247398 248122 248361 "CLIF" 248843 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243620 245544 245585 "CLAGG" 246514 NIL CLAGG (NIL T) -9 NIL 247050 NIL) (-149 242042 242499 243082 "CLAGG-" 243087 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241586 241671 241811 "CINTSLPE" 241951 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 239087 239558 240106 "CHVAR" 241114 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238330 238850 238878 "CHARZ" 238883 T CHARZ (NIL) -9 NIL 238898 NIL) (-145 238084 238124 238202 "CHARPOL" 238284 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237211 237764 237792 "CHARNZ" 237839 T CHARNZ (NIL) -9 NIL 237895 NIL) (-143 235200 235901 236236 "CHAR" 236896 T CHAR (NIL) -8 NIL NIL NIL) (-142 234926 234987 235015 "CFCAT" 235126 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234171 234282 234464 "CDEN" 234810 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230163 233324 233604 "CCLASS" 233911 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229470 229613 229776 "CATEGORY" 230020 T -10 (NIL) -8 NIL NIL NIL) (-138 229134 229389 229437 "CATCTOR" 229442 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228608 228834 228933 "CATAST" 229055 T CATAST (NIL) -8 NIL NIL NIL) (-136 228111 228329 228421 "CASEAST" 228536 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223163 224140 224893 "CARTEN" 227414 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222271 222419 222640 "CARTEN2" 223010 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220613 221421 221678 "CARD" 222034 T CARD (NIL) -8 NIL NIL NIL) (-132 220216 220417 220492 "CAPSLAST" 220558 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219588 219916 219944 "CACHSET" 220076 T CACHSET (NIL) -9 NIL 220153 NIL) (-130 219084 219380 219408 "CABMON" 219458 T CABMON (NIL) -9 NIL 219514 NIL) (-129 218107 218630 218766 "BYTE" 218929 T BYTE (NIL) -8 NIL NIL 219045) (-128 213516 217575 217738 "BYTEBUF" 217964 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211073 213208 213315 "BTREE" 213442 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208571 210721 210843 "BTOURN" 210983 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 205988 208041 208082 "BTCAT" 208150 NIL BTCAT (NIL T) -9 NIL 208227 NIL) (-124 205655 205735 205884 "BTCAT-" 205889 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 200947 204798 204826 "BTAGG" 205048 T BTAGG (NIL) -9 NIL 205209 NIL) (-122 200437 200562 200768 "BTAGG-" 200773 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197481 199715 199930 "BSTREE" 200254 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196619 196745 196929 "BRILL" 197337 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193318 195345 195386 "BRAGG" 196035 NIL BRAGG (NIL T) -9 NIL 196293 NIL) (-118 191847 192253 192808 "BRAGG-" 192813 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185111 191193 191377 "BPADICRT" 191695 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183461 185048 185093 "BPADIC" 185098 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183159 183189 183303 "BOUNDZRO" 183425 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178674 179765 180632 "BOP" 182312 T BOP (NIL) -8 NIL NIL NIL) (-113 176295 176739 177259 "BOP1" 178187 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 174997 175719 175912 "BOOLEAN" 176122 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174359 174737 174791 "BMODULE" 174796 NIL BMODULE (NIL T T) -9 NIL 174861 NIL) (-110 170189 174157 174230 "BITS" 174306 T BITS (NIL) -8 NIL NIL NIL) (-109 169601 169723 169865 "BINDING" 170067 T BINDING (NIL) -8 NIL NIL NIL) (-108 163646 169200 169347 "BINARY" 169474 T BINARY (NIL) -8 NIL NIL NIL) (-107 161473 162901 162942 "BGAGG" 163202 NIL BGAGG (NIL T) -9 NIL 163339 NIL) (-106 161304 161336 161427 "BGAGG-" 161432 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160402 160688 160893 "BFUNCT" 161119 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159092 159270 159558 "BEZOUT" 160226 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155609 157944 158274 "BBTREE" 158795 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155343 155396 155424 "BASTYPE" 155543 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155196 155224 155297 "BASTYPE-" 155302 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154630 154706 154858 "BALFACT" 155107 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153513 154045 154231 "AUTOMOR" 154475 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153239 153244 153270 "ATTREG" 153275 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151518 151936 152288 "ATTRBUT" 152905 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151153 151346 151412 "ATTRAST" 151470 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150689 150802 150828 "ATRIG" 151029 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150498 150539 150626 "ATRIG-" 150631 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150169 150329 150355 "ASTCAT" 150360 T ASTCAT (NIL) -9 NIL 150390 NIL) (-92 149896 149955 150074 "ASTCAT-" 150079 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148093 149672 149760 "ASTACK" 149839 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146598 146895 147260 "ASSOCEQ" 147775 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145630 146257 146381 "ASP9" 146505 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145394 145578 145617 "ASP8" 145622 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144263 144999 145141 "ASP80" 145283 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143162 143898 144030 "ASP7" 144162 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142116 142839 142957 "ASP78" 143075 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141085 141796 141913 "ASP77" 142030 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 139997 140723 140854 "ASP74" 140985 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138897 139632 139764 "ASP73" 139896 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138001 138723 138823 "ASP6" 138828 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 136949 137678 137796 "ASP55" 137914 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135899 136623 136742 "ASP50" 136861 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 134987 135600 135710 "ASP4" 135820 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134075 134688 134798 "ASP49" 134908 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132860 133614 133782 "ASP42" 133964 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131637 132393 132563 "ASP41" 132747 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130587 131314 131432 "ASP35" 131550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130352 130535 130574 "ASP34" 130579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130089 130156 130232 "ASP33" 130307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 128984 129724 129856 "ASP31" 129988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128749 128932 128971 "ASP30" 128976 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128484 128553 128629 "ASP29" 128704 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128249 128432 128471 "ASP28" 128476 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128014 128197 128236 "ASP27" 128241 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127098 127712 127823 "ASP24" 127934 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126175 126900 127012 "ASP20" 127017 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125263 125876 125986 "ASP1" 126096 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124207 124937 125056 "ASP19" 125175 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 123944 124011 124087 "ASP12" 124162 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122796 123543 123687 "ASP10" 123831 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120695 122640 122731 "ARRAY2" 122736 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116511 120343 120457 "ARRAY1" 120612 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115543 115716 115937 "ARRAY12" 116334 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109902 111773 111848 "ARR2CAT" 114478 NIL ARR2CAT (NIL T T T) -9 NIL 115236 NIL) (-56 107336 108080 109034 "ARR2CAT-" 109039 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106930 107163 107242 "ARITY" 107275 T ARITY (NIL) -8 NIL NIL NIL) (-54 105678 105830 106136 "APPRULE" 106766 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105329 105377 105496 "APPLYORE" 105624 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104303 104594 104789 "ANY" 105152 T ANY (NIL) -8 NIL NIL NIL) (-51 103581 103704 103861 "ANY1" 104177 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101146 102018 102345 "ANTISYM" 103305 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100661 100850 100947 "ANON" 101067 T ANON (NIL) -8 NIL NIL NIL) (-48 94793 99200 99654 "AN" 100225 T AN (NIL) -8 NIL NIL NIL) (-47 91049 92403 92454 "AMR" 93202 NIL AMR (NIL T T) -9 NIL 93802 NIL) (-46 90161 90382 90745 "AMR-" 90750 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74711 90078 90139 "ALIST" 90144 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71548 74305 74474 "ALGSC" 74629 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68104 68658 69265 "ALGPKG" 70988 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67381 67482 67666 "ALGMFACT" 67990 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63120 63805 64460 "ALGMANIP" 66904 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54526 62746 62896 "ALGFF" 63053 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53722 53853 54032 "ALGFACT" 54384 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52787 53353 53391 "ALGEBRA" 53396 NIL ALGEBRA (NIL T) -9 NIL 53437 NIL) (-37 52505 52564 52696 "ALGEBRA-" 52701 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34764 50507 50559 "ALAGG" 50695 NIL ALAGG (NIL T T) -9 NIL 50856 NIL) (-35 34300 34413 34439 "AHYP" 34640 T AHYP (NIL) -9 NIL NIL NIL) (-34 33231 33479 33505 "AGG" 34004 T AGG (NIL) -9 NIL 34283 NIL) (-33 32665 32827 33041 "AGG-" 33046 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30342 30764 31182 "AF" 32307 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29849 30067 30157 "ADDAST" 30270 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29118 29376 29532 "ACPLOT" 29711 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18410 26331 26382 "ACFS" 27093 NIL ACFS (NIL T) -9 NIL 27332 NIL) (-28 16424 16914 17689 "ACFS-" 17694 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14591 14617 "ACF" 15496 T ACF (NIL) -9 NIL 15908 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 3193505 3193510 3193515 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3193490 3193495 3193500 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3193475 3193480 3193485 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3193460 3193465 3193470 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1282 3192636 3193335 3193412 "ZMOD" 3193417 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1281 3191746 3191910 3192119 "ZLINDEP" 3192468 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1280 3181050 3182814 3184786 "ZDSOLVE" 3189876 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1279 3180296 3180437 3180626 "YSTREAM" 3180896 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1278 3178107 3179597 3179801 "XRPOLY" 3180139 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1277 3174695 3175978 3176553 "XPR" 3177579 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1276 3172451 3174026 3174230 "XPOLY" 3174526 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1275 3170242 3171576 3171631 "XPOLYC" 3171919 NIL XPOLYC (NIL T T) -9 NIL 3172032 NIL) (-1274 3166660 3168759 3169147 "XPBWPOLY" 3169900 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3162571 3164823 3164865 "XF" 3165486 NIL XF (NIL T) -9 NIL 3165886 NIL) (-1272 3162192 3162280 3162449 "XF-" 3162454 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1271 3157526 3158781 3158836 "XFALG" 3161008 NIL XFALG (NIL T T) -9 NIL 3161797 NIL) (-1270 3156659 3156763 3156968 "XEXPPKG" 3157418 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1269 3154803 3156509 3156605 "XDPOLY" 3156610 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1268 3153748 3154314 3154357 "XALG" 3154362 NIL XALG (NIL T) -9 NIL 3154473 NIL) (-1267 3147217 3151725 3152219 "WUTSET" 3153340 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1266 3145508 3146269 3146592 "WP" 3147028 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1265 3145137 3145330 3145400 "WHILEAST" 3145460 T WHILEAST (NIL) -8 NIL NIL NIL) (-1264 3144636 3144854 3144948 "WHEREAST" 3145065 T WHEREAST (NIL) -8 NIL NIL NIL) (-1263 3143522 3143720 3144015 "WFFINTBS" 3144433 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1262 3141426 3141853 3142315 "WEIER" 3143094 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1261 3140573 3140997 3141039 "VSPACE" 3141175 NIL VSPACE (NIL T) -9 NIL 3141249 NIL) (-1260 3140411 3140438 3140529 "VSPACE-" 3140534 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1259 3140219 3140262 3140330 "VOID" 3140365 T VOID (NIL) -8 NIL NIL NIL) (-1258 3138355 3138714 3139120 "VIEW" 3139835 T VIEW (NIL) -7 NIL NIL NIL) (-1257 3134780 3135418 3136155 "VIEWDEF" 3137640 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1256 3124116 3126328 3128501 "VIEW3D" 3132629 T VIEW3D (NIL) -8 NIL NIL NIL) (-1255 3116398 3118027 3119606 "VIEW2D" 3122559 T VIEW2D (NIL) -8 NIL NIL NIL) (-1254 3111802 3116168 3116260 "VECTOR" 3116341 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1253 3110379 3110638 3110956 "VECTOR2" 3111532 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1252 3103906 3108163 3108206 "VECTCAT" 3109199 NIL VECTCAT (NIL T) -9 NIL 3109785 NIL) (-1251 3102920 3103174 3103564 "VECTCAT-" 3103569 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1250 3102401 3102571 3102691 "VARIABLE" 3102835 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1249 3102334 3102339 3102369 "UTYPE" 3102374 T UTYPE (NIL) -9 NIL NIL NIL) (-1248 3101164 3101318 3101580 "UTSODETL" 3102160 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1247 3098604 3099064 3099588 "UTSODE" 3100705 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1246 3090480 3096230 3096719 "UTS" 3098173 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1245 3081723 3087047 3087090 "UTSCAT" 3088202 NIL UTSCAT (NIL T) -9 NIL 3088959 NIL) (-1244 3079078 3079793 3080782 "UTSCAT-" 3080787 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1243 3078705 3078748 3078881 "UTS2" 3079029 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1242 3072978 3075543 3075586 "URAGG" 3077656 NIL URAGG (NIL T) -9 NIL 3078379 NIL) (-1241 3069917 3070780 3071903 "URAGG-" 3071908 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1240 3065641 3068531 3069003 "UPXSSING" 3069581 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1239 3057743 3064888 3065161 "UPXS" 3065426 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1238 3050856 3057647 3057719 "UPXSCONS" 3057724 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1237 3041101 3047851 3047913 "UPXSCCA" 3048487 NIL UPXSCCA (NIL T T) -9 NIL 3048720 NIL) (-1236 3040739 3040824 3040998 "UPXSCCA-" 3041003 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1235 3030837 3037360 3037403 "UPXSCAT" 3038051 NIL UPXSCAT (NIL T) -9 NIL 3038659 NIL) (-1234 3030267 3030346 3030525 "UPXS2" 3030752 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1233 3028921 3029174 3029525 "UPSQFREE" 3030010 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1232 3022709 3025723 3025778 "UPSCAT" 3026939 NIL UPSCAT (NIL T T) -9 NIL 3027713 NIL) (-1231 3021913 3022120 3022447 "UPSCAT-" 3022452 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1230 3007763 3015761 3015804 "UPOLYC" 3017905 NIL UPOLYC (NIL T) -9 NIL 3019126 NIL) (-1229 2999092 3001517 3004664 "UPOLYC-" 3004669 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1228 2998719 2998762 2998895 "UPOLYC2" 2999043 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1227 2990293 2998402 2998531 "UP" 2998638 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1226 2989632 2989739 2989903 "UPMP" 2990182 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1225 2989185 2989266 2989405 "UPDIVP" 2989545 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1224 2987753 2988002 2988318 "UPDECOMP" 2988934 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1223 2986988 2987100 2987285 "UPCDEN" 2987637 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1222 2986507 2986576 2986725 "UP2" 2986913 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1221 2985024 2985711 2985988 "UNISEG" 2986265 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1220 2984239 2984366 2984571 "UNISEG2" 2984867 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1219 2983299 2983479 2983705 "UNIFACT" 2984055 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1218 2967266 2982476 2982727 "ULS" 2983106 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1217 2955306 2967170 2967242 "ULSCONS" 2967247 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1216 2937922 2949864 2949926 "ULSCCAT" 2950564 NIL ULSCCAT (NIL T T) -9 NIL 2950852 NIL) (-1215 2936972 2937217 2937605 "ULSCCAT-" 2937610 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1214 2926847 2933284 2933327 "ULSCAT" 2934190 NIL ULSCAT (NIL T) -9 NIL 2934920 NIL) (-1213 2926277 2926356 2926535 "ULS2" 2926762 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1212 2925414 2925889 2925990 "UINT8" 2926101 T UINT8 (NIL) -8 NIL NIL 2926180) (-1211 2924550 2925025 2925126 "UINT32" 2925237 T UINT32 (NIL) -8 NIL NIL 2925316) (-1210 2923686 2924161 2924262 "UINT16" 2924373 T UINT16 (NIL) -8 NIL NIL 2924452) (-1209 2922089 2923012 2923042 "UFD" 2923254 T UFD (NIL) -9 NIL 2923368 NIL) (-1208 2921883 2921929 2922024 "UFD-" 2922029 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1207 2920965 2921148 2921364 "UDVO" 2921689 T UDVO (NIL) -7 NIL NIL NIL) (-1206 2918781 2919190 2919661 "UDPO" 2920529 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1205 2918714 2918719 2918749 "TYPE" 2918754 T TYPE (NIL) -9 NIL NIL NIL) (-1204 2918501 2918669 2918700 "TYPEAST" 2918705 T TYPEAST (NIL) -8 NIL NIL NIL) (-1203 2917472 2917674 2917914 "TWOFACT" 2918295 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1202 2916544 2916881 2917116 "TUPLE" 2917272 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1201 2914235 2914754 2915293 "TUBETOOL" 2916027 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1200 2913084 2913289 2913530 "TUBE" 2914028 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1199 2907848 2912056 2912339 "TS" 2912836 NIL TS (NIL T) -8 NIL NIL NIL) (-1198 2896515 2900607 2900704 "TSETCAT" 2905973 NIL TSETCAT (NIL T T T T) -9 NIL 2907504 NIL) (-1197 2891250 2892847 2894738 "TSETCAT-" 2894743 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1196 2885513 2886359 2887301 "TRMANIP" 2890386 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1195 2884954 2885017 2885180 "TRIMAT" 2885445 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1194 2882750 2882987 2883351 "TRIGMNIP" 2884703 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1193 2882270 2882383 2882413 "TRIGCAT" 2882626 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1192 2881939 2882018 2882159 "TRIGCAT-" 2882164 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1191 2878836 2880797 2881078 "TREE" 2881693 NIL TREE (NIL T) -8 NIL NIL NIL) (-1190 2878110 2878638 2878668 "TRANFUN" 2878703 T TRANFUN (NIL) -9 NIL 2878769 NIL) (-1189 2877389 2877580 2877860 "TRANFUN-" 2877865 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1188 2877193 2877225 2877286 "TOPSP" 2877350 T TOPSP (NIL) -7 NIL NIL NIL) (-1187 2876541 2876656 2876810 "TOOLSIGN" 2877074 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1186 2875202 2875718 2875957 "TEXTFILE" 2876324 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1185 2873141 2873655 2874084 "TEX" 2874795 T TEX (NIL) -8 NIL NIL NIL) (-1184 2872922 2872953 2873025 "TEX1" 2873104 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1183 2872570 2872633 2872723 "TEMUTL" 2872854 T TEMUTL (NIL) -7 NIL NIL NIL) (-1182 2870724 2871004 2871329 "TBCMPPK" 2872293 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1181 2862612 2868884 2868940 "TBAGG" 2869340 NIL TBAGG (NIL T T) -9 NIL 2869551 NIL) (-1180 2857682 2859170 2860924 "TBAGG-" 2860929 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1179 2857066 2857173 2857318 "TANEXP" 2857571 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1178 2850567 2856923 2857016 "TABLE" 2857021 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1177 2849979 2850078 2850216 "TABLEAU" 2850464 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1176 2844587 2845807 2847055 "TABLBUMP" 2848765 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1175 2844015 2844115 2844243 "SYSTEM" 2844481 T SYSTEM (NIL) -7 NIL NIL NIL) (-1174 2840478 2841173 2841956 "SYSSOLP" 2843266 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1173 2839535 2840002 2840115 "SYSNNI" 2840301 NIL SYSNNI (NIL NIL) -8 NIL NIL 2840380) (-1172 2838988 2839393 2839435 "SYSINT" 2839440 NIL SYSINT (NIL NIL) -8 NIL NIL 2839448) (-1171 2835322 2836249 2836965 "SYNTAX" 2838294 T SYNTAX (NIL) -8 NIL NIL NIL) (-1170 2832480 2833082 2833714 "SYMTAB" 2834712 T SYMTAB (NIL) -8 NIL NIL NIL) (-1169 2827729 2828631 2829614 "SYMS" 2831519 T SYMS (NIL) -8 NIL NIL NIL) (-1168 2825001 2827187 2827417 "SYMPOLY" 2827534 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1167 2824518 2824593 2824716 "SYMFUNC" 2824913 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1166 2820570 2821830 2822643 "SYMBOL" 2823727 T SYMBOL (NIL) -8 NIL NIL NIL) (-1165 2814109 2815798 2817518 "SWITCH" 2818872 T SWITCH (NIL) -8 NIL NIL NIL) (-1164 2807379 2812930 2813233 "SUTS" 2813864 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1163 2799480 2806626 2806899 "SUPXS" 2807164 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1162 2791010 2799098 2799224 "SUP" 2799389 NIL SUP (NIL T) -8 NIL NIL NIL) (-1161 2790169 2790296 2790513 "SUPFRACF" 2790878 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1160 2789790 2789849 2789962 "SUP2" 2790104 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1159 2788203 2788477 2788840 "SUMRF" 2789489 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1158 2787517 2787583 2787782 "SUMFS" 2788124 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1157 2771524 2786694 2786945 "SULS" 2787324 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1156 2771153 2771346 2771416 "SUCHTAST" 2771476 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1155 2770475 2770678 2770818 "SUCH" 2771061 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1154 2764369 2765381 2766340 "SUBSPACE" 2769563 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1153 2763799 2763889 2764053 "SUBRESP" 2764257 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1152 2757168 2758464 2759775 "STTF" 2762535 NIL STTF (NIL T) -7 NIL NIL NIL) (-1151 2751341 2752461 2753608 "STTFNC" 2756068 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1150 2742656 2744523 2746317 "STTAYLOR" 2749582 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1149 2735900 2742520 2742603 "STRTBL" 2742608 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1148 2731291 2735855 2735886 "STRING" 2735891 T STRING (NIL) -8 NIL NIL NIL) (-1147 2726179 2730664 2730694 "STRICAT" 2730753 T STRICAT (NIL) -9 NIL 2730815 NIL) (-1146 2718989 2723798 2724409 "STREAM" 2725603 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1145 2718499 2718576 2718720 "STREAM3" 2718906 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1144 2717481 2717664 2717899 "STREAM2" 2718312 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1143 2717169 2717221 2717314 "STREAM1" 2717423 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1142 2716185 2716366 2716597 "STINPROD" 2716985 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1141 2715763 2715947 2715977 "STEP" 2716057 T STEP (NIL) -9 NIL 2716135 NIL) (-1140 2709306 2715662 2715739 "STBL" 2715744 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1139 2704480 2708527 2708570 "STAGG" 2708723 NIL STAGG (NIL T) -9 NIL 2708812 NIL) (-1138 2702182 2702784 2703656 "STAGG-" 2703661 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1137 2700377 2701952 2702044 "STACK" 2702125 NIL STACK (NIL T) -8 NIL NIL NIL) (-1136 2693102 2698518 2698974 "SREGSET" 2700007 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1135 2685528 2686896 2688409 "SRDCMPK" 2691708 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1134 2678495 2682968 2682998 "SRAGG" 2684301 T SRAGG (NIL) -9 NIL 2684909 NIL) (-1133 2677512 2677767 2678146 "SRAGG-" 2678151 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1132 2672007 2676459 2676880 "SQMATRIX" 2677138 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1131 2665756 2668725 2669452 "SPLTREE" 2671352 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1130 2661746 2662412 2663058 "SPLNODE" 2665182 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1129 2660793 2661026 2661056 "SPFCAT" 2661500 T SPFCAT (NIL) -9 NIL NIL NIL) (-1128 2659530 2659740 2660004 "SPECOUT" 2660551 T SPECOUT (NIL) -7 NIL NIL NIL) (-1127 2651182 2652926 2652956 "SPADXPT" 2657348 T SPADXPT (NIL) -9 NIL 2659382 NIL) (-1126 2650943 2650983 2651052 "SPADPRSR" 2651135 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1125 2649126 2650898 2650929 "SPADAST" 2650934 T SPADAST (NIL) -8 NIL NIL NIL) (-1124 2641097 2642844 2642887 "SPACEC" 2647260 NIL SPACEC (NIL T) -9 NIL 2649076 NIL) (-1123 2639268 2641029 2641078 "SPACE3" 2641083 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1122 2638020 2638191 2638482 "SORTPAK" 2639073 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1121 2636070 2636373 2636792 "SOLVETRA" 2637684 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1120 2635081 2635303 2635577 "SOLVESER" 2635843 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1119 2630301 2631182 2632184 "SOLVERAD" 2634133 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1118 2626116 2626725 2627454 "SOLVEFOR" 2629668 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1117 2620413 2625465 2625562 "SNTSCAT" 2625567 NIL SNTSCAT (NIL T T T T) -9 NIL 2625637 NIL) (-1116 2614556 2618736 2619127 "SMTS" 2620103 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1115 2609007 2614444 2614521 "SMP" 2614526 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1114 2607166 2607467 2607865 "SMITH" 2608704 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1113 2600061 2604217 2604320 "SMATCAT" 2605671 NIL SMATCAT (NIL NIL T T T) -9 NIL 2606221 NIL) (-1112 2597001 2597824 2599002 "SMATCAT-" 2599007 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1111 2594714 2596237 2596280 "SKAGG" 2596541 NIL SKAGG (NIL T) -9 NIL 2596676 NIL) (-1110 2591056 2594130 2594325 "SINT" 2594512 T SINT (NIL) -8 NIL NIL 2594685) (-1109 2590828 2590866 2590932 "SIMPAN" 2591012 T SIMPAN (NIL) -7 NIL NIL NIL) (-1108 2590135 2590363 2590503 "SIG" 2590710 T SIG (NIL) -8 NIL NIL NIL) (-1107 2588973 2589194 2589469 "SIGNRF" 2589894 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1106 2587778 2587929 2588220 "SIGNEF" 2588802 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1105 2587111 2587361 2587485 "SIGAST" 2587676 T SIGAST (NIL) -8 NIL NIL NIL) (-1104 2584801 2585255 2585761 "SHP" 2586652 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1103 2578707 2584702 2584778 "SHDP" 2584783 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1102 2578306 2578472 2578502 "SGROUP" 2578595 T SGROUP (NIL) -9 NIL 2578657 NIL) (-1101 2578164 2578190 2578263 "SGROUP-" 2578268 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1100 2575000 2575697 2576420 "SGCF" 2577463 T SGCF (NIL) -7 NIL NIL NIL) (-1099 2569395 2574447 2574544 "SFRTCAT" 2574549 NIL SFRTCAT (NIL T T T T) -9 NIL 2574588 NIL) (-1098 2562819 2563834 2564970 "SFRGCD" 2568378 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1097 2555947 2557018 2558204 "SFQCMPK" 2561752 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1096 2555569 2555658 2555768 "SFORT" 2555888 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1095 2554714 2555409 2555530 "SEXOF" 2555535 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1094 2553848 2554595 2554663 "SEX" 2554668 T SEX (NIL) -8 NIL NIL NIL) (-1093 2549387 2550076 2550171 "SEXCAT" 2553108 NIL SEXCAT (NIL T T T T T) -9 NIL 2553686 NIL) (-1092 2546567 2549321 2549369 "SET" 2549374 NIL SET (NIL T) -8 NIL NIL NIL) (-1091 2544818 2545280 2545585 "SETMN" 2546308 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1090 2544424 2544550 2544580 "SETCAT" 2544697 T SETCAT (NIL) -9 NIL 2544782 NIL) (-1089 2544204 2544256 2544355 "SETCAT-" 2544360 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1088 2540591 2542665 2542708 "SETAGG" 2543578 NIL SETAGG (NIL T) -9 NIL 2543918 NIL) (-1087 2540049 2540165 2540402 "SETAGG-" 2540407 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1086 2539519 2539745 2539846 "SEQAST" 2539970 T SEQAST (NIL) -8 NIL NIL NIL) (-1085 2538718 2539012 2539073 "SEGXCAT" 2539359 NIL SEGXCAT (NIL T T) -9 NIL 2539479 NIL) (-1084 2537774 2538384 2538566 "SEG" 2538571 NIL SEG (NIL T) -8 NIL NIL NIL) (-1083 2536753 2536967 2537010 "SEGCAT" 2537532 NIL SEGCAT (NIL T) -9 NIL 2537753 NIL) (-1082 2535802 2536132 2536332 "SEGBIND" 2536588 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1081 2535423 2535482 2535595 "SEGBIND2" 2535737 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1080 2535024 2535224 2535301 "SEGAST" 2535368 T SEGAST (NIL) -8 NIL NIL NIL) (-1079 2534243 2534369 2534573 "SEG2" 2534868 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1078 2533680 2534178 2534225 "SDVAR" 2534230 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1077 2525970 2533450 2533580 "SDPOL" 2533585 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1076 2524563 2524829 2525148 "SCPKG" 2525685 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1075 2523699 2523879 2524079 "SCOPE" 2524385 T SCOPE (NIL) -8 NIL NIL NIL) (-1074 2522920 2523053 2523232 "SCACHE" 2523554 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1073 2522592 2522752 2522782 "SASTCAT" 2522787 T SASTCAT (NIL) -9 NIL 2522800 NIL) (-1072 2522106 2522427 2522503 "SAOS" 2522538 T SAOS (NIL) -8 NIL NIL NIL) (-1071 2521671 2521706 2521879 "SAERFFC" 2522065 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1070 2515645 2521568 2521648 "SAE" 2521653 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1069 2515238 2515273 2515432 "SAEFACT" 2515604 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1068 2513559 2513873 2514274 "RURPK" 2514904 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1067 2512195 2512474 2512786 "RULESET" 2513393 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1066 2509382 2509885 2510350 "RULE" 2511876 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1065 2509021 2509176 2509259 "RULECOLD" 2509334 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1064 2508519 2508738 2508832 "RSTRCAST" 2508949 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1063 2503368 2504162 2505082 "RSETGCD" 2507718 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1062 2492625 2497677 2497774 "RSETCAT" 2501893 NIL RSETCAT (NIL T T T T) -9 NIL 2502990 NIL) (-1061 2490552 2491091 2491915 "RSETCAT-" 2491920 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1060 2482939 2484314 2485834 "RSDCMPK" 2489151 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2480944 2481385 2481459 "RRCC" 2482545 NIL RRCC (NIL T T) -9 NIL 2482889 NIL) (-1058 2480295 2480469 2480748 "RRCC-" 2480753 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1057 2479765 2479991 2480092 "RPTAST" 2480216 T RPTAST (NIL) -8 NIL NIL NIL) (-1056 2453771 2463358 2463425 "RPOLCAT" 2474089 NIL RPOLCAT (NIL T T T) -9 NIL 2477248 NIL) (-1055 2445271 2447609 2450731 "RPOLCAT-" 2450736 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1054 2436318 2443482 2443964 "ROUTINE" 2444811 T ROUTINE (NIL) -8 NIL NIL NIL) (-1053 2433151 2435944 2436084 "ROMAN" 2436200 T ROMAN (NIL) -8 NIL NIL NIL) (-1052 2431426 2432011 2432271 "ROIRC" 2432956 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1051 2427819 2430062 2430092 "RNS" 2430396 T RNS (NIL) -9 NIL 2430669 NIL) (-1050 2426328 2426711 2427245 "RNS-" 2427320 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1049 2425777 2426159 2426189 "RNG" 2426194 T RNG (NIL) -9 NIL 2426215 NIL) (-1048 2425169 2425531 2425574 "RMODULE" 2425636 NIL RMODULE (NIL T) -9 NIL 2425678 NIL) (-1047 2424005 2424099 2424435 "RMCAT2" 2425070 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1046 2420882 2423351 2423648 "RMATRIX" 2423767 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1045 2413824 2416058 2416173 "RMATCAT" 2419532 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2420514 NIL) (-1044 2413199 2413346 2413653 "RMATCAT-" 2413658 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1043 2412766 2412841 2412969 "RINTERP" 2413118 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1042 2411899 2412419 2412449 "RING" 2412505 T RING (NIL) -9 NIL 2412591 NIL) (-1041 2411691 2411735 2411832 "RING-" 2411837 NIL RING- (NIL T) -8 NIL NIL NIL) (-1040 2410532 2410769 2411027 "RIDIST" 2411455 T RIDIST (NIL) -7 NIL NIL NIL) (-1039 2401848 2410000 2410206 "RGCHAIN" 2410380 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1038 2401224 2401604 2401645 "RGBCSPC" 2401703 NIL RGBCSPC (NIL T) -9 NIL 2401755 NIL) (-1037 2400408 2400763 2400804 "RGBCMDL" 2401036 NIL RGBCMDL (NIL T) -9 NIL 2401150 NIL) (-1036 2397402 2398016 2398686 "RF" 2399772 NIL RF (NIL T) -7 NIL NIL NIL) (-1035 2397048 2397111 2397214 "RFFACTOR" 2397333 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1034 2396773 2396808 2396905 "RFFACT" 2397007 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1033 2394890 2395254 2395636 "RFDIST" 2396413 T RFDIST (NIL) -7 NIL NIL NIL) (-1032 2394343 2394435 2394598 "RETSOL" 2394792 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1031 2393979 2394059 2394102 "RETRACT" 2394235 NIL RETRACT (NIL T) -9 NIL 2394322 NIL) (-1030 2393828 2393853 2393940 "RETRACT-" 2393945 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1029 2393457 2393650 2393720 "RETAST" 2393780 T RETAST (NIL) -8 NIL NIL NIL) (-1028 2386311 2393110 2393237 "RESULT" 2393352 T RESULT (NIL) -8 NIL NIL NIL) (-1027 2384937 2385580 2385779 "RESRING" 2386214 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1026 2384573 2384622 2384720 "RESLATC" 2384874 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1025 2384279 2384313 2384420 "REPSQ" 2384532 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1024 2381701 2382281 2382883 "REP" 2383699 T REP (NIL) -7 NIL NIL NIL) (-1023 2381399 2381433 2381544 "REPDB" 2381660 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1022 2375309 2376688 2377911 "REP2" 2380211 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1021 2371686 2372367 2373175 "REP1" 2374536 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1020 2364412 2369827 2370283 "REGSET" 2371316 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1019 2363225 2363560 2363810 "REF" 2364197 NIL REF (NIL T) -8 NIL NIL NIL) (-1018 2362602 2362705 2362872 "REDORDER" 2363109 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1017 2358607 2361815 2362042 "RECLOS" 2362430 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1016 2357659 2357840 2358055 "REALSOLV" 2358414 T REALSOLV (NIL) -7 NIL NIL NIL) (-1015 2357505 2357546 2357576 "REAL" 2357581 T REAL (NIL) -9 NIL 2357616 NIL) (-1014 2353988 2354790 2355674 "REAL0Q" 2356670 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1013 2349589 2350577 2351638 "REAL0" 2352969 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1012 2349087 2349306 2349400 "RDUCEAST" 2349517 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1011 2348492 2348564 2348771 "RDIV" 2349009 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1010 2347560 2347734 2347947 "RDIST" 2348314 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1009 2346157 2346444 2346816 "RDETRS" 2347268 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1008 2343969 2344423 2344961 "RDETR" 2345699 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1007 2342580 2342858 2343262 "RDEEFS" 2343685 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1006 2341075 2341381 2341813 "RDEEF" 2342268 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1005 2335336 2338211 2338241 "RCFIELD" 2339536 T RCFIELD (NIL) -9 NIL 2340266 NIL) (-1004 2333400 2333904 2334600 "RCFIELD-" 2334675 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1003 2329716 2331501 2331544 "RCAGG" 2332628 NIL RCAGG (NIL T) -9 NIL 2333093 NIL) (-1002 2329344 2329438 2329601 "RCAGG-" 2329606 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1001 2328679 2328791 2328956 "RATRET" 2329228 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1000 2328232 2328299 2328420 "RATFACT" 2328607 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-999 2327547 2327667 2327817 "RANDSRC" 2328102 T RANDSRC (NIL) -7 NIL NIL NIL) (-998 2327284 2327328 2327399 "RADUTIL" 2327496 T RADUTIL (NIL) -7 NIL NIL NIL) (-997 2320446 2326126 2326434 "RADIX" 2327008 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-996 2312103 2320290 2320418 "RADFF" 2320423 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-995 2311755 2311830 2311858 "RADCAT" 2312015 T RADCAT (NIL) -9 NIL NIL NIL) (-994 2311540 2311588 2311685 "RADCAT-" 2311690 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-993 2309691 2311315 2311404 "QUEUE" 2311484 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-992 2306267 2309628 2309673 "QUAT" 2309678 NIL QUAT (NIL T) -8 NIL NIL NIL) (-991 2305905 2305948 2306075 "QUATCT2" 2306218 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-990 2299652 2302954 2302994 "QUATCAT" 2303774 NIL QUATCAT (NIL T) -9 NIL 2304540 NIL) (-989 2295796 2296833 2298220 "QUATCAT-" 2298314 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-988 2293316 2294880 2294921 "QUAGG" 2295296 NIL QUAGG (NIL T) -9 NIL 2295471 NIL) (-987 2292948 2293141 2293209 "QQUTAST" 2293268 T QQUTAST (NIL) -8 NIL NIL NIL) (-986 2291873 2292346 2292518 "QFORM" 2292820 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-985 2283085 2288290 2288330 "QFCAT" 2288988 NIL QFCAT (NIL T) -9 NIL 2289989 NIL) (-984 2278657 2279858 2281449 "QFCAT-" 2281543 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-983 2278295 2278338 2278465 "QFCAT2" 2278608 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-982 2277755 2277865 2277995 "QEQUAT" 2278185 T QEQUAT (NIL) -8 NIL NIL NIL) (-981 2270903 2271974 2273158 "QCMPACK" 2276688 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-980 2268479 2268900 2269328 "QALGSET" 2270558 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-979 2267724 2267898 2268130 "QALGSET2" 2268299 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-978 2266415 2266638 2266955 "PWFFINTB" 2267497 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-977 2264597 2264765 2265119 "PUSHVAR" 2266229 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-976 2260515 2261569 2261610 "PTRANFN" 2263494 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-975 2258917 2259208 2259530 "PTPACK" 2260226 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-974 2258549 2258606 2258715 "PTFUNC2" 2258854 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-973 2253076 2257421 2257462 "PTCAT" 2257758 NIL PTCAT (NIL T) -9 NIL 2257911 NIL) (-972 2252734 2252769 2252893 "PSQFR" 2253035 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-971 2251329 2251627 2251961 "PSEUDLIN" 2252432 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-970 2238099 2240463 2242787 "PSETPK" 2249089 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-969 2231143 2233857 2233953 "PSETCAT" 2236974 NIL PSETCAT (NIL T T T T) -9 NIL 2237788 NIL) (-968 2228979 2229613 2230434 "PSETCAT-" 2230439 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-967 2228328 2228493 2228521 "PSCURVE" 2228789 T PSCURVE (NIL) -9 NIL 2228956 NIL) (-966 2224684 2226166 2226231 "PSCAT" 2227075 NIL PSCAT (NIL T T T) -9 NIL 2227315 NIL) (-965 2223747 2223963 2224363 "PSCAT-" 2224368 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-964 2222479 2223112 2223317 "PRTITION" 2223562 T PRTITION (NIL) -8 NIL NIL NIL) (-963 2221981 2222200 2222292 "PRTDAST" 2222407 T PRTDAST (NIL) -8 NIL NIL NIL) (-962 2211079 2213285 2215473 "PRS" 2219843 NIL PRS (NIL T T) -7 NIL NIL NIL) (-961 2208937 2210429 2210469 "PRQAGG" 2210652 NIL PRQAGG (NIL T) -9 NIL 2210754 NIL) (-960 2208323 2208552 2208580 "PROPLOG" 2208765 T PROPLOG (NIL) -9 NIL 2208887 NIL) (-959 2205493 2206137 2206601 "PROPFRML" 2207891 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-958 2204953 2205063 2205193 "PROPERTY" 2205383 T PROPERTY (NIL) -8 NIL NIL NIL) (-957 2199038 2203119 2203939 "PRODUCT" 2204179 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-956 2196351 2198496 2198730 "PR" 2198849 NIL PR (NIL T T) -8 NIL NIL NIL) (-955 2196147 2196179 2196238 "PRINT" 2196312 T PRINT (NIL) -7 NIL NIL NIL) (-954 2195487 2195604 2195756 "PRIMES" 2196027 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-953 2193552 2193953 2194419 "PRIMELT" 2195066 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-952 2193281 2193330 2193358 "PRIMCAT" 2193482 T PRIMCAT (NIL) -9 NIL NIL NIL) (-951 2189442 2193219 2193264 "PRIMARR" 2193269 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-950 2188449 2188627 2188855 "PRIMARR2" 2189260 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-949 2188092 2188148 2188259 "PREASSOC" 2188387 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-948 2187567 2187700 2187728 "PPCURVE" 2187933 T PPCURVE (NIL) -9 NIL 2188069 NIL) (-947 2187189 2187362 2187445 "PORTNUM" 2187504 T PORTNUM (NIL) -8 NIL NIL NIL) (-946 2184548 2184947 2185539 "POLYROOT" 2186770 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-945 2178493 2184152 2184312 "POLY" 2184421 NIL POLY (NIL T) -8 NIL NIL NIL) (-944 2177876 2177934 2178168 "POLYLIFT" 2178429 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-943 2174151 2174600 2175229 "POLYCATQ" 2177421 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-942 2160968 2166326 2166391 "POLYCAT" 2169905 NIL POLYCAT (NIL T T T) -9 NIL 2171833 NIL) (-941 2154418 2156279 2158663 "POLYCAT-" 2158668 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-940 2154005 2154073 2154193 "POLY2UP" 2154344 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-939 2153637 2153694 2153803 "POLY2" 2153942 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-938 2152322 2152561 2152837 "POLUTIL" 2153411 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-937 2150677 2150954 2151285 "POLTOPOL" 2152044 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-936 2146195 2150613 2150659 "POINT" 2150664 NIL POINT (NIL T) -8 NIL NIL NIL) (-935 2144382 2144739 2145114 "PNTHEORY" 2145840 T PNTHEORY (NIL) -7 NIL NIL NIL) (-934 2142801 2143098 2143510 "PMTOOLS" 2144080 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-933 2142394 2142472 2142589 "PMSYM" 2142717 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-932 2141904 2141973 2142147 "PMQFCAT" 2142319 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-931 2141259 2141369 2141525 "PMPRED" 2141781 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-930 2140655 2140741 2140902 "PMPREDFS" 2141160 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-929 2139298 2139506 2139891 "PMPLCAT" 2140417 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-928 2138830 2138909 2139061 "PMLSAGG" 2139213 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-927 2138305 2138381 2138562 "PMKERNEL" 2138748 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-926 2137922 2137997 2138110 "PMINS" 2138224 NIL PMINS (NIL T) -7 NIL NIL NIL) (-925 2137350 2137419 2137635 "PMFS" 2137847 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-924 2136578 2136696 2136901 "PMDOWN" 2137227 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-923 2135741 2135900 2136082 "PMASS" 2136416 T PMASS (NIL) -7 NIL NIL NIL) (-922 2135015 2135126 2135289 "PMASSFS" 2135627 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-921 2134670 2134738 2134832 "PLOTTOOL" 2134941 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-920 2129292 2130481 2131629 "PLOT" 2133542 T PLOT (NIL) -8 NIL NIL NIL) (-919 2125106 2126140 2127061 "PLOT3D" 2128391 T PLOT3D (NIL) -8 NIL NIL NIL) (-918 2124018 2124195 2124430 "PLOT1" 2124910 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-917 2099412 2104084 2108935 "PLEQN" 2119284 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-916 2098730 2098852 2099032 "PINTERP" 2099277 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-915 2098423 2098470 2098573 "PINTERPA" 2098677 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-914 2097671 2098192 2098279 "PI" 2098319 T PI (NIL) -8 NIL NIL 2098386) (-913 2096068 2097009 2097037 "PID" 2097219 T PID (NIL) -9 NIL 2097353 NIL) (-912 2095793 2095830 2095918 "PICOERCE" 2096025 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-911 2095113 2095252 2095428 "PGROEB" 2095649 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-910 2090700 2091514 2092419 "PGE" 2094228 T PGE (NIL) -7 NIL NIL NIL) (-909 2088824 2089070 2089436 "PGCD" 2090417 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-908 2088162 2088265 2088426 "PFRPAC" 2088708 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-907 2084842 2086710 2087063 "PFR" 2087841 NIL PFR (NIL T) -8 NIL NIL NIL) (-906 2083231 2083475 2083800 "PFOTOOLS" 2084589 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-905 2081764 2082003 2082354 "PFOQ" 2082988 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-904 2080237 2080449 2080812 "PFO" 2081548 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-903 2076825 2080126 2080195 "PF" 2080200 NIL PF (NIL NIL) -8 NIL NIL NIL) (-902 2074259 2075496 2075524 "PFECAT" 2076109 T PFECAT (NIL) -9 NIL 2076493 NIL) (-901 2073704 2073858 2074072 "PFECAT-" 2074077 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-900 2072308 2072559 2072860 "PFBRU" 2073453 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-899 2070175 2070526 2070958 "PFBR" 2071959 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-898 2066091 2067551 2068227 "PERM" 2069532 NIL PERM (NIL T) -8 NIL NIL NIL) (-897 2061357 2062298 2063168 "PERMGRP" 2065254 NIL 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2041819 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-884 2035273 2035330 2035439 "PATTERN2" 2035578 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-883 2033030 2033418 2033875 "PATTERN1" 2034862 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-882 2030425 2030979 2031460 "PATRES" 2032595 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-881 2029989 2030056 2030188 "PATRES2" 2030352 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-880 2027872 2028277 2028684 "PATMATCH" 2029656 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-879 2027408 2027591 2027632 "PATMAB" 2027739 NIL PATMAB (NIL T) -9 NIL 2027822 NIL) (-878 2025953 2026262 2026520 "PATLRES" 2027213 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-877 2025499 2025622 2025663 "PATAB" 2025668 NIL PATAB (NIL T) -9 NIL 2025840 NIL) (-876 2022980 2023512 2024085 "PARTPERM" 2024946 T PARTPERM (NIL) -7 NIL NIL NIL) (-875 2022601 2022664 2022766 "PARSURF" 2022911 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-874 2022233 2022290 2022399 "PARSU2" 2022538 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-873 2021997 2022037 2022104 "PARSER" 2022186 T PARSER (NIL) -7 NIL NIL NIL) (-872 2021618 2021681 2021783 "PARSCURV" 2021928 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-871 2021250 2021307 2021416 "PARSC2" 2021555 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-870 2020889 2020947 2021044 "PARPCURV" 2021186 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-869 2020521 2020578 2020687 "PARPC2" 2020826 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-868 2020041 2020127 2020246 "PAN2EXPR" 2020422 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-867 2018847 2019162 2019390 "PALETTE" 2019833 T PALETTE (NIL) -8 NIL NIL NIL) (-866 2017315 2017852 2018212 "PAIR" 2018533 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-865 2011221 2016574 2016768 "PADICRC" 2017170 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-864 2004485 2010567 2010751 "PADICRAT" 2011069 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-863 2002835 2004422 2004467 "PADIC" 2004472 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-862 2000045 2001575 2001615 "PADICCT" 2002196 NIL PADICCT (NIL NIL) -9 NIL 2002478 NIL) (-861 1999002 1999202 1999470 "PADEPAC" 1999832 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-860 1998214 1998347 1998553 "PADE" 1998864 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-859 1996636 1997422 1997702 "OWP" 1998018 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-858 1995709 1996241 1996413 "OVAR" 1996504 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-857 1994973 1995094 1995255 "OUT" 1995568 T OUT (NIL) -7 NIL NIL NIL) (-856 1983880 1986082 1988282 "OUTFORM" 1992793 T OUTFORM (NIL) -8 NIL NIL NIL) (-855 1983216 1983477 1983604 "OUTBFILE" 1983773 T OUTBFILE (NIL) -8 NIL NIL NIL) (-854 1982523 1982688 1982716 "OUTBCON" 1983034 T OUTBCON (NIL) -9 NIL 1983200 NIL) (-853 1982124 1982236 1982393 "OUTBCON-" 1982398 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-852 1981532 1981853 1981942 "OSI" 1982055 T OSI (NIL) -8 NIL NIL NIL) (-851 1981088 1981400 1981428 "OSGROUP" 1981433 T OSGROUP (NIL) -9 NIL 1981455 NIL) (-850 1979833 1980060 1980345 "ORTHPOL" 1980835 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-849 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(NIL) -9 NIL 1958823 NIL) (-837 1954855 1956849 1957258 "ORDCOMP" 1957887 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-836 1954121 1954248 1954434 "ORDCOMP2" 1954715 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-835 1950729 1951612 1952426 "OPTPROB" 1953327 T OPTPROB (NIL) -8 NIL NIL NIL) (-834 1947531 1948170 1948874 "OPTPACK" 1950045 T OPTPACK (NIL) -7 NIL NIL NIL) (-833 1945244 1945984 1946012 "OPTCAT" 1946831 T OPTCAT (NIL) -9 NIL 1947481 NIL) (-832 1944687 1944921 1945026 "OPSIG" 1945159 T OPSIG (NIL) -8 NIL NIL NIL) (-831 1944455 1944494 1944560 "OPQUERY" 1944641 T OPQUERY (NIL) -7 NIL NIL NIL) (-830 1941621 1942766 1943270 "OP" 1943984 NIL OP (NIL T) -8 NIL NIL NIL) (-829 1941156 1941327 1941368 "OPERCAT" 1941503 NIL OPERCAT (NIL T) -9 NIL 1941571 NIL) (-828 1941002 1941029 1941115 "OPERCAT-" 1941120 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-827 1937847 1939799 1940168 "ONECOMP" 1940666 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-826 1937152 1937267 1937441 "ONECOMP2" 1937719 NIL ONECOMP2 (NIL T 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"OFMONOID" 1917894 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-812 1913822 1914321 1914366 "ODVAR" 1914371 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-811 1911280 1913567 1913722 "ODR" 1913727 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-810 1903624 1911056 1911182 "ODPOL" 1911187 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-809 1897500 1903496 1903601 "ODP" 1903606 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-808 1896266 1896481 1896756 "ODETOOLS" 1897274 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-807 1893235 1893891 1894607 "ODESYS" 1895599 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-806 1888117 1889025 1890050 "ODERTRIC" 1892310 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-805 1887543 1887625 1887819 "ODERED" 1888029 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-804 1884431 1884979 1885656 "ODERAT" 1886966 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-803 1881391 1881855 1882452 "ODEPRRIC" 1883960 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-802 1879361 1879930 1880416 "ODEPROB" 1880925 T ODEPROB (NIL) -8 NIL NIL NIL) (-801 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1845173 1845615 1845643 "OCAMON" 1845648 T OCAMON (NIL) -9 NIL 1845669 NIL) (-788 1844730 1845045 1845073 "OASGP" 1845078 T OASGP (NIL) -9 NIL 1845098 NIL) (-787 1844017 1844480 1844508 "OAMONS" 1844548 T OAMONS (NIL) -9 NIL 1844591 NIL) (-786 1843457 1843864 1843892 "OAMON" 1843897 T OAMON (NIL) -9 NIL 1843917 NIL) (-785 1842761 1843253 1843281 "OAGROUP" 1843286 T OAGROUP (NIL) -9 NIL 1843306 NIL) (-784 1842451 1842501 1842589 "NUMTUBE" 1842705 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-783 1836024 1837542 1839078 "NUMQUAD" 1840935 T NUMQUAD (NIL) -7 NIL NIL NIL) (-782 1831780 1832768 1833793 "NUMODE" 1835019 T NUMODE (NIL) -7 NIL NIL NIL) (-781 1829161 1830015 1830043 "NUMINT" 1830966 T NUMINT (NIL) -9 NIL 1831730 NIL) (-780 1828109 1828306 1828524 "NUMFMT" 1828963 T NUMFMT (NIL) -7 NIL NIL NIL) (-779 1814468 1817413 1819945 "NUMERIC" 1825616 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-778 1808865 1813917 1814012 "NTSCAT" 1814017 NIL NTSCAT (NIL T T T T) -9 NIL 1814056 NIL) (-777 1808059 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1776713 1777536 1777791 "NNI" 1778138 T NNI (NIL) -8 NIL NIL 1778373) (-764 1775133 1775446 1775810 "NLINSOL" 1776381 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-763 1771401 1772369 1773268 "NIPROB" 1774254 T NIPROB (NIL) -8 NIL NIL NIL) (-762 1770158 1770392 1770694 "NFINTBAS" 1771163 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-761 1769332 1769808 1769849 "NETCLT" 1770021 NIL NETCLT (NIL T) -9 NIL 1770103 NIL) (-760 1768040 1768271 1768552 "NCODIV" 1769100 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-759 1767802 1767839 1767914 "NCNTFRAC" 1767997 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-758 1765982 1766346 1766766 "NCEP" 1767427 NIL NCEP (NIL T) -7 NIL NIL NIL) (-757 1764893 1765632 1765660 "NASRING" 1765770 T NASRING (NIL) -9 NIL 1765844 NIL) (-756 1764688 1764732 1764826 "NASRING-" 1764831 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-755 1763841 1764340 1764368 "NARNG" 1764485 T NARNG (NIL) -9 NIL 1764576 NIL) (-754 1763533 1763600 1763734 "NARNG-" 1763739 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-753 1762412 1762619 1762854 "NAGSP" 1763318 T NAGSP (NIL) -7 NIL NIL NIL) (-752 1753684 1755368 1757041 "NAGS" 1760759 T NAGS (NIL) -7 NIL NIL NIL) (-751 1752232 1752540 1752871 "NAGF07" 1753373 T NAGF07 (NIL) -7 NIL NIL NIL) (-750 1746770 1748061 1749368 "NAGF04" 1750945 T NAGF04 (NIL) -7 NIL NIL NIL) (-749 1739738 1741352 1742985 "NAGF02" 1745157 T NAGF02 (NIL) -7 NIL NIL NIL) (-748 1734962 1736062 1737179 "NAGF01" 1738641 T NAGF01 (NIL) -7 NIL NIL NIL) (-747 1728590 1730156 1731741 "NAGE04" 1733397 T NAGE04 (NIL) -7 NIL NIL NIL) (-746 1719759 1721880 1724010 "NAGE02" 1726480 T NAGE02 (NIL) -7 NIL NIL NIL) (-745 1715712 1716659 1717623 "NAGE01" 1718815 T NAGE01 (NIL) -7 NIL NIL NIL) (-744 1713507 1714041 1714599 "NAGD03" 1715174 T NAGD03 (NIL) -7 NIL NIL NIL) (-743 1705257 1707185 1709139 "NAGD02" 1711573 T NAGD02 (NIL) -7 NIL NIL NIL) (-742 1699068 1700493 1701933 "NAGD01" 1703837 T NAGD01 (NIL) -7 NIL NIL NIL) (-741 1695277 1696099 1696936 "NAGC06" 1698251 T NAGC06 (NIL) -7 NIL NIL NIL) (-740 1693742 1694074 1694430 "NAGC05" 1694941 T NAGC05 (NIL) -7 NIL NIL NIL) (-739 1693118 1693237 1693381 "NAGC02" 1693618 T NAGC02 (NIL) -7 NIL NIL NIL) (-738 1692178 1692735 1692775 "NAALG" 1692854 NIL NAALG (NIL T) -9 NIL 1692915 NIL) (-737 1692013 1692042 1692132 "NAALG-" 1692137 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-736 1685963 1687071 1688258 "MULTSQFR" 1690909 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-735 1685282 1685357 1685541 "MULTFACT" 1685875 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-734 1678375 1682245 1682298 "MTSCAT" 1683368 NIL MTSCAT (NIL T T) -9 NIL 1683882 NIL) (-733 1678087 1678141 1678233 "MTHING" 1678315 NIL MTHING (NIL T) -7 NIL NIL NIL) (-732 1677879 1677912 1677972 "MSYSCMD" 1678047 T MSYSCMD (NIL) -7 NIL NIL NIL) (-731 1673991 1676634 1676954 "MSET" 1677592 NIL MSET (NIL T) -8 NIL NIL NIL) (-730 1671086 1673552 1673593 "MSETAGG" 1673598 NIL MSETAGG (NIL T) -9 NIL 1673632 NIL) (-729 1666969 1668465 1669210 "MRING" 1670386 NIL MRING (NIL T T) -8 NIL NIL NIL) (-728 1666535 1666602 1666733 "MRF2" 1666896 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-727 1666153 1666188 1666332 "MRATFAC" 1666494 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-726 1663765 1664060 1664491 "MPRFF" 1665858 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-725 1657825 1663619 1663716 "MPOLY" 1663721 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-724 1657315 1657350 1657558 "MPCPF" 1657784 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-723 1656829 1656872 1657056 "MPC3" 1657266 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-722 1656024 1656105 1656326 "MPC2" 1656744 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-721 1654325 1654662 1655052 "MONOTOOL" 1655684 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-720 1653576 1653867 1653895 "MONOID" 1654114 T MONOID (NIL) -9 NIL 1654261 NIL) (-719 1653122 1653241 1653422 "MONOID-" 1653427 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-718 1643981 1649889 1649948 "MONOGEN" 1650622 NIL MONOGEN (NIL T T) -9 NIL 1651078 NIL) (-717 1641199 1641934 1642934 "MONOGEN-" 1643053 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-716 1640058 1640478 1640506 "MONADWU" 1640898 T MONADWU (NIL) -9 NIL 1641136 NIL) (-715 1639430 1639589 1639837 "MONADWU-" 1639842 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-714 1638815 1639033 1639061 "MONAD" 1639268 T MONAD (NIL) -9 NIL 1639380 NIL) (-713 1638500 1638578 1638710 "MONAD-" 1638715 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-712 1636816 1637413 1637692 "MOEBIUS" 1638253 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-711 1636208 1636586 1636626 "MODULE" 1636631 NIL MODULE (NIL T) -9 NIL 1636657 NIL) (-710 1635776 1635872 1636062 "MODULE-" 1636067 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-709 1633491 1634140 1634467 "MODRING" 1635600 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-708 1630477 1631596 1632117 "MODOP" 1633020 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-707 1629092 1629544 1629821 "MODMONOM" 1630340 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-706 1618899 1627383 1627797 "MODMON" 1628729 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-705 1616090 1617743 1618019 "MODFIELD" 1618774 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-704 1615094 1615371 1615561 "MMLFORM" 1615920 T MMLFORM (NIL) -8 NIL NIL NIL) (-703 1614620 1614663 1614842 "MMAP" 1615045 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-702 1612837 1613570 1613611 "MLO" 1614034 NIL MLO (NIL T) -9 NIL 1614276 NIL) (-701 1610204 1610719 1611321 "MLIFT" 1612318 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-700 1609595 1609679 1609833 "MKUCFUNC" 1610115 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-699 1609194 1609264 1609387 "MKRECORD" 1609518 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-698 1608242 1608403 1608631 "MKFUNC" 1609005 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-697 1607630 1607734 1607890 "MKFLCFN" 1608125 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-696 1607173 1607540 1607599 "MKCHSET" 1607604 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-695 1606450 1606552 1606737 "MKBCFUNC" 1607066 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-694 1603192 1606004 1606140 "MINT" 1606334 T MINT (NIL) -8 NIL NIL NIL) (-693 1602004 1602247 1602524 "MHROWRED" 1602947 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-692 1597430 1600539 1600944 "MFLOAT" 1601619 T MFLOAT (NIL) -8 NIL NIL NIL) (-691 1596787 1596863 1597034 "MFINFACT" 1597342 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-690 1593102 1593950 1594834 "MESH" 1595923 T MESH (NIL) -7 NIL NIL NIL) (-689 1591492 1591804 1592157 "MDDFACT" 1592789 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-688 1588334 1590651 1590692 "MDAGG" 1590947 NIL MDAGG (NIL T) -9 NIL 1591090 NIL) (-687 1578112 1587627 1587834 "MCMPLX" 1588147 T MCMPLX (NIL) -8 NIL NIL NIL) (-686 1577253 1577399 1577599 "MCDEN" 1577961 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-685 1575143 1575413 1575793 "MCALCFN" 1576983 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-684 1574068 1574308 1574541 "MAYBE" 1574949 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-683 1571680 1572203 1572765 "MATSTOR" 1573539 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-682 1567686 1571052 1571300 "MATRIX" 1571465 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-681 1563455 1564159 1564895 "MATLIN" 1567043 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-680 1553609 1556747 1556824 "MATCAT" 1561704 NIL MATCAT (NIL T T T) -9 NIL 1563121 NIL) (-679 1549973 1550986 1552342 "MATCAT-" 1552347 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-678 1548567 1548720 1549053 "MATCAT2" 1549808 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-677 1546679 1547003 1547387 "MAPPKG3" 1548242 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-676 1545660 1545833 1546055 "MAPPKG2" 1546503 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-675 1544159 1544443 1544770 "MAPPKG1" 1545366 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-674 1543265 1543565 1543742 "MAPPAST" 1544002 T MAPPAST (NIL) -8 NIL NIL NIL) (-673 1542876 1542934 1543057 "MAPHACK3" 1543201 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-672 1542468 1542529 1542643 "MAPHACK2" 1542808 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-671 1541906 1542009 1542151 "MAPHACK1" 1542359 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-670 1540012 1540606 1540910 "MAGMA" 1541634 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-669 1539518 1539736 1539827 "MACROAST" 1539941 T MACROAST (NIL) -8 NIL NIL NIL) (-668 1535985 1537757 1538218 "M3D" 1539090 NIL M3D (NIL T) -8 NIL NIL NIL) (-667 1530139 1534354 1534395 "LZSTAGG" 1535177 NIL LZSTAGG (NIL T) -9 NIL 1535472 NIL) (-666 1526113 1527270 1528727 "LZSTAGG-" 1528732 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-665 1523227 1524004 1524491 "LWORD" 1525658 NIL LWORD (NIL T) -8 NIL NIL NIL) (-664 1522830 1523031 1523106 "LSTAST" 1523172 T LSTAST (NIL) -8 NIL NIL NIL) (-663 1516031 1522601 1522735 "LSQM" 1522740 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-662 1515255 1515394 1515622 "LSPP" 1515886 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-661 1513067 1513368 1513824 "LSMP" 1514944 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-660 1509846 1510520 1511250 "LSMP1" 1512369 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-659 1503771 1509013 1509054 "LSAGG" 1509116 NIL LSAGG (NIL T) -9 NIL 1509194 NIL) (-658 1500466 1501390 1502603 "LSAGG-" 1502608 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-657 1498092 1499610 1499859 "LPOLY" 1500261 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-656 1497674 1497759 1497882 "LPEFRAC" 1498001 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-655 1496021 1496768 1497021 "LO" 1497506 NIL LO (NIL T T T) -8 NIL NIL NIL) (-654 1495673 1495785 1495813 "LOGIC" 1495924 T LOGIC (NIL) -9 NIL 1496005 NIL) (-653 1495535 1495558 1495629 "LOGIC-" 1495634 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-652 1494728 1494868 1495061 "LODOOPS" 1495391 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-651 1492186 1494644 1494710 "LODO" 1494715 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-650 1490724 1490959 1491312 "LODOF" 1491933 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-649 1487080 1489477 1489518 "LODOCAT" 1489956 NIL LODOCAT (NIL T) -9 NIL 1490167 NIL) (-648 1486813 1486871 1486998 "LODOCAT-" 1487003 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-647 1484168 1486654 1486772 "LODO2" 1486777 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-646 1481638 1484105 1484150 "LODO1" 1484155 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-645 1480498 1480663 1480975 "LODEEF" 1481461 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-644 1475784 1478628 1478669 "LNAGG" 1479616 NIL LNAGG (NIL T) -9 NIL 1480060 NIL) (-643 1474931 1475145 1475487 "LNAGG-" 1475492 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-642 1471094 1471856 1472495 "LMOPS" 1474346 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-641 1470489 1470851 1470892 "LMODULE" 1470953 NIL LMODULE (NIL T) -9 NIL 1470995 NIL) (-640 1467735 1470134 1470257 "LMDICT" 1470399 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-639 1467461 1467643 1467703 "LITERAL" 1467708 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-638 1460688 1466407 1466705 "LIST" 1467196 NIL LIST (NIL T) -8 NIL NIL NIL) (-637 1460213 1460287 1460426 "LIST3" 1460608 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-636 1459220 1459398 1459626 "LIST2" 1460031 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-635 1457354 1457666 1458065 "LIST2MAP" 1458867 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-634 1456084 1456720 1456761 "LINEXP" 1457016 NIL LINEXP (NIL T) -9 NIL 1457165 NIL) (-633 1454731 1454991 1455288 "LINDEP" 1455836 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-632 1451498 1452217 1452994 "LIMITRF" 1453986 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-631 1449774 1450069 1450485 "LIMITPS" 1451193 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-630 1444229 1449285 1449513 "LIE" 1449595 NIL LIE (NIL T T) -8 NIL NIL NIL) (-629 1443278 1443721 1443761 "LIECAT" 1443901 NIL LIECAT (NIL T) -9 NIL 1444052 NIL) (-628 1443119 1443146 1443234 "LIECAT-" 1443239 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-627 1435731 1442568 1442733 "LIB" 1442974 T LIB (NIL) -8 NIL NIL NIL) (-626 1431368 1432249 1433184 "LGROBP" 1434848 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-625 1429234 1429508 1429870 "LF" 1431089 NIL LF (NIL T T) -7 NIL NIL NIL) (-624 1428074 1428766 1428794 "LFCAT" 1429001 T LFCAT (NIL) -9 NIL 1429140 NIL) (-623 1424978 1425606 1426294 "LEXTRIPK" 1427438 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-622 1421749 1422548 1423051 "LEXP" 1424558 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-621 1421252 1421470 1421562 "LETAST" 1421677 T LETAST (NIL) -8 NIL NIL NIL) (-620 1419650 1419963 1420364 "LEADCDET" 1420934 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-619 1418840 1418914 1419143 "LAZM3PK" 1419571 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-618 1413795 1416917 1417455 "LAUPOL" 1418352 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-617 1413360 1413404 1413572 "LAPLACE" 1413745 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-616 1411334 1412461 1412712 "LA" 1413193 NIL LA (NIL T T T) -8 NIL NIL NIL) (-615 1410415 1410965 1411006 "LALG" 1411068 NIL LALG (NIL T) -9 NIL 1411127 NIL) (-614 1410129 1410188 1410324 "LALG-" 1410329 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-613 1409964 1409988 1410029 "KVTFROM" 1410091 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-612 1408767 1409181 1409410 "KTVLOGIC" 1409755 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-611 1408602 1408626 1408667 "KRCFROM" 1408729 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-610 1407506 1407693 1407992 "KOVACIC" 1408402 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-609 1407341 1407365 1407406 "KONVERT" 1407468 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-608 1407176 1407200 1407241 "KOERCE" 1407303 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-607 1404910 1405670 1406063 "KERNEL" 1406815 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-606 1404412 1404493 1404623 "KERNEL2" 1404824 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-605 1398263 1402951 1403005 "KDAGG" 1403382 NIL KDAGG (NIL T T) -9 NIL 1403588 NIL) (-604 1397792 1397916 1398121 "KDAGG-" 1398126 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-603 1390967 1397453 1397608 "KAFILE" 1397670 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-602 1385422 1390478 1390706 "JORDAN" 1390788 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-601 1384828 1385071 1385192 "JOINAST" 1385321 T JOINAST (NIL) -8 NIL NIL NIL) (-600 1384674 1384733 1384788 "JAVACODE" 1384793 T JAVACODE (NIL) -8 NIL NIL NIL) (-599 1380973 1382879 1382933 "IXAGG" 1383862 NIL IXAGG (NIL T T) -9 NIL 1384321 NIL) (-598 1379892 1380198 1380617 "IXAGG-" 1380622 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-597 1375472 1379814 1379873 "IVECTOR" 1379878 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-596 1374238 1374475 1374741 "ITUPLE" 1375239 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-595 1372674 1372851 1373157 "ITRIGMNP" 1374060 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-594 1371419 1371623 1371906 "ITFUN3" 1372450 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-593 1371051 1371108 1371217 "ITFUN2" 1371356 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-592 1368888 1369913 1370212 "ITAYLOR" 1370785 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-591 1357871 1363025 1364188 "ISUPS" 1367758 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-590 1356975 1357115 1357351 "ISUMP" 1357718 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-589 1352239 1356776 1356855 "ISTRING" 1356928 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-588 1351742 1351960 1352052 "ISAST" 1352167 T ISAST (NIL) -8 NIL NIL NIL) (-587 1350952 1351033 1351249 "IRURPK" 1351656 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-586 1349888 1350089 1350329 "IRSN" 1350732 T IRSN (NIL) -7 NIL NIL NIL) (-585 1347917 1348272 1348708 "IRRF2F" 1349526 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-584 1347664 1347702 1347778 "IRREDFFX" 1347873 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-583 1346279 1346538 1346837 "IROOT" 1347397 NIL IROOT (NIL T) -7 NIL NIL NIL) (-582 1342911 1343963 1344655 "IR" 1345619 NIL IR (NIL T) -8 NIL NIL NIL) (-581 1340524 1341019 1341585 "IR2" 1342389 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-580 1339596 1339709 1339930 "IR2F" 1340407 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-579 1339387 1339421 1339481 "IPRNTPK" 1339556 T IPRNTPK (NIL) -7 NIL NIL NIL) (-578 1336006 1339276 1339345 "IPF" 1339350 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-577 1334369 1335931 1335988 "IPADIC" 1335993 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-576 1333709 1333929 1334059 "IP4ADDR" 1334259 T IP4ADDR (NIL) -8 NIL NIL NIL) (-575 1333209 1333413 1333523 "IOMODE" 1333619 T IOMODE (NIL) -8 NIL NIL NIL) (-574 1332282 1332806 1332933 "IOBFILE" 1333102 T IOBFILE (NIL) -8 NIL NIL NIL) (-573 1331770 1332186 1332214 "IOBCON" 1332219 T IOBCON (NIL) -9 NIL 1332240 NIL) (-572 1331267 1331325 1331515 "INVLAPLA" 1331706 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-571 1320916 1323269 1325655 "INTTR" 1328931 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-570 1317260 1318002 1318866 "INTTOOLS" 1320101 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-569 1316846 1316937 1317054 "INTSLPE" 1317163 T INTSLPE (NIL) -7 NIL NIL NIL) (-568 1314841 1316769 1316828 "INTRVL" 1316833 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-567 1312443 1312955 1313530 "INTRF" 1314326 NIL INTRF (NIL T) -7 NIL NIL NIL) (-566 1311854 1311951 1312093 "INTRET" 1312341 NIL INTRET (NIL T) -7 NIL NIL NIL) (-565 1309851 1310240 1310710 "INTRAT" 1311462 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-564 1307079 1307662 1308288 "INTPM" 1309336 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-563 1303782 1304381 1305126 "INTPAF" 1306465 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-562 1298961 1299923 1300974 "INTPACK" 1302751 T INTPACK (NIL) -7 NIL NIL NIL) (-561 1295873 1298690 1298817 "INT" 1298854 T INT (NIL) -8 NIL NIL NIL) (-560 1295125 1295277 1295485 "INTHERTR" 1295715 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-559 1294564 1294644 1294832 "INTHERAL" 1295039 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-558 1292410 1292853 1293310 "INTHEORY" 1294127 T INTHEORY (NIL) -7 NIL NIL NIL) (-557 1283718 1285339 1287118 "INTG0" 1290762 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-556 1264291 1269081 1273891 "INTFTBL" 1278928 T INTFTBL (NIL) -8 NIL NIL NIL) (-555 1263540 1263678 1263851 "INTFACT" 1264150 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-554 1260925 1261371 1261935 "INTEF" 1263094 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-553 1259392 1260097 1260125 "INTDOM" 1260426 T INTDOM (NIL) -9 NIL 1260633 NIL) (-552 1258761 1258935 1259177 "INTDOM-" 1259182 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-551 1255256 1257145 1257199 "INTCAT" 1257998 NIL INTCAT (NIL T) -9 NIL 1258318 NIL) (-550 1254729 1254831 1254959 "INTBIT" 1255148 T INTBIT (NIL) -7 NIL NIL NIL) (-549 1253400 1253554 1253868 "INTALG" 1254574 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-548 1252857 1252947 1253117 "INTAF" 1253304 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-547 1246311 1252667 1252807 "INTABL" 1252812 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-546 1245771 1246184 1246212 "INT8" 1246217 T INT8 (NIL) -8 NIL NIL 1246225) (-545 1245230 1245643 1245671 "INT32" 1245676 T INT32 (NIL) -8 NIL NIL 1245684) (-544 1244689 1245102 1245130 "INT16" 1245135 T INT16 (NIL) -8 NIL NIL 1245143) (-543 1239704 1242378 1242406 "INS" 1243340 T INS (NIL) -9 NIL 1244005 NIL) (-542 1236944 1237715 1238689 "INS-" 1238762 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1235719 1235946 1236244 "INPSIGN" 1236697 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1234837 1234954 1235151 "INPRODPF" 1235599 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1233731 1233848 1234085 "INPRODFF" 1234717 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1232731 1232883 1233143 "INNMFACT" 1233567 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1231928 1232025 1232213 "INMODGCD" 1232630 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1230437 1230681 1231005 "INFSP" 1231673 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1229621 1229738 1229921 "INFPROD0" 1230317 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1226503 1227686 1228201 "INFORM" 1229114 T INFORM (NIL) -8 NIL NIL NIL) (-533 1226113 1226173 1226271 "INFORM1" 1226438 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1225636 1225725 1225839 "INFINITY" 1226019 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1224812 1225356 1225457 "INETCLTS" 1225555 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1223429 1223678 1223999 "INEP" 1224560 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1222705 1223326 1223391 "INDE" 1223396 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1222269 1222337 1222454 "INCRMAPS" 1222632 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1221087 1221538 1221744 "INBFILE" 1222083 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1216398 1217323 1218267 "INBFF" 1220175 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1215306 1215575 1215603 "INBCON" 1216116 T INBCON (NIL) -9 NIL 1216382 NIL) (-524 1214558 1214781 1215057 "INBCON-" 1215062 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1214060 1214279 1214371 "INAST" 1214486 T INAST (NIL) -8 NIL NIL NIL) (-522 1213514 1213739 1213845 "IMPTAST" 1213974 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1210008 1213358 1213462 "IMATRIX" 1213467 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208720 1208843 1209158 "IMATQF" 1209864 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206940 1207167 1207504 "IMATLIN" 1208476 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201566 1206864 1206922 "ILIST" 1206927 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199519 1201426 1201539 "IIARRAY2" 1201544 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194952 1199430 1199494 "IFF" 1199499 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194326 1194569 1194685 "IFAST" 1194856 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189369 1193618 1193806 "IFARRAY" 1194183 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188576 1189273 1189346 "IFAMON" 1189351 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188160 1188225 1188279 "IEVALAB" 1188486 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187835 1187903 1188063 "IEVALAB-" 1188068 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187493 1187749 1187812 "IDPO" 1187817 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186770 1187382 1187457 "IDPOAMS" 1187462 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1186104 1186659 1186734 "IDPOAM" 1186739 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185189 1185439 1185492 "IDPC" 1185905 NIL IDPC (NIL T T) -9 NIL 1186054 NIL) (-506 1184685 1185081 1185154 "IDPAM" 1185159 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1184088 1184577 1184650 "IDPAG" 1184655 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183856 1184003 1184053 "IDENT" 1184058 T IDENT (NIL) -8 NIL NIL NIL) (-503 1180111 1180959 1181854 "IDECOMP" 1183013 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172985 1174034 1175081 "IDEAL" 1179147 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172149 1172261 1172460 "ICDEN" 1172869 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171248 1171629 1171776 "ICARD" 1172022 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169308 1169621 1170026 "IBPTOOLS" 1170925 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164942 1168928 1169041 "IBITS" 1169227 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161665 1162241 1162936 "IBATOOL" 1164359 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159445 1159906 1160439 "IBACHIN" 1161200 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157322 1159291 1159394 "IARRAY2" 1159399 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153475 1157248 1157305 "IARRAY1" 1157310 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147469 1151887 1152368 "IAN" 1153014 T IAN (NIL) -8 NIL NIL NIL) (-492 1146980 1147037 1147210 "IALGFACT" 1147406 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146508 1146621 1146649 "HYPCAT" 1146856 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1146046 1146163 1146349 "HYPCAT-" 1146354 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145668 1145841 1145924 "HOSTNAME" 1145983 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145513 1145550 1145591 "HOMOTOP" 1145596 NIL HOMOTOP (NIL T) -9 NIL 1145629 NIL) (-487 1142192 1143523 1143564 "HOAGG" 1144545 NIL HOAGG (NIL T) -9 NIL 1145224 NIL) (-486 1140786 1141185 1141711 "HOAGG-" 1141716 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134828 1140383 1140531 "HEXADEC" 1140658 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133576 1133798 1134061 "HEUGCD" 1134605 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132679 1133413 1133543 "HELLFDIV" 1133548 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130907 1132456 1132544 "HEAP" 1132623 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130198 1130459 1130593 "HEADAST" 1130793 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1124118 1130113 1130175 "HDP" 1130180 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117869 1123753 1123905 "HDMP" 1124019 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117194 1117333 1117497 "HB" 1117725 T HB (NIL) -7 NIL NIL NIL) (-477 1110691 1117040 1117144 "HASHTBL" 1117149 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110194 1110412 1110504 "HASAST" 1110619 T HASAST (NIL) -8 NIL NIL NIL) (-475 1108006 1109816 1109998 "HACKPI" 1110032 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103701 1107859 1107972 "GTSET" 1107977 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097227 1103579 1103677 "GSTBL" 1103682 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089540 1096258 1096523 "GSERIES" 1097018 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088707 1089098 1089126 "GROUP" 1089329 T GROUP (NIL) -9 NIL 1089463 NIL) (-470 1088073 1088232 1088483 "GROUP-" 1088488 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086442 1086761 1087148 "GROEBSOL" 1087750 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085382 1085644 1085695 "GRMOD" 1086224 NIL GRMOD (NIL T T) -9 NIL 1086392 NIL) (-467 1085150 1085186 1085314 "GRMOD-" 1085319 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080476 1081504 1082504 "GRIMAGE" 1084170 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078943 1079203 1079527 "GRDEF" 1080172 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078387 1078503 1078644 "GRAY" 1078822 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077600 1077980 1078031 "GRALG" 1078184 NIL GRALG (NIL T T) -9 NIL 1078277 NIL) (-462 1077261 1077334 1077497 "GRALG-" 1077502 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1074065 1076846 1077024 "GPOLSET" 1077168 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073419 1073476 1073734 "GOSPER" 1074002 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069178 1069857 1070383 "GMODPOL" 1073118 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068183 1068367 1068605 "GHENSEL" 1068990 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062234 1063077 1064104 "GENUPS" 1067267 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061931 1061982 1062071 "GENUFACT" 1062177 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061343 1061420 1061585 "GENPGCD" 1061849 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060817 1060852 1061065 "GENMFACT" 1061302 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059385 1059640 1059947 "GENEEZ" 1060560 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053298 1058996 1059158 "GDMP" 1059308 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042675 1047069 1048175 "GCNAALG" 1052281 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1041102 1041930 1041958 "GCDDOM" 1042213 T GCDDOM (NIL) -9 NIL 1042370 NIL) (-449 1040572 1040699 1040914 "GCDDOM-" 1040919 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039244 1039429 1039733 "GB" 1040351 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027864 1030190 1032582 "GBINTERN" 1036935 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025701 1025993 1026414 "GBF" 1027539 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024482 1024647 1024914 "GBEUCLID" 1025517 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023831 1023956 1024105 "GAUSSFAC" 1024353 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022198 1022500 1022814 "GALUTIL" 1023550 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020506 1020780 1021104 "GALPOLYU" 1021925 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017871 1018161 1018568 "GALFACTU" 1020203 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009677 1011176 1012784 "GALFACT" 1016303 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1007065 1007723 1007751 "FVFUN" 1008907 T FVFUN (NIL) -9 NIL 1009627 NIL) (-438 1006331 1006513 1006541 "FVC" 1006832 T FVC (NIL) -9 NIL 1007015 NIL) (-437 1005973 1006128 1006209 "FUNCTION" 1006283 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003744 1004295 1004761 "FT" 1005527 T FT (NIL) -8 NIL NIL NIL) (-435 1002562 1003045 1003248 "FTEM" 1003561 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000818 1001107 1001511 "FSUPFACT" 1002253 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999215 999504 999836 "FST" 1000506 T FST (NIL) -8 NIL NIL NIL) (-432 998386 998492 998687 "FSRED" 999097 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 997065 997320 997674 "FSPRMELT" 998101 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994150 994588 995087 "FSPECF" 996628 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976210 984653 984693 "FS" 988541 NIL FS (NIL T) -9 NIL 990830 NIL) (-428 964860 967850 971906 "FS-" 972203 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964374 964428 964605 "FSINT" 964801 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962701 963367 963670 "FSERIES" 964153 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961715 961831 962062 "FSCINT" 962581 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957949 960659 960700 "FSAGG" 961070 NIL FSAGG (NIL T) -9 NIL 961329 NIL) (-423 955711 956312 957108 "FSAGG-" 957203 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954753 954896 955123 "FSAGG2" 955564 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952408 952687 953241 "FS2UPS" 954471 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951990 952033 952188 "FS2" 952359 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950847 951018 951327 "FS2EXPXP" 951815 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950273 950388 950540 "FRUTIL" 950727 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941728 945768 947126 "FR" 948947 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936803 939446 939486 "FRNAALG" 940882 NIL FRNAALG (NIL T) -9 NIL 941489 NIL) (-415 932481 933552 934827 "FRNAALG-" 935577 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 932119 932162 932289 "FRNAAF2" 932432 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930526 930973 931268 "FRMOD" 931931 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928305 928909 929226 "FRIDEAL" 930317 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927500 927587 927876 "FRIDEAL2" 928212 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926633 927047 927088 "FRETRCT" 927093 NIL FRETRCT (NIL T) -9 NIL 927269 NIL) (-409 925745 925976 926327 "FRETRCT-" 926332 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922957 924133 924192 "FRAMALG" 925074 NIL FRAMALG (NIL T T) -9 NIL 925366 NIL) (-407 921091 921546 922176 "FRAMALG-" 922399 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 915049 920566 920842 "FRAC" 920847 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914685 914742 914849 "FRAC2" 914986 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914321 914378 914485 "FR2" 914622 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908994 911846 911874 "FPS" 912993 T FPS (NIL) -9 NIL 913550 NIL) (-402 908443 908552 908716 "FPS-" 908862 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905897 907532 907560 "FPC" 907785 T FPC (NIL) -9 NIL 907927 NIL) (-400 905690 905730 905827 "FPC-" 905832 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904568 905178 905219 "FPATMAB" 905224 NIL FPATMAB (NIL T) -9 NIL 905376 NIL) (-398 902268 902744 903170 "FPARFRAC" 904205 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897662 898160 898842 "FORTRAN" 901700 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895378 895878 896417 "FORT" 897143 T FORT (NIL) -7 NIL NIL NIL) (-395 893054 893616 893644 "FORTFN" 894704 T FORTFN (NIL) -9 NIL 895328 NIL) (-394 892818 892868 892896 "FORTCAT" 892955 T FORTCAT (NIL) -9 NIL 893017 NIL) (-393 890951 891434 891824 "FORMULA" 892448 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890739 890769 890838 "FORMULA1" 890915 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890262 890314 890487 "FORDER" 890681 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889358 889522 889715 "FOP" 890089 T FOP (NIL) -7 NIL NIL NIL) (-389 887966 888638 888812 "FNLA" 889240 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886721 887110 887138 "FNCAT" 887598 T FNCAT (NIL) -9 NIL 887858 NIL) (-387 886287 886680 886708 "FNAME" 886713 T FNAME (NIL) -8 NIL NIL NIL) (-386 884950 885879 885907 "FMTC" 885912 T FMTC (NIL) -9 NIL 885948 NIL) (-385 881312 882473 883102 "FMONOID" 884354 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880531 881054 881203 "FM" 881208 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877955 878601 878629 "FMFUN" 879773 T FMFUN (NIL) -9 NIL 880481 NIL) (-382 877224 877405 877433 "FMC" 877723 T FMC (NIL) -9 NIL 877905 NIL) (-381 874418 875252 875306 "FMCAT" 876501 NIL FMCAT (NIL T T) -9 NIL 876996 NIL) (-380 873311 874184 874284 "FM1" 874363 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 871085 871501 871995 "FLOATRP" 872862 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864709 868814 869435 "FLOAT" 870484 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862147 862647 863225 "FLOATCP" 864176 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860956 861760 861801 "FLINEXP" 861806 NIL FLINEXP (NIL T) -9 NIL 861899 NIL) (-375 860110 860345 860673 "FLINEXP-" 860678 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859186 859330 859554 "FLASORT" 859962 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856403 857245 857297 "FLALG" 858524 NIL FLALG (NIL T T) -9 NIL 858991 NIL) (-372 850187 853889 853930 "FLAGG" 855192 NIL FLAGG (NIL T) -9 NIL 855844 NIL) (-371 848913 849252 849742 "FLAGG-" 849747 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847955 848098 848325 "FLAGG2" 848766 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844930 845904 845963 "FINRALG" 847091 NIL FINRALG (NIL T T) -9 NIL 847599 NIL) (-368 844090 844319 844658 "FINRALG-" 844663 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843496 843709 843737 "FINITE" 843933 T FINITE (NIL) -9 NIL 844040 NIL) (-366 835954 838115 838155 "FINAALG" 841822 NIL FINAALG (NIL T) -9 NIL 843275 NIL) (-365 831295 832336 833480 "FINAALG-" 834859 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830690 831050 831153 "FILE" 831225 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829374 829686 829740 "FILECAT" 830424 NIL FILECAT (NIL T T) -9 NIL 830640 NIL) (-362 827242 828736 828764 "FIELD" 828804 T FIELD (NIL) -9 NIL 828884 NIL) (-361 825862 826247 826758 "FIELD-" 826763 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823740 824497 824844 "FGROUP" 825548 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822830 822994 823214 "FGLMICPK" 823572 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818697 822755 822812 "FFX" 822817 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818298 818359 818494 "FFSLPE" 818630 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814291 815070 815866 "FFPOLY" 817534 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813795 813831 814040 "FFPOLY2" 814249 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809681 813714 813777 "FFP" 813782 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 805114 809592 809656 "FF" 809661 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800275 804457 804647 "FFNBX" 804968 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795249 799410 799668 "FFNBP" 800129 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789917 794533 794744 "FFNB" 795082 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788749 788947 789262 "FFINTBAS" 789714 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784977 787156 787184 "FFIELDC" 787804 T FFIELDC (NIL) -9 NIL 788180 NIL) (-347 783640 784010 784507 "FFIELDC-" 784512 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783210 783255 783379 "FFHOM" 783582 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780908 781392 781909 "FFF" 782725 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776561 780650 780751 "FFCGX" 780851 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772228 776293 776400 "FFCGP" 776504 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767446 771955 772063 "FFCG" 772164 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749279 758317 758403 "FFCAT" 763568 NIL FFCAT (NIL T T T) -9 NIL 765019 NIL) (-340 744477 745524 746838 "FFCAT-" 748068 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743888 743931 744166 "FFCAT2" 744428 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 733100 736860 738080 "FEXPR" 742740 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 732100 732535 732576 "FEVALAB" 732660 NIL FEVALAB (NIL T) -9 NIL 732921 NIL) (-336 731259 731469 731807 "FEVALAB-" 731812 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729852 730642 730845 "FDIV" 731158 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726918 727633 727748 "FDIVCAT" 729316 NIL FDIVCAT (NIL T T T T) -9 NIL 729753 NIL) (-333 726680 726707 726877 "FDIVCAT-" 726882 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725900 725987 726264 "FDIV2" 726587 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724586 724845 725134 "FCPAK1" 725631 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723714 724086 724227 "FCOMP" 724477 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707451 710864 714402 "FC" 720196 T FC (NIL) -8 NIL NIL NIL) (-328 700030 704015 704055 "FAXF" 705857 NIL FAXF (NIL T) -9 NIL 706549 NIL) (-327 697309 697964 698789 "FAXF-" 699254 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692409 696685 696861 "FARRAY" 697166 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687662 689694 689747 "FAMR" 690770 NIL FAMR (NIL T T) -9 NIL 691230 NIL) (-324 686552 686854 687289 "FAMR-" 687294 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685748 686474 686527 "FAMONOID" 686532 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683560 684244 684297 "FAMONC" 685238 NIL FAMONC (NIL T T) -9 NIL 685624 NIL) (-321 682252 683314 683451 "FAGROUP" 683456 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 680047 680366 680769 "FACUTIL" 681933 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679146 679331 679553 "FACTFUNC" 679857 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671551 678397 678609 "EXPUPXS" 679002 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 669034 669574 670160 "EXPRTUBE" 670985 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665228 665820 666557 "EXPRODE" 668373 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650602 663883 664311 "EXPR" 664832 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 645009 645596 646409 "EXPR2UPS" 649900 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644645 644702 644809 "EXPR2" 644946 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 636050 643777 644074 "EXPEXPAN" 644482 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635877 636007 636036 "EXIT" 636041 T EXIT (NIL) -8 NIL NIL NIL) (-310 635384 635601 635692 "EXITAST" 635806 T EXITAST (NIL) -8 NIL NIL NIL) (-309 635011 635073 635186 "EVALCYC" 635316 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634552 634670 634711 "EVALAB" 634881 NIL EVALAB (NIL T) -9 NIL 634985 NIL) (-307 634033 634155 634376 "EVALAB-" 634381 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631501 632769 632797 "EUCDOM" 633352 T EUCDOM (NIL) -9 NIL 633702 NIL) (-305 629906 630348 630938 "EUCDOM-" 630943 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617446 620204 622954 "ESTOOLS" 627176 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 617078 617135 617244 "ESTOOLS2" 617383 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616829 616871 616951 "ESTOOLS1" 617030 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610734 612462 612490 "ES" 615258 T ES (NIL) -9 NIL 616667 NIL) (-300 605682 606968 608785 "ES-" 608949 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 602057 602817 603597 "ESCONT" 604922 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601802 601834 601916 "ESCONT1" 602019 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601477 601527 601627 "ES2" 601746 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 601107 601165 601274 "ES1" 601413 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600323 600452 600628 "ERROR" 600951 T ERROR (NIL) -7 NIL NIL NIL) (-294 593826 600182 600273 "EQTBL" 600278 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586383 589140 590589 "EQ" 592410 NIL -3367 (NIL T) -8 NIL NIL NIL) (-292 586015 586072 586181 "EQ2" 586320 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581307 582353 583446 "EP" 584954 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579889 580190 580507 "ENV" 581010 T ENV (NIL) -8 NIL NIL NIL) (-289 579068 579588 579616 "ENTIRER" 579621 T ENTIRER (NIL) -9 NIL 579667 NIL) (-288 575570 577023 577393 "EMR" 578867 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574714 574899 574953 "ELTAGG" 575333 NIL ELTAGG (NIL T T) -9 NIL 575544 NIL) (-286 574433 574495 574636 "ELTAGG-" 574641 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574222 574251 574305 "ELTAB" 574389 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573348 573494 573693 "ELFUTS" 574073 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 573090 573146 573174 "ELEMFUN" 573279 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572960 572981 573049 "ELEMFUN-" 573054 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567851 571060 571101 "ELAGG" 572041 NIL ELAGG (NIL T) -9 NIL 572504 NIL) (-280 566136 566570 567233 "ELAGG-" 567238 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564793 565073 565368 "ELABEXPR" 565861 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557659 559460 560287 "EFUPXS" 564069 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 551109 552910 553720 "EFULS" 556935 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548531 548889 549368 "EFSTRUC" 550741 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537603 539168 540728 "EF" 547046 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536704 537088 537237 "EAB" 537474 T EAB (NIL) -8 NIL NIL NIL) (-273 535913 536663 536691 "E04UCFA" 536696 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 535122 535872 535900 "E04NAFA" 535905 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534331 535081 535109 "E04MBFA" 535114 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533540 534290 534318 "E04JAFA" 534323 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532751 533499 533527 "E04GCFA" 533532 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531962 532710 532738 "E04FDFA" 532743 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531171 531921 531949 "E04DGFA" 531954 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525349 526696 528060 "E04AGNT" 529827 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 524055 524535 524575 "DVARCAT" 525050 NIL DVARCAT (NIL T) -9 NIL 525249 NIL) (-264 523259 523471 523785 "DVARCAT-" 523790 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516159 523058 523187 "DSMP" 523192 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510969 512104 513172 "DROPT" 515111 T DROPT (NIL) -8 NIL NIL NIL) (-261 510634 510693 510791 "DROPT1" 510904 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505749 506875 508012 "DROPT0" 509517 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 504094 504419 504805 "DRAWPT" 505383 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498681 499604 500683 "DRAW" 503068 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498314 498367 498485 "DRAWHACK" 498622 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 497045 497314 497605 "DRAWCX" 498043 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496561 496629 496780 "DRAWCURV" 496971 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 487032 488991 491106 "DRAWCFUN" 494466 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483845 485727 485768 "DQAGG" 486397 NIL DQAGG (NIL T) -9 NIL 486670 NIL) (-252 472124 478823 478906 "DPOLCAT" 480758 NIL DPOLCAT (NIL T T T T) -9 NIL 481303 NIL) (-251 466963 468309 470267 "DPOLCAT-" 470272 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 460118 466824 466922 "DPMO" 466927 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453176 459898 460065 "DPMM" 460070 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452840 453095 453143 "DOMCTOR" 453148 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452135 452362 452499 "DOMAIN" 452723 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445886 451770 451922 "DMP" 452036 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445486 445542 445686 "DLP" 445824 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439356 444813 445003 "DLIST" 445328 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436200 438209 438250 "DLAGG" 438800 NIL DLAGG (NIL T) -9 NIL 439030 NIL) (-242 435013 435643 435671 "DIVRING" 435763 T DIVRING (NIL) -9 NIL 435846 NIL) (-241 434250 434440 434740 "DIVRING-" 434745 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432352 432709 433115 "DISPLAY" 433864 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426294 432266 432329 "DIRPROD" 432334 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425142 425345 425610 "DIRPROD2" 426087 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414405 420357 420410 "DIRPCAT" 420820 NIL DIRPCAT (NIL NIL T) -9 NIL 421660 NIL) (-236 411731 412373 413254 "DIRPCAT-" 413591 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 411018 411178 411364 "DIOSP" 411565 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407720 409930 409971 "DIOPS" 410405 NIL DIOPS (NIL T) -9 NIL 410634 NIL) (-233 407269 407383 407574 "DIOPS-" 407579 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406161 406755 406783 "DIFRING" 406970 T DIFRING (NIL) -9 NIL 407080 NIL) (-231 405807 405884 406036 "DIFRING-" 406041 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403612 404850 404891 "DIFEXT" 405254 NIL DIFEXT (NIL T) -9 NIL 405548 NIL) (-229 401897 402325 402991 "DIFEXT-" 402996 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399219 401429 401470 "DIAGG" 401475 NIL DIAGG (NIL T) -9 NIL 401495 NIL) (-227 398603 398760 399012 "DIAGG-" 399017 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 394068 397562 397839 "DHMATRIX" 398372 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389680 390589 391599 "DFSFUN" 393078 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384796 388611 388923 "DFLOAT" 389388 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 383024 383305 383701 "DFINTTLS" 384504 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 380089 381045 381445 "DERHAM" 382690 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377938 379864 379953 "DEQUEUE" 380033 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377153 377286 377482 "DEGRED" 377800 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373548 374293 375146 "DEFINTRF" 376381 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 371075 371544 372143 "DEFINTEF" 373067 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370452 370695 370810 "DEFAST" 370980 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364494 370049 370197 "DECIMAL" 370324 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 362006 362464 362970 "DDFACT" 364038 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361602 361645 361796 "DBLRESP" 361957 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359501 359835 360195 "DBASE" 361369 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358770 358981 359127 "DATAARY" 359400 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357903 358729 358757 "D03FAFA" 358762 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 357037 357862 357890 "D03EEFA" 357895 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354987 355453 355942 "D03AGNT" 356568 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354303 354946 354974 "D02EJFA" 354979 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353619 354262 354290 "D02CJFA" 354295 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352935 353578 353606 "D02BHFA" 353611 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352251 352894 352922 "D02BBFA" 352927 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345449 347037 348643 "D02AGNT" 350665 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343218 343740 344286 "D01WGTS" 344923 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342313 343177 343205 "D01TRNS" 343210 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341408 342272 342300 "D01GBFA" 342305 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340503 341367 341395 "D01FCFA" 341400 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339598 340462 340490 "D01ASFA" 340495 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338693 339557 339585 "D01AQFA" 339590 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337788 338652 338680 "D01APFA" 338685 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336883 337747 337775 "D01ANFA" 337780 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335978 336842 336870 "D01AMFA" 336875 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 335073 335937 335965 "D01ALFA" 335970 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334168 335032 335060 "D01AKFA" 335065 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333263 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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))
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(-543))) ((*1 *1 *1) (-12 (-5 *1 (-885 *2)) (-4 *2 (-1090)))) @@ -973,38 +754,54 @@ ((*1 *1 *1) (-12 (-5 *1 (-1130 *2 *3)) (-4 *2 (-13 (-1090) (-34))) (-4 *3 (-13 (-1090) (-34)))))) -(((*1 *2 *3) - (-12 (-4 *4 (-787)) (-4 *5 (-844)) (-4 *6 (-306)) (-5 *2 (-417 *3)) - (-5 *1 (-736 *4 *5 *6 *3)) (-4 *3 (-942 *6 *4 *5))))) -(((*1 *2 *1 *1) (-12 (-5 *2 (-561)) (-5 *1 (-378))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1271 *3 *4)) (-4 *3 (-844)) (-4 *4 (-1042)) + (-5 *2 (-2 (|:| |k| (-813 *3)) (|:| |c| *4)))))) +(((*1 *2 *3 *4 *4 *5 *3 *6) + (|partial| -12 (-5 *4 (-607 *3)) (-5 *5 (-638 *3)) (-5 *6 (-1162 *3)) + (-4 *3 (-13 (-429 *7) (-27) (-1190))) + (-4 *7 (-13 (-450) (-1031 (-561)) (-844) (-146) (-634 (-561)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-638 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-557 *7 *3 *8)) (-4 *8 (-1090)))) + ((*1 *2 *3 *4 *4 *5 *4 *3 *6) + (|partial| -12 (-5 *4 (-607 *3)) (-5 *5 (-638 *3)) + (-5 *6 (-406 (-1162 *3))) (-4 *3 (-13 (-429 *7) 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(-224)))) + (-5 *2 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))) + (-5 *1 (-191))))) +(((*1 *2 *1) + (-12 (-5 *2 (-638 (-561))) (-5 *1 (-997 *3)) (-14 *3 (-561))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-609 *2) (-171))) (-5 *2 (-885 *4)) (-5 *1 (-169 *4 *5 *3)) (-4 *4 (-1090)) (-4 *3 (-165 *5)))) @@ -1013,13 +810,13 @@ (-5 *2 (-638 (-1084 (-837 (-224))))) (-5 *1 (-304)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-856)) (-5 *3 (-561)) (-5 *1 (-393)))) ((*1 *1 *2) - (-12 (-5 *2 (-1253 *3)) (-4 *3 (-171)) (-4 *1 (-408 *3 *4)) - (-4 *4 (-1229 *3)))) + (-12 (-5 *2 (-1254 *3)) (-4 *3 (-171)) (-4 *1 (-408 *3 *4)) + (-4 *4 (-1230 *3)))) ((*1 *2 *1) - (-12 (-4 *1 (-408 *3 *4)) (-4 *3 (-171)) (-4 *4 (-1229 *3)) - (-5 *2 (-1253 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 *3)) (-4 *3 (-171)) (-4 *1 (-416 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-416 *3)) (-4 *3 (-171)) (-5 *2 (-1253 *3)))) + (-12 (-4 *1 (-408 *3 *4)) (-4 *3 (-171)) (-4 *4 (-1230 *3)) + (-5 *2 (-1254 *3)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 *3)) (-4 *3 (-171)) (-4 *1 (-416 *3)))) + ((*1 *2 *1) (-12 (-4 *1 (-416 *3)) (-4 *3 (-171)) (-5 *2 (-1254 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-417 *1)) (-4 *1 (-429 *3)) (-4 *3 (-553)) (-4 *3 (-844)))) @@ -1030,16 +827,16 @@ ((*1 *2 *1) (-12 (-4 *1 (-609 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) (-12 (-4 *1 (-613 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) - (-12 (-4 *3 (-171)) (-4 *1 (-718 *3 *2)) (-4 *2 (-1229 *3)))) + (-12 (-4 *3 (-171)) (-4 *1 (-718 *3 *2)) (-4 *2 (-1230 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-638 (-885 *3))) (-5 *1 (-885 *3)) (-4 *3 (-1090)))) ((*1 *1 *2) (-12 (-5 *2 (-945 *3)) (-4 *3 (-1042)) (-4 *1 (-1056 *3 *4 *5)) (-4 *5 (-609 (-1166))) (-4 *4 (-787)) (-4 *5 (-844)))) ((*1 *1 *2) - (-4007 + (-4050 (-12 (-5 *2 (-945 (-561))) (-4 *1 (-1056 *3 *4 *5)) - (-12 (-2159 (-4 *3 (-38 (-406 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(-14 *5 (-638 (-1166))) - (-5 *2 (-774 *4 (-858 *6))) (-5 *1 (-1279 *4 *5 *6)) + (-5 *2 (-774 *4 (-858 *6))) (-5 *1 (-1280 *4 *5 *6)) (-14 *6 (-638 (-1166))))) ((*1 *2 *3) (-12 (-5 *3 (-945 *4)) (-4 *4 (-13 (-842) (-306) (-146) (-1015))) - (-5 *2 (-945 (-1017 (-406 *4)))) (-5 *1 (-1279 *4 *5 *6)) + (-5 *2 (-945 (-1017 (-406 *4)))) (-5 *1 (-1280 *4 *5 *6)) (-14 *5 (-638 (-1166))) (-14 *6 (-638 (-1166))))) ((*1 *2 *3) (-12 (-5 *3 (-774 *4 (-858 *6))) (-4 *4 (-13 (-842) (-306) (-146) (-1015))) (-14 *6 (-638 (-1166))) - (-5 *2 (-945 (-1017 (-406 *4)))) (-5 *1 (-1279 *4 *5 *6)) + (-5 *2 (-945 (-1017 (-406 *4)))) (-5 *1 (-1280 *4 *5 *6)) (-14 *5 (-638 (-1166))))) ((*1 *2 *3) (-12 (-5 *3 (-1162 *4)) (-4 *4 (-13 (-842) (-306) (-146) (-1015))) - (-5 *2 (-1162 (-1017 (-406 *4)))) (-5 *1 (-1279 *4 *5 *6)) + (-5 *2 (-1162 (-1017 (-406 *4)))) (-5 *1 (-1280 *4 *5 *6)) (-14 *5 (-638 (-1166))) (-14 *6 (-638 (-1166))))) ((*1 *2 *3) (-12 (-5 *3 (-1136 *4 (-529 (-858 *6)) (-858 *6) (-774 *4 (-858 *6)))) 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(-5 *2 (-1254)) (-5 *1 (-259)))) + (-12 (-5 *3 (-638 (-936 (-224)))) (-5 *2 (-1255)) (-5 *1 (-259)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-638 (-936 (-224)))) (-5 *4 (-638 (-262))) - (-5 *2 (-1254)) (-5 *1 (-259)))) + (-5 *2 (-1255)) (-5 *1 (-259)))) ((*1 *2 *3 *3 *3) - (-12 (-5 *3 (-638 (-224))) (-5 *2 (-1255)) (-5 *1 (-259)))) + (-12 (-5 *3 (-638 (-224))) (-5 *2 (-1256)) (-5 *1 (-259)))) ((*1 *2 *3 *3 *3 *4) - (-12 (-5 *3 (-638 (-224))) (-5 *4 (-638 (-262))) (-5 *2 (-1255)) + (-12 (-5 *3 (-638 (-224))) (-5 *4 (-638 (-262))) (-5 *2 (-1256)) (-5 *1 (-259))))) (((*1 *1 *2 *1) (-12 (-4 *1 (-21)) (-5 *2 (-561)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-765)))) @@ -1605,10 +1363,10 @@ ((*1 *1 *2 *1) (-12 (-5 *1 (-385 *2)) (-4 *2 (-1090)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-638 (-1166))) (-4 *4 (-171)) - (-4 *6 (-237 (-3498 *3) (-765))) + (-4 *6 (-237 (-3548 *3) (-765))) (-14 *7 - (-1 (-112) (-2 (|:| -2413 *5) (|:| -4196 *6)) - (-2 (|:| -2413 *5) (|:| -4196 *6)))) + (-1 (-112) (-2 (|:| -2442 *5) (|:| -4181 *6)) + (-2 (|:| -2442 *5) (|:| -4181 *6)))) (-5 *1 (-459 *3 *4 *5 *6 *7 *2)) (-4 *5 (-844)) (-4 *2 (-942 *4 *6 (-858 *3))))) ((*1 *1 *1 *2) @@ -1619,7 +1377,7 @@ (-12 (-4 *2 (-362)) (-4 *3 (-787)) (-4 *4 (-844)) (-5 *1 (-502 *2 *3 *4 *5)) (-4 *5 (-942 *2 *3 *4)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-1253 *3)) (-4 *3 (-348)) (-5 *1 (-526 *3)))) + (-12 (-5 *2 (-1254 *3)) (-4 *3 (-348)) (-5 *1 (-526 *3)))) ((*1 *1 *1 *1) (-5 *1 (-534))) ((*1 *1 *1 *2) (-12 (-5 *2 (-561)) (-5 *1 (-592 *3)) (-4 *3 (-1042)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-592 *2)) (-4 *2 (-1042)))) @@ -1654,7 +1412,7 @@ ((*1 *1 *1 *1) (-5 *1 (-856))) ((*1 *1 *1 *1) (-12 (-5 *1 (-885 *2)) (-4 *2 (-1090)))) ((*1 *2 *3 *2) - (-12 (-5 *2 (-1253 *4)) (-4 *4 (-1229 *3)) (-4 *3 (-553)) + (-12 (-5 *2 (-1254 *4)) (-4 *4 (-1230 *3)) (-4 *3 (-553)) (-5 *1 (-962 *3 *4)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1048 *2)) (-4 *2 (-1049)))) ((*1 *1 *1 *1) (-4 *1 (-1102))) @@ -1676,21 +1434,17 @@ ((*1 *2 *3 *2) (-12 (-5 *2 (-936 (-224))) (-5 *3 (-224)) (-5 *1 (-1201)))) ((*1 *1 *1 *2) - (-12 (-4 *1 (-1251 *2)) (-4 *2 (-1205)) (-4 *2 (-720)))) + (-12 (-4 *1 (-1252 *2)) (-4 *2 (-1205)) (-4 *2 (-720)))) ((*1 *1 *2 *1) - (-12 (-4 *1 (-1251 *2)) (-4 *2 (-1205)) (-4 *2 (-720)))) + (-12 (-4 *1 (-1252 *2)) (-4 *2 (-1205)) (-4 *2 (-720)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-561)) (-4 *1 (-1251 *3)) (-4 *3 (-1205)) (-4 *3 (-21)))) + (-12 (-5 *2 (-561)) (-4 *1 (-1252 *3)) (-4 *3 (-1205)) (-4 *3 (-21)))) ((*1 *1 *2 *1) - (-12 (-4 *1 (-1270 *2 *3)) (-4 *2 (-844)) (-4 *3 (-1042)))) + (-12 (-4 *1 (-1271 *2 *3)) (-4 *2 (-844)) (-4 *3 (-1042)))) ((*1 *1 *1 *2) - (-12 (-4 *1 (-1270 *3 *2)) (-4 *3 (-844)) (-4 *2 (-1042)))) + (-12 (-4 *1 (-1271 *3 *2)) (-4 *3 (-844)) (-4 *2 (-1042)))) ((*1 *1 *1 *2) - (-12 (-5 *1 (-1276 *2 *3)) (-4 *2 (-1042)) (-4 *3 (-840))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-638 (-2 (|:| |totdeg| (-765)) (|:| -4158 *3)))) - (-5 *4 (-765)) (-4 *3 (-942 *5 *6 *7)) (-4 *5 (-450)) (-4 *6 (-787)) - (-4 *7 (-844)) (-5 *1 (-447 *5 *6 *7 *3))))) + (-12 (-5 *1 (-1277 *2 *3)) (-4 *2 (-1042)) (-4 *3 (-840))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1042)) (-4 *4 (-786)))) @@ -1744,8 +1498,8 @@ (-4 *6 (-844)) (-5 *2 (-315 *6)) (-5 *1 (-313 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-335 *5 *6 *7 *8)) (-4 *5 (-362)) - (-4 *6 (-1229 *5)) (-4 *7 (-1229 (-406 *6))) (-4 *8 (-341 *5 *6 *7)) - (-4 *9 (-362)) (-4 *10 (-1229 *9)) (-4 *11 (-1229 (-406 *10))) + (-4 *6 (-1230 *5)) (-4 *7 (-1230 (-406 *6))) (-4 *8 (-341 *5 *6 *7)) + (-4 *9 (-362)) (-4 *10 (-1230 *9)) (-4 *11 (-1230 (-406 *10))) (-5 *2 (-335 *9 *10 *11 *12)) (-5 *1 (-332 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-341 *9 *10 *11)))) @@ -1753,9 +1507,9 @@ (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-337 *3)) (-4 *3 (-1090)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1209)) (-4 *8 (-1209)) - (-4 *6 (-1229 *5)) (-4 *7 (-1229 (-406 *6))) (-4 *9 (-1229 *8)) + (-4 *6 (-1230 *5)) (-4 *7 (-1230 (-406 *6))) (-4 *9 (-1230 *8)) (-4 *2 (-341 *8 *9 *10)) (-5 *1 (-339 *5 *6 *7 *4 *8 *9 *10 *2)) - (-4 *4 (-341 *5 *6 *7)) (-4 *10 (-1229 (-406 *9))))) + (-4 *4 (-341 *5 *6 *7)) (-4 *10 (-1230 (-406 *9))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1205)) (-4 *6 (-1205)) (-4 *2 (-372 *6)) (-5 *1 (-370 *5 *4 *6 *2)) (-4 *4 (-372 *5)))) @@ -1770,9 +1524,9 @@ (-4 *6 (-553)) (-5 *2 (-406 *6)) (-5 *1 (-405 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-412 *5 *6 *7 *8)) (-4 *5 (-306)) - (-4 *6 (-985 *5)) (-4 *7 (-1229 *6)) + (-4 *6 (-985 *5)) (-4 *7 (-1230 *6)) (-4 *8 (-13 (-408 *6 *7) (-1031 *6))) (-4 *9 (-306)) - (-4 *10 (-985 *9)) (-4 *11 (-1229 *10)) + (-4 *10 (-985 *9)) (-4 *11 (-1230 *10)) (-5 *2 (-412 *9 *10 *11 *12)) (-5 *1 (-411 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-13 (-408 *10 *11) (-1031 *10))))) @@ -1798,9 +1552,9 @@ (-4 *6 (-362)) (-5 *2 (-582 *6)) (-5 *1 (-581 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -2246 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -3413 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-362)) (-4 *6 (-362)) - (-5 *2 (-2 (|:| -2246 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -3413 *6) (|:| |coeff| *6))) (-5 *1 (-581 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -1857,9 +1611,9 @@ (-4 *4 (-680 *5 *6 *7)) (-4 *9 (-372 *8)) (-4 *10 (-372 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-553)) (-4 *7 (-553)) - (-4 *6 (-1229 *5)) (-4 *2 (-1229 (-406 *8))) - (-5 *1 (-703 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1229 (-406 *6))) - (-4 *8 (-1229 *7)))) + (-4 *6 (-1230 *5)) (-4 *2 (-1230 (-406 *8))) + (-5 *1 (-703 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1230 (-406 *6))) + (-4 *8 (-1230 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1042)) (-4 *9 (-1042)) (-4 *5 (-844)) (-4 *6 (-787)) (-4 *2 (-942 *9 *7 *5)) @@ -1919,7 +1673,7 @@ (-4 *8 (-1042)) (-4 *6 (-787)) (-4 *2 (-13 (-1090) - (-10 -8 (-15 -1813 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-765)))))) + (-10 -8 (-15 -1810 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ 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(-12 (-5 *1 (-330 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-338 *2 *3 *4)) (-14 *2 (-638 (-1166))) @@ -2410,62 +2394,36 @@ (-12 (-5 *2 (-1146 *3)) (-4 *3 (-38 (-406 (-561)))) (-5 *1 (-1152 *3)))) ((*1 *1 *1) (-4 *1 (-1193)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-406 (-945 *5))) (-5 *4 (-1166)) - (-4 *5 (-13 (-306) (-844) (-146))) (-5 *2 (-638 (-293 (-315 *5)))) - (-5 *1 (-1119 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-406 (-945 *4))) (-4 *4 (-13 (-306) (-844) (-146))) - (-5 *2 (-638 (-293 (-315 *4)))) (-5 *1 (-1119 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-293 (-406 (-945 *5)))) (-5 *4 (-1166)) - (-4 *5 (-13 (-306) (-844) (-146))) (-5 *2 (-638 (-293 (-315 *5)))) - (-5 *1 (-1119 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-293 (-406 (-945 *4)))) - (-4 *4 (-13 (-306) (-844) (-146))) (-5 *2 (-638 (-293 (-315 *4)))) - (-5 *1 (-1119 *4)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-638 (-406 (-945 *5)))) (-5 *4 (-638 (-1166))) - (-4 *5 (-13 (-306) (-844) (-146))) - (-5 *2 (-638 (-638 (-293 (-315 *5))))) (-5 *1 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(-844)) (-4 *4 (-1042)) + (-5 *2 (-813 *3)))) + ((*1 *2 *1) + (-12 (-4 *2 (-840)) (-5 *1 (-1277 *3 *2)) (-4 *3 (-1042))))) +(((*1 *1) (-5 *1 (-156))) + ((*1 *2 *1) (-12 (-4 *1 (-1037 *2)) (-4 *2 (-23))))) +(((*1 *2 *2 *1) + (-12 (-4 *1 (-1198 *3 *4 *5 *2)) (-4 *3 (-553)) (-4 *4 (-787)) + (-4 *5 (-844)) (-4 *2 (-1056 *3 *4 *5))))) (((*1 *2 *1) (-12 (-5 *2 (-1115 (-561) (-607 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) - (-12 (-4 *3 (-985 *2)) (-4 *4 (-1229 *3)) (-4 *2 (-306)) + (-12 (-4 *3 (-985 *2)) (-4 *4 (-1230 *3)) (-4 *2 (-306)) (-5 *1 (-412 *2 *3 *4 *5)) (-4 *5 (-13 (-408 *3 *4) (-1031 *3))))) ((*1 *2 *1) (-12 (-4 *3 (-553)) (-4 *3 (-844)) (-5 *2 (-1115 *3 (-607 *1))) @@ -2478,23 +2436,22 @@ (-12 (-4 *4 (-171)) (-4 *2 (|SubsetCategory| (-720) *4)) (-5 *1 (-655 *3 *4 *2)) (-4 *3 (-711 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-985 *2)) (-4 *2 (-553))))) -(((*1 *2 *1) - (-12 (-5 *2 (-638 (-2 (|:| |k| (-1166)) (|:| |c| (-1275 *3))))) - (-5 *1 (-1275 *3)) (-4 *3 (-1042)))) - ((*1 *2 *1) - (-12 (-5 *2 (-638 (-2 (|:| |k| *3) (|:| |c| (-1277 *3 *4))))) - (-5 *1 (-1277 *3 *4)) (-4 *3 (-844)) (-4 *4 (-1042))))) -(((*1 *1) (-5 *1 (-436)))) -(((*1 *1 *1 *1) (-5 *1 (-112))) ((*1 *1 *1 *1) (-4 *1 (-123)))) +(((*1 *2 *1) (-12 (-5 *2 (-1125)) (-5 *1 (-515))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1166)) + (-5 *2 + (-2 (|:| |zeros| (-1146 (-224))) (|:| |ones| (-1146 (-224))) + (|:| |singularities| (-1146 (-224))))) + (-5 *1 (-105))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-844) (-553))) (-5 *1 (-275 *3 *2)) (-4 *2 (-13 (-429 *3) (-995))))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-406 (-561)))) (-4 *4 (-1244 *3)) - (-5 *1 (-277 *3 *4 *2)) (-4 *2 (-1215 *3 *4)))) + (-12 (-4 *3 (-38 (-406 (-561)))) (-4 *4 (-1245 *3)) + (-5 *1 (-277 *3 *4 *2)) (-4 *2 (-1216 *3 *4)))) ((*1 *2 *2) - (-12 (-4 *3 (-38 (-406 (-561)))) (-4 *4 (-1213 *3)) - (-5 *1 (-278 *3 *4 *2 *5)) (-4 *2 (-1236 *3 *4)) (-4 *5 (-976 *4)))) + (-12 (-4 *3 (-38 (-406 (-561)))) (-4 *4 (-1214 *3)) + (-5 *1 (-278 *3 *4 *2 *5)) (-4 *2 (-1237 *3 *4)) (-4 *5 (-976 *4)))) ((*1 *1 *2) (-12 (-5 *1 (-330 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-338 *2 *3 *4)) (-14 *2 (-638 (-1166))) @@ -2506,44 +2463,59 @@ (-12 (-5 *2 (-1146 *3)) (-4 *3 (-38 (-406 (-561)))) (-5 *1 (-1152 *3)))) ((*1 *1 *1) (-4 *1 (-1193)))) -(((*1 *1 *1) (-4 *1 (-1134)))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-682 *7)) (-5 *3 (-638 *7)) (-4 *7 (-942 *4 *6 *5)) - (-4 *4 (-13 (-306) (-146))) (-4 *5 (-13 (-844) (-609 (-1166)))) - (-4 *6 (-787)) (-5 *1 (-917 *4 *5 *6 *7))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-133))))) -(((*1 *2) - (-12 (-4 *3 (-553)) (-5 *2 (-638 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-416 *3))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1148)) (-5 *2 (-1258)) (-5 *1 (-1255))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-1165)) (-5 *1 (-329))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-1229 *2)) (-4 *2 (-1042)) (-4 *2 (-553))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-638 *1)) (-4 *1 (-1056 *4 *5 *6)) (-4 *4 (-1042)) - (-4 *5 (-787)) (-4 *6 (-844)) (-5 *2 (-112)))) - ((*1 *2 *1 *1) - (-12 (-4 *1 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(-315 (-224))) + (|:| |abserr| (-224)) (|:| |relerr| (-224)))) + (-5 *2 (-1028))))) +(((*1 *2 *1) (-12 (-4 *1 (-1124 *3)) (-4 *3 (-1042)) (-5 *2 (-112))))) +(((*1 *2 *1) + (-12 (-4 *1 (-165 *3)) (-4 *3 (-171)) (-4 *3 (-543)) (-5 *2 (-112)))) ((*1 *2 *1) - (-12 (-4 *1 (-1198 *3 *4 *5 *6)) (-4 *3 (-553)) (-4 *4 (-787)) - (-4 *5 (-844)) (-4 *6 (-1056 *3 *4 *5)) (-5 *2 (-112)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-1198 *4 *5 *6 *3)) (-4 *4 (-553)) (-4 *5 (-787)) - (-4 *6 (-844)) (-4 *3 (-1056 *4 *5 *6)) (-5 *2 (-112))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-844) (-450))) (-5 *1 (-1196 *3 *2)) - (-4 *2 (-13 (-429 *3) (-1190)))))) + (-12 (-5 *2 (-112)) (-5 *1 (-417 *3)) (-4 *3 (-543)) (-4 *3 (-553)))) + ((*1 *2 *1) (-12 (-4 *1 (-543)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-4 *1 (-791 *3)) (-4 *3 (-171)) (-4 *3 (-543)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-827 *3)) (-4 *3 (-543)) (-4 *3 (-1090)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-837 *3)) (-4 *3 (-543)) (-4 *3 (-1090)))) + ((*1 *2 *1) + (-12 (-4 *1 (-990 *3)) (-4 *3 (-171)) (-4 *3 (-543)) (-5 *2 (-112)))) + ((*1 *2 *3) + (-12 (-5 *2 (-112)) (-5 *1 (-1001 *3)) (-4 *3 (-1031 (-406 (-561))))))) (((*1 *1 *2) (-12 (-5 *2 (-638 *3)) (-4 *3 (-1205)) (-4 *1 (-150 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-638 (-2 (|:| -4196 (-765)) (|:| -2262 *4) (|:| |num| *4)))) - (-4 *4 (-1229 *3)) (-4 *3 (-13 (-362) (-146))) (-5 *1 (-398 *3 *4)))) + (-5 *2 (-638 (-2 (|:| -4181 (-765)) (|:| -2298 *4) (|:| |num| *4)))) + (-4 *4 (-1230 *3)) (-4 *3 (-13 (-362) (-146))) (-5 *1 (-398 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-433)) (|:| -2630 "void"))) (-5 *3 (-638 (-945 (-561)))) (-5 *4 (-112)) (-5 *1 (-436)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-433)) (|:| -2630 "void"))) (-5 *3 (-638 (-1166))) (-5 *4 (-112)) (-5 *1 (-436)))) ((*1 *2 *1) (-12 (-5 *2 (-1146 *3)) (-5 *1 (-596 *3)) (-4 *3 (-1205)))) @@ -2563,24 +2535,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-707 *2 *3 *4)) (-4 *2 (-844)) (-4 *3 (-1090)) (-14 *4 - (-1 (-112) (-2 (|:| -2413 *2) (|:| -4196 *3)) - (-2 (|:| -2413 *2) (|:| -4196 *3)))))) + (-1 (-112) (-2 (|:| -2442 *2) (|:| -4181 *3)) + (-2 (|:| -2442 *2) (|:| -4181 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-504)) (-5 *3 (-1108)) (-5 *1 (-832)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-866 *2 *3)) (-4 *2 (-1205)) (-4 *3 (-1205)))) ((*1 *1 *2) - (-12 (-5 *2 (-638 (-2 (|:| -2252 (-1166)) (|:| -2654 *4)))) + (-12 (-5 *2 (-638 (-2 (|:| -2285 (-1166)) (|:| -2677 *4)))) (-4 *4 (-1090)) (-5 *1 (-882 *3 *4)) (-4 *3 (-1090)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-638 *5)) (-4 *5 (-13 (-1090) (-34))) (-5 *2 (-638 (-1130 *3 *5))) (-5 *1 (-1130 *3 *5)) (-4 *3 (-13 (-1090) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-638 (-2 (|:| |val| *4) (|:| -1510 *5)))) + (-12 (-5 *3 (-638 (-2 (|:| |val| *4) (|:| -1495 *5)))) (-4 *4 (-13 (-1090) (-34))) (-4 *5 (-13 (-1090) (-34))) (-5 *2 (-638 (-1130 *4 *5))) (-5 *1 (-1130 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1510 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -1495 *4))) (-4 *3 (-13 (-1090) (-34))) (-4 *4 (-13 (-1090) (-34))) (-5 *1 (-1130 *3 *4)))) ((*1 *1 *2 *3) @@ -2605,8 +2577,8 @@ (-12 (-5 *1 (-1155 *2 *3)) (-4 *2 (-1090)) (-4 *3 (-1090))))) (((*1 *2 *1) (-12 (-5 *2 (-1115 (-561) (-607 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) - (-12 (-4 *3 (-306)) (-4 *4 (-985 *3)) (-4 *5 (-1229 *4)) - (-5 *2 (-1253 *6)) (-5 *1 (-412 *3 *4 *5 *6)) + (-12 (-4 *3 (-306)) (-4 *4 (-985 *3)) (-4 *5 (-1230 *4)) + (-5 *2 (-1254 *6)) (-5 *1 (-412 *3 *4 *5 *6)) (-4 *6 (-13 (-408 *4 *5) (-1031 *4))))) ((*1 *2 *1) (-12 (-4 *3 (-1042)) (-4 *3 (-844)) (-5 *2 (-1115 *3 (-607 *1))) @@ -2619,95 +2591,108 @@ (-12 (-4 *3 (-171)) (-4 *2 (-711 *3)) (-5 *1 (-655 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-720) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-985 *2)) (-4 *2 (-553))))) -(((*1 *2) - (-12 (-4 *3 (-553)) (-5 *2 (-638 *4)) (-5 *1 (-43 *3 *4)) - (-4 *4 (-416 *3))))) 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"void"))) + (-14 *3 (-1166)) (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2630 "void"))) (-14 *5 (-638 (-1166))) (-14 *6 (-1170)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-5 *1 (-397 *3 *4 *5 *6)) (-14 *3 (-1166)) - (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) + (-14 *4 (-3 (|:| |fst| (-433)) (|:| -2630 "void"))) (-14 *5 (-638 (-1166))) (-14 *6 (-1170)))) ((*1 *1 *2) (-12 (-5 *2 (-330 *4)) (-4 *4 (-13 (-844) (-21))) @@ -2863,28 +2848,28 @@ ((*1 *1 *2) (-12 (-5 *2 (-433)) (-5 *1 (-436)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1170)) (|:| -3481 (-638 (-329))))) + (-5 *2 (-2 (|:| |localSymbols| (-1170)) (|:| -3529 (-638 (-329))))) (-4 *1 (-438)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-4 *1 (-438)))) ((*1 *1 *2) (-12 (-5 *2 (-638 (-329))) (-4 *1 (-438)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-692))) (-4 *1 (-438)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-692))) (-4 *1 (-438)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1170)) (|:| -3481 (-638 (-329))))) + (-5 *2 (-2 (|:| |localSymbols| (-1170)) (|:| -3529 (-638 (-329))))) (-4 *1 (-439)))) ((*1 *1 *2) (-12 (-5 *2 (-329)) (-4 *1 (-439)))) ((*1 *1 *2) (-12 (-5 *2 (-638 (-329))) (-4 *1 (-439)))) ((*1 *1 *2) - (-12 (-5 *2 (-1253 (-406 (-945 *3)))) (-4 *3 (-171)) - (-14 *6 (-1253 (-682 *3))) (-5 *1 (-451 *3 *4 *5 *6)) + (-12 (-5 *2 (-1254 (-406 (-945 *3)))) (-4 *3 (-171)) + (-14 *6 (-1254 (-682 *3))) (-5 *1 (-451 *3 *4 *5 *6)) (-14 *4 (-914)) (-14 *5 (-638 (-1166))))) ((*1 *1 *2) (-12 (-5 *2 (-638 (-638 (-936 (-224))))) (-5 *1 (-466)))) ((*1 *2 *1) (-12 (-5 *2 (-856)) (-5 *1 (-466)))) ((*1 *1 *2) - (-12 (-5 *2 (-1238 *3 *4 *5)) (-4 *3 (-1042)) (-14 *4 (-1166)) + (-12 (-5 *2 (-1239 *3 *4 *5)) (-4 *3 (-1042)) (-14 *4 (-1166)) (-14 *5 *3) (-5 *1 (-472 *3 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-1249 *4)) (-14 *4 (-1166)) (-5 *1 (-472 *3 *4 *5)) + (-12 (-5 *2 (-1250 *4)) (-14 *4 (-1166)) (-5 *1 (-472 *3 *4 *5)) (-4 *3 (-1042)) (-14 *5 *3))) ((*1 *1 *2) (-12 (-5 *2 (-1115 (-561) (-607 (-493)))) (-5 *1 (-493)))) ((*1 *1 *2) (-12 (-5 *2 (-1148)) (-5 *1 (-500)))) @@ -2899,10 +2884,10 @@ ((*1 *1 *2) (-12 (-4 *1 (-611 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) (-12 (-4 *1 (-615 *2)) (-4 *2 (-1042)))) ((*1 *2 *1) - (-12 (-5 *2 (-1273 *3 *4)) (-5 *1 (-622 *3 *4 *5)) (-4 *3 (-844)) + (-12 (-5 *2 (-1274 *3 *4)) (-5 *1 (-622 *3 *4 *5)) (-4 *3 (-844)) (-4 *4 (-13 (-171) (-711 (-406 (-561))))) (-14 *5 (-914)))) ((*1 *2 *1) - (-12 (-5 *2 (-1268 *3 *4)) (-5 *1 (-622 *3 *4 *5)) (-4 *3 (-844)) + (-12 (-5 *2 (-1269 *3 *4)) (-5 *1 (-622 *3 *4 *5)) (-4 *3 (-844)) (-4 *4 (-13 (-171) (-711 (-406 (-561))))) (-14 *5 (-914)))) ((*1 *1 *2) (-12 (-4 *3 (-171)) (-5 *1 (-630 *3 *2)) (-4 *2 (-738 *3)))) @@ -2939,7 +2924,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-638 (-2 (|:| -4188 *3) (|:| -3044 *4)))) + (-12 (-5 *2 (-638 (-2 (|:| -4226 *3) (|:| -3077 *4)))) (-4 *3 (-1042)) (-4 *4 (-720)) (-5 *1 (-729 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-561)) (-4 *1 (-757)))) ((*1 *1 *2) @@ -2948,25 +2933,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) - (|:| -2290 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (|:| |mdnia| (-2 (|:| |fn| (-315 (-224))) - (|:| -2290 (-638 (-1084 (-837 (-224))))) + (|:| -2185 (-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))))) (-5 *1 (-763)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-315 (-224))) - (|:| -2290 (-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) + (|:| -2185 (-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-763)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) - (|:| -2290 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-763)))) ((*1 *2 *3) (-12 (-5 *2 (-768)) (-5 *1 (-767 *3)) (-4 *3 (-1205)))) @@ -2974,7 +2959,7 @@ (-12 (-5 *2 (-2 (|:| |xinit| (-224)) (|:| |xend| (-224)) - (|:| |fn| (-1253 (-315 (-224)))) (|:| |yinit| (-638 (-224))) + (|:| |fn| (-1254 (-315 (-224)))) (|:| |yinit| (-638 (-224))) (|:| |intvals| (-638 (-224))) (|:| |g| (-315 (-224))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-802)))) @@ -2984,23 +2969,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-315 (-224))) (|:| -3721 (-638 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3767 (-638 (-224))) (|:| |lb| (-638 (-837 (-224)))) (|:| |cf| (-638 (-315 (-224)))) (|:| |ub| (-638 (-837 (-224)))))) (|:| |lsa| (-2 (|:| |lfn| (-638 (-315 (-224)))) - (|:| -3721 (-638 (-224))))))) + (|:| -3767 (-638 (-224))))))) (-5 *1 (-835)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-638 (-315 (-224)))) (|:| -3721 (-638 (-224))))) + (-2 (|:| |lfn| (-638 (-315 (-224)))) (|:| -3767 (-638 (-224))))) (-5 *1 (-835)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-315 (-224))) (|:| -3721 (-638 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3767 (-638 (-224))) (|:| |lb| (-638 (-837 (-224)))) (|:| |cf| (-638 (-315 (-224)))) (|:| |ub| (-638 (-837 (-224)))))) (-5 *1 (-835)))) @@ -3040,7 +3025,7 @@ (-4 *4 (-13 (-844) (-553))))) ((*1 *1 *2) (-12 (-5 *2 (-1166)) (-5 *1 (-959 *3)) (-4 *3 (-960)))) ((*1 *1 *2) (-12 (-5 *1 (-959 *2)) (-4 *2 (-960)))) - ((*1 *2 *3) (-12 (-5 *2 (-1258)) (-5 *1 (-1026 *3)) (-4 *3 (-1205)))) + ((*1 *2 *3) (-12 (-5 *2 (-1259)) (-5 *1 (-1026 *3)) (-4 *3 (-1205)))) ((*1 *2 *3) (-12 (-5 *3 (-311)) (-5 *1 (-1026 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) (-12 (-4 *3 (-362)) (-4 *4 (-787)) (-4 *5 (-844)) @@ -3059,13 +3044,13 @@ ((*1 *2 *3) (-12 (-5 *2 (-1146 *3)) (-5 *1 (-1150 *3)) (-4 *3 (-1042)))) ((*1 *1 *2) - (-12 (-5 *2 (-1249 *4)) (-14 *4 (-1166)) (-5 *1 (-1157 *3 *4 *5)) + (-12 (-5 *2 (-1250 *4)) (-14 *4 (-1166)) (-5 *1 (-1157 *3 *4 *5)) (-4 *3 (-1042)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1249 *4)) (-14 *4 (-1166)) (-5 *1 (-1164 *3 *4 *5)) + (-12 (-5 *2 (-1250 *4)) (-14 *4 (-1166)) (-5 *1 (-1164 *3 *4 *5)) (-4 *3 (-1042)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1226 *4 *3)) (-4 *3 (-1042)) (-14 *4 (-1166)) + (-12 (-5 *2 (-1227 *4 *3)) (-4 *3 (-1042)) (-14 *4 (-1166)) (-14 *5 *3) (-5 *1 (-1164 *3 *4 *5)))) ((*1 *1 *2) (-12 (-5 *2 (-1166)) (-5 *1 (-1165)))) ((*1 *2 *1) (-12 (-5 *2 (-1178 (-1166) (-436))) (-5 *1 (-1170)))) @@ -3079,46 +3064,44 @@ (-12 (-5 *2 (-945 *3)) (-4 *3 (-1042)) (-5 *1 (-1199 *3)))) ((*1 *1 *2) (-12 (-5 *2 (-1166)) (-5 *1 (-1199 *3)) (-4 *3 (-1042)))) ((*1 *1 *2) - (-12 (-5 *2 (-1249 *4)) (-14 *4 (-1166)) (-5 *1 (-1217 *3 *4 *5)) + (-12 (-5 *2 (-1250 *4)) (-14 *4 (-1166)) (-5 *1 (-1218 *3 *4 *5)) (-4 *3 (-1042)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1084 *3)) (-4 *3 (-1205)) (-5 *1 (-1220 *3)))) + (-12 (-5 *2 (-1084 *3)) (-4 *3 (-1205)) (-5 *1 (-1221 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-1249 *4)) (-14 *4 (-1166)) (-5 *1 (-1245 *3 *4 *5)) + (-12 (-5 *2 (-1250 *4)) (-14 *4 (-1166)) (-5 *1 (-1246 *3 *4 *5)) (-4 *3 (-1042)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1226 *4 *3)) (-4 *3 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(-52)) (-5 *1 (-51 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) @@ -3173,47 +3156,47 @@ ((*1 *1 *2) (|partial| -12 (-5 *2 (-315 (-561))) (-4 *1 (-395)))) ((*1 *1 *2) (|partial| -12 (-5 *2 (-315 (-378))) (-4 *1 (-395)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-406 (-945 (-561))))) (-4 *1 (-439)))) + (|partial| -12 (-5 *2 (-1254 (-406 (-945 (-561))))) (-4 *1 (-439)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-406 (-945 (-378))))) (-4 *1 (-439)))) + (|partial| -12 (-5 *2 (-1254 (-406 (-945 (-378))))) (-4 *1 (-439)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-945 (-561)))) (-4 *1 (-439)))) + (|partial| -12 (-5 *2 (-1254 (-945 (-561)))) (-4 *1 (-439)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-945 (-378)))) (-4 *1 (-439)))) + (|partial| -12 (-5 *2 (-1254 (-945 (-378)))) (-4 *1 (-439)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-315 (-561)))) (-4 *1 (-439)))) + (|partial| -12 (-5 *2 (-1254 (-315 (-561)))) (-4 *1 (-439)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1253 (-315 (-378)))) (-4 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+ (-14 *6 (-1166)) (-14 *7 *5) (-5 *2 (-406 (-1227 *6 *5))) + (-5 *1 (-861 *5 *6 *7))))) +(((*1 *2 *2) (-12 (-5 *2 (-638 (-1148))) (-5 *1 (-396))))) +(((*1 *1 *2 *3) + (-12 (-5 *2 (-1254 *3)) (-4 *3 (-1230 *4)) (-4 *4 (-1209)) + (-4 *1 (-341 *4 *3 *5)) (-4 *5 (-1230 (-406 *3)))))) (((*1 *2 *3) (-12 (-5 *2 (-638 (-1148))) (-5 *1 (-240)) (-5 *3 (-1148)))) ((*1 *2 *2) (-12 (-5 *2 (-638 (-1148))) (-5 *1 (-240)))) ((*1 *1 *2) (-12 (-5 *2 (-156)) (-5 *1 (-867))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-885 *4)) (-4 *4 (-1090)) (-5 *1 (-883 *4 *3)) + (-4 *3 (-1205)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-52)) (-5 *1 (-885 *3)) (-4 *3 (-1090))))) (((*1 *2 *1) (|partial| -12 (-4 *3 (-450)) (-4 *4 (-844)) (-4 *5 (-787)) (-5 *2 (-112)) (-5 *1 (-980 *3 *4 *5 *6)) @@ -3512,24 +3489,10 @@ ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1130 *3 *4)) (-4 *3 (-13 (-1090) (-34))) (-4 *4 (-13 (-1090) (-34)))))) -(((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-112)) (-4 *6 (-450)) (-4 *7 (-787)) - (-4 *8 (-844)) (-4 *9 (-1056 *6 *7 *8)) - (-5 *2 - (-2 (|:| -3360 (-638 *9)) (|:| -1510 *4) (|:| |ineq| (-638 *9)))) - (-5 *1 (-981 *6 *7 *8 *9 *4)) (-5 *3 (-638 *9)) - (-4 *4 (-1062 *6 *7 *8 *9)))) - ((*1 *2 *3 *4 *3 *5 *5 *5 *5 *5) - (|partial| -12 (-5 *5 (-112)) (-4 *6 (-450)) (-4 *7 (-787)) - (-4 *8 (-844)) (-4 *9 (-1056 *6 *7 *8)) - (-5 *2 - (-2 (|:| -3360 (-638 *9)) (|:| -1510 *4) (|:| |ineq| (-638 *9)))) - (-5 *1 (-1097 *6 *7 *8 *9 *4)) (-5 *3 (-638 *9)) - (-4 *4 (-1062 *6 *7 *8 *9))))) -(((*1 *2 *3 *3 *4 *5) - (-12 (-5 *3 (-638 (-945 *6))) (-5 *4 (-638 (-1166))) (-4 *6 (-450)) - (-5 *2 (-638 (-638 *7))) (-5 *1 (-536 *6 *7 *5)) (-4 *7 (-362)) - (-4 *5 (-13 (-362) (-842)))))) +(((*1 *1) (-5 *1 (-156))) + ((*1 *2 *1) (-12 (-4 *1 (-1037 *2)) (-4 *2 (-23))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-885 *3)) (-4 *3 (-1090))))) +(((*1 *2 *1 *1) (-12 (-4 *1 (-553)) (-5 *2 (-112))))) (((*1 *1 *1 *2) (-12 (-5 *2 (-1148)) (-5 *1 (-114)))) ((*1 *2 *2 *3) (-12 (-5 *3 (-1148)) (-4 *4 (-844)) (-5 *1 (-922 *4 *2)) @@ -3537,62 +3500,68 @@ ((*1 *2 *3 *4) (-12 (-5 *3 (-1166)) (-5 *4 (-1148)) (-5 *2 (-315 (-561))) (-5 *1 (-923))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-791 *2)) (-4 *2 (-171)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-992 *3)) (-4 *3 (-171)) (-5 *1 (-793 *3))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1168 (-406 (-561)))) (-5 *1 (-189)) (-5 *3 (-561))))) -(((*1 *2 *1 *1) - (-12 +(((*1 *2 *2) (-12 (-5 *2 (-561)) (-5 *1 (-920))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-844) (-553))) (-5 *1 (-275 *3 *2)) + (-4 *2 (-13 (-429 *3) (-995)))))) +(((*1 *2) (-12 (-5 *2 (-638 (-1148))) (-5 *1 (-1257))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-682 *3)) (-4 *3 (-1042)) (-5 *1 (-683 *3))))) +(((*1 *2 *2 *3) + (|partial| -12 + (-5 *3 (-638 (-2 (|:| |func| *2) (|:| |pole| (-112))))) + (-4 *2 (-13 (-429 *4) (-995))) (-4 *4 (-13 (-844) (-553))) + (-5 *1 (-275 *4 *2))))) +(((*1 *2 *3 *3 *2) + (|partial| -12 (-5 *2 (-765)) + (-4 *3 (-13 (-720) (-367) (-10 -7 (-15 ** (*3 *3 (-561)))))) + (-5 *1 (-245 *3))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1162 *9)) (-5 *4 (-638 *7)) (-5 *5 (-638 (-638 *8))) + (-4 *7 (-844)) (-4 *8 (-306)) (-4 *9 (-942 *8 *6 *7)) (-4 *6 (-787)) (-5 *2 - (-2 (|:| |polnum| (-776 *3)) (|:| |polden| *3) (|:| -1364 (-765)))) - (-5 *1 (-776 *3)) (-4 *3 (-1042)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844)) - (-5 *2 (-2 (|:| |polnum| *1) (|:| |polden| *1) (|:| -1364 (-765)))) - (-4 *1 (-1056 *3 *4 *5))))) -(((*1 *1 *2) (-12 (-5 *1 (-684 *2)) (-4 *2 (-608 (-856)))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-450)) (-4 *5 (-787)) (-4 *6 (-844)) - (-4 *7 (-1056 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-981 *4 *5 *6 *7 *3)) (-4 *3 (-1062 *4 *5 *6 *7)))) + (-2 (|:| |upol| (-1162 *8)) (|:| |Lval| (-638 *8)) + (|:| |Lfact| + (-638 (-2 (|:| -1633 (-1162 *8)) (|:| -4181 (-561))))) + (|:| |ctpol| *8))) + (-5 *1 (-736 *6 *7 *8 *9))))) +(((*1 *2) (-12 (-5 *2 (-867)) (-5 *1 (-1257)))) + ((*1 *2 *2) (-12 (-5 *2 (-867)) (-5 *1 (-1257))))) +(((*1 *1 *1 *1) (-4 *1 (-543)))) +(((*1 *1) (-4 *1 (-348))) + ((*1 *2 *3) + (-12 (-5 *3 (-638 *5)) (-4 *5 (-429 *4)) + (-4 *4 (-13 (-553) (-844) (-146))) + (-5 *2 + (-2 (|:| |primelt| *5) (|:| |poly| (-638 (-1162 *5))) + (|:| |prim| (-1162 *5)))) + (-5 *1 (-431 *4 *5)))) ((*1 *2 *3 *3) - (-12 (-4 *4 (-450)) (-4 *5 (-787)) (-4 *6 (-844)) - (-4 *7 (-1056 *4 *5 *6)) (-5 *2 (-112)) - (-5 *1 (-1097 *4 *5 *6 *7 *3)) (-4 *3 (-1062 *4 *5 *6 *7))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-682 *3)) - (-4 *3 (-13 (-306) (-10 -8 (-15 -3422 ((-417 $) $))))) - (-4 *4 (-1229 *3)) (-5 *1 (-497 *3 *4 *5)) (-4 *5 (-408 *3 *4))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-1 *5 *5)) (-4 *5 (-1229 *4)) (-4 *4 (-1209)) - (-4 *6 (-1229 (-406 *5))) + (-12 (-4 *4 (-13 (-553) (-844) (-146))) (-5 *2 - (-2 (|:| |num| *1) (|:| |den| *5) (|:| |derivden| *5) - (|:| |gd| *5))) - (-4 *1 (-341 *4 *5 *6))))) -(((*1 *1 *2) (-12 (-5 *2 (-156)) (-5 *1 (-867))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1146 (-638 (-561)))) (-5 *3 (-638 (-561))) - (-5 *1 (-876))))) -(((*1 *1) (-5 *1 (-143))) ((*1 *1 *1) (-5 *1 (-856)))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-638 - (-2 (|:| -1569 (-765)) - (|:| |eqns| - (-638 - (-2 (|:| |det| *7) (|:| |rows| (-638 (-561))) - (|:| |cols| (-638 (-561)))))) - (|:| |fgb| (-638 *7))))) - (-4 *7 (-942 *4 *6 *5)) (-4 *4 (-13 (-306) (-146))) - (-4 *5 (-13 (-844) (-609 (-1166)))) (-4 *6 (-787)) (-5 *2 (-765)) - (-5 *1 (-917 *4 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-638 (-561))) (-5 *2 (-561)) (-5 *1 (-484 *4)) - (-4 *4 (-1229 *2))))) + (-2 (|:| |primelt| *3) (|:| |pol1| (-1162 *3)) + (|:| |pol2| (-1162 *3)) (|:| |prim| (-1162 *3)))) + (-5 *1 (-431 *4 *3)) (-4 *3 (-27)) (-4 *3 (-429 *4)))) + ((*1 *2 *3 *4 *3 *4) + (-12 (-5 *3 (-945 *5)) (-5 *4 (-1166)) (-4 *5 (-13 (-362) (-146))) + (-5 *2 + (-2 (|:| |coef1| (-561)) (|:| |coef2| (-561)) + (|:| |prim| (-1162 *5)))) + (-5 *1 (-953 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-638 (-945 *5))) (-5 *4 (-638 (-1166))) + (-4 *5 (-13 (-362) (-146))) + (-5 *2 + (-2 (|:| -4226 (-638 (-561))) (|:| |poly| (-638 (-1162 *5))) + (|:| |prim| (-1162 *5)))) + (-5 *1 (-953 *5)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-638 (-945 *6))) (-5 *4 (-638 (-1166))) (-5 *5 (-1166)) + (-4 *6 (-13 (-362) (-146))) + (-5 *2 + (-2 (|:| -4226 (-638 (-561))) (|:| |poly| (-638 (-1162 *6))) + (|:| |prim| (-1162 *6)))) + (-5 *1 (-953 *6))))) (((*1 *2 *3) (-12 (-5 *3 (-1148)) (-5 *2 (-311)) (-5 *1 (-295)))) ((*1 *2 *3) (-12 (-5 *3 (-638 (-1148))) (-5 *2 (-311)) (-5 *1 (-295)))) @@ -3600,10 +3569,30 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-638 (-1148))) (-5 *3 (-1148)) (-5 *2 (-311)) (-5 *1 (-295))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-638 (-638 (-638 *4)))) (-5 *3 (-638 *4)) (-4 *4 (-844)) - (-5 *1 (-1176 *4))))) -(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-875 *2)) (-4 *2 (-1205))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1124 *3)) (-4 *3 (-1042)) (-5 *2 (-638 (-936 *3))))) + ((*1 *1 *2) + (-12 (-5 *2 (-638 (-936 *3))) (-4 *3 (-1042)) (-4 *1 (-1124 *3)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-638 (-638 *3))) (-4 *1 (-1124 *3)) (-4 *3 (-1042)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-638 (-936 *3))) (-4 *1 (-1124 *3)) (-4 *3 (-1042))))) +(((*1 *2 *3 *3 *3) + (|partial| -12 + (-4 *4 (-13 (-146) (-27) (-1031 (-561)) (-1031 (-406 (-561))))) + (-4 *5 (-1230 *4)) (-5 *2 (-1162 (-406 *5))) (-5 *1 (-610 *4 *5)) + (-5 *3 (-406 *5)))) + ((*1 *2 *3 *3 *3 *4) + (|partial| -12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1230 *5)) + (-4 *5 (-13 (-146) (-27) (-1031 (-561)) (-1031 (-406 (-561))))) + (-5 *2 (-1162 (-406 *6))) (-5 *1 (-610 *5 *6)) (-5 *3 (-406 *6))))) +(((*1 *2 *3) + (-12 (-4 *4 (-38 (-406 (-561)))) + (-5 *2 (-2 (|:| -4213 (-1146 *4)) (|:| -3002 (-1146 *4)))) + (-5 *1 (-1152 *4)) (-5 *3 (-1146 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-479 *4 *5)) (-14 *4 (-638 (-1166))) (-4 *5 (-1042)) + (-5 *2 (-945 *5)) (-5 *1 (-937 *4 *5))))) (((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) (-12 (-5 *2 (-945 (-378))) (-5 *1 (-338 *3 *4 *5)) @@ -3647,30 +3636,30 @@ ((*1 *1 *2) (-12 (-5 *2 (-945 (-378))) (-4 *1 (-395)))) ((*1 *1 *2) (-12 (-5 *2 (-315 (-561))) (-4 *1 (-395)))) ((*1 *1 *2) (-12 (-5 *2 (-315 (-378))) (-4 *1 (-395)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-406 (-945 (-561))))) (-4 *1 (-439)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-406 (-945 (-378))))) (-4 *1 (-439)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-945 (-561)))) (-4 *1 (-439)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-945 (-378)))) (-4 *1 (-439)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-315 (-561)))) (-4 *1 (-439)))) - ((*1 *1 *2) (-12 (-5 *2 (-1253 (-315 (-378)))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-406 (-945 (-561))))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-406 (-945 (-378))))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-945 (-561)))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-945 (-378)))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-315 (-561)))) (-4 *1 (-439)))) + ((*1 *1 *2) (-12 (-5 *2 (-1254 (-315 (-378)))) (-4 *1 (-439)))) ((*1 *2 *1) (-12 (-5 *2 (-3 (|:| |nia| (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) - (|:| -2290 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (|:| |mdnia| (-2 (|:| |fn| (-315 (-224))) - (|:| -2290 (-638 (-1084 (-837 (-224))))) + (|:| -2185 (-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))))) (-5 *1 (-763)))) ((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |xinit| (-224)) (|:| |xend| (-224)) - (|:| |fn| (-1253 (-315 (-224)))) (|:| |yinit| (-638 (-224))) + (|:| |fn| (-1254 (-315 (-224)))) (|:| |yinit| (-638 (-224))) (|:| |intvals| (-638 (-224))) (|:| |g| (-315 (-224))) (|:| |abserr| (-224)) (|:| |relerr| (-224)))) (-5 *1 (-802)))) @@ -3679,13 +3668,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-315 (-224))) (|:| -3721 (-638 (-224))) + (-2 (|:| |fn| (-315 (-224))) (|:| -3767 (-638 (-224))) (|:| |lb| (-638 (-837 (-224)))) (|:| |cf| (-638 (-315 (-224)))) (|:| |ub| (-638 (-837 (-224)))))) (|:| |lsa| (-2 (|:| |lfn| (-638 (-315 (-224)))) - (|:| -3721 (-638 (-224))))))) + (|:| -3767 (-638 (-224))))))) (-5 *1 (-835)))) ((*1 *2 *1) (-12 @@ -3704,26 +3693,26 @@ (-4 *4 (-787)) (-4 *5 (-844)) (-4 *1 (-969 *3 *4 *5 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-1031 *2)) (-4 *2 (-1205)))) ((*1 *1 *2) - (-4007 + (-4050 (-12 (-5 *2 (-945 *3)) - (-12 (-2159 (-4 *3 (-38 (-406 (-561))))) - (-2159 (-4 *3 (-38 (-561)))) (-4 *5 (-609 (-1166)))) + (-12 (-2186 (-4 *3 (-38 (-406 (-561))))) + (-2186 (-4 *3 (-38 (-561)))) (-4 *5 (-609 (-1166)))) (-4 *3 (-1042)) (-4 *1 (-1056 *3 *4 *5)) (-4 *4 (-787)) (-4 *5 (-844))) (-12 (-5 *2 (-945 *3)) - (-12 (-2159 (-4 *3 (-543))) (-2159 (-4 *3 (-38 (-406 (-561))))) + (-12 (-2186 (-4 *3 (-543))) (-2186 (-4 *3 (-38 (-406 (-561))))) (-4 *3 (-38 (-561))) (-4 *5 (-609 (-1166)))) (-4 *3 (-1042)) (-4 *1 (-1056 *3 *4 *5)) (-4 *4 (-787)) (-4 *5 (-844))) (-12 (-5 *2 (-945 *3)) - (-12 (-2159 (-4 *3 (-985 (-561)))) (-4 *3 (-38 (-406 (-561)))) + (-12 (-2186 (-4 *3 (-985 (-561)))) (-4 *3 (-38 (-406 (-561)))) (-4 *5 (-609 (-1166)))) (-4 *3 (-1042)) (-4 *1 (-1056 *3 *4 *5)) (-4 *4 (-787)) (-4 *5 (-844))))) ((*1 *1 *2) - (-4007 + (-4050 (-12 (-5 *2 (-945 (-561))) (-4 *1 (-1056 *3 *4 *5)) - (-12 (-2159 (-4 *3 (-38 (-406 (-561))))) (-4 *3 (-38 (-561))) + (-12 (-2186 (-4 *3 (-38 (-406 (-561))))) (-4 *3 (-38 (-561))) (-4 *5 (-609 (-1166)))) (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844))) (-12 (-5 *2 (-945 (-561))) (-4 *1 (-1056 *3 *4 *5)) @@ -3733,895 +3722,678 @@ (-12 (-5 *2 (-945 (-406 (-561)))) (-4 *1 (-1056 *3 *4 *5)) (-4 *3 (-38 (-406 (-561)))) (-4 *5 (-609 (-1166))) (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844))))) -(((*1 *2 *2 *3 *4 *5) - (-12 (-5 *2 (-638 *9)) (-5 *3 (-1 (-112) *9)) - (-5 *4 (-1 (-112) *9 *9)) (-5 *5 (-1 *9 *9 *9)) - (-4 *9 (-1056 *6 *7 *8)) (-4 *6 (-553)) (-4 *7 (-787)) - (-4 *8 (-844)) (-5 *1 (-970 *6 *7 *8 *9))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1084 (-837 (-378)))) (-5 *2 (-1084 (-837 (-224)))) - (-5 *1 (-304))))) -(((*1 *2 *1) (-12 (-5 *2 (-638 (-561))) (-5 *1 (-274))))) (((*1 *2 *3 *3) - (-12 (-4 *4 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(-526 *3)))) ((*1 *1 *1 *1) (-5 *1 (-534))) ((*1 *1 *2 *3) (-12 (-4 *4 (-171)) (-5 *1 (-616 *2 *4 *3)) (-4 *2 (-38 *4)) @@ -14315,65 +14409,52 @@ (-4 *5 (-237 *4 *2)) (-4 *6 (-237 *3 *2)) (-4 *2 (-362)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-1146 *3)) (-4 *3 (-1042)) (-5 *1 (-1150 *3)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1260 *2)) (-4 *2 (-362)))) + ((*1 *1 *1 *2) (-12 (-4 *1 (-1261 *2)) (-4 *2 (-362)))) ((*1 *1 *1 *1) (|partial| -12 (-4 *2 (-362)) (-4 *2 (-1042)) (-4 *3 (-844)) (-4 *4 (-787)) (-14 *6 (-638 *3)) - (-5 *1 (-1265 *2 *3 *4 *5 *6 *7 *8)) (-4 *5 (-942 *2 *4 *3)) + (-5 *1 (-1266 *2 *3 *4 *5 *6 *7 *8)) (-4 *5 (-942 *2 *4 *3)) (-14 *7 (-638 (-765))) (-14 *8 (-765)))) ((*1 *1 *1 *2) - (-12 (-5 *1 (-1276 *2 *3)) (-4 *2 (-362)) (-4 *2 (-1042)) + (-12 (-5 *1 (-1277 *2 *3)) (-4 *2 (-362)) (-4 *2 (-1042)) (-4 *3 (-840))))) (((*1 *2 *3 *2) - (-12 (-4 *1 (-781)) (-5 *2 (-1028)) - (-5 *3 - (-2 (|:| |fn| (-315 (-224))) - (|:| -2290 (-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) - (|:| 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(-638 (-1084 (-837 (-224))))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))))) + ((*1 *2 *3 *2) + (-12 (-4 *1 (-781)) (-5 *2 (-1028)) + (-5 *3 + (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224))))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1230 *2)) (-4 *2 (-1042))))) (((*1 *2 *1) (-12 (-4 *1 (-165 *2)) (-4 *2 (-171)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-553) (-844) (-1031 (-561)))) (-5 *2 (-315 *4)) @@ -15078,41 +15219,68 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-450) (-844) (-1031 (-561)) (-634 (-561)))) (-5 *1 (-1194 *3 *2)) (-4 *2 (-13 (-27) (-1190) (-429 *3)))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-765)) (-4 *5 (-553)) - (-5 *2 (-2 (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-962 *5 *3)) (-4 *3 (-1229 *5))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-638 (-945 *4))) (-5 *3 (-638 (-1166))) (-4 *4 (-450)) - (-5 *1 (-911 *4))))) -(((*1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| |mval| (-682 *3)) (|:| |invmval| (-682 *3)) - (|:| 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(|:| |cols| (-638 (-561)))))) + (|:| |fgb| (-638 *7))))) + (-4 *7 (-942 *4 *6 *5)) (-4 *4 (-13 (-306) (-146))) + (-4 *5 (-13 (-844) (-609 (-1166)))) (-4 *6 (-787)) (-5 *2 (-765)) + (-5 *1 (-917 *4 *5 *6 *7))))) +(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) + (-12 (-5 *3 (-561)) (-5 *4 (-682 (-224))) (-5 *2 (-1028)) + (-5 *1 (-746))))) (((*1 *2 *1) (-12 (-4 *1 (-165 *2)) (-4 *2 (-171)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-553) (-844) (-1031 (-561)))) (-5 *2 (-315 *4)) @@ -15122,64 +15290,43 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-450) (-844) (-1031 (-561)) (-634 (-561)))) (-5 *1 (-1194 *3 *2)) (-4 *2 (-13 (-27) (-1190) (-429 *3)))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-638 (-607 (-48)))) (-5 *1 (-48)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-607 (-48))) (-5 *1 (-48)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-1162 (-48))) (-5 *3 (-638 (-607 (-48)))) (-5 *1 (-48)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-1162 (-48))) (-5 *3 (-607 (-48))) (-5 *1 (-48)))) - ((*1 *2 *1) (-12 (-4 *1 (-165 *2)) (-4 *2 (-171)))) - ((*1 *2 *3) - (-12 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*1 *1 *2) (-12 (-4 *1 (-1134)) (-5 *2 (-143))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-1166)) (-5 *6 (-112)) + (-4 *7 (-13 (-306) (-844) (-146) (-1031 (-561)) (-634 (-561)))) + (-4 *3 (-13 (-1190) (-952) (-29 *7))) + (-5 *2 + (-3 (|:| |f1| (-837 *3)) (|:| |f2| (-638 (-837 *3))) + (|:| |fail| "failed") (|:| |pole| "potentialPole"))) + (-5 *1 (-218 *7 *3)) (-5 *5 (-837 *3))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-1056 *2 *3 *4)) (-4 *2 (-1042)) (-4 *3 (-787)) + (-4 *4 (-844)) (-4 *2 (-553)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1056 *2 *3 *4)) (-4 *2 (-1042)) (-4 *3 (-787)) + (-4 *4 (-844)) (-4 *2 (-553))))) +(((*1 *1 *2) (-12 (-5 *2 (-561)) (-5 *1 (-1053)))) + ((*1 *1 *2) (-12 (-5 *2 (-1166)) (-5 *1 (-1053))))) (((*1 *1 *1) (-12 (-5 *1 (-338 *2 *3 *4)) (-14 *2 (-638 (-1166))) (-14 *3 (-638 (-1166))) (-4 *4 (-386)))) @@ -15189,42 +15336,28 @@ ((*1 *1 *2) (-12 (-5 *2 (-406 (-561))) (-4 *1 (-1005)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1005)) (-5 *2 (-914)))) ((*1 *1 *1) (-4 *1 (-1005)))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-25)) (-4 *3 (-844)) (-5 *2 (-638 *1)) - (-4 *1 (-429 *3)))) - ((*1 *2 *1) - (|partial| -12 (-5 *2 (-638 (-885 *3))) (-5 *1 (-885 *3)) - (-4 *3 (-1090)))) - ((*1 *2 *1) - (|partial| -12 (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844)) - (-5 *2 (-638 *1)) (-4 *1 (-942 *3 *4 *5)))) - ((*1 *2 *3) - (|partial| -12 (-4 *4 (-787)) (-4 *5 (-844)) (-4 *6 (-1042)) - (-4 *7 (-942 *6 *4 *5)) (-5 *2 (-638 *3)) - (-5 *1 (-943 *4 *5 *6 *7 *3)) - (-4 *3 - (-13 (-362) - (-10 -8 (-15 -4022 ($ *7)) (-15 -4030 (*7 $)) - (-15 -4045 (*7 $)))))))) -(((*1 *1 *1) (|partial| -4 *1 (-1141)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-765)) (-5 *4 (-1253 *2)) (-4 *5 (-306)) - (-4 *6 (-985 *5)) (-4 *2 (-13 (-408 *6 *7) (-1031 *6))) - (-5 *1 (-412 *5 *6 *7 *2)) (-4 *7 (-1229 *6))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-914)) (-5 *3 (-638 (-262))) (-5 *1 (-260)))) - ((*1 *1 *2) (-12 (-5 *2 (-914)) (-5 *1 (-262))))) +(((*1 *2 *1) (-12 (-5 *2 (-638 (-1171))) (-5 *1 (-182))))) (((*1 *2 *2 *3) - (-12 (-5 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(-638 (-48))) (-5 *2 (-417 *3)) (-5 *1 (-39 *3)) - (-4 *3 (-1229 (-48))))) + (-4 *3 (-1230 (-48))))) ((*1 *2 *3) - (-12 (-5 *2 (-417 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1229 (-48))))) + (-12 (-5 *2 (-417 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1230 (-48))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-638 (-48))) (-4 *5 (-844)) (-4 *6 (-787)) (-5 *2 (-417 *3)) (-5 *1 (-42 *5 *6 *3)) (-4 *3 (-942 (-48) *6 *5)))) @@ -15234,33 +15367,33 @@ (-5 *1 (-42 *5 *6 *7)) (-5 *3 (-1162 *7)))) ((*1 *2 *3) (-12 (-4 *4 (-306)) (-5 *2 (-417 *3)) (-5 *1 (-166 *4 *3)) - (-4 *3 (-1229 (-168 *4))))) + (-4 *3 (-1230 (-168 *4))))) ((*1 *2 *3 *4 *5) (-12 (-5 *5 (-112)) (-4 *4 (-13 (-362) (-842))) (-5 *2 (-417 *3)) - (-5 *1 (-180 *4 *3)) (-4 *3 (-1229 (-168 *4))))) + (-5 *1 (-180 *4 *3)) (-4 *3 (-1230 (-168 *4))))) ((*1 *2 *3 *4) (-12 (-4 *4 (-13 (-362) (-842))) (-5 *2 (-417 *3)) - (-5 *1 (-180 *4 *3)) (-4 *3 (-1229 (-168 *4))))) + (-5 *1 (-180 *4 *3)) (-4 *3 (-1230 (-168 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-362) (-842))) (-5 *2 (-417 *3)) - (-5 *1 (-180 *4 *3)) (-4 *3 (-1229 (-168 *4))))) + (-5 *1 (-180 *4 *3)) (-4 *3 (-1230 (-168 *4))))) ((*1 *2 *3) (-12 (-4 *4 (-348)) (-5 *2 (-417 *3)) (-5 *1 (-215 *4 *3)) - (-4 *3 (-1229 *4)))) + (-4 *3 (-1230 *4)))) ((*1 *2 *3) - (-12 (-5 *2 (-417 *3)) (-5 *1 (-440 *3)) (-4 *3 (-1229 (-561))))) + (-12 (-5 *2 (-417 *3)) (-5 *1 (-440 *3)) (-4 *3 (-1230 (-561))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-765)) (-5 *2 (-417 *3)) (-5 *1 (-440 *3)) - (-4 *3 (-1229 (-561))))) + (-4 *3 (-1230 (-561))))) ((*1 *2 *3 *4) (-12 (-5 *4 (-638 (-765))) (-5 *2 (-417 *3)) (-5 *1 (-440 *3)) - (-4 *3 (-1229 (-561))))) + (-4 *3 (-1230 (-561))))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-638 (-765))) (-5 *5 (-765)) (-5 *2 (-417 *3)) - (-5 *1 (-440 *3)) (-4 *3 (-1229 (-561))))) + (-5 *1 (-440 *3)) (-4 *3 (-1230 (-561))))) ((*1 *2 *3 *4 *4) (-12 (-5 *4 (-765)) (-5 *2 (-417 *3)) (-5 *1 (-440 *3)) - (-4 *3 (-1229 (-561))))) + (-4 *3 (-1230 (-561))))) ((*1 *2 *3) (-12 (-5 *2 (-417 (-168 (-561)))) (-5 *1 (-444)) (-5 *3 (-168 (-561))))) @@ -15268,8 +15401,8 @@ (-12 (-4 *4 (-13 (-844) - (-10 -8 (-15 -4174 ((-1166) $)) - (-15 -2389 ((-3 $ "failed") (-1166)))))) + (-10 -8 (-15 -4216 ((-1166) $)) + (-15 -2421 ((-3 $ "failed") (-1166)))))) (-4 *5 (-787)) (-4 *7 (-553)) (-5 *2 (-417 *3)) (-5 *1 (-454 *4 *5 *6 *7 *3)) (-4 *6 (-553)) (-4 *3 (-942 *7 *5 *4)))) @@ -15277,9 +15410,9 @@ (-12 (-4 *4 (-306)) (-5 *2 (-417 (-1162 *4))) (-5 *1 (-456 *4)) (-5 *3 (-1162 *4)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1229 *5)) (-4 *5 (-362)) + (-12 (-5 *4 (-1 (-417 *6) *6)) (-4 *6 (-1230 *5)) (-4 *5 (-362)) (-4 *7 (-13 (-362) (-146) (-718 *5 *6))) (-5 *2 (-417 *3)) - (-5 *1 (-492 *5 *6 *7 *3)) (-4 *3 (-1229 *7)))) + (-5 *1 (-492 *5 *6 *7 *3)) (-4 *3 (-1230 *7)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-417 (-1162 *7)) (-1162 *7))) (-4 *7 (-13 (-306) (-146))) (-4 *5 (-844)) (-4 *6 (-787)) @@ -15294,19 +15427,19 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-638 *5) *6)) (-4 *5 (-13 (-362) (-146) (-1031 (-561)) (-1031 (-406 (-561))))) - (-4 *6 (-1229 *5)) (-5 *2 (-638 (-646 (-406 *6)))) + (-4 *6 (-1230 *5)) (-5 *2 (-638 (-646 (-406 *6)))) (-5 *1 (-650 *5 *6)) (-5 *3 (-646 (-406 *6))))) ((*1 *2 *3) (-12 (-4 *4 (-27)) (-4 *4 (-13 (-362) (-146) (-1031 (-561)) (-1031 (-406 (-561))))) - (-4 *5 (-1229 *4)) (-5 *2 (-638 (-646 (-406 *5)))) + (-4 *5 (-1230 *4)) (-5 *2 (-638 (-646 (-406 *5)))) (-5 *1 (-650 *4 *5)) (-5 *3 (-646 (-406 *5))))) ((*1 *2 *3) (-12 (-5 *3 (-813 *4)) (-4 *4 (-844)) (-5 *2 (-638 (-665 *4))) (-5 *1 (-665 *4)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-561)) (-5 *2 (-638 *3)) (-5 *1 (-689 *3)) - (-4 *3 (-1229 *4)))) + (-4 *3 (-1230 *4)))) ((*1 *2 *3) (-12 (-4 *4 (-844)) (-4 *5 (-787)) (-4 *6 (-348)) (-5 *2 (-417 *3)) (-5 *1 (-691 *4 *5 *6 *3)) (-4 *3 (-942 *6 *5 *4)))) @@ -15318,13 +15451,13 @@ (-12 (-4 *4 (-787)) (-4 *5 (-13 (-844) - (-10 -8 (-15 -4174 ((-1166) $)) - (-15 -2389 ((-3 $ "failed") (-1166)))))) + (-10 -8 (-15 -4216 ((-1166) $)) + (-15 -2421 ((-3 $ "failed") (-1166)))))) (-4 *6 (-306)) (-5 *2 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+15585,112 @@ (-12 (-5 *4 (-1082 (-406 (-945 *5)))) (-5 *3 (-406 (-945 *5))) (-4 *5 (-13 (-553) (-844) (-1031 (-561)))) (-5 *2 (-3 *3 (-315 *5))) (-5 *1 (-1159 *5))))) -(((*1 *2 *3 *4 *5 *3) - (-12 (-5 *4 (-1 *7 *7)) - (-5 *5 (-1 (-3 (-2 (|:| -2246 *6) (|:| |coeff| *6)) "failed") *6)) - (-4 *6 (-362)) (-4 *7 (-1229 *6)) +(((*1 *2 *2) (-12 (-5 *2 (-682 (-315 (-561)))) (-5 *1 (-1024))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-846 *2)) (-4 *2 (-1042)) (-4 *2 (-362))))) +(((*1 *1 *2) (-12 (-5 *1 (-226 *2)) (-4 *2 (-13 (-362) (-1190)))))) +(((*1 *1 *2 *1) (-12 (-4 *1 (-107 *2)) (-4 *2 (-1205)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-844)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-126 *2)) (-4 *2 (-844)))) + ((*1 *1 *1 *1 *2) + (-12 (-5 *2 (-561)) (-4 *1 (-281 *3)) (-4 *3 (-1205)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-561)) (-4 *1 (-281 *2)) (-4 *2 (-1205)))) + ((*1 *1 *2) + (-12 (-5 *2 - (-3 (-2 (|:| |answer| (-406 *7)) (|:| |a0| *6)) - (-2 (|:| -2246 (-406 *7)) (|:| |coeff| (-406 *7))) "failed")) - (-5 *1 (-571 *6 *7)) (-5 *3 (-406 *7))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-936 (-224))) (-5 *2 (-1258)) (-5 *1 (-466))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-844) (-553))) (-5 *1 (-275 *3 *2)) - (-4 *2 (-13 (-429 *3) (-995)))))) -(((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-844))))) -(((*1 *2 *3) - (-12 (-5 *3 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) - (-5 *2 (-1258)) (-5 *1 (-1169)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1166)) - (-5 *4 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) (-5 *2 (-1258)) - (-5 *1 (-1169)))) - ((*1 *2 *3 *4 *1) - (-12 (-5 *3 (-1166)) - (-5 *4 (-3 (|:| |fst| (-433)) (|:| -2609 "void"))) (-5 *2 (-1258)) - (-5 *1 (-1169))))) -(((*1 *2 *3 *3 *3 *4 *5) - (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1229 *6)) - (-4 *6 (-13 (-362) (-146) (-1031 *4))) (-5 *4 (-561)) + (-2 + (|:| -2285 + (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (|:| -2677 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1146 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2185 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))))) + (-5 *1 (-556)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-765)) (-4 *1 (-688 *2)) (-4 *2 (-1090)))) + ((*1 *1 *2) + (-12 (-5 *2 - (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) - (|:| -3360 - (-2 (|:| |b| *3) (|:| |c| *3) (|:| 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(-1090))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1205)))) ((*1 *1 *1) (-12 (-5 *1 (-665 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-670 *2)) (-4 *2 (-844)))) @@ -15615,7 +15727,42 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-561)) (-5 *1 (-856)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-842) (-362))) (-5 *1 (-1052 *2 *3)) - (-4 *3 (-1229 *2))))) + (-4 *3 (-1230 *2))))) +(((*1 *1 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1042)) (-4 *3 (-786)))) + ((*1 *1 *1) + (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1042)) (-14 *3 (-638 (-1166))))) + ((*1 *1 *1) + (-12 (-5 *1 (-222 *2 *3)) (-4 *2 (-13 (-1042) (-844))) + (-14 *3 (-638 (-1166))))) + ((*1 *1 *1) + (-12 (-4 *1 (-381 *2 *3)) (-4 *2 (-1042)) (-4 *3 (-1090)))) + ((*1 *1 *1) + (-12 (-14 *2 (-638 (-1166))) (-4 *3 (-171)) + (-4 *5 (-237 (-3548 *2) (-765))) + (-14 *6 + (-1 (-112) (-2 (|:| -2442 *4) (|:| -4181 *5)) + (-2 (|:| -2442 *4) (|:| -4181 *5)))) + (-5 *1 (-459 *2 *3 *4 *5 *6 *7)) (-4 *4 (-844)) + (-4 *7 (-942 *3 *5 (-858 *2))))) + ((*1 *1 *1) (-12 (-4 *1 (-507 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(-1090)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-1249 *5)) (-14 *5 (-1166)) (-4 *6 (-1042)) - (-5 *2 (-1226 *5 (-945 *6))) (-5 *1 (-940 *5 *6)) (-5 *3 (-945 *6)))) + (-12 (-5 *4 (-1250 *5)) (-14 *5 (-1166)) (-4 *6 (-1042)) + (-5 *2 (-1227 *5 (-945 *6))) (-5 *1 (-940 *5 *6)) (-5 *3 (-945 *6)))) ((*1 *2 *1) (-12 (-4 *1 (-942 *3 *4 *5)) (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844)) (-5 *2 (-1162 *3)))) @@ -15639,89 +15786,49 @@ (-5 *1 (-943 *5 *4 *6 *7 *3)) (-4 *3 (-13 (-362) - (-10 -8 (-15 -4022 ($ *7)) (-15 -4030 (*7 $)) (-15 -4045 (*7 $))))))) + (-10 -8 (-15 -4064 ($ *7)) (-15 -4077 (*7 $)) (-15 -4088 (*7 $))))))) ((*1 *2 *3 *4 *2) (-12 (-5 *2 (-1162 *3)) (-4 *3 (-13 (-362) - (-10 -8 (-15 -4022 ($ *7)) (-15 -4030 (*7 $)) (-15 -4045 (*7 $))))) + (-10 -8 (-15 -4064 ($ *7)) (-15 -4077 (*7 $)) (-15 -4088 (*7 $))))) (-4 *7 (-942 *6 *5 *4)) (-4 *5 (-787)) (-4 *4 (-844)) (-4 *6 (-1042)) (-5 *1 (-943 *5 *4 *6 *7 *3)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1166)) (-4 *5 (-553)) (-5 *2 (-406 (-1162 (-406 (-945 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(-5 *3 (-1254 *4)) (-4 *4 (-348)) (-5 *2 (-1162 *4)) + (-5 *1 (-526 *4))))) +(((*1 *2 *2 *3 *3) + (-12 (-5 *2 (-1254 *4)) (-5 *3 (-1110)) (-4 *4 (-348)) + (-5 *1 (-526 *4))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1205)))) ((*1 *1 *1) (-12 (-5 *1 (-665 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-670 *2)) (-4 *2 (-844)))) @@ -15729,71 +15836,41 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-561)) (-5 *1 (-856)))) ((*1 *2 *1) (-12 (-4 *2 (-13 (-842) (-362))) (-5 *1 (-1052 *2 *3)) - (-4 *3 (-1229 *2))))) -(((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-914)) (-5 *4 (-1148)) (-5 *2 (-1258)) (-5 *1 (-1254))))) -(((*1 *2 *1) (-12 (-5 *2 (-638 (-1166))) (-5 *1 (-1170))))) + (-4 *3 (-1230 *2))))) +(((*1 *2) (-12 (-5 *2 (-378)) (-5 *1 (-1033))))) (((*1 *2 *1) (-12 (-4 *3 (-1042)) (-4 *4 (-787)) (-4 *5 (-844)) (-5 *2 (-638 *1)) (-4 *1 (-942 *3 *4 *5))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-682 *3)) (-4 *3 (-1042)) (-5 *1 (-683 *3))))) (((*1 *2 *1) (-12 (-5 *2 (-638 (-607 *1))) (-4 *1 (-301))))) +(((*1 *2 *1 *1) 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(-1042)) + (-4 *6 (-237 *4 *5)) (-4 *7 (-237 *3 *5)) (-4 *5 (-553)) + (-5 *2 (-765))))) +(((*1 *2 *3 *4 *4 *3) + (|partial| -12 (-5 *4 (-607 *3)) + (-4 *3 (-13 (-429 *5) (-27) (-1190))) + (-4 *5 (-13 (-450) (-1031 (-561)) (-844) (-146) (-634 (-561)))) + (-5 *2 (-2 (|:| -3413 *3) (|:| |coeff| *3))) + (-5 *1 (-563 *5 *3 *6)) (-4 *6 (-1090))))) (((*1 *2 *3) (-12 (-5 *3 (-1166)) (-4 *4 (-13 (-450) (-844) (-1031 (-561)) (-634 (-561)))) @@ -16350,58 +16441,65 @@ (-4 *6 (-13 (-450) (-844) (-1031 *5) (-634 *5))) (-5 *5 (-561)) (-5 *2 (-52)) (-5 *1 (-314 *6 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *7 (-561))) (-5 *4 (-293 *7)) (-5 *5 (-1220 (-561))) + (-12 (-5 *3 (-1 *7 (-561))) (-5 *4 (-293 *7)) (-5 *5 (-1221 (-561))) (-4 *7 (-13 (-27) (-1190) (-429 *6))) (-4 *6 (-13 (-553) (-844) (-1031 (-561)) (-634 (-561)))) (-5 *2 (-52)) (-5 *1 (-457 *6 *7)))) ((*1 *2 *3 *4 *5 *6) - (-12 (-5 *4 (-1166)) (-5 *5 (-293 *3)) (-5 *6 (-1220 (-561))) + (-12 (-5 *4 (-1166)) (-5 *5 (-293 *3)) (-5 *6 (-1221 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(-1148)) (-5 *2 (-1259)) (-5 *1 (-704)))) + ((*1 *2 *1) (-12 (-5 *2 (-1259)) (-5 *1 (-1185)))) + ((*1 *2 *1 *3) (-12 (-5 *3 (-561)) (-5 *2 (-1259)) (-5 *1 (-1185))))) +(((*1 *2 *2 *3) (-12 (-5 *3 (-561)) (-5 *1 (-1179 *2)) (-4 *2 (-362))))) +(((*1 *2) (-12 (-5 *2 (-638 *3)) (-5 *1 (-1074 *3)) (-4 *3 (-131))))) +(((*1 *2 *1) (-12 (-5 *2 (-1166)) (-5 *1 (-523))))) (((*1 *1 *2 *1) - (-12 (|has| *1 (-6 -4390)) (-4 *1 (-150 *2)) (-4 *2 (-1205)) + (-12 (|has| *1 (-6 -4399)) (-4 *1 (-150 *2)) (-4 *2 (-1205)) (-4 *2 (-1090)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4390)) (-4 *1 (-150 *3)) + (-12 (-5 *2 (-1 (-112) *3)) (|has| *1 (-6 -4399)) (-4 *1 (-150 *3)) (-4 *3 (-1205)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-112) *3)) (-4 *1 (-667 *3)) (-4 *3 (-1205)))) @@ -16413,36 +16511,22 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1130 *3 *4)) (-4 *3 (-13 (-1090) (-34))) (-4 *4 (-13 (-1090) (-34))) (-5 *1 (-1131 *3 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-682 *8)) (-4 *8 (-942 *5 *7 *6)) - (-4 *5 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(-1148) (-1171))) - (-5 *1 (-1171))))) +(((*1 *2 *1) (-12 (-4 *1 (-184)) (-5 *2 (-638 (-112)))))) +(((*1 *2) + (-12 + (-5 *2 (-2 (|:| -3140 (-638 (-1166))) (|:| -2438 (-638 (-1166))))) + (-5 *1 (-1207))))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-1254 *4)) (-5 *3 (-765)) (-4 *4 (-348)) + (-5 *1 (-526 *4))))) +(((*1 *2 *2) + (-12 (-4 *3 (-348)) (-4 *4 (-328 *3)) (-4 *5 (-1230 *4)) + (-5 *1 (-771 *3 *4 *5 *2 *6)) (-4 *2 (-1230 *5)) (-14 *6 (-914)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-765)) (-4 *1 (-1273 *3)) (-4 *3 (-362)) (-4 *3 (-367)))) + ((*1 *1 *1) (-12 (-4 *1 (-1273 *2)) (-4 *2 (-362)) (-4 *2 (-367))))) +(((*1 *2 *3) (-12 (-5 *3 (-378)) (-5 *2 (-224)) (-5 *1 (-1257)))) + ((*1 *2) (-12 (-5 *2 (-224)) (-5 *1 (-1257))))) (((*1 *2 *3) (-12 (-5 *3 (-1166)) (-4 *4 (-13 (-450) (-844) (-1031 (-561)) (-634 (-561)))) @@ -16477,45 +16561,80 @@ (-4 *6 (-13 (-553) (-844) (-1031 (-561)) (-634 (-561)))) (-5 *2 (-52)) (-5 *1 (-457 *6 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *7 (-561))) (-5 *4 (-293 *7)) 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(-842)))))) -(((*1 *2 *3 *2) (-12 (-5 *3 (-765)) (-5 *1 (-850 *2)) (-4 *2 (-171)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1162 (-561))) (-5 *1 (-935)) (-5 *3 (-561))))) -(((*1 *2) (-12 (-5 *2 (-1137 (-1148))) (-5 *1 (-390))))) -(((*1 *1 *1) (-5 *1 (-1054)))) -(((*1 *2 *3 *4 *4 *4 *4 *5 *5) - (-12 (-5 *3 (-1 (-378) (-378))) (-5 *4 (-378)) - (-5 *2 - (-2 (|:| -2484 *4) (|:| -3941 *4) (|:| |totalpts| (-561)) - (|:| |success| (-112)))) - (-5 *1 (-783)) (-5 *5 (-561))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1252 *2)) (-4 *2 (-1205)) (-4 *2 (-995)) + (-4 *2 (-1042))))) +(((*1 *2 *1) (-12 (-5 *2 (-768)) (-5 *1 (-52))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4390)) (-4 *1 (-150 *2)) (-4 *2 (-1205)) + (-12 (|has| *1 (-6 -4399)) (-4 *1 (-150 *2)) (-4 *2 (-1205)) (-4 *2 (-1090))))) -(((*1 *2 *1) (-12 (-5 *2 (-768)) (-5 *1 (-52))))) +(((*1 *1 *1 *1) (-5 *1 (-856)))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-638 + (-2 + (|:| -2285 + (-2 (|:| |var| (-1166)) (|:| |fn| (-315 (-224))) + (|:| -2185 (-1084 (-837 (-224)))) (|:| |abserr| (-224)) + (|:| |relerr| (-224)))) + (|:| -2677 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1146 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2185 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-556))))) (((*1 *1 *2 *2 *3) (-12 (-5 *2 (-765)) (-4 *3 (-1205)) (-4 *1 (-57 *3 *4 *5)) (-4 *4 (-372 *3)) (-4 *5 (-372 *3)))) @@ 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-(((*1 *2 *1) (-12 (-5 *2 (-765)) (-5 *1 (-898 *3)) (-4 *3 (-1090))))) -(((*1 *2 *1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-170)))) - ((*1 *2 *1) (-12 (-5 *2 (-1258)) (-5 *1 (-1254)))) - ((*1 *2 *1) (-12 (-5 *2 (-1258)) (-5 *1 (-1255))))) -(((*1 *2 *3 *4 *3 *4 *4 *4) - (-12 (-5 *3 (-682 (-224))) (-5 *4 (-561)) (-5 *2 (-1028)) - (-5 *1 (-750))))) -(((*1 *1 *2 *2 *1) (-12 (-5 *1 (-640 *2)) (-4 *2 (-1090))))) + (-12 (-5 *2 (-856)) (-5 *1 (-389 *3 *4 *5)) (-14 *3 (-765)) + (-14 *4 (-765)) (-4 *5 (-171))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |stiffness| (-378)) (|:| |stability| (-378)) - (|:| |expense| (-378)) (|:| |accuracy| (-378)) - (|:| |intermediateResults| (-378)))) - (-5 *2 (-1028)) (-5 *1 (-304))))) + (-12 (-5 *3 (-638 *2)) (-4 *2 (-429 *4)) (-5 *1 (-157 *4 *2)) + (-4 *4 (-13 (-844) (-553)))))) +(((*1 *2 *3 *4 *2) + (-12 (-5 *2 (-638 (-638 (-638 *5)))) (-5 *3 (-1 (-112) *5 *5)) + (-5 *4 (-638 *5)) (-4 *5 (-844)) (-5 *1 (-1176 *5))))) (((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-315 (-224))) (-5 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*3) - (|partial| -12 (-5 *3 (-945 *4)) (-4 *4 (-1042)) (-4 *4 (-609 *2)) - (-5 *2 (-378)) (-5 *1 (-779 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-945 *5)) (-5 *4 (-914)) (-4 *5 (-1042)) - (-4 *5 (-609 *2)) (-5 *2 (-378)) (-5 *1 (-779 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-406 (-945 *4))) (-4 *4 (-553)) - (-4 *4 (-609 *2)) (-5 *2 (-378)) (-5 *1 (-779 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-406 (-945 *5))) (-5 *4 (-914)) (-4 *5 (-553)) - (-4 *5 (-609 *2)) (-5 *2 (-378)) (-5 *1 (-779 *5)))) - ((*1 *2 *3) - (|partial| -12 (-5 *3 (-315 *4)) (-4 *4 (-553)) (-4 *4 (-844)) - (-4 *4 (-609 *2)) (-5 *2 (-378)) (-5 *1 (-779 *4)))) - ((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-315 *5)) (-5 *4 (-914)) (-4 *5 (-553)) - (-4 *5 (-844)) (-4 *5 (-609 *2)) (-5 *2 (-378)) - (-5 *1 (-779 *5))))) -(((*1 *2 *1) (-12 (-5 *2 (-638 (-1148))) (-5 *1 (-393))))) -(((*1 *1 *1 *2) - (-12 - (-5 *2 - (-2 (|:| -1313 (-638 (-856))) (|:| -2090 (-638 (-856))) - (|:| |presup| (-638 (-856))) (|:| -1351 (-638 (-856))) - (|:| |args| (-638 (-856))))) - (-5 *1 (-1166)))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-638 (-638 (-856)))) (-5 *1 (-1166))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-976 *2)) (-4 *2 (-1190))))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-465)))) + ((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-465))))) (((*1 *2 *2 *2) - (-12 (-4 *3 (-1205)) (-5 *1 (-181 *3 *2)) (-4 *2 (-667 *3))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1093 *3 *4 *5 *6 *7)) (-4 *3 (-1090)) (-4 *4 (-1090)) - (-4 *5 (-1090)) (-4 *6 (-1090)) (-4 *7 (-1090)) (-5 *2 (-112))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1148)) (-5 *2 (-311)) (-5 *1 (-823))))) -(((*1 *2) - (-12 (-4 *4 (-171)) (-5 *2 (-112)) (-5 *1 (-365 *3 *4)) - (-4 *3 (-366 *4)))) - ((*1 *2) (-12 (-4 *1 (-366 *3)) (-4 *3 (-171)) (-5 *2 (-112))))) + (-12 (-4 *3 (-362)) (-5 *1 (-760 *2 *3)) (-4 *2 (-702 *3)))) + ((*1 *1 *1 *1) (-12 (-4 *1 (-846 *2)) (-4 *2 (-1042)) (-4 *2 (-362))))) +(((*1 *1 *2) + (|partial| -12 (-5 *2 (-813 *3)) (-4 *3 (-844)) (-5 *1 (-665 *3))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-253 *2)) (-4 *2 (-1205))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-170))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-638 *2)) (-4 *2 (-543)) (-5 *1 (-158 *2))))) +(((*1 *1 *2) (-12 (-5 *2 (-638 (-856))) (-5 *1 (-856)))) + ((*1 *1 *1 *1) (-5 *1 (-856)))) (((*1 *1 *1) (-12 (-5 *1 (-670 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-813 *2)) (-4 *2 (-844)))) ((*1 *1 *1) (-12 (-5 *1 (-886 *2)) (-4 *2 (-844)))) @@ -16632,17 +16732,17 @@ (|partial| -12 (-4 *1 (-1198 *2 *3 *4 *5)) (-4 *2 (-553)) (-4 *3 (-787)) (-4 *4 (-844)) (-4 *5 (-1056 *2 *3 *4)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-765)) (-4 *1 (-1241 *3)) (-4 *3 (-1205)))) - ((*1 *1 *1) (-12 (-4 *1 (-1241 *2)) (-4 *2 (-1205))))) + (-12 (-5 *2 (-765)) (-4 *1 (-1242 *3)) (-4 *3 (-1205)))) + ((*1 *1 *1) (-12 (-4 *1 (-1242 *2)) (-4 *2 (-1205))))) (((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-406 *5)) (-4 *4 (-1209)) (-4 *5 (-1229 *4)) - (-5 *1 (-147 *4 *5 *2)) (-4 *2 (-1229 *3)))) + (-12 (-5 *3 (-406 *5)) (-4 *4 (-1209)) (-4 *5 (-1230 *4)) + (-5 *1 (-147 *4 *5 *2)) (-4 *2 (-1230 *3)))) ((*1 *2 *3) (-12 (-5 *3 (-1168 (-406 (-561)))) (-5 *2 (-406 (-561))) (-5 *1 (-189)))) ((*1 *2 *2 *3 *4) (-12 (-5 *2 (-682 (-315 (-224)))) (-5 *3 (-638 (-1166))) - (-5 *4 (-1253 (-315 (-224)))) (-5 *1 (-204)))) + (-5 *4 (-1254 (-315 (-224)))) (-5 *1 (-204)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-638 (-293 *3))) (-4 *3 (-308 *3)) (-4 *3 (-1090)) (-4 *3 (-1205)) (-5 *1 (-293 *3)))) @@ -16731,44 +16831,31 @@ ((*1 *2 *2 *3) (-12 (-5 *2 (-1146 *3)) (-4 *3 (-1042)) (-5 *1 (-1150 *3)))) ((*1 *2 *1 *3) - (-12 (-4 *1 (-1231 *3 *4)) (-4 *3 (-1042)) (-4 *4 (-786)) + (-12 (-4 *1 (-1232 *3 *4)) (-4 *3 (-1042)) (-4 *4 (-786)) (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1146 *3))))) -(((*1 *2 *3) - (-12 (-4 *4 (-450)) (-4 *4 (-553)) (-4 *5 (-787)) (-4 *6 (-844)) - (-5 *2 (-638 *3)) (-5 *1 (-970 *4 *5 *6 *3)) - (-4 *3 (-1056 *4 *5 *6))))) -(((*1 *2 *1) - (-12 (-5 *2 (-638 (-52))) (-5 *1 (-885 *3)) (-4 *3 (-1090))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-450)) (-4 *6 (-787)) 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(-129)))))) +(((*1 *2 *3) (-12 (-5 *3 (-1148)) (-5 *2 (-1259)) (-5 *1 (-435))))) +(((*1 *1 *1 *2) + (-12 (-5 *1 (-642 *2 *3 *4)) (-4 *2 (-1090)) (-4 *3 (-23)) + (-14 *4 *3)))) +(((*1 *2) (-12 (-4 *3 (-171)) (-5 *2 (-1254 *1)) (-4 *1 (-366 *3))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1090)) (-4 *5 (-1090)) + (-4 *6 (-1090)) (-5 *2 (-1 *6 *5 *4)) (-5 *1 (-677 *4 *5 *6))))) (((*1 *2 *1) (-12 (-4 *1 (-599 *3 *2)) (-4 *3 (-1090)) (-4 *3 (-844)) (-4 *2 (-1205)))) @@ -16781,64 +16868,46 @@ (|partial| -12 (-4 *1 (-1198 *3 *4 *5 *2)) (-4 *3 (-553)) (-4 *4 (-787)) (-4 *5 (-844)) (-4 *2 (-1056 *3 *4 *5)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-765)) (-4 *1 (-1241 *3)) (-4 *3 (-1205)))) - ((*1 *2 *1) (-12 (-4 *1 (-1241 *2)) (-4 *2 (-1205))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-406 (-561))) (-4 *5 (-787)) (-4 *6 (-844)) - (-4 *7 (-553)) (-4 *8 (-942 *7 *5 *6)) - (-5 *2 (-2 (|:| -4196 (-765)) (|:| -4188 *9) (|:| |radicand| *9))) - (-5 *1 (-946 *5 *6 *7 *8 *9)) (-5 *4 (-765)) - (-4 *9 - (-13 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(-362)) (-4 *7 (-1229 *5)) (-4 *4 (-718 *5 *7)) - (-5 *2 (-2 (|:| -3327 (-682 *6)) (|:| |vec| (-1253 *5)))) - (-5 *1 (-805 *5 *6 *7 *4 *3)) (-4 *6 (-649 *5)) (-4 *3 (-649 *4))))) + (-12 (-5 *3 (-638 (-1 (-112) *8))) (-4 *8 (-1056 *5 *6 *7)) + (-4 *5 (-553)) (-4 *6 (-787)) (-4 *7 (-844)) + (-5 *2 (-2 (|:| |goodPols| (-638 *8)) (|:| |badPols| (-638 *8)))) + (-5 *1 (-970 *5 *6 *7 *8)) (-5 *4 (-638 *8))))) +(((*1 *2 *2) (-12 (-5 *1 (-675 *2)) (-4 *2 (-1090))))) +(((*1 *1 *2 *2) (-12 (-4 *1 (-165 *2)) (-4 *2 (-171))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1148)) (-5 *2 (-1259)) (-5 *1 (-1256))))) +(((*1 *1 *1) (-5 *1 (-1054)))) +(((*1 *2 *1) + (-12 (-5 *2 (-765)) (-5 *1 (-1154 *3 *4)) (-14 *3 (-914)) + (-4 *4 (-1042))))) +(((*1 *2 *3 *3 *1) + (-12 (-4 *4 (-450)) (-4 *5 (-787)) (-4 *6 (-844)) + (-4 *3 (-1056 *4 *5 *6)) (-5 *2 (-3 *3 (-638 *1))) + (-4 *1 (-1062 *4 *5 *6 *3))))) +(((*1 *1 *1 *2) (-12 (-5 *2 (-1166)) (-5 *1 (-1054))))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-638 (-1166))) (-5 *3 (-1166)) (-5 *1 (-534)))) ((*1 *2 *3 *2) @@ -16850,6 +16919,15 @@ ((*1 *2 *3 *2 *4) (-12 (-5 *4 (-638 (-1166))) (-5 *2 (-1166)) (-5 *1 (-698 *3)) (-4 *3 (-609 (-534)))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1124 *3)) (-4 *3 (-1042)) + (-5 *2 + (-2 (|:| -3233 (-765)) (|:| |curves| (-765)) + (|:| |polygons| (-765)) (|:| |constructs| (-765))))))) +(((*1 *2 *3) + (-12 (-5 *3 (-638 *7)) (-4 *7 (-1056 *4 *5 *6)) (-4 *4 (-553)) + (-4 *5 (-787)) (-4 *6 (-844)) (-5 *2 (-112)) + (-5 *1 (-970 *4 *5 *6 *7))))) (((*1 *2 *1 *3) (-12 (-5 *2 (-406 (-561))) (-5 *1 (-117 *4)) (-14 *4 *3) (-5 *3 (-561)))) @@ -16863,50 +16941,19 @@ ((*1 *2 *1 *1) (-12 (-4 *1 (-1005)) (-5 *2 (-406 (-561))))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1059 *2 *3)) (-4 *2 (-13 (-842) (-362))) - (-4 *3 (-1229 *2)))) + (-4 *3 (-1230 *2)))) ((*1 *2 *1 *3) - (-12 (-4 *1 (-1231 *2 *3)) (-4 *3 (-786)) - (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -4022 (*2 (-1166)))) + (-12 (-4 *1 (-1232 *2 *3)) (-4 *3 (-786)) + (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 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*1)) - (-4 *1 (-1062 *4 *5 *6 *3)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1198 *3 *4 *5 *2)) (-4 *3 (-553)) (-4 *4 (-787)) - (-4 *5 (-844)) (-4 *2 (-1056 *3 *4 *5)))) - ((*1 *1 *1 *2) - (-12 (-4 *1 (-1231 *3 *2)) (-4 *3 (-1042)) (-4 *2 (-786))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-45 (-1148) (-768))) (-5 *1 (-114))))) -(((*1 *2 *1 *1) - (|partial| -12 (-4 *1 (-1056 *3 *4 *5)) (-4 *3 (-1042)) - (-4 *4 (-787)) (-4 *5 (-844)) (-5 *2 (-112))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-362)) (-5 *1 (-760 *2 *3)) (-4 *2 (-702 *3)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-846 *2)) (-4 *2 (-1042)) (-4 *2 (-362))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-976 *2)) (-4 *2 (-1190))))) +(((*1 *2 *1) + (-12 (-5 *2 (-866 (-959 *3) (-959 *3))) (-5 *1 (-959 *3)) + (-4 *3 (-960))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-638 (-315 (-224)))) (|:| -3721 (-638 (-224))))) + (-2 (|:| |lfn| (-638 (-315 (-224)))) (|:| -3767 (-638 (-224))))) (-5 *2 (-638 (-1166))) (-5 *1 (-266)))) ((*1 *2 *3) (-12 (-5 *3 (-1162 *7)) (-4 *7 (-942 *6 *4 *5)) (-4 *4 (-787)) @@ -16928,7 +16975,7 @@ (-5 *1 (-943 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-362) - (-10 -8 (-15 -4022 ($ *7)) (-15 -4030 (*7 $)) (-15 -4045 (*7 $))))))) + (-10 -8 (-15 -4064 ($ *7)) (-15 -4077 (*7 $)) (-15 -4088 (*7 $))))))) ((*1 *2 *1) (-12 (-5 *2 (-1092 (-1166))) (-5 *1 (-959 *3)) (-4 *3 (-960)))) ((*1 *2 *1) @@ -16940,61 +16987,54 @@ ((*1 *2 *3) (-12 (-5 *3 (-406 (-945 *4))) (-4 *4 (-553)) (-5 *2 (-638 (-1166))) (-5 *1 (-1036 *4))))) -(((*1 *2 *3) - (|partial| -12 (-4 *4 (-13 (-553) (-146))) - (-5 *2 (-2 (|:| -1605 *3) (|:| -1621 *3))) (-5 *1 (-1223 *4 *3)) - (-4 *3 (-1229 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-791 *2)) (-4 *2 (-171))))) -(((*1 *2 *2) - (-12 (-5 *2 (-638 *6)) (-4 *6 (-1056 *3 *4 *5)) (-4 *3 (-553)) - (-4 *4 (-787)) (-4 *5 (-844)) (-5 *1 (-970 *3 *4 *5 *6))))) -(((*1 *2 *3 *3 *4 *4 *3 *4 *4 *3 *3 *3) - (-12 (-5 *3 (-561)) (-5 *4 (-682 (-224))) (-5 *2 (-1028)) - (-5 *1 (-746))))) -(((*1 *1 *1 *1) (-12 (-4 *1 (-372 *2)) (-4 *2 (-1205)) (-4 *2 (-844)))) - 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\ No newline at end of file |