From a4baedf72d3abfe9f74ee1dade09a454c0ae7c00 Mon Sep 17 00:00:00 2001 From: dos-reis Date: Wed, 7 Jan 2009 07:54:17 +0000 Subject: * interp/sys-utility.boot (readByteFromFile): Tidy. (makeByteBuffer): Set fill pointer. (connectToHostAndPort): Define here. (readByteFromStreamSocket): Likewise. (writeByteToStreamSocket): Likewise. * interp/sys-os.boot (doConnectToHostAndPort): Rename from connectot$NetworkClientSocket. (doReadByteFromStreamSocket): Rename from readByteFromStreamSocket. (doWriteByteToStreamSocket): Rename from writeByteToStreamSocket. * algebra/net.spad.pamphlet: Use Maybe Byte. * algebra/data.spad.pamphlet (ByteBuffer): Fix fill pointer thinko. --- ChangeLog | 4 + contrib/examples/time-client.input | 29 + src/ChangeLog | 14 + src/algebra/data.spad.pamphlet | 9 +- src/algebra/net.spad.pamphlet | 94 +- src/interp/sys-os.boot | 10 +- src/interp/sys-utility.boot | 29 +- src/share/algebra/browse.daase | 644 +- src/share/algebra/category.daase | 1212 +- src/share/algebra/compress.daase | 1308 +- src/share/algebra/interp.daase | 8780 ++++----- src/share/algebra/operation.daase | 33827 ++++++++++++++++++----------------- 12 files changed, 23008 insertions(+), 22952 deletions(-) create mode 100755 contrib/examples/time-client.input diff --git a/ChangeLog b/ChangeLog index 06c7faf3..771d1b6f 100644 --- a/ChangeLog +++ b/ChangeLog @@ -1,3 +1,7 @@ +2009-01-07 Gabriel Dos Reis + + * contrib/examples/time-client.input: New. + 2009-01-03 Gabriel Dos Reis * Makefile.pamphlet (AXIOM_SRC_TARGETS): Add all-databases. diff --git a/contrib/examples/time-client.input b/contrib/examples/time-client.input new file mode 100755 index 00000000..4bb9dcbd --- /dev/null +++ b/contrib/examples/time-client.input @@ -0,0 +1,29 @@ +#!/usr/bin/env open-axiom + +-- This little script is a simple example of how to use +-- the client socket domain in OpenAxiom. +-- It connects to a time server, read the time and print it +-- on the standard output. +-- Contributed by Gabriel Dos Reis. + +s := connectTo(host "time-a.nist.gov", port 13)$INETCLTS + +-- Give up if conection failed. We try only once. +s case nothing => + print message("connection failed")$OutputForm + +-- Read initial linefeed character +readByte! s case nothing => + messagePrint("could not read first linefeed character")$OutputForm + +text := empty()$ByteBuffer -- container of the actual line +buf := byteBuffer 256 -- temporary buffer to read into + +-- Accumulate data until end of input. +while readBytes!(s::INETCLTS,buf) > 0 repeat + text := concat(text,buf) +close! s + +-- Show what we got. We should actually try to remove last +-- linefeed character. +messagePrint(text::String)$OutputForm diff --git a/src/ChangeLog b/src/ChangeLog index 8b621478..4346f47e 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,17 @@ +2009-01-07 Gabriel Dos Reis + + * interp/sys-utility.boot (readByteFromFile): Tidy. + (makeByteBuffer): Set fill pointer. + (connectToHostAndPort): Define here. + (readByteFromStreamSocket): Likewise. + (writeByteToStreamSocket): Likewise. + * interp/sys-os.boot (doConnectToHostAndPort): Rename from + connectot$NetworkClientSocket. + (doReadByteFromStreamSocket): Rename from readByteFromStreamSocket. + (doWriteByteToStreamSocket): Rename from writeByteToStreamSocket. + * algebra/net.spad.pamphlet: Use Maybe Byte. + * algebra/data.spad.pamphlet (ByteBuffer): Fix fill pointer thinko. + 2009-01-06 Gabriel Dos Reis * algebra/net.spad.pamphlet (resolve$Hostname): Return a Maybe %. diff --git a/src/algebra/data.spad.pamphlet b/src/algebra/data.spad.pamphlet index d684c59d..a46ab663 100644 --- a/src/algebra/data.spad.pamphlet +++ b/src/algebra/data.spad.pamphlet @@ -81,8 +81,11 @@ ByteBuffer(): Public == Private where ++ setLength!(buf,n) sets the number of active bytes in the ++ `buf'. Error if `n' is more than the capacity. Private == add + makeByteBuffer(n: NonNegativeInteger): % == + makeByteBuffer(n)$Lisp + byteBuffer n == - buf := makeByteBuffer(n)$Lisp + buf := makeByteBuffer n setLength!(buf,0) buf @@ -127,7 +130,7 @@ ByteBuffer(): Public == Private where s construct l == - buf := byteBuffer(#l) + buf := makeByteBuffer(#l) for b in l for i in 0.. repeat buf.i := b buf @@ -135,7 +138,7 @@ ByteBuffer(): Public == Private where concat(x: %, y:%) == nx := #x ny := #y - buf := byteBuffer(nx + ny) + buf := makeByteBuffer(nx + ny) for i in 0..(nx - 1) repeat buf.i := x.i for i in 0..(ny - 1) repeat diff --git a/src/algebra/net.spad.pamphlet b/src/algebra/net.spad.pamphlet index 05d15354..4f2ded2a 100644 --- a/src/algebra/net.spad.pamphlet +++ b/src/algebra/net.spad.pamphlet @@ -37,25 +37,24 @@ Conduit(): Category == with ++ Description: ++ This category describes input byte stream conduits. InputByteConduit(): Category == Conduit with - readByteIfCan!: % -> SingleInteger - ++ readByteIfCan!(cond) attempts to read a byte from the + readByte!: % -> Maybe Byte + ++ readByte!(cond) attempts to read a byte from the ++ input conduit `cond'. Returns the read byte if successful, - ++ otherwise return -1. - ++ Note: Ideally, the return value should have been of type - ++ Maybe Byte; but that would have implied allocating - ++ a cons cell for every read attempt, which is overkill. - readBytes!: (%,ByteBuffer) -> SingleInteger + ++ 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 readBytes!(cond,buf) == - count: NonNegativeInteger := 0 - b : SingleInteger - while count < capacity buf and ((b := readByteIfCan! cond) >= 0) repeat - qsetelt!(buf,count,b : Byte) - count := count + 1 - setLength!(buf,count)::SingleInteger + count := 0@NonNegativeInteger + while count < capacity buf repeat + case readByte! cond is + b@Byte => + qsetelt!(buf,count,b) + count := count + 1 + otherwise => break + setLength!(buf,count) @ @@ -69,22 +68,19 @@ InputByteConduit(): Category == Conduit with ++ Description: ++ This category describes output byte stream conduits. OutputByteConduit(): Category == Conduit with - writeByteIfCan!: (%,Byte) -> SingleInteger - ++ writeByteIfCan!(c,b) attempts to write the byte `b' on + writeByte!: (%,Byte) -> Maybe Byte + ++ writeByte!(c,b) attempts to write the byte `b' on ++ the conduit `c'. Returns the written byte if successful, - ++ otherwise, returns -1. - ++ Note: Ideally, the return value should have been of type - ++ Maybe Byte; but that would have implied allocating - ++ a cons cell for every write attempt, which is overkill. - writeBytes!: (%,ByteBuffer) -> SingleInteger + ++ 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 writeBytes!(cond,buf) == - count: SingleInteger := 0 + count := 0@NonNegativeInteger while count < capacity buf and - writeByteIfCan!(cond,qelt(buf,count)) >= 0 repeat + writeByte!(cond,qelt(buf,count)) case Byte repeat count := count + 1 count @@ -143,10 +139,10 @@ InputBinaryFile(): Public == Private where per [openBinaryFile(f,input$IOMode)$Lisp,f::FileName,false] isOpen? ifile == not null? rep(ifile).stream - readByteIfCan! ifile == + readByte! ifile == isOpen? ifile => - b: SingleInteger := readByteFromFile(rep(ifile).stream)$Lisp - if b < 0@SingleInteger then + b: Maybe Byte := readByteFromFile(rep(ifile).stream)$Lisp + if b case nothing then rep(ifile).eof := true b error "file is not open" @@ -165,7 +161,6 @@ InputBinaryFile(): Public == Private where position!(ifile,p) == isOpen? ifile => FILE_-POSITION(rep(ifile).stream,p)$Lisp - p error "file is not open" coerce(ifile: %): OutputForm == rep(ifile).filename::OutputForm @@ -200,7 +195,7 @@ OutputBinaryFile(): Public == Private where per [openBinaryFile(f,output$IOMode)$Lisp,f::FileName] isOpen? ifile == not null? rep(ifile).stream - writeByteIfCan!(ifile,b) == + writeByte!(ifile,b) == isOpen? ifile => writeByteToFile(rep(ifile).stream,b)$Lisp error "file is not open" close! ifile == @@ -338,50 +333,45 @@ InetClientStreamSocket(): Public == Private where Public == Join(NetworkClientSocket IP4Address, CoercibleTo OutputForm) with connectTo: (Hostname, PortNumber) -> Maybe % Private == add - -- we hope that a small integer is OK on all platform Host == Union(IP4Address,Hostname) - Rep == Record(%host: Host, %port: PortNumber, %sock: SingleInteger) + -- we hope that a small integer is OK on all platforms + Rep == Record(%host: Host, %port: PortNumber, %sock: Maybe SingleInteger) connectTo(ip: IP4Address, p: PortNumber) == - s: SingleInteger := connectToHostAndPort(ip,4,p)$Lisp - s = -1::SingleInteger => nothing + s: Maybe SingleInteger := connectToHostAndPort(ip,4,p)$Lisp + s case nothing => nothing just per [ip::Host,p,s] connectTo(h: Hostname, p: PortNumber) == (ip := resolve(h)$IP4Address) case nothing => nothing - s: SingleInteger := connectToHostAndPort(ip@IP4Address,4,p)$Lisp - s = -1::SingleInteger => nothing + s: Maybe SingleInteger := connectToHostAndPort(ip@IP4Address,4,p)$Lisp + s case nothing => nothing just per [h::Host,p,s] isConnected? s == - rep(s).%sock ~= -1::SingleInteger + rep(s).%sock case SingleInteger readBytes!(x,b) == - n: SingleInteger := + not isConnected? x => error "socket is not connected" + n: NonNegativeInteger := readFromStreamSocket(rep(x).%sock,b, capacity b)$Lisp - if n <= 0 then close! x - else setLength!(b,n : NonNegativeInteger) - n - readByteIfCan! x == - r: SingleInteger := readByteFromStreamSocket(rep(x).%sock)$Lisp - if r < 0 then close! x - r + setLength!(b,n) + + readByte! x == + not isConnected? x => error "socket is not connected" + readByteFromStreamSocket(rep(x).%sock)$Lisp writeBytes!(x,b) == - n: SingleInteger := - writeToStreamSocket(rep(x).%sock,b, capacity b)$Lisp - if n <= 0 then close! x - else setLength!(b,n : NonNegativeInteger) - n + not isConnected? x => error "socket is not connected" + writeToStreamSocket(rep(x).%sock,b, #b)$Lisp - writeByteIfCan!(x,b) == - r: SingleInteger := writeByteToStreamSocket(rep(x).%sock,b)$Lisp - if r < 0 then close! x - r + writeByte!(x,b) == + not isConnected? x => error "socket is not connected" + writeByteToStreamSocket(rep(x).%sock,b)$Lisp close! x == closeSocket(rep(x).%sock)$Lisp - rep(x).%sock := -1::SingleInteger + rep(x).%sock := nothing x coerce(x: %): OutputForm == diff --git a/src/interp/sys-os.boot b/src/interp/sys-os.boot index d41ccfc7..2e9bf84b 100644 --- a/src/interp/sys-os.boot +++ b/src/interp/sys-os.boot @@ -1,4 +1,4 @@ --- Copyright (C) 2007-2008 Gabriel Dos Reis. +-- Copyright (C) 2007-2009 Gabriel Dos Reis. -- All rights reserved. -- -- Redistribution and use in source and binary forms, with or without @@ -125,17 +125,17 @@ import oa__get__host__address: (string, int, writeonly buffer byte) -> int ++ Return -1 on failure, otherwise the file descriptor corresponding ++ to the obtained client socket. import oa__connect__ip__port__stream: (readonly buffer byte,int,int) -> int - for connectToHostAndPort + for doConnectToHostAndPort ++ Try to read bytes of data from socket. ++ Return -1 for failure; number of read bytes, otherwise. import oa__socket__read: (int,writeonly buffer byte,int) -> int for readFromStreamSocket -++ Try to read a byte socket from a socket. +++ Try read a byte socket from a socket. ++ Return -1 on failure; byte read, otherwise. import oa__socket__read__byte: int -> int - for readByteFromStreamSocket + for doReadByteFromStreamSocket ++ Try to write bytes of data to socket. ++ Return -1 on failure; actual bytes written, otherwise. @@ -145,7 +145,7 @@ import oa__socket__write: (int,readonly buffer byte,int) -> int ++ Try to write a byte to socket. ++ Return -1 on failure; the written byte, otherwise. import oa__socket__write__byte: (int,int) -> int - for writeByteToStreamSocket + for doWriteByteToStreamSocket import oa__close__socket: int -> int for closeSocket diff --git a/src/interp/sys-utility.boot b/src/interp/sys-utility.boot index 3fcbdf9c..510f5080 100644 --- a/src/interp/sys-utility.boot +++ b/src/interp/sys-utility.boot @@ -261,14 +261,11 @@ openBinaryFile(file,mode) == KEYWORD::ELEMENT_-TYPE,"%Byte") ++ Attemp to read a byte from input file `ifile'. If not end of -++ file, return the read byte; otherwise -1. -readByteFromFile: %Thing -> %Short +++ file, return the read byte; %nothing. readByteFromFile ifile == - byte := READ_-BYTE(ifile,false) => byte - -1 + READ_-BYTE(ifile,false,%nothing) ++ Write byte `b' to output binary file `ofile'. -writeByteToFile: (%Thing,%Byte) -> %Short writeByteToFile(ofile,b) == WRITE_-BYTE(b,ofile) @@ -276,11 +273,31 @@ closeFile file == CLOSE file nil +--% Socket I/O + +++ Attempt to establish a client TCP/IP socket connection. The IP numeric +++ address is specified by the first argument; second argument is the +++ version of IP used (4 or 6); third argument is the desired port. +++ Return %nothing on failure, otherwise the file descriptor corresponding +++ to the obtained client socket. +connectToHostAndPort(addr,prot,port) == + (socket := doConnectToHostAndPort(addr,prot,port)) < 0 => %nothing + socket + +++ Attempt to read a byte from the socket `s'. If unsuccessful, +++ return %nothing. +readByteFromStreamSocket s == + (byte := doReadByteFromStreamSocket s) < 0 => %nothing + COERCE(byte,"%Byte") + +writeByteToStreamSocket(s,b) == + (byte := doWriteByteToStreamSocket(s,b)) < 0 => %nothing + COERCE(byte,"%Byte") --% makeByteBuffer(n,b == 0) == MAKE_-ARRAY(n,KEYWORD::ELEMENT_-TYPE,"%Byte", - KEYWORD::FILL_-POINTER,0, KEYWORD::INITIAL_-ELEMENT,b) + KEYWORD::FILL_-POINTER,true, KEYWORD::INITIAL_-ELEMENT,b) quoteForm t == ["QUOTE",t] diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index d3719ea1..ca84745d 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2276380 . 3440285145) +(2275580 . 3440300497) (-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 @@ -56,7 +56,7 @@ 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 -3199) +(-32 R -3189) ((|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 -1028) (QUOTE (-558))))) @@ -88,11 +88,11 @@ NIL ((|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 -3199 UP UPUP -2522) +(-40 -3189 UP UPUP -3142) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3996 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3996 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3996 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) -(-41 R -3199) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3994 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3994 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3994 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +(-41 R -3189) ((|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 (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -429) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-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."))) ((-4383 . T) (-4384 . T)) -((-3996 (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|))))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|))))))) +((-3994 (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|))))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3199) +(-54 |Base| R -3189) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-61 -3149) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-61 -3179) ((|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 -3149) +(-62 -3179) ((|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 -3149) +(-63 -3179) ((|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 -3149) +(-64 -3179) ((|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 -3149) +(-65 -3179) ((|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 -3149) +(-66 -3179) ((|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 -3149) +(-67 -3179) ((|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 -3149) +(-68 -3179) ((|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 -3149) +(-69 -3179) ((|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 -3149) +(-70 -3179) ((|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 -3149) +(-71 -3179) ((|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 -3149) +(-72 -3179) ((|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 -3149) +(-73 -3179) ((|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 -3149) +(-74 -3179) ((|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 -3149) +(-77 -3179) ((|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 -3149) +(-78 -3179) ((|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 -3149) +(-79 -3179) ((|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 -3149) +(-80 -3179) ((|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 -3149) +(-81 -3179) ((|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 -3149) +(-82 -3179) ((|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 -3149) +(-83 -3179) ((|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 -3149) +(-84 -3179) ((|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 -3149) +(-85 -3179) ((|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 -3149) +(-86 -3179) ((|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 -3149) +(-87 -3179) ((|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 -3149) +(-88 -3179) ((|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 -3149) +(-89 -3179) ((|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 @@ -295,7 +295,7 @@ NIL (-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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ 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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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 @@ -363,7 +363,7 @@ 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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|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 -3199 UP) +(-115 -3189 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 @@ -399,7 +399,7 @@ 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}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3996 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (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 (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))))) +((|HasCategory| (-116 |#1|) (QUOTE (-899))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-146))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-116 |#1|) (QUOTE (-1012))) (|HasCategory| (-116 |#1|) (QUOTE (-811))) (-3994 (|HasCategory| (-116 |#1|) (QUOTE (-811))) (|HasCategory| (-116 |#1|) (QUOTE (-841)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-1138))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-116 |#1|) (QUOTE (-232))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (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 (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-116 |#1|) (QUOTE (-899)))) (|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 @@ -415,7 +415,7 @@ 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"))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3996 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) +((-3994 (-12 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129)))))) (-3994 (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -308) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-129) (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087)))) (|HasCategory| (-129) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-129) (QUOTE (-1087))) (|HasCategory| (-129) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-129) (QUOTE (-1087))) (|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 @@ -464,11 +464,11 @@ NIL ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4385 "*") . T)) NIL -(-134 |minix| -4352 S T$) +(-134 |minix| -1470 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -4352 R) +(-135 |minix| -1470 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -491,7 +491,7 @@ 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}."))) ((-4383 . T) (-4373 . T) (-4384 . T)) -((-3996 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-3994 (-12 (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-367))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|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 @@ -516,7 +516,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4380 . T)) NIL -(-147 -3199 UP UPUP) +(-147 -3189 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 @@ -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 -3199) +(-157 R -3189) ((|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 @@ -590,7 +590,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (QUOTE (-543))) (|HasCategory| |#2| (QUOTE (-992))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasCategory| |#2| (QUOTE (-1048))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4379)) (|HasAttribute| |#2| (QUOTE -4382)) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-841)))) (-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}."))) -((-4376 -3996 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4376 -3994 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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}."))) -((-4376 -3996 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|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 -631) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-819)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1185)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -606) 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(|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-348))))) +((-4376 -3994 (|has| |#1| (-550)) (-12 (|has| |#1| (-306)) (|has| |#1| (-899)))) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4379 |has| |#1| (-6 -4379)) (-4382 |has| |#1| (-6 -4382)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-348)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|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 -631) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-367)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-819)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-841)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1012)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-1185)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -606) 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(|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-899)))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-899))))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (QUOTE (-1048))) (-12 (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-1185)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-232))) (-12 (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasAttribute| |#1| (QUOTE -4379)) (|HasAttribute| |#1| (QUOTE -4382)) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-899)))) (|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 @@ -676,7 +676,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors."))) NIL NIL -(-187 R -3199) +(-187 R -3189) ((|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 -3199 UP UPUP R) +(-214 -3189 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 -3199 FP) +(-215 -3189 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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-218 R -3199) +(-218 R -3189) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -815,18 +815,18 @@ NIL (-221 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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}."))) ((-4380 . T)) NIL -(-223 R -3199) +(-223 R -3189) ((|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}."))) -((-1395 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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)}.}"))) @@ -835,7 +835,7 @@ 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}"))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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 @@ -872,22 +872,22 @@ NIL ((|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 -4352 R) +(-236 S -1470 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 (-784))) (|HasCategory| |#3| (QUOTE (-839))) (|HasAttribute| |#3| (QUOTE -4380)) (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-367))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (QUOTE (-1087)))) -(-237 -4352 R) +(-237 -1470 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"))) ((-4377 |has| |#2| (-1039)) (-4378 |has| |#2| (-1039)) (-4380 |has| |#2| (-6 -4380)) ((-4385 "*") |has| |#2| (-171)) (-4383 . T)) NIL -(-238 -4352 A B) +(-238 -1470 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 -4352 R) +(-239 -1470 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."))) ((-4377 |has| |#2| (-1039)) (-4378 |has| |#2| (-1039)) (-4380 |has| |#2| (-6 -4380)) ((-4385 "*") |has| |#2| (-171)) (-4383 . 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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 @@ -907,7 +907,7 @@ 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}"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|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 @@ -915,7 +915,7 @@ 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.")) 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(|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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(QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-3994 (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (|HasCategory| |#3| (QUOTE (-717))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163)))))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558))))) (-3994 (|HasCategory| |#3| (QUOTE (-1039))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1087)))) (-3994 (|HasAttribute| |#3| (QUOTE -4380)) (-12 (|HasCategory| |#3| (QUOTE (-232))) (|HasCategory| |#3| (QUOTE (-1039)))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#3| (QUOTE (-1039))) (|HasCategory| |#3| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|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 @@ -983,7 +983,7 @@ 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"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#3| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#3| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|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 -3199) +(-275 R -3189) ((|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 -3199) +(-276 R -3189) ((|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 @@ -1080,7 +1080,7 @@ NIL ((|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| -1783 -2297 |exactQuo|) +(-288 S R |Mod| -2915 -3391 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL @@ -1102,21 +1102,21 @@ NIL NIL (-293 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-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 -3199 S) +(-296 -3189 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 -3199) +(-297 E -3189) ((|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 @@ -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 -3199) +(-309 -3189) ((|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 @@ -1179,7 +1179,7 @@ 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}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1012))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (-3996 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1138))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))) (-3996 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))))) +((|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1012))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (-3994 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-811))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-1138))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-232))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -308) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (LIST (QUOTE -285) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1232) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-306))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-543))) (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-841))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))) (-3994 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-144))) (-12 (|HasCategory| (-1232 |#1| |#2| |#3| |#4|) (QUOTE (-899))) (|HasCategory| $ (QUOTE (-144)))))) (-313 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -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."))) -((-4380 -3996 (-2113 (|has| |#1| (-1039)) (|has| |#1| (-631 (-558)))) (-12 (|has| |#1| (-550)) (-3996 (-2113 (|has| |#1| (-1039)) (|has| |#1| (-631 (-558)))) (|has| |#1| (-1039)) (|has| |#1| (-471)))) (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4381 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(-25))) (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))))) (-3994 (|HasCategory| |#1| (QUOTE (-471))) (|HasCategory| |#1| (QUOTE (-1039)))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| $ (QUOTE (-1039))) (|HasCategory| $ (LIST (QUOTE -1028) (QUOTE (-558))))) +(-316 R -3189) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1203,7 +1203,7 @@ 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."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3221) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|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 @@ -1235,12 +1235,12 @@ 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."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) -(-327 S -3199) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +(-327 S -3189) ((|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 -3199) +(-328 -3189) ((|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL @@ -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 -3199 UP UPUP R) +(-333 S -3189 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 -3199 UP UPUP R) +(-334 -3189 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 -3199 UP UPUP R) +(-335 -3189 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 @@ -1288,26 +1288,26 @@ NIL ((|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 -3199 UP UPUP) +(-340 S -3189 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 -3199 UP UPUP) +(-341 -3189 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."))) ((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3994 (|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3994 (|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 @@ -1324,31 +1324,31 @@ NIL ((|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-349 R UP -3199) +(-349 R UP -3189) ((|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3994 (|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3994 (|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}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#1|) (QUOTE (-144)))) +((-3994 (|HasCategory| (-900 |#1|) (QUOTE (-144))) (|HasCategory| (-900 |#1|) (QUOTE (-367)))) (|HasCategory| (-900 |#1|) (QUOTE (-146))) (|HasCategory| (-900 |#1|) (QUOTE (-367))) (|HasCategory| (-900 |#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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) -(-355 -3199 GF) +((-3994 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +(-355 -3189 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 @@ -1356,14 +1356,14 @@ 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 -3199 FP FPP) +(-357 -3189 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}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-367)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-144)))) +((-3994 (|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 @@ -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}."))) -((-4366 . T) (-4374 . T) (-1395 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-4366 . T) (-4374 . T) (-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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}."))) @@ -1492,7 +1492,7 @@ NIL ((|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 -3199 UP UPUP R) +(-391 -3189 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 -3149 |returnType| -1314 |symbols|) +(-397 -3179 |returnType| -2164 |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 -3199 UP) +(-398 -3189 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1542,7 +1542,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4366)) (|HasAttribute| |#1| (QUOTE -4374))) (-403) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-1395 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . 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."))) @@ -1555,7 +1555,7 @@ 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."))) ((-4370 -12 (|has| |#1| (-6 -4381)) (|has| |#1| (-450)) (|has| |#1| (-6 -4370))) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3996 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (QUOTE (-811))) (-3994 (|HasCategory| |#1| (QUOTE (-811))) (|HasCategory| |#1| (QUOTE (-841)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-819))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 (-819)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-543))) (-12 (|HasAttribute| |#1| (QUOTE -4381)) (|HasAttribute| |#1| (QUOTE -4370)) (|HasCategory| |#1| (QUOTE (-450)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-412 R -3199 UP A) +(-412 R -3189 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4380 . T)) NIL -(-413 R -3199 UP A |ibasis|) +(-413 R -3189 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 -1028) (|devaluate| |#2|)))) @@ -1599,7 +1599,7 @@ 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."))) ((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-450)))) +((|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -308) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -285) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-1204))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-1204)))) (|HasCategory| |#1| (QUOTE (-1012))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 -890) (QUOTE (-1163)))) (|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 @@ -1628,7 +1628,7 @@ NIL ((|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4383 . T) (-4373 . T) (-4384 . T)) NIL -(-425 R -3199) +(-425 R -3189) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4370 -12 (|has| |#1| (-6 -4370)) (|has| |#2| (-6 -4370))) (-4377 . T) (-4378 . T) (-4380 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4370)) (|HasAttribute| |#2| (QUOTE -4370)))) -(-427 R -3199) +(-427 R -3189) ((|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 -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-471))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -606) (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}."))) -((-4380 -3996 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-550)) (-4375 |has| |#1| (-550))) +((-4380 -3994 (|has| |#1| (-1039)) (|has| |#1| (-471))) (-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-550)) (-4375 |has| |#1| (-550))) NIL -(-430 R -3199) +(-430 R -3189) ((|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 -3199) +(-431 R -3189) ((|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 -3199) +(-432 R -3189) ((|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 -3199 UP) +(-434 R -3189 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 -1028) (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 -3199) +(-441 R UP -3189) ((|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 @@ -1739,7 +1739,7 @@ NIL (-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"))) (((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|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 @@ -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| -3199 R) +(-469 |lv| -3189 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 @@ -1819,11 +1819,11 @@ 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."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3221) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|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."))) ((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087)))) (-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)}"))) ((-4384 . T) (-4383 . T)) @@ -1839,7 +1839,7 @@ 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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-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 @@ -1847,11 +1847,11 @@ 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"))) (((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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(QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-839))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (|HasCategory| (-558) (QUOTE (-841))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (QUOTE (-1039)))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163))))) (-3994 (|HasCategory| |#2| (QUOTE (-1039))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-481) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1859,8 +1859,8 @@ 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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) -(-483 -3199 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +(-483 -3189 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 @@ -1871,7 +1871,7 @@ 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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1896,7 +1896,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-492 -3199 UP |AlExt| |AlPol|) +(-492 -3189 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 @@ -1907,16 +1907,16 @@ NIL (-494 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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 -3199) +(-497 R UP -3189) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1936,7 +1936,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-502 -3199 |Expon| |VarSet| |DPoly|) +(-502 -3189 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-1163))))) @@ -1987,7 +1987,7 @@ NIL (-514 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|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 @@ -1995,15 +1995,15 @@ 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}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((-3996 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#1|) (QUOTE (-144)))) +((-3994 (|HasCategory| (-575 |#1|) (QUOTE (-144))) (|HasCategory| (-575 |#1|) (QUOTE (-367)))) (|HasCategory| (-575 |#1|) (QUOTE (-146))) (|HasCategory| (-575 |#1|) (QUOTE (-367))) (|HasCategory| (-575 |#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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|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 @@ -2015,7 +2015,7 @@ NIL (-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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-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!| (((|SingleInteger|) $ (|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.")) (|readByteIfCan!| (((|SingleInteger|) $) "\\spad{readByteIfCan!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise return \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every read attempt,{} which is overkill.}"))) +((|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}."))) NIL NIL (-525) -((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|SingleInteger|) $ (|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.")) (|readByteIfCan!| (((|SingleInteger|) $) "\\spad{readByteIfCan!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise return \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every read attempt,{} which is overkill.}"))) +((|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}."))) 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 -3199 |Par|) +(-530 K -3189 |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 -3199 |Par|) +(-536 K -3189 |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 @@ -2107,12 +2107,12 @@ NIL (-544 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) -(-545 R -3199) +((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853))))) +(-545 R -3189) ((|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 -(-546 R0 -3199 UP UPUP R) +(-546 R0 -3189 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 @@ -2122,7 +2122,7 @@ NIL NIL (-548 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."))) -((-1395 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1422 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-549 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."))) @@ -2132,7 +2132,7 @@ NIL ((|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."))) ((-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-551 R -3199) +(-551 R -3189) ((|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 @@ -2144,7 +2144,7 @@ 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 -(-554 R -3199 L) +(-554 R -3189 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 -646) (|devaluate| |#2|)))) @@ -2152,11 +2152,11 @@ 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 -(-556 -3199 UP UPUP R) +(-556 -3189 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 -(-557 -3199 UP) +(-557 -3189 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 @@ -2168,15 +2168,15 @@ NIL ((|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 -(-560 R -3199 L) +(-560 R -3189 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 -646) (|devaluate| |#2|)))) -(-561 R -3199) +(-561 R -3189) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1126)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-621))))) -(-562 -3199 UP) +(-562 -3189 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 @@ -2184,27 +2184,27 @@ 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 -(-564 -3199) +(-564 -3189) ((|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 (-565 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."))) -((-1395 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1422 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-566) ((|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 -(-567 R -3199) +(-567 R -3189) ((|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 -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-283))) (|HasCategory| |#2| (QUOTE (-621))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-283)))) (|HasCategory| |#1| (QUOTE (-550)))) -(-568 -3199 UP) +(-568 -3189 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 -(-569 R -3199) +(-569 R -3189) ((|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 @@ -2236,15 +2236,15 @@ NIL ((|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 -(-577 R -3199) +(-577 R -3189) ((|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 -(-578 E -3199) +(-578 E -3189) ((|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 -(-579 -3199) +(-579 -3189) ((|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}."))) ((-4378 . T) (-4377 . T)) ((|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-1163))))) @@ -2275,7 +2275,7 @@ NIL (-586 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3996 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-3994 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-3994 (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-587 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 @@ -2283,7 +2283,7 @@ NIL (-588 |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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-558)) (|devaluate| |#1|)))) (|HasCategory| (-558) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-558)))))) (-589 |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.}"))) ((-4378 |has| |#1| (-550)) (-4377 |has| |#1| (-550)) ((-4385 "*") |has| |#1| (-550)) (-4376 |has| |#1| (-550)) (-4380 . T)) @@ -2296,7 +2296,7 @@ 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 -(-592 R -3199 FG) +(-592 R -3189 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 @@ -2307,7 +2307,7 @@ NIL (-594 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-595 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2326,12 +2326,12 @@ NIL NIL (-599 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4380 -3996 (-2113 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) -((-3996 (|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|)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4380 -3994 (-2157 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) +((-3994 (|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|)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-600 |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."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| (-1145) (QUOTE (-841))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (LIST (QUOTE -605) (QUOTE (-853))))) (-601 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 @@ -2356,7 +2356,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-607 -3199 UP) +(-607 -3189 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2384,7 +2384,7 @@ NIL ((|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}."))) ((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-839)))) -(-614 R -3199) +(-614 R -3189) ((|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 @@ -2416,18 +2416,18 @@ 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 -(-622 R -3199) +(-622 R -3189) ((|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 -(-623 |lv| -3199) +(-623 |lv| -3189) ((|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 (-624) ((|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."))) ((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1145))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-1145) (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (QUOTE (-1087)))) (-625 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2438,8 +2438,8 @@ NIL NIL (-627 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4380 -3996 (-2113 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) -((-3996 (|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|)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) +((-4380 -3994 (-2157 (|has| |#2| (-366 |#1|)) (|has| |#1| (-550))) (-12 (|has| |#2| (-416 |#1|)) (|has| |#1| (-550)))) (-4378 . T) (-4377 . T)) +((-3994 (|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|)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (LIST (QUOTE -416) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -366) (|devaluate| |#1|)))) (-628 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 @@ -2451,7 +2451,7 @@ NIL (-630 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 -((-2104 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) +((-2143 (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-362)))) (-631 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4380 . T)) @@ -2471,7 +2471,7 @@ NIL (-635 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-636 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2479,7 +2479,7 @@ NIL (-637 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-638 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2496,7 +2496,7 @@ NIL ((|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 -(-642 R -3199 L) +(-642 R -3189 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 @@ -2516,11 +2516,11 @@ NIL ((|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}."))) ((-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-647 -3199 UP) +(-647 -3189 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)))) -(-648 A -2181) +(-648 A -2511) ((|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}}"))) ((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) @@ -2556,11 +2556,11 @@ NIL ((|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}."))) ((-4384 . T) (-4383 . T)) NIL -(-657 -3199) +(-657 -3189) ((|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 -(-658 -3199 |Row| |Col| M) +(-658 -3189 |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 @@ -2571,7 +2571,7 @@ NIL (-660 |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."))) ((-4380 . T) (-4383 . T) (-4377 . T) (-4378 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3996 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (|HasCategory| |#2| (QUOTE (-550))) (-3994 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-661) ((|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 @@ -2591,7 +2591,7 @@ NIL (-665 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 -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (QUOTE (-1039))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-666) ((|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 @@ -2647,7 +2647,7 @@ NIL (-679 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."))) ((-4383 . T) (-4384 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-306))) (|HasCategory| |#1| (QUOTE (-550))) (|HasAttribute| |#1| (QUOTE (-4385 "*"))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-680 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 @@ -2656,7 +2656,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "autoCoerce is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spad{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} 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|) "maybe(\\spad{x}) injects the value \\spad{`x'} into \\%."))) NIL NIL -(-682 S -3199 FLAF FLAS) +(-682 S -3189 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 @@ -2667,7 +2667,7 @@ NIL (-684) ((|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"))) ((-4376 . T) (-4381 |has| (-689) (-362)) (-4375 |has| (-689) (-362)) (-4382 |has| (-689) (-6 -4382)) (-4379 |has| (-689) (-6 -4379)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-689) (QUOTE (-146))) (|HasCategory| (-689) (QUOTE (-144))) (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-367))) (|HasCategory| (-689) (QUOTE (-362))) (-3996 (|HasCategory| (-689) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-232))) (-3996 (|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-348)))) (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (LIST (QUOTE -285) (QUOTE (-689)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -308) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-689)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-689) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-689) (LIST (QUOTE -606) 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(|HasCategory| (-689) (QUOTE (-362))) (|HasCategory| (-689) (QUOTE (-899)))) (-12 (|HasCategory| (-689) (QUOTE (-348))) (|HasCategory| (-689) (QUOTE (-899))))) (|HasCategory| (-689) (QUOTE (-543))) (-12 (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-1185)))) (|HasCategory| (-689) (QUOTE (-1048))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-362)))) (-3994 (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-550)))) (-12 (|HasCategory| (-689) (QUOTE (-232))) (|HasCategory| (-689) (QUOTE (-362)))) (-12 (|HasCategory| (-689) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-689) (QUOTE (-362)))) (|HasCategory| (-689) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-689) (QUOTE (-841))) (|HasCategory| (-689) (QUOTE (-550))) (|HasAttribute| (-689) (QUOTE -4382)) (|HasAttribute| (-689) (QUOTE -4379)) (-12 (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-144)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-689) (QUOTE (-306))) (|HasCategory| (-689) (QUOTE (-899)))) (|HasCategory| (-689) (QUOTE (-348))))) (-685 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}."))) ((-4384 . T)) @@ -2680,13 +2680,13 @@ NIL ((|constructor| (NIL "\\indented{1}{} 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 -(-688 OV E -3199 PG) +(-688 OV E -3189 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 (-689) ((|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}"))) -((-1395 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) +((-1422 . T) (-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-690 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."))) @@ -2716,7 +2716,7 @@ 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 -(-697 S -2921 I) +(-697 S -3042 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 @@ -2736,14 +2736,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding 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 -(-702 R |Mod| -1783 -2297 |exactQuo|) +(-702 R |Mod| -2915 -3391 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-703 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-704 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2752,7 +2752,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4378 |has| |#1| (-171)) (-4377 |has| |#1| (-171)) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146)))) -(-706 R |Mod| -1783 -2297 |exactQuo|) +(-706 R |Mod| -2915 -3391 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4380 . T)) NIL @@ -2764,7 +2764,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4378 . T) (-4377 . T)) NIL -(-709 -3199) +(-709 -3189) ((|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]]}."))) ((-4380 . T)) NIL @@ -2800,7 +2800,7 @@ 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 -(-718 -3199 UP) +(-718 -3189 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 @@ -2819,7 +2819,7 @@ NIL (-722 |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."))) (((-4385 "*") |has| |#2| (-171)) (-4376 |has| |#2| (-550)) (-4381 |has| |#2| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3996 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-171))) (-3994 (|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (QUOTE (-550)))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-855 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#2| (QUOTE (-841))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362))) (|HasAttribute| |#2| (QUOTE -4381)) (|HasCategory| |#2| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-723 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 @@ -2952,11 +2952,11 @@ 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 -(-756 -3199) +(-756 -3189) ((|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 -(-757 P -3199) +(-757 P -3189) ((|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 @@ -2964,7 +2964,7 @@ NIL NIL NIL NIL -(-759 UP -3199) +(-759 UP -3189) ((|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 @@ -2980,7 +2980,7 @@ NIL ((|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."))) (((-4385 "*") . T)) NIL -(-763 R -3199) +(-763 R -3189) ((|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 @@ -3000,7 +3000,7 @@ 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 -(-768 -3199 |ExtF| |SUEx| |ExtP| |n|) +(-768 -3189 |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 @@ -3015,7 +3015,7 @@ NIL (-771 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."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) 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|#1| (QUOTE (-543)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-558))))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-1163)))) (-2143 (|HasCategory| |#1| (LIST (QUOTE -982) (QUOTE (-558))))))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-772 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3023,7 +3023,7 @@ NIL (-773 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4379 |has| |#1| (-362)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1069) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-774 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 @@ -3084,23 +3084,23 @@ NIL ((|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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4377 . T) (-4378 . T) (-4380 . T)) NIL -(-789 -3996 R OS S) +(-789 -3994 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-790 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3996 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -285) (|devaluate| |#1|) (|devaluate| |#1|))) (-3994 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-989 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (-791) ((|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 -(-792 R -3199 L) +(-792 R -3189 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 -(-793 R -3199) +(-793 R -3189) ((|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 @@ -3108,7 +3108,7 @@ 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 -(-795 R -3199) +(-795 R -3189) ((|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 @@ -3116,11 +3116,11 @@ 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 -(-797 -3199 UP UPUP R) +(-797 -3189 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 -(-798 -3199 UP L LQ) +(-798 -3189 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 @@ -3128,38 +3128,38 @@ 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 -(-800 -3199 UP L LQ) +(-800 -3189 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 -(-801 -3199 UP) +(-801 -3189 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 -(-802 -3199 L UP A LO) +(-802 -3189 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 -(-803 -3199 UP) +(-803 -3189 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)))) -(-804 -3199 LO) +(-804 -3189 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) 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(|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 -(-805 -3199 LODO) +(-805 -3189 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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|#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-1087)))) (|HasAttribute| |#2| (QUOTE -4380)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))))) (-807 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"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-809 (-1163)) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-808 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4385 "*") |has| |#2| (-362)) (-4376 |has| |#2| (-362)) (-4381 |has| |#2| (-362)) (-4375 |has| |#2| (-362)) (-4380 . T) (-4378 . T) (-4377 . T)) @@ -3227,7 +3227,7 @@ NIL (-824 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."))) ((-4380 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3996 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-839))) (-3994 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-825 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 @@ -3267,12 +3267,12 @@ NIL (-834 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4380 |has| |#1| (-839))) -((|HasCategory| |#1| (QUOTE (-839))) (-3996 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3996 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-839))) (-3994 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-839)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (-3994 (|HasCategory| |#1| (QUOTE (-839))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-543))) (|HasCategory| |#1| (QUOTE (-21)))) (-835) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-836 -4352 S) +(-836 -1470 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 @@ -3308,11 +3308,11 @@ NIL ((|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 (-550)))) -(-845 R |sigma| -4150) +(-845 R |sigma| -3691) ((|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."))) ((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-362)))) -(-846 |x| R |sigma| -4150) +(-846 |x| R |sigma| -3691) ((|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}."))) ((-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| |#2| (QUOTE (-171))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-450))) (|HasCategory| |#2| (QUOTE (-362)))) @@ -3329,11 +3329,11 @@ NIL NIL NIL (-850 S) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) +((|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}."))) NIL NIL (-851) -((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|SingleInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,{}b)} write bytes from buffer \\spad{`b'} onto the conduit \\spad{`c'}. The actual number of written bytes is returned.")) (|writeByteIfCan!| (((|SingleInteger|) $ (|Byte|)) "\\spad{writeByteIfCan!(c,{}b)} attempts to write the byte \\spad{`b'} on the conduit \\spad{`c'}. Returns the written byte if successful,{} otherwise,{} returns \\spad{-1}. Note: Ideally,{} the return value should have been of type \\indented{2}{Maybe Byte; but that would have implied allocating} \\indented{2}{a cons cell for every write attempt,{} which is overkill.}"))) +((|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}."))) NIL NIL (-852) @@ -3375,15 +3375,15 @@ NIL (-861 |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)."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3996 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) +((|HasCategory| (-860 |#1|) (QUOTE (-899))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-146))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-860 |#1|) (QUOTE (-1012))) (|HasCategory| (-860 |#1|) (QUOTE (-811))) (-3994 (|HasCategory| (-860 |#1|) (QUOTE (-811))) (|HasCategory| (-860 |#1|) (QUOTE (-841)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-1138))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| (-860 |#1|) (QUOTE (-232))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -512) (QUOTE (-1163)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -308) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (LIST (QUOTE -285) (LIST (QUOTE -860) (|devaluate| |#1|)) (LIST (QUOTE -860) (|devaluate| |#1|)))) (|HasCategory| (-860 |#1|) (QUOTE (-306))) (|HasCategory| (-860 |#1|) (QUOTE (-543))) (|HasCategory| (-860 |#1|) (QUOTE (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-860 |#1|) (QUOTE (-899)))) (|HasCategory| (-860 |#1|) (QUOTE (-144))))) (-862 |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)}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3996 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) +((|HasCategory| |#2| (QUOTE (-899))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-1012))) (|HasCategory| |#2| (QUOTE (-811))) (-3994 (|HasCategory| |#2| (QUOTE (-811))) (|HasCategory| |#2| (QUOTE (-841)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-1138))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 (-841))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-899)))) (|HasCategory| |#2| (QUOTE (-144))))) (-863 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 (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))))) (-864) ((|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 @@ -3439,7 +3439,7 @@ NIL (-877 |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 (-2104 (|HasCategory| |#2| (QUOTE (-1039)))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2104 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) +((-12 (-2143 (|HasCategory| |#2| (QUOTE (-1039)))) (-2143 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (-12 (|HasCategory| |#2| (QUOTE (-1039))) (-2143 (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-1163))))) (-878 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 @@ -3448,7 +3448,7 @@ 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 -(-880 R -2921) +(-880 R -3042) ((|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 @@ -3472,7 +3472,7 @@ 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 -(-886 UP -3199) +(-886 UP -3189) ((|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 @@ -3495,7 +3495,7 @@ NIL (-891 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 (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-892 |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 @@ -3511,7 +3511,7 @@ NIL (-895 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."))) ((-4380 . T)) -((-3996 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) +((-3994 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#1| (QUOTE (-841)))) (-896 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 @@ -3532,7 +3532,7 @@ NIL ((|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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) ((|HasCategory| $ (QUOTE (-146))) (|HasCategory| $ (QUOTE (-144))) (|HasCategory| $ (QUOTE (-367)))) -(-901 R0 -3199 UP UPUP R) +(-901 R0 -3189 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 @@ -3560,7 +3560,7 @@ 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 -(-908 -3199) +(-908 -3189) ((|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 @@ -3576,11 +3576,11 @@ NIL ((|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}."))) (((-4385 "*") . T)) NIL -(-912 -3199 P) +(-912 -3189 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-913 |xx| -3199) +(-913 |xx| -3189) ((|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 @@ -3604,7 +3604,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-919 R -3199) +(-919 R -3189) ((|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 @@ -3616,7 +3616,7 @@ 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 -(-922 S R -3199) +(-922 S R -3189) ((|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 @@ -3636,11 +3636,11 @@ 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 -876) (|devaluate| |#1|)))) -(-927 R -3199 -2921) +(-927 R -3189 -3042) ((|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 -(-928 -2921) +(-928 -3042) ((|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 @@ -3663,7 +3663,7 @@ NIL (-933 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-934 |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 @@ -3688,7 +3688,7 @@ NIL ((|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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL -(-940 E V R P -3199) +(-940 E V R P -3189) ((|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 @@ -3699,8 +3699,8 @@ NIL (-942 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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) -(-943 E V R P -3199) +((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| (-1163) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +(-943 E V R P -3189) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-450)))) @@ -3723,12 +3723,12 @@ NIL (-948 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-949) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-950 -3199) +(-950 -3189) ((|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 @@ -3743,11 +3743,11 @@ NIL (-953 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}"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4381))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-130)))) (|HasAttribute| |#1| (QUOTE -4381))) (-954 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"))) ((-4380 -12 (|has| |#2| (-471)) (|has| |#1| (-471)))) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 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(|HasCategory| |#2| (QUOTE (-717))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-3996 (-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 (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 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(|HasCategory| |#2| (QUOTE (-717))))) (-12 (|HasCategory| |#1| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-367)))) (-3994 (-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 (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-784))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#2| (QUOTE (-841))))) (-955) ((|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 @@ -3828,7 +3828,7 @@ 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 -(-975 K R UP -3199) +(-975 K R UP -3189) ((|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 @@ -3887,11 +3887,11 @@ NIL (-989 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.}"))) ((-4376 |has| |#1| (-289)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 -890) (QUOTE (-1163)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-289))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -512) (QUOTE (-1163)) (|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 -890) (QUOTE (-1163)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-1048))) (|HasCategory| |#1| (QUOTE (-543)))) (-990 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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-991 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3900,14 +3900,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-993 -3199 UP UPUP |radicnd| |n|) +(-993 -3189 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4376 |has| (-406 |#2|) (-362)) (-4381 |has| (-406 |#2|) (-362)) (-4375 |has| (-406 |#2|) (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3996 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3996 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3996 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) +((|HasCategory| (-406 |#2|) (QUOTE (-144))) (|HasCategory| (-406 |#2|) (QUOTE (-146))) (|HasCategory| (-406 |#2|) (QUOTE (-348))) (-3994 (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (|HasCategory| (-406 |#2|) (QUOTE (-362))) (|HasCategory| (-406 |#2|) (QUOTE (-367))) (-3994 (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (QUOTE (-348)))) (-3994 (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-348))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 |#2|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-12 (|HasCategory| (-406 |#2|) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-406 |#2|) (QUOTE (-362)))) (-12 (|HasCategory| (-406 |#2|) (QUOTE (-232))) (|HasCategory| (-406 |#2|) (QUOTE (-362))))) (-994 |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."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3996 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) +((|HasCategory| (-558) (QUOTE (-899))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-1163)))) (|HasCategory| (-558) (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-146))) (|HasCategory| (-558) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-1012))) (|HasCategory| (-558) (QUOTE (-811))) (-3994 (|HasCategory| (-558) (QUOTE (-811))) (|HasCategory| (-558) (QUOTE (-841)))) (|HasCategory| (-558) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-1138))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| (-558) (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| (-558) (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| (-558) (QUOTE (-232))) (|HasCategory| (-558) (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| (-558) (LIST (QUOTE -512) (QUOTE (-1163)) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -308) (QUOTE (-558)))) (|HasCategory| (-558) (LIST (QUOTE -285) (QUOTE (-558)) (QUOTE (-558)))) (|HasCategory| (-558) (QUOTE (-306))) (|HasCategory| (-558) (QUOTE (-543))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-558) (LIST (QUOTE -631) (QUOTE (-558)))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| (-558) (QUOTE (-899)))) (|HasCategory| (-558) (QUOTE (-144))))) (-995) ((|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 @@ -3940,19 +3940,19 @@ NIL ((|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}}"))) ((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) NIL -(-1003 R -3199) +(-1003 R -3189) ((|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 -(-1004 R -3199) +(-1004 R -3189) ((|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 -(-1005 -3199 UP) +(-1005 -3189 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 -(-1006 -3199 UP) +(-1006 -3189 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 @@ -3987,8 +3987,8 @@ NIL (-1014 |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"))) ((-4376 . T) (-4381 . T) (-4375 . T) (-4378 . T) (-4377 . T) ((-4385 "*") . T) (-4380 . T)) -((-3996 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) -(-1015 -3199 L) +((-3994 (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-406 (-558)) (LIST (QUOTE -1028) (QUOTE (-558))))) +(-1015 -3189 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 @@ -4024,14 +4024,14 @@ 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 -(-1024 -3199 |Expon| |VarSet| |FPol| |LFPol|) +(-1024 -3189 |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"))) (((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL (-1025) ((|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.}"))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1026) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4088,7 +4088,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4380 . T)) NIL -(-1040 |xx| -3199) +(-1040 |xx| -3189) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4103,7 +4103,7 @@ NIL (-1043 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4383 . T) (-4378 . T) (-4377 . T)) -((-3996 (-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 (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) +((-3994 (-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 (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#3| (QUOTE (-171))) (|HasCategory| |#3| (QUOTE (-362)))) (|HasCategory| |#3| (QUOTE (-362))) (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (QUOTE (-306))) (|HasCategory| |#3| (QUOTE (-550))) (|HasCategory| |#3| (QUOTE (-171))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853))))) (-1044 |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 @@ -4135,7 +4135,7 @@ NIL (-1051) ((|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}"))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -3528) (QUOTE (-52))))))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3996 (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (QUOTE (-1163))) (LIST (QUOTE |:|) (QUOTE -1925) (QUOTE (-52))))))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-52) (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| (-52) (QUOTE (-1087))) (|HasCategory| (-52) (LIST (QUOTE -308) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (QUOTE (-1087))) (|HasCategory| (-1163) (QUOTE (-841))) (|HasCategory| (-52) (QUOTE (-1087))) (-3994 (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-52) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (LIST (QUOTE -605) (QUOTE (-853))))) (-1052 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 @@ -4180,11 +4180,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1063 |Base| R -3199) +(-1063 |Base| R -3189) ((|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 -(-1064 |Base| R -3199) +(-1064 |Base| R -3189) ((|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 @@ -4199,7 +4199,7 @@ NIL (-1067 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."))) ((-4376 |has| |#1| (-362)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) +((|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-348))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-348)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-367))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (QUOTE (-348)))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-348))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362)))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163))))) (-12 (|HasCategory| |#1| (QUOTE (-232))) (|HasCategory| |#1| (QUOTE (-362))))) (-1068 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 @@ -4227,7 +4227,7 @@ NIL (-1074 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"))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . 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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 @@ -4287,7 +4287,7 @@ NIL (-1089 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. 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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 ().")) 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|#3| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#3| (QUOTE (-1087)))) (|HasAttribute| |#3| (QUOTE -4380)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#3| (QUOTE (-1087))) (|HasCategory| |#3| (LIST (QUOTE -308) (|devaluate| |#3|))))) (-1101 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 @@ -4340,7 +4340,7 @@ 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 -(-1103 R -3199) +(-1103 R -3189) ((|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 @@ -4379,16 +4379,16 @@ NIL (-1112 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."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-6 -4381)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (QUOTE (-899))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3996 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) +((|HasCategory| |#1| (QUOTE (-899))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-378)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-378))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -876) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -876) (QUOTE (-558))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-378)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -606) (LIST (QUOTE -882) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534))))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| |#1| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-362))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1113 |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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4378 . T) (-4377 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-144))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-362)))) (-1114 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}"))) ((-4384 . T) (-4383 . T)) NIL -(-1115 UP -3199) +(-1115 UP -3189) ((|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 @@ -4443,11 +4443,11 @@ NIL (-1128 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3996 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))) (-3994 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -308) (LIST (QUOTE -1127) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1127 |#1| |#2|) (QUOTE (-1087))))) (|HasCategory| (-1127 |#1| |#2|) (LIST (QUOTE -605) (QUOTE (-853))))) (-1129 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4380 . T) (-4372 |has| |#2| (-6 (-4385 "*"))) (-4383 . T) (-4377 . T) (-4378 . T)) -((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3996 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3996 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) +((|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232))) (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (LIST (QUOTE -1028) (QUOTE (-558)))) (-3994 (-12 (|HasCategory| |#2| (QUOTE (-232))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))))) (|HasCategory| |#2| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| |#2| (QUOTE (-306))) (|HasCategory| |#2| (QUOTE (-550))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-362))) (-3994 (|HasAttribute| |#2| (QUOTE (-4385 "*"))) (|HasCategory| |#2| (LIST (QUOTE -631) (QUOTE (-558)))) (|HasCategory| |#2| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#2| (QUOTE (-232)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-171)))) (-1130 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4467,7 +4467,7 @@ NIL (-1134 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4383 . T) (-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1135 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 @@ -4479,7 +4479,7 @@ NIL (-1137 |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."))) ((-4384 . T)) -((-12 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2055) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3528) (|devaluate| |#2|)))))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3996 (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (QUOTE (-1087)))) +((-12 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -308) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2176) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1925) (|devaluate| |#2|)))))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| |#2| (QUOTE (-1087)))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -606) (QUOTE (-534)))) (-12 (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -308) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-841))) (-3994 (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#2| (QUOTE (-1087))) (|HasCategory| |#2| (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (LIST (QUOTE -605) (QUOTE (-853)))) (|HasCategory| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (QUOTE (-1087)))) (-1138) ((|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 @@ -4503,7 +4503,7 @@ NIL (-1143 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."))) ((-4384 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) +((-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1087))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (-1144) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4384 . T) (-4383 . T)) @@ -4511,11 +4511,11 @@ NIL (-1145) NIL ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) +((-3994 (-12 (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143))))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (|HasCategory| (-143) (LIST (QUOTE -606) (QUOTE (-534)))) (|HasCategory| (-143) (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| (-143) (QUOTE (-1087))) (|HasCategory| (-143) (LIST (QUOTE -308) (QUOTE (-143)))))) (-1146 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4383 . T) (-4384 . 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(|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*(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 = sum(i+j=k,{}a)}.")) (|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 @@ -4546,9 +4546,9 @@ NIL NIL (-1154 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-450))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-1138))) (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasCategory| |#1| (QUOTE (-232))) (|HasAttribute| |#1| (QUOTE -4381)) (|HasCategory| |#1| (QUOTE (-450))) (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (-3994 (-12 (|HasCategory| $ (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-899)))) (|HasCategory| |#1| (QUOTE (-144))))) (-1160 |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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4381 |has| |#1| (-362)) (-4375 |has| |#1| (-362)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3996 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3221) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (|HasCategory| |#1| (QUOTE (-171))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558))) (|devaluate| |#1|)))) (|HasCategory| (-406 (-558)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-3994 (|HasCategory| |#1| (QUOTE (-362))) (|HasCategory| |#1| (QUOTE (-550)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -406) (QUOTE (-558)))))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1161 |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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3221) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1162) ((|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 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))}."))) (((-4385 "*") |has| (-1231 |#2| |#3| |#4|) (-171)) (-4376 |has| (-1231 |#2| |#3| |#4|) (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3996 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) +((|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-144))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-146))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-171))) (-3994 (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558)))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| (-1231 |#2| |#3| |#4|) (LIST (QUOTE -1028) (QUOTE (-558)))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-362))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-450))) (|HasCategory| (-1231 |#2| |#3| |#4|) (QUOTE (-550)))) (-1233 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3221) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-1185))) (|HasSignature| |#2| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1337) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1163))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#2| (QUOTE (-362)))) (-1237 |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."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) @@ -4883,12 +4883,12 @@ NIL (-1238 |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}."))) (((-4385 "*") |has| |#1| (-171)) (-4376 |has| |#1| (-550)) (-4377 . T) (-4378 . T) (-4380 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3996 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3996 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -3221) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -2664) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasCategory| |#1| (QUOTE (-550))) (-3994 (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-550)))) (|HasCategory| |#1| (QUOTE (-171))) (|HasCategory| |#1| (QUOTE (-144))) (|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (LIST (QUOTE -890) (QUOTE (-1163)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-762)) (|devaluate| |#1|)))) (|HasCategory| (-762) (QUOTE (-1099))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasSignature| |#1| (LIST (QUOTE -3940) (LIST (|devaluate| |#1|) (QUOTE (-1163)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-762))))) (|HasCategory| |#1| (QUOTE (-362))) (-3994 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-1185))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -406) (QUOTE (-558))))) (|HasSignature| |#1| (LIST (QUOTE -1337) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1163))))) (|HasSignature| |#1| (LIST (QUOTE -4078) (LIST (LIST (QUOTE -635) (QUOTE (-1163))) (|devaluate| |#1|))))))) (-1239 |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=f(y,{}y',{}..,{}y)} such that \\spad{y(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 -(-1240 -3199 UP L UTS) +(-1240 -3189 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 (-550)))) @@ -4915,7 +4915,7 @@ NIL (-1246 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."))) ((-4384 . T) (-4383 . T)) -((-3996 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3996 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3996 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) +((-3994 (-12 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-3994 (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853))))) (|HasCategory| |#1| (LIST (QUOTE -606) (QUOTE (-534)))) (-3994 (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-841))) (|HasCategory| (-558) (QUOTE (-841))) (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#1| (QUOTE (-1039))) (-12 (|HasCategory| |#1| (QUOTE (-992))) (|HasCategory| |#1| (QUOTE (-1039)))) (|HasCategory| |#1| (LIST (QUOTE -605) (QUOTE (-853)))) (-12 (|HasCategory| |#1| (QUOTE (-1087))) (|HasCategory| |#1| (LIST (QUOTE -308) (|devaluate| |#1|))))) (-1247) ((|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 @@ -4948,7 +4948,7 @@ NIL ((|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 -(-1255 K R UP -3199) +(-1255 K R UP -3189) ((|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 @@ -4984,11 +4984,11 @@ NIL ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4376 |has| |#2| (-6 -4376)) (-4378 . T) (-4377 . T) (-4380 . T)) NIL -(-1264 S -3199) +(-1264 S -3189) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-367))) (|HasCategory| |#2| (QUOTE (-144))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1265 -3199) +(-1265 -3189) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4375 . T) (-4381 . T) (-4376 . T) ((-4385 "*") . T) (-4377 . T) (-4378 . T) (-4380 . T)) NIL @@ -5044,4 +5044,4 @@ NIL NIL NIL NIL -((-3 NIL 2276360 2276365 2276370 2276375) (-2 NIL 2276340 2276345 2276350 2276355) (-1 NIL 2276320 2276325 2276330 2276335) (0 NIL 2276300 2276305 2276310 2276315) (-1274 "ZMOD.spad" 2276109 2276122 2276238 2276295) (-1273 "ZLINDEP.spad" 2275153 2275164 2276099 2276104) (-1272 "ZDSOLVE.spad" 2265002 2265024 2275143 2275148) (-1271 "YSTREAM.spad" 2264495 2264506 2264992 2264997) (-1270 "XRPOLY.spad" 2263715 2263735 2264351 2264420) (-1269 "XPR.spad" 2261506 2261519 2263433 2263532) (-1268 "XPOLY.spad" 2261061 2261072 2261362 2261431) (-1267 "XPOLYC.spad" 2260378 2260394 2260987 2261056) (-1266 "XPBWPOLY.spad" 2258815 2258835 2260158 2260227) (-1265 "XF.spad" 2257276 2257291 2258717 2258810) (-1264 "XF.spad" 2255717 2255734 2257160 2257165) (-1263 "XFALG.spad" 2252741 2252757 2255643 2255712) (-1262 "XEXPPKG.spad" 2251992 2252018 2252731 2252736) (-1261 "XDPOLY.spad" 2251606 2251622 2251848 2251917) (-1260 "XALG.spad" 2251266 2251277 2251562 2251601) (-1259 "WUTSET.spad" 2247105 2247122 2250912 2250939) (-1258 "WP.spad" 2246304 2246348 2246963 2247030) (-1257 "WHILEAST.spad" 2246102 2246111 2246294 2246299) (-1256 "WHEREAST.spad" 2245773 2245782 2246092 2246097) (-1255 "WFFINTBS.spad" 2243336 2243358 2245763 2245768) (-1254 "WEIER.spad" 2241550 2241561 2243326 2243331) (-1253 "VSPACE.spad" 2241223 2241234 2241518 2241545) (-1252 "VSPACE.spad" 2240916 2240929 2241213 2241218) (-1251 "VOID.spad" 2240593 2240602 2240906 2240911) (-1250 "VIEW.spad" 2238215 2238224 2240583 2240588) (-1249 "VIEWDEF.spad" 2233412 2233421 2238205 2238210) (-1248 "VIEW3D.spad" 2217247 2217256 2233402 2233407) (-1247 "VIEW2D.spad" 2204984 2204993 2217237 2217242) (-1246 "VECTOR.spad" 2203659 2203670 2203910 2203937) (-1245 "VECTOR2.spad" 2202286 2202299 2203649 2203654) (-1244 "VECTCAT.spad" 2200186 2200197 2202254 2202281) (-1243 "VECTCAT.spad" 2197894 2197907 2199964 2199969) (-1242 "VARIABLE.spad" 2197674 2197689 2197884 2197889) (-1241 "UTYPE.spad" 2197318 2197327 2197664 2197669) (-1240 "UTSODETL.spad" 2196611 2196635 2197274 2197279) (-1239 "UTSODE.spad" 2194799 2194819 2196601 2196606) (-1238 "UTS.spad" 2189588 2189616 2193266 2193363) (-1237 "UTSCAT.spad" 2187039 2187055 2189486 2189583) (-1236 "UTSCAT.spad" 2184134 2184152 2186583 2186588) (-1235 "UTS2.spad" 2183727 2183762 2184124 2184129) (-1234 "URAGG.spad" 2178359 2178370 2183717 2183722) (-1233 "URAGG.spad" 2172955 2172968 2178315 2178320) (-1232 "UPXSSING.spad" 2170598 2170624 2172036 2172169) (-1231 "UPXS.spad" 2167746 2167774 2168730 2168879) (-1230 "UPXSCONS.spad" 2165503 2165523 2165878 2166027) (-1229 "UPXSCCA.spad" 2164068 2164088 2165349 2165498) (-1228 "UPXSCCA.spad" 2162775 2162797 2164058 2164063) (-1227 "UPXSCAT.spad" 2161356 2161372 2162621 2162770) (-1226 "UPXS2.spad" 2160897 2160950 2161346 2161351) (-1225 "UPSQFREE.spad" 2159309 2159323 2160887 2160892) (-1224 "UPSCAT.spad" 2156902 2156926 2159207 2159304) (-1223 "UPSCAT.spad" 2154201 2154227 2156508 2156513) (-1222 "UPOLYC.spad" 2149179 2149190 2154043 2154196) (-1221 "UPOLYC.spad" 2144049 2144062 2148915 2148920) (-1220 "UPOLYC2.spad" 2143518 2143537 2144039 2144044) (-1219 "UP.spad" 2140675 2140690 2141068 2141221) (-1218 "UPMP.spad" 2139565 2139578 2140665 2140670) (-1217 "UPDIVP.spad" 2139128 2139142 2139555 2139560) (-1216 "UPDECOMP.spad" 2137365 2137379 2139118 2139123) (-1215 "UPCDEN.spad" 2136572 2136588 2137355 2137360) (-1214 "UP2.spad" 2135934 2135955 2136562 2136567) (-1213 "UNISEG.spad" 2135287 2135298 2135853 2135858) (-1212 "UNISEG2.spad" 2134780 2134793 2135243 2135248) (-1211 "UNIFACT.spad" 2133881 2133893 2134770 2134775) (-1210 "ULS.spad" 2124433 2124461 2125526 2125955) (-1209 "ULSCONS.spad" 2116827 2116847 2117199 2117348) (-1208 "ULSCCAT.spad" 2114556 2114576 2116673 2116822) (-1207 "ULSCCAT.spad" 2112393 2112415 2114512 2114517) (-1206 "ULSCAT.spad" 2110609 2110625 2112239 2112388) (-1205 "ULS2.spad" 2110121 2110174 2110599 2110604) (-1204 "UFD.spad" 2109186 2109195 2110047 2110116) (-1203 "UFD.spad" 2108313 2108324 2109176 2109181) (-1202 "UDVO.spad" 2107160 2107169 2108303 2108308) (-1201 "UDPO.spad" 2104587 2104598 2107116 2107121) (-1200 "TYPE.spad" 2104519 2104528 2104577 2104582) (-1199 "TYPEAST.spad" 2104438 2104447 2104509 2104514) (-1198 "TWOFACT.spad" 2103088 2103103 2104428 2104433) (-1197 "TUPLE.spad" 2102572 2102583 2102987 2102992) (-1196 "TUBETOOL.spad" 2099409 2099418 2102562 2102567) (-1195 "TUBE.spad" 2098050 2098067 2099399 2099404) (-1194 "TS.spad" 2096639 2096655 2097615 2097712) (-1193 "TSETCAT.spad" 2083766 2083783 2096607 2096634) (-1192 "TSETCAT.spad" 2070879 2070898 2083722 2083727) (-1191 "TRMANIP.spad" 2065245 2065262 2070585 2070590) (-1190 "TRIMAT.spad" 2064204 2064229 2065235 2065240) (-1189 "TRIGMNIP.spad" 2062721 2062738 2064194 2064199) (-1188 "TRIGCAT.spad" 2062233 2062242 2062711 2062716) (-1187 "TRIGCAT.spad" 2061743 2061754 2062223 2062228) (-1186 "TREE.spad" 2060314 2060325 2061350 2061377) (-1185 "TRANFUN.spad" 2060145 2060154 2060304 2060309) (-1184 "TRANFUN.spad" 2059974 2059985 2060135 2060140) (-1183 "TOPSP.spad" 2059648 2059657 2059964 2059969) (-1182 "TOOLSIGN.spad" 2059311 2059322 2059638 2059643) (-1181 "TEXTFILE.spad" 2057868 2057877 2059301 2059306) (-1180 "TEX.spad" 2055000 2055009 2057858 2057863) (-1179 "TEX1.spad" 2054556 2054567 2054990 2054995) (-1178 "TEMUTL.spad" 2054111 2054120 2054546 2054551) (-1177 "TBCMPPK.spad" 2052204 2052227 2054101 2054106) (-1176 "TBAGG.spad" 2051240 2051263 2052184 2052199) (-1175 "TBAGG.spad" 2050284 2050309 2051230 2051235) (-1174 "TANEXP.spad" 2049660 2049671 2050274 2050279) (-1173 "TABLE.spad" 2048071 2048094 2048341 2048368) (-1172 "TABLEAU.spad" 2047552 2047563 2048061 2048066) (-1171 "TABLBUMP.spad" 2044335 2044346 2047542 2047547) (-1170 "SYSTEM.spad" 2043609 2043618 2044325 2044330) (-1169 "SYSSOLP.spad" 2041082 2041093 2043599 2043604) (-1168 "SYNTAX.spad" 2037352 2037361 2041072 2041077) (-1167 "SYMTAB.spad" 2035408 2035417 2037342 2037347) (-1166 "SYMS.spad" 2031393 2031402 2035398 2035403) (-1165 "SYMPOLY.spad" 2030400 2030411 2030482 2030609) (-1164 "SYMFUNC.spad" 2029875 2029886 2030390 2030395) (-1163 "SYMBOL.spad" 2027302 2027311 2029865 2029870) (-1162 "SWITCH.spad" 2024059 2024068 2027292 2027297) (-1161 "SUTS.spad" 2020958 2020986 2022526 2022623) (-1160 "SUPXS.spad" 2018093 2018121 2019090 2019239) (-1159 "SUP.spad" 2014862 2014873 2015643 2015796) (-1158 "SUPFRACF.spad" 2013967 2013985 2014852 2014857) (-1157 "SUP2.spad" 2013357 2013370 2013957 2013962) (-1156 "SUMRF.spad" 2012323 2012334 2013347 2013352) (-1155 "SUMFS.spad" 2011956 2011973 2012313 2012318) (-1154 "SULS.spad" 2002495 2002523 2003601 2004030) (-1153 "SUCHTAST.spad" 2002264 2002273 2002485 2002490) (-1152 "SUCH.spad" 2001944 2001959 2002254 2002259) (-1151 "SUBSPACE.spad" 1993951 1993966 2001934 2001939) (-1150 "SUBRESP.spad" 1993111 1993125 1993907 1993912) (-1149 "STTF.spad" 1989210 1989226 1993101 1993106) (-1148 "STTFNC.spad" 1985678 1985694 1989200 1989205) (-1147 "STTAYLOR.spad" 1978076 1978087 1985559 1985564) (-1146 "STRTBL.spad" 1976581 1976598 1976730 1976757) (-1145 "STRING.spad" 1975990 1975999 1976004 1976031) (-1144 "STRICAT.spad" 1975778 1975787 1975958 1975985) (-1143 "STREAM.spad" 1972636 1972647 1975303 1975318) (-1142 "STREAM3.spad" 1972181 1972196 1972626 1972631) (-1141 "STREAM2.spad" 1971249 1971262 1972171 1972176) (-1140 "STREAM1.spad" 1970953 1970964 1971239 1971244) (-1139 "STINPROD.spad" 1969859 1969875 1970943 1970948) (-1138 "STEP.spad" 1969060 1969069 1969849 1969854) (-1137 "STBL.spad" 1967586 1967614 1967753 1967768) (-1136 "STAGG.spad" 1966661 1966672 1967576 1967581) (-1135 "STAGG.spad" 1965734 1965747 1966651 1966656) (-1134 "STACK.spad" 1965085 1965096 1965341 1965368) (-1133 "SREGSET.spad" 1962789 1962806 1964731 1964758) (-1132 "SRDCMPK.spad" 1961334 1961354 1962779 1962784) (-1131 "SRAGG.spad" 1956431 1956440 1961302 1961329) (-1130 "SRAGG.spad" 1951548 1951559 1956421 1956426) (-1129 "SQMATRIX.spad" 1949164 1949182 1950080 1950167) (-1128 "SPLTREE.spad" 1943716 1943729 1948600 1948627) (-1127 "SPLNODE.spad" 1940304 1940317 1943706 1943711) (-1126 "SPFCAT.spad" 1939081 1939090 1940294 1940299) (-1125 "SPECOUT.spad" 1937631 1937640 1939071 1939076) (-1124 "SPADXPT.spad" 1929770 1929779 1937621 1937626) (-1123 "spad-parser.spad" 1929235 1929244 1929760 1929765) (-1122 "SPADAST.spad" 1928936 1928945 1929225 1929230) (-1121 "SPACEC.spad" 1912949 1912960 1928926 1928931) (-1120 "SPACE3.spad" 1912725 1912736 1912939 1912944) (-1119 "SORTPAK.spad" 1912270 1912283 1912681 1912686) (-1118 "SOLVETRA.spad" 1910027 1910038 1912260 1912265) (-1117 "SOLVESER.spad" 1908547 1908558 1910017 1910022) (-1116 "SOLVERAD.spad" 1904557 1904568 1908537 1908542) (-1115 "SOLVEFOR.spad" 1902977 1902995 1904547 1904552) (-1114 "SNTSCAT.spad" 1902577 1902594 1902945 1902972) (-1113 "SMTS.spad" 1900837 1900863 1902142 1902239) (-1112 "SMP.spad" 1898276 1898296 1898666 1898793) (-1111 "SMITH.spad" 1897119 1897144 1898266 1898271) (-1110 "SMATCAT.spad" 1895229 1895259 1897063 1897114) (-1109 "SMATCAT.spad" 1893271 1893303 1895107 1895112) (-1108 "SKAGG.spad" 1892232 1892243 1893239 1893266) (-1107 "SINT.spad" 1891058 1891067 1892098 1892227) (-1106 "SIMPAN.spad" 1890786 1890795 1891048 1891053) (-1105 "SIG.spad" 1890114 1890123 1890776 1890781) (-1104 "SIGNRF.spad" 1889222 1889233 1890104 1890109) (-1103 "SIGNEF.spad" 1888491 1888508 1889212 1889217) (-1102 "SIGAST.spad" 1887872 1887881 1888481 1888486) (-1101 "SHP.spad" 1885790 1885805 1887828 1887833) (-1100 "SHDP.spad" 1875501 1875528 1876010 1876141) (-1099 "SGROUP.spad" 1875109 1875118 1875491 1875496) (-1098 "SGROUP.spad" 1874715 1874726 1875099 1875104) (-1097 "SGCF.spad" 1867596 1867605 1874705 1874710) (-1096 "SFRTCAT.spad" 1866524 1866541 1867564 1867591) (-1095 "SFRGCD.spad" 1865587 1865607 1866514 1866519) (-1094 "SFQCMPK.spad" 1860224 1860244 1865577 1865582) (-1093 "SFORT.spad" 1859659 1859673 1860214 1860219) (-1092 "SEXOF.spad" 1859502 1859542 1859649 1859654) (-1091 "SEX.spad" 1859394 1859403 1859492 1859497) (-1090 "SEXCAT.spad" 1856945 1856985 1859384 1859389) (-1089 "SET.spad" 1855245 1855256 1856366 1856405) (-1088 "SETMN.spad" 1853679 1853696 1855235 1855240) (-1087 "SETCAT.spad" 1853164 1853173 1853669 1853674) (-1086 "SETCAT.spad" 1852647 1852658 1853154 1853159) (-1085 "SETAGG.spad" 1849168 1849179 1852627 1852642) (-1084 "SETAGG.spad" 1845697 1845710 1849158 1849163) (-1083 "SEQAST.spad" 1845400 1845409 1845687 1845692) (-1082 "SEGXCAT.spad" 1844522 1844535 1845390 1845395) (-1081 "SEG.spad" 1844335 1844346 1844441 1844446) (-1080 "SEGCAT.spad" 1843242 1843253 1844325 1844330) (-1079 "SEGBIND.spad" 1842314 1842325 1843197 1843202) (-1078 "SEGBIND2.spad" 1842010 1842023 1842304 1842309) (-1077 "SEGAST.spad" 1841724 1841733 1842000 1842005) (-1076 "SEG2.spad" 1841149 1841162 1841680 1841685) (-1075 "SDVAR.spad" 1840425 1840436 1841139 1841144) (-1074 "SDPOL.spad" 1837815 1837826 1838106 1838233) (-1073 "SCPKG.spad" 1835894 1835905 1837805 1837810) (-1072 "SCOPE.spad" 1835039 1835048 1835884 1835889) (-1071 "SCACHE.spad" 1833721 1833732 1835029 1835034) (-1070 "SASTCAT.spad" 1833630 1833639 1833711 1833716) (-1069 "SAOS.spad" 1833502 1833511 1833620 1833625) (-1068 "SAERFFC.spad" 1833215 1833235 1833492 1833497) (-1067 "SAE.spad" 1831390 1831406 1832001 1832136) (-1066 "SAEFACT.spad" 1831091 1831111 1831380 1831385) (-1065 "RURPK.spad" 1828732 1828748 1831081 1831086) (-1064 "RULESET.spad" 1828173 1828197 1828722 1828727) (-1063 "RULE.spad" 1826377 1826401 1828163 1828168) (-1062 "RULECOLD.spad" 1826229 1826242 1826367 1826372) (-1061 "RSTRCAST.spad" 1825946 1825955 1826219 1826224) (-1060 "RSETGCD.spad" 1822324 1822344 1825936 1825941) (-1059 "RSETCAT.spad" 1812108 1812125 1822292 1822319) (-1058 "RSETCAT.spad" 1801912 1801931 1812098 1812103) (-1057 "RSDCMPK.spad" 1800364 1800384 1801902 1801907) (-1056 "RRCC.spad" 1798748 1798778 1800354 1800359) (-1055 "RRCC.spad" 1797130 1797162 1798738 1798743) (-1054 "RPTAST.spad" 1796832 1796841 1797120 1797125) (-1053 "RPOLCAT.spad" 1776192 1776207 1796700 1796827) (-1052 "RPOLCAT.spad" 1755266 1755283 1775776 1775781) (-1051 "ROUTINE.spad" 1751129 1751138 1753913 1753940) (-1050 "ROMAN.spad" 1750457 1750466 1750995 1751124) (-1049 "ROIRC.spad" 1749537 1749569 1750447 1750452) (-1048 "RNS.spad" 1748440 1748449 1749439 1749532) (-1047 "RNS.spad" 1747429 1747440 1748430 1748435) (-1046 "RNG.spad" 1747164 1747173 1747419 1747424) (-1045 "RMODULE.spad" 1746802 1746813 1747154 1747159) (-1044 "RMCAT2.spad" 1746210 1746267 1746792 1746797) (-1043 "RMATRIX.spad" 1745034 1745053 1745377 1745416) (-1042 "RMATCAT.spad" 1740567 1740598 1744990 1745029) (-1041 "RMATCAT.spad" 1735990 1736023 1740415 1740420) (-1040 "RINTERP.spad" 1735878 1735898 1735980 1735985) (-1039 "RING.spad" 1735348 1735357 1735858 1735873) (-1038 "RING.spad" 1734826 1734837 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"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 2275560 2275565 2275570 2275575) (-2 NIL 2275540 2275545 2275550 2275555) (-1 NIL 2275520 2275525 2275530 2275535) (0 NIL 2275500 2275505 2275510 2275515) (-1274 "ZMOD.spad" 2275309 2275322 2275438 2275495) (-1273 "ZLINDEP.spad" 2274353 2274364 2275299 2275304) (-1272 "ZDSOLVE.spad" 2264202 2264224 2274343 2274348) (-1271 "YSTREAM.spad" 2263695 2263706 2264192 2264197) (-1270 "XRPOLY.spad" 2262915 2262935 2263551 2263620) (-1269 "XPR.spad" 2260706 2260719 2262633 2262732) (-1268 "XPOLY.spad" 2260261 2260272 2260562 2260631) (-1267 "XPOLYC.spad" 2259578 2259594 2260187 2260256) (-1266 "XPBWPOLY.spad" 2258015 2258035 2259358 2259427) (-1265 "XF.spad" 2256476 2256491 2257917 2258010) (-1264 "XF.spad" 2254917 2254934 2256360 2256365) (-1263 "XFALG.spad" 2251941 2251957 2254843 2254912) (-1262 "XEXPPKG.spad" 2251192 2251218 2251931 2251936) (-1261 "XDPOLY.spad" 2250806 2250822 2251048 2251117) (-1260 "XALG.spad" 2250466 2250477 2250762 2250801) (-1259 "WUTSET.spad" 2246305 2246322 2250112 2250139) (-1258 "WP.spad" 2245504 2245548 2246163 2246230) (-1257 "WHILEAST.spad" 2245302 2245311 2245494 2245499) (-1256 "WHEREAST.spad" 2244973 2244982 2245292 2245297) (-1255 "WFFINTBS.spad" 2242536 2242558 2244963 2244968) (-1254 "WEIER.spad" 2240750 2240761 2242526 2242531) (-1253 "VSPACE.spad" 2240423 2240434 2240718 2240745) (-1252 "VSPACE.spad" 2240116 2240129 2240413 2240418) (-1251 "VOID.spad" 2239793 2239802 2240106 2240111) (-1250 "VIEW.spad" 2237415 2237424 2239783 2239788) (-1249 "VIEWDEF.spad" 2232612 2232621 2237405 2237410) (-1248 "VIEW3D.spad" 2216447 2216456 2232602 2232607) (-1247 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(-1210 "ULS.spad" 2123633 2123661 2124726 2125155) (-1209 "ULSCONS.spad" 2116027 2116047 2116399 2116548) (-1208 "ULSCCAT.spad" 2113756 2113776 2115873 2116022) (-1207 "ULSCCAT.spad" 2111593 2111615 2113712 2113717) (-1206 "ULSCAT.spad" 2109809 2109825 2111439 2111588) (-1205 "ULS2.spad" 2109321 2109374 2109799 2109804) (-1204 "UFD.spad" 2108386 2108395 2109247 2109316) (-1203 "UFD.spad" 2107513 2107524 2108376 2108381) (-1202 "UDVO.spad" 2106360 2106369 2107503 2107508) (-1201 "UDPO.spad" 2103787 2103798 2106316 2106321) (-1200 "TYPE.spad" 2103719 2103728 2103777 2103782) (-1199 "TYPEAST.spad" 2103638 2103647 2103709 2103714) (-1198 "TWOFACT.spad" 2102288 2102303 2103628 2103633) (-1197 "TUPLE.spad" 2101772 2101783 2102187 2102192) (-1196 "TUBETOOL.spad" 2098609 2098618 2101762 2101767) (-1195 "TUBE.spad" 2097250 2097267 2098599 2098604) (-1194 "TS.spad" 2095839 2095855 2096815 2096912) (-1193 "TSETCAT.spad" 2082966 2082983 2095807 2095834) (-1192 "TSETCAT.spad" 2070079 2070098 2082922 2082927) (-1191 "TRMANIP.spad" 2064445 2064462 2069785 2069790) (-1190 "TRIMAT.spad" 2063404 2063429 2064435 2064440) (-1189 "TRIGMNIP.spad" 2061921 2061938 2063394 2063399) (-1188 "TRIGCAT.spad" 2061433 2061442 2061911 2061916) (-1187 "TRIGCAT.spad" 2060943 2060954 2061423 2061428) (-1186 "TREE.spad" 2059514 2059525 2060550 2060577) (-1185 "TRANFUN.spad" 2059345 2059354 2059504 2059509) (-1184 "TRANFUN.spad" 2059174 2059185 2059335 2059340) (-1183 "TOPSP.spad" 2058848 2058857 2059164 2059169) (-1182 "TOOLSIGN.spad" 2058511 2058522 2058838 2058843) (-1181 "TEXTFILE.spad" 2057068 2057077 2058501 2058506) (-1180 "TEX.spad" 2054200 2054209 2057058 2057063) (-1179 "TEX1.spad" 2053756 2053767 2054190 2054195) (-1178 "TEMUTL.spad" 2053311 2053320 2053746 2053751) (-1177 "TBCMPPK.spad" 2051404 2051427 2053301 2053306) (-1176 "TBAGG.spad" 2050440 2050463 2051384 2051399) (-1175 "TBAGG.spad" 2049484 2049509 2050430 2050435) (-1174 "TANEXP.spad" 2048860 2048871 2049474 2049479) (-1173 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T)) @@ -797,7 +797,7 @@ ((((-635 |#1|)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#2|) |has| |#2| (-308 |#2|))) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -807,7 +807,7 @@ (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T)) (|has| |#2| (-367)) -(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) @@ -821,8 +821,8 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((($) . T) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-112)) . T)) @@ -846,26 +846,26 @@ ((((-853)) . T)) ((((-1168)) . T)) (|has| |#1| (-811)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-841)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-550)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (((-558)) . T)) (|has| |#1| (-899)) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-853)) . 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T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-558)) . T)) -((($) . T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) . T)) +((($) |has| |#1| (-550)) ((|#1|) . T) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-558)) . T)) +((($) . T) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) . T)) (|has| |#1| (-819)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) (|has| |#1| (-1087)) @@ -908,29 +908,29 @@ (((|#3|) |has| |#3| (-1087))) (|has| |#3| (-367)) (((|#1|) . T) (((-853)) . 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T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#) ((|#2|) . T) (((-558)) . T)) (((|#1| |#2| |#3|) . T)) -(-3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +(-3994 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) (|has| $ (-146)) (|has| $ (-146)) ((((-1168)) . T)) @@ -938,14 +938,14 @@ ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) ((($ $) |has| |#1| (-285 $ $)) ((|#1| $) |has| |#1| (-285 |#1| |#1|))) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) ((((-1163)) . T)) (|has| |#1| (-550)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) @@ -956,7 +956,7 @@ (|has| |#1| (-146)) (|has| |#1| (-144)) (|has| |#4| (-839)) -(((|#2| (-239 (-1450 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-239 (-1596 |#1|) (-762)) (-855 |#1|)) . T)) (|has| |#3| (-839)) (((|#1| (-529 |#3|) |#3|) . T)) (|has| |#1| (-146)) @@ -970,20 +970,20 @@ (|has| |#1| (-144)) ((((-406 (-558))) |has| |#2| (-362)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3996 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#1| (-348)) (|has| |#1| (-367))) ((((-1129 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-171)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-232)) (|has| |#2| (-1039))) -(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) -(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) +(((|#2|) . T) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +(-3994 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3994 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-689)) . T)) -(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-550)) (((|#1|) . T)) (((|#1|) . T)) @@ -1007,11 +1007,11 @@ (((|#1| (-406 (-558))) . T)) (((|#3|) . T) (((-604 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -((((-558)) -3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +((((-558)) -3994 (|has| |#2| (-171)) (|has| |#2| (-839)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039))) ((|#2|) -3994 (|has| |#2| (-171)) (|has| |#2| (-1087))) (((-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1019,8 +1019,8 @@ ((((-853)) . T)) ((((-853)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) |has| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (-308 (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))))) ((((-853)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1031,10 +1031,10 @@ ((($ $) . T) ((#0=(-855 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-308 |#1|))) @@ -1122,11 +1122,11 @@ (|has| |#1| (-367)) ((((-1163) $) |has| |#1| (-512 (-1163) $)) (($ $) |has| |#1| (-308 $)) ((|#1| |#1|) |has| |#1| (-308 |#1|)) (((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|))) ((((-1163)) |has| |#1| (-890 (-1163)))) -(-3996 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) +(-3994 (-12 (|has| |#1| (-232)) (|has| |#1| (-362))) (|has| |#1| (-348))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-387) |#1|) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-1087)) (((|#2|) . T) (((-853)) . T)) ((((-853)) . T)) @@ -1134,8 +1134,8 @@ ((((-900 |#1|)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) -((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) -3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1144,16 +1144,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (((|#1| |#1|) . T)) (((#0=(-860 |#1|)) |has| #0# (-308 #0#))) -((((-558)) . 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T)) (|has| |#1| (-1185)) (((#0=(-558) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) ((((-406 (-558))) . T) (($) . T)) @@ -1164,8 +1164,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (|has| |#1| (-362)) ((((-558)) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) . T) ((#0=(-406 (-558)) #0#) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((($ $) . T) ((#0=(-406 (-558)) #0#) -3994 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1| |#1|) . T)) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -1180,14 +1180,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-839)) (|has| |#1| (-839)) -((($) . T) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) +((($) . 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T)) +((((-853)) -3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) ((((-1145) (-52)) . T)) @@ -1196,10 +1196,10 @@ ((((-558)) |has| #0=(-406 |#2|) (-631 (-558))) ((#0#) . T)) ((($) . T) (((-558)) . T)) ((((-558) (-143)) . T)) -((((-558) (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T) ((|#1| |#2|) . T)) +((((-558) (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T) ((|#1| |#2|) . T)) ((((-406 (-558))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-853)) . T)) ((((-900 |#1|)) . T)) (|has| |#1| (-362)) @@ -1226,21 +1226,21 @@ ((((-853)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-558) (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T) ((|#1| |#2|) . 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T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +(((|#2|) -3994 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-1039))) (($) |has| |#2| (-171))) (|has| $ (-146)) ((((-406 |#2|)) . T)) ((((-883 |#1|)) . T) ((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) @@ -1328,11 +1328,11 @@ (((|#3|) |has| |#3| (-171))) (|has| |#1| (-146)) (|has| |#1| (-144)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) (((|#1|) . T)) (|has| |#2| (-232)) @@ -1369,7 +1369,7 @@ ((((-989 |#1|)) . T) ((|#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-406 (-558))) . T) (((-406 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1159 |#1|)) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) @@ -1377,9 +1377,9 @@ (|has| |#1| (-841)) (((|#2|) . T)) ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) ((((-558) |#2|) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#2|) . T)) ((((-558) |#3|) . T)) (((|#2|) . T)) @@ -1394,7 +1394,7 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#2|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) #0#) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((#0=(-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) #0#) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))))) (((|#2| |#2|) . T)) (((|#1|) . T)) (|has| |#2| (-362)) @@ -1427,19 +1427,19 @@ (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1| |#2|) . T)) ((((-558) (-143)) . T)) -(((#0=(-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) #0#) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) -((($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +(((#0=(-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) #0#) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((($) -3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (|has| |#1| (-841)) (((|#2| (-762) (-1069)) . T)) (((|#1| |#2|) . T)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-171)) (|has| |#1| (-550))) (|has| |#1| (-782)) (((|#1|) |has| |#1| (-171))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3996 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) -(-3996 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) +(-3994 (|has| |#1| (-146)) (-12 (|has| |#1| (-362)) (|has| |#2| (-146)))) +(-3994 (|has| |#1| (-144)) (-12 (|has| |#1| (-362)) (|has| |#2| (-144)))) (((|#4|) . T)) (|has| |#1| (-144)) ((((-1145) |#1|) . T)) @@ -1453,10 +1453,10 @@ (((|#3|) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) -(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-841)) (|has| |#1| (-1087))) (((|#1|) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . T)) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087))) (((-948 |#1|)) . T)) (|has| |#1| (-839)) (|has| |#1| (-839)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) @@ -1470,8 +1470,8 @@ ((($) . T)) ((((-387) (-1145)) . T)) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-853)) -3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2055 (-1145)) (|:| -3528 #0#))) . T)) +((((-853)) -3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-605 (-853))) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((-1246 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2176 (-1145)) (|:| -1925 #0#))) . T)) (((|#1|) . T)) ((((-853)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) @@ -1479,7 +1479,7 @@ (|has| |#2| (-144)) (|has| |#2| (-146)) (|has| |#1| (-471)) -(-3996 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3994 (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) (|has| |#1| (-362)) ((((-853)) . T)) (|has| |#1| (-38 (-406 (-558)))) @@ -1490,8 +1490,8 @@ (|has| |#1| (-839)) ((((-853)) . T)) (((|#2|) . T)) -((((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) -(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550)))) +((((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1238 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) +(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550)))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#2|) . T) (((-558)) . T) (((-810 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1500,7 +1500,7 @@ ((((-853)) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) -(((|#2| (-480 (-1450 |#1|) (-762)) (-855 |#1|)) . T)) +(((|#2| (-480 (-1596 |#1|) (-762)) (-855 |#1|)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1| (-529 (-1163)) (-1163)) . T)) (((|#1|) . T)) @@ -1520,16 +1520,16 @@ (|has| |#1| (-146)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-1163) (-52)) . T)) ((($ $) . T)) (((|#1| (-558)) . T)) ((((-900 |#1|)) . T)) -(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +(((|#1|) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039))) (($) -3994 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) (|has| |#1| (-841)) (|has| |#1| (-841)) @@ -1547,11 +1547,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) (|has| |#2| (-841)) (|has| |#1| (-841)) -(((|#3|) -3996 (|has| |#3| (-171)) (|has| |#3| (-362)))) -(-3996 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) +(((|#3|) -3994 (|has| |#3| (-171)) (|has| |#3| (-362)))) +(-3994 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-899))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) ((((-558) |#2|) . T)) -(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3994 (|has| |#2| (-171)) (|has| |#2| (-362)))) (|has| |#1| (-348)) (((|#3| |#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) (((|#2|) . T) (((-558)) . T)) @@ -1560,7 +1560,7 @@ (|has| |#1| (-811)) (|has| |#1| (-811)) (((|#1|) . T)) -(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-839)) (|has| |#1| (-839)) (|has| |#1| (-839)) @@ -1569,13 +1569,13 @@ ((((-558)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-1163)) |has| |#1| (-890 (-1163))) (((-1069)) . T)) (((|#1|) . T)) (|has| |#1| (-839)) -(((#0=(-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) #0#) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))))) +(((#0=(-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) #0#) |has| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (-308 (-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-1087)) ((((-853)) . T) (((-1168)) . T)) @@ -1594,11 +1594,11 @@ (((|#1| (-762) (-1069)) . T)) (((|#3|) . T)) ((((-143)) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3996 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3994 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) (((|#1|) . T)) ((((-143)) . T)) (((|#2|) |has| |#2| (-171))) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((|#1|) . T)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -1621,32 +1621,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) ((((-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((|#1|) |has| |#1| (-171)) (($) |has| |#1| (-550))) -((((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) -(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550)))) +((((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-362)) ((|#1|) |has| |#1| (-171))) +(((|#1|) |has| |#1| (-171)) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550)))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) ((((-662 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1655,7 +1655,7 @@ ((((-853)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) ((((-1168)) . T)) ((((-406 (-558))) . T) (($) . T) (((-406 |#1|)) . T) ((|#1|) . T) (((-558)) . T)) (((|#3|) . T) (((-558)) . T) (((-604 $)) . T)) @@ -1663,12 +1663,12 @@ ((((-853)) . T)) ((((-853)) . T)) (((|#2|) . T)) -(-3996 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) -(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) +(-3994 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) (|has| |#1| (-1185)) (|has| |#1| (-1185)) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (|has| |#1| (-1185)) (|has| |#1| (-1185)) (((|#3| |#3|) . T)) @@ -1681,16 +1681,16 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((((-1145) (-52)) . T)) (|has| |#1| (-1087)) -(-3996 (|has| |#2| (-811)) (|has| |#2| (-841))) +(-3994 (|has| |#2| (-811)) (|has| |#2| (-841))) (((|#1|) . T)) (((|#1|) |has| |#1| (-171)) (($) . T)) -((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3994 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3994 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((($) . T)) ((((-1161 |#1| |#2| |#3|)) -12 (|has| (-1161 |#1| |#2| |#3|) (-308 (-1161 |#1| |#2| |#3|))) (|has| |#1| (-362)))) ((((-853)) . T)) ((((-558)) . T) (($) . T)) ((((-762)) . T)) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) ((($) . T) (((-558)) . T)) @@ -1698,29 +1698,29 @@ (|has| |#2| (-899)) (|has| |#1| (-362)) (((|#2|) |has| |#2| (-1087))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-534)) . T) (((-406 (-1159 (-558)))) . T) (((-224)) . T) (((-378)) . T)) ((((-378)) . T) (((-224)) . T) (((-853)) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) (|has| |#1| (-899)) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-899))) ((($) . T) ((|#2|) . T)) -(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((($ $) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((($ $) . T)) ((((-558) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-558)) . T)) ((((-112)) . T)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-38 (-406 (-558)))) (((|#1| (-558)) . T)) ((($) . T)) @@ -1742,7 +1742,7 @@ (((|#1| (-1210 |#1| |#2| |#3|)) . T)) (((|#1| (-762)) . T)) (((|#1|) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-853)) . T)) (|has| |#1| (-1087)) ((((-1145) |#1|) . T)) @@ -1762,18 +1762,18 @@ (((|#1|) . T)) ((((-558)) . T)) ((((-853)) . T)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) (((|#3|) . T)) -(-3996 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3994 (|has| |#3| (-171)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|)) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3996 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) +((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-604 $)) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) -3994 (-12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-762)) . T)) -((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (((|#1|) |has| |#1| (-308 |#1|))) ((((-1232 |#1| |#2| |#3| |#4|)) . T)) ((((-558)) |has| |#1| (-876 (-558))) (((-378)) |has| |#1| (-876 (-378)))) @@ -1781,7 +1781,7 @@ (|has| |#1| (-550)) (((|#1|) . T)) ((((-853)) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))))) (((|#1|) |has| |#1| (-171))) ((($) |has| |#1| (-550)) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) @@ -1789,7 +1789,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1087))) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) -(((|#2|) -3996 (|has| |#2| (-171)) (|has| |#2| (-362)))) +(((|#2|) -3994 (|has| |#2| (-171)) (|has| |#2| (-362)))) ((((-1231 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-811)) @@ -1799,8 +1799,8 @@ (|has| |#1| (-839)) (|has| |#1| (-839)) (((|#1| (-558) (-1069)) . T)) -(-3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +(-3994 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (|has| |#1| (-841)) @@ -1813,33 +1813,33 @@ (|has| |#1| (-1087)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-1087)) -((((-558)) -3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) +((((-558)) -3994 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)))) (((|#1|) . T)) (|has| |#1| (-1087)) ((((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((|#2|) |has| |#1| (-362))) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) -((((-679 (-338 (-3870) (-3870 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +((((-679 (-338 (-3952) (-3952 (QUOTE X) (QUOTE HESS)) (-689)))) . T)) (((|#2|) |has| |#2| (-171))) (((|#1|) |has| |#1| (-171))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) ((((-853)) . T)) (|has| |#3| (-839)) ((((-853)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-853)) . T)) -(((|#1| |#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1| |#1|) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#1|) . T)) ((((-558)) . T)) ((((-558)) . T)) -(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) +(((|#1|) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-1039)))) (((|#2|) |has| |#2| (-362))) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-841)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) |has| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-899))) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) |has| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (-308 (-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) ((((-853)) . T)) ((((-853)) . T)) @@ -1870,25 +1870,25 @@ (|has| |#1| (-144)) ((((-558)) . T) ((|#1|) . T) (($) . T) (((-406 (-558))) . T) (((-1163)) |has| |#1| (-1028 (-1163)))) (((|#1| |#2|) . T)) -((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3996 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) +((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) -3994 (|has| |#1| (-839)) (|has| |#1| (-1028 (-558)))) ((|#1|) . T)) ((((-143)) . T)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (((|#1|) . T)) -(-3996 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-171)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-558)) . T)) ((((-853)) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| (-406 |#2|) (-232)) ((((-635 |#1|)) . T)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-1039))) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))))) (|has| |#1| (-362)) (((|#1|) |has| |#1| (-171))) (((|#1| |#1|) . T)) @@ -1915,7 +1915,7 @@ (((|#1| (-406 (-558)) (-1069)) . T)) (((|#1| (-762) (-1069)) . T)) (((#0=(-406 |#2|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-558)) -3996 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) +(((|#1|) . T) (((-558)) -3994 (|has| (-406 (-558)) (-1028 (-558))) (|has| |#1| (-1028 (-558)))) (((-406 (-558))) . T)) (((|#1| (-594 |#1| |#3|) (-594 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -1936,25 +1936,25 @@ (((|#2|) |has| |#2| (-171))) (|has| |#2| (-839)) ((((-558)) . T) ((|#2|) . T) (((-406 (-558))) |has| |#2| (-1028 (-406 (-558))))) -((((-112)) |has| |#1| (-1087)) (((-853)) -3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) +((((-112)) |has| |#1| (-1087)) (((-853)) -3994 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))) . T)) ((((-853)) . T)) ((((-558) |#1|) . T)) ((((-853)) . T)) ((((-689)) . T) (((-406 (-558))) . T) (((-558)) . T)) (((|#1| |#1|) |has| |#1| (-171))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|))))) +(((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|))))) ((((-378)) . T)) ((((-689)) . T)) ((((-406 (-558))) . #0=(|has| |#2| (-362))) (($) . #0#)) (((|#1|) |has| |#1| (-171))) ((((-406 (-942 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-841)) @@ -1965,14 +1965,14 @@ (((|#3|) |has| |#3| (-1039))) ((((-1163)) |has| |#2| (-890 (-1163)))) ((((-853)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-406 (-558))) . T) (($) . T)) (|has| |#1| (-471)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-367)) (|has| |#1| (-362)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-471)) (|has| |#1| (-550)) (|has| |#1| (-1039)) (|has| |#1| (-1099))) (|has| |#1| (-38 (-406 (-558)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1993,11 +1993,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-841)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) |has| (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)) (-308 (-2 (|:| -2055 |#1|) (|:| -3528 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) |has| (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)) (-308 (-2 (|:| -2176 |#1|) (|:| -1925 |#2|)))) ((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2015,11 +2015,11 @@ ((((-534)) |has| |#1| (-606 (-534))) (((-882 (-558))) |has| |#1| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#1| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#1| (-1012))) (((-224)) . #0#)) (((|#1|) |has| |#1| (-362))) ((((-853)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((($ $) . T) (((-604 $) $) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) ((($) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T) (((-406 (-558))) . T)) -((($) -3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) +((($) -3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (|has| |#1| (-362)) @@ -2030,11 +2030,11 @@ ((((-378)) . T)) (((|#3|) -12 (|has| |#3| (-308 |#3|)) (|has| |#3| (-1087)))) ((((-853)) . T)) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-899))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-899))) (((|#1|) . T)) (|has| |#1| (-841)) (|has| |#1| (-841)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-534)) |has| |#1| (-606 (-534)))) (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) ((((-762)) . T)) @@ -2045,13 +2045,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((((-558)) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (((#0=(-1231 |#2| |#3| |#4|)) . T) (((-406 (-558))) |has| #0# (-38 (-406 (-558)))) (($) . T)) ((((-558)) . T)) (|has| |#1| (-362)) -(-3996 (-12 (|has| (-1238 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-3996 (-12 (|has| (-1238 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-3994 (-12 (|has| (-1238 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-3994 (-12 (|has| (-1238 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-362)) (|has| |#1| (-144)) (|has| |#1| (-146)) @@ -2066,23 +2066,23 @@ (((|#2|) . T)) (|has| |#1| (-1087)) (((|#1| |#2|) . T)) -((((-558)) . T) ((|#1|) . T) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-1028 (-406 (-558)))))) +((((-558)) . T) ((|#1|) . T) (((-406 (-558))) -3994 (|has| |#1| (-362)) (|has| |#1| (-1028 (-406 (-558)))))) (((|#1|) . T) (((-558)) |has| |#1| (-631 (-558)))) (((|#3|) |has| |#3| (-171))) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) ((((-853)) . T)) ((((-558)) . T)) (((|#1| $) |has| |#1| (-285 |#1| |#1|))) ((((-406 (-558))) . T) (($) . T) (((-406 |#1|)) . T) ((|#1|) . T)) ((((-942 |#1|)) . T) (((-853)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3996 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -3994 (|has| |#1| (-289)) (|has| |#1| (-362))) ((#0=(-406 (-558)) #0#) |has| |#1| (-362))) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) ((((-942 |#1|)) . T)) ((($) . T)) ((((-558) |#1|) . T)) ((((-1163)) |has| (-406 |#2|) (-890 (-1163)))) -(((|#1|) . T) (($) -3996 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) +(((|#1|) . T) (($) -3994 (|has| |#1| (-289)) (|has| |#1| (-362))) (((-406 (-558))) |has| |#1| (-362))) ((((-534)) |has| |#2| (-606 (-534)))) ((((-679 |#2|)) . T) (((-853)) . T)) (((|#1|) . T)) @@ -2090,8 +2090,8 @@ (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) ((((-860 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3996 (|has| |#4| (-784)) (|has| |#4| (-839))) -(-3996 (|has| |#3| (-784)) (|has| |#3| (-839))) +(-3994 (|has| |#4| (-784)) (|has| |#4| (-839))) +(-3994 (|has| |#3| (-784)) (|has| |#3| (-839))) ((((-853)) . T)) ((((-853)) . T)) (((|#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) @@ -2107,17 +2107,17 @@ ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) ((((-406 (-558))) . T) (($) . T)) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-1204))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-1204))) ((($) . T)) ((((-406 (-558))) |has| #0=(-406 |#2|) (-1028 (-406 (-558)))) (((-558)) |has| #0# (-1028 (-558))) ((#0#) . T)) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| (-762)) . T)) (|has| |#1| (-841)) (((|#1|) . T) (((-558)) |has| |#1| (-631 (-558)))) -((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3996 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) +((($) -3994 (|has| |#1| (-362)) (|has| |#1| (-348))) (((-406 (-558))) -3994 (|has| |#1| (-362)) (|has| |#1| (-348))) ((|#1|) . T)) ((((-558)) . T)) (|has| |#1| (-38 (-406 (-558)))) -((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))))) +((((-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))) |has| (-2 (|:| -2176 (-1145)) (|:| -1925 (-52))) (-308 (-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))))) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) (|has| |#1| (-839)) (|has| |#1| (-38 (-406 (-558)))) @@ -2140,29 +2140,29 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) -(((|#2|) . T) (((-558)) . T) (($) -3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . T) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558)))))) +(((|#2|) . T) (((-558)) . T) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . T) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558)))))) (((|#1| |#2|) . T)) ((((-143)) . T)) ((((-771 |#1| (-855 |#2|))) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (|has| |#1| (-1185)) ((((-853)) . T)) (((|#1|) . T)) -(-3996 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) +(-3994 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-171)) (|has| |#3| (-362)) (|has| |#3| (-367)) (|has| |#3| (-717)) (|has| |#3| (-784)) (|has| |#3| (-839)) (|has| |#3| (-1039)) (|has| |#3| (-1087))) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|))) (((|#2|) . T)) -((($ $) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) +((($ $) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) ((((-900 |#1|)) . T)) ((($) . T)) ((((-406 (-942 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -((($) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-534)) |has| |#4| (-606 (-534)))) ((((-853)) . T) (((-635 |#4|)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-839)) -(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) |has| (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|)) (-308 (-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))))) +(((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087))) (((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) |has| (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|)) (-308 (-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))))) (|has| |#1| (-1087)) (|has| |#1| (-362)) (|has| |#1| (-841)) @@ -2171,16 +2171,16 @@ (((|#1|) . T)) ((((-662 |#1|)) . T)) ((($) . T) (((-406 (-558))) . T)) -((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3996 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) +((($) -3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-362))) ((|#1|) |has| |#1| (-171))) (|has| |#1| (-144)) (|has| |#1| (-146)) -(-3996 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) -(-3996 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) +(-3994 (-12 (|has| (-1161 |#1| |#2| |#3|) (-146)) (|has| |#1| (-362))) (|has| |#1| (-146))) +(-3994 (-12 (|has| (-1161 |#1| |#2| |#3|) (-144)) (|has| |#1| (-362))) (|has| |#1| (-144))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-146)) (|has| |#1| (-144)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) (|has| |#1| (-839)) (((|#1| |#2|) . T)) @@ -2204,9 +2204,9 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -(((|#1|) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)))) +(((|#1|) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)))) ((((-315 |#1|)) . T)) (((|#2|) |has| |#2| (-362))) (((|#2|) . T)) @@ -2228,13 +2228,13 @@ (|has| |#1| (-144)) (|has| |#1| (-146)) ((($ $) . T)) -(-3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) (|has| |#1| (-550)) (((|#2|) . T)) ((((-558)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#1|) . T)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) ((((-575 |#1|)) . T)) ((($) . T)) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) @@ -2250,7 +2250,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1231 |#2| |#3| |#4|)) . T) (((-558)) . T) (((-1232 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-406 (-558))) . T)) -((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-558)) -3996 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1028 (-558))) (|has| |#1| (-1039))) ((|#1|) . T) (((-604 $)) . T) (($) |has| |#1| (-550)) (((-406 (-558))) -3996 (|has| |#1| (-550)) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) +((((-48)) -12 (|has| |#1| (-550)) (|has| |#1| (-1028 (-558)))) (((-558)) -3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1028 (-558))) (|has| |#1| (-1039))) ((|#1|) . T) (((-604 $)) . T) (($) |has| |#1| (-550)) (((-406 (-558))) -3994 (|has| |#1| (-550)) (|has| |#1| (-1028 (-406 (-558))))) (((-406 (-942 |#1|))) |has| |#1| (-550)) (((-942 |#1|)) |has| |#1| (-1039)) (((-1163)) . T)) ((((-406 (-558))) |has| |#2| (-1028 (-406 (-558)))) (((-558)) |has| |#2| (-1028 (-558))) ((|#2|) . T) (((-855 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-406 (-558))) . T)) ((((-1112 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-558)) |has| |#1| (-1028 (-558))) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558))))) @@ -2263,12 +2263,12 @@ (((|#1| |#2|) . T)) ((((-1163) |#1|) . T)) (((|#4|) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1163) (-52)) . T)) ((((-1231 |#2| |#3| |#4|) (-318 |#2| |#3| |#4|)) . T)) ((((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) (((-558)) |has| |#1| (-1028 (-558))) ((|#1|) . T)) ((((-853)) . T)) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-367)) (|has| |#2| (-717)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039)) (|has| |#2| (-1087))) (((#0=(-1232 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-171)) ((#0=(-406 (-558)) #0#) |has| |#1| (-550)) (($ $) |has| |#1| (-550))) (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) @@ -2288,14 +2288,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((|#2| |#3|) . T)) -(-3996 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#2| (-362)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1| (-529 |#2|)) . T)) (((|#1| (-762)) . T)) (((|#1| (-529 (-1075 (-1163)))) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (|has| |#2| (-899)) -(-3996 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3994 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-853)) . T)) ((($ $) . T) ((#0=(-1231 |#2| |#3| |#4|) #0#) . T) ((#1=(-406 (-558)) #1#) |has| #0# (-38 (-406 (-558))))) ((((-900 |#1|)) . T)) @@ -2304,14 +2304,14 @@ ((((-853)) . T)) ((($) . T)) ((($) . T)) -(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-362)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1231 |#2| |#3| |#4|)) . T) (((-406 (-558))) |has| #0# (-38 (-406 (-558))))) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(-3996 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3996 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) +(-3994 (-12 (|has| |#1| (-306)) (|has| |#1| (-899))) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039))) ((((-558)) |has| |#1| (-631 (-558))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-853)) . T)) @@ -2344,27 +2344,27 @@ (((|#1|) |has| |#1| (-171))) ((((-853)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-308 |#4|)) (|has| |#4| (-1087)))) -(((|#2|) -3996 (|has| |#2| (-6 (-4385 "*"))) (|has| |#2| (-171)))) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(((|#2|) -3994 (|has| |#2| (-6 (-4385 "*"))) (|has| |#2| (-171)))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#2| (-841)) (|has| |#2| (-899)) (|has| |#1| (-899)) (((|#2|) |has| |#2| (-171))) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) ((((-853)) . T)) ((((-853)) . T)) ((((-534)) . T) (((-558)) . T) (((-882 (-558))) . T) (((-378)) . T) (((-224)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))) . T)) (((|#1|) . T)) ((((-853)) . T)) (((|#1| |#2|) . T)) (((|#1| (-406 (-558))) . T)) (((|#1|) . T)) -(-3996 (|has| |#1| (-289)) (|has| |#1| (-362))) +(-3994 (|has| |#1| (-289)) (|has| |#1| (-362))) ((((-143)) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) (|has| |#1| (-839)) @@ -2380,7 +2380,7 @@ ((((-853)) . T)) ((((-853)) . T)) ((((-186)) . T) (((-853)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2393,7 +2393,7 @@ ((((-853)) . T)) ((((-1145)) . T)) ((((-1163) |#1|) |has| |#1| (-512 (-1163) |#1|)) ((|#1| |#1|) |has| |#1| (-308 |#1|))) -((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) (|has| |#1| (-841)) ((((-853)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) @@ -2405,16 +2405,16 @@ (((|#2|) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T)) ((($) . T) (((-558)) . T) (((-406 (-558))) . T) (((-604 $)) . T)) -(-3996 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) -(-3996 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3994 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) +(-3994 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-1163) (-52)) . T)) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3996 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) -(-3996 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-839)) (|has| |#2| (-1039))) (|has| |#1| (-899)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) (|has| |#1| (-899)) @@ -2431,12 +2431,12 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (|has| |#1| (-811)) (((#0=(-900 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((((-406 |#2|)) . T)) (|has| |#1| (-839)) -((((-1186 |#1|)) . T) (((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-1186 |#1|)) . T) (((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) . T) ((#1=(-558) #1#) . T) (($ $) . T)) ((((-900 |#1|)) . T) (($) . T) (((-406 (-558))) . T)) (((|#2|) |has| |#2| (-1039)) (((-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) @@ -2447,11 +2447,11 @@ (((|#2|) . T)) ((((-853)) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T) (((-558)) . T)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2055 (-1163)) (|:| -3528 #0#))) . T)) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2176 (-1163)) (|:| -1925 #0#))) . T)) (|has| |#1| (-348)) ((((-558)) . T)) ((((-853)) . T)) @@ -2459,14 +2459,14 @@ (((#0=(-1232 |#1| |#2| |#3| |#4|) $) |has| #0# (-285 #0# #0#))) (|has| |#1| (-362)) (((#0=(-1069) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) (((#0=(-406 (-558)) #0#) . T) ((#1=(-689) #1#) . T) (($ $) . T)) ((((-315 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) |has| |#1| (-362))) (|has| |#1| (-1087)) (((|#1|) . T)) -(((|#1|) -3996 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) -(((|#1|) -3996 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3994 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) +(((|#1|) -3994 (|has| |#2| (-366 |#1|)) (|has| |#2| (-416 |#1|)))) (((|#2|) . T)) ((((-406 (-558))) . T) (((-689)) . T) (($) . T)) ((((-573)) . T)) @@ -2489,7 +2489,7 @@ (((|#1|) . T)) ((((-558)) . T)) (((|#2|) . T) (((-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((|#1|) . T) (($) . T) (((-558)) . T)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((|#2|) . T) (((-558)) |has| |#2| (-631 (-558)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2527,7 +2527,7 @@ (|has| |#2| (-1012)) ((($) . T)) (|has| |#1| (-899)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2535,9 +2535,9 @@ ((($) . T)) (|has| |#1| (-362)) ((((-900 |#1|)) . T)) -((($) -3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) -(-3996 (|has| |#1| (-367)) (|has| |#1| (-841))) +(-3994 (|has| |#1| (-367)) (|has| |#1| (-841))) (((|#1|) . T)) ((((-762)) . T)) ((((-853)) . T)) @@ -2548,16 +2548,16 @@ ((((-558)) . T) (($) . T)) ((((-558)) . T) (($) . T)) ((((-762) |#1|) . T)) -(((|#2| (-239 (-1450 |#1|) (-762))) . T)) +(((|#2| (-239 (-1596 |#1|) (-762))) . T)) (((|#1| (-529 |#3|)) . T)) ((((-406 (-558))) . T)) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((((-1145)) . T) (((-853)) . T)) -(((#0=(-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) #0#) |has| (-2 (|:| -2055 (-1163)) (|:| -3528 (-52))) (-308 (-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))))) +(((#0=(-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) #0#) |has| (-2 (|:| -2176 (-1163)) (|:| -1925 (-52))) (-308 (-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))))) ((((-1145)) . T)) (|has| |#1| (-899)) (|has| |#2| (-362)) -(-3996 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-130)) (|has| |#2| (-171)) (|has| |#2| (-362)) (|has| |#2| (-784)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) (((|#1|) . T)) @@ -2574,11 +2574,11 @@ (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-306)) (|has| |#1| (-362)) (|has| |#1| (-348))) (|has| |#1| (-38 (-406 (-558)))) (-12 (|has| |#1| (-543)) (|has| |#1| (-819))) ((((-853)) . T)) -((((-1163)) -3996 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) +((((-1163)) -3994 (-12 (|has| |#1| (-15 * (|#1| (-558) |#1|))) (|has| |#1| (-890 (-1163)))) (-12 (|has| |#1| (-362)) (|has| |#2| (-890 (-1163)))))) (|has| |#1| (-362)) ((((-1163)) -12 (|has| |#1| (-15 * (|#1| (-406 (-558)) |#1|))) (|has| |#1| (-890 (-1163))))) (|has| |#1| (-362)) @@ -2589,7 +2589,7 @@ (((|#2|) |has| |#1| (-362))) (((|#2|) |has| |#1| (-362))) ((((-558)) . T) (($) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) @@ -2614,9 +2614,9 @@ ((((-378)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-378)))) (((-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-876 (-558))))) (|has| |#1| (-362)) (((|#1| |#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) (|has| |#1| (-362)) (|has| |#1| (-550)) (((|#1|) . T)) @@ -2625,22 +2625,22 @@ ((((-1145)) . T) (((-1163)) . T) (((-224)) . T) (((-558)) . T)) (((|#1|) . T)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . 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T)) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-1145) |#1|) . T)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-367))) (|has| |#1| (-146)) ((((-575 |#1|)) . T)) ((($) . T)) @@ -2648,7 +2648,7 @@ (|has| |#1| (-550)) (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558)))) -(-3996 (|has| |#1| (-144)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-348))) (|has| |#1| (-146)) ((((-853)) . T)) ((($) . T)) @@ -2675,7 +2675,7 @@ ((((-853)) . T)) ((((-900 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2697,7 +2697,7 @@ ((((-558)) . T)) ((((-853)) . T)) ((((-558)) . T)) -(-3996 (|has| |#2| (-784)) (|has| |#2| (-839))) +(-3994 (|has| |#2| (-784)) (|has| |#2| (-839))) ((((-168 (-378))) . T) (((-224)) . T) (((-378)) . T)) ((((-853)) . T)) ((((-853)) . T)) @@ -2709,9 +2709,9 @@ (((|#1|) . T) (($) . T) (((-406 (-558))) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) -(-3996 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +(-3994 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-471)) (|has| |#1| (-717)) (|has| |#1| (-890 (-1163))) (|has| |#1| (-1039)) (|has| |#1| (-1099)) (|has| |#1| (-1087))) (|has| |#1| (-1138)) ((((-558) |#1|) . T)) (((|#1|) . T)) @@ -2730,8 +2730,8 @@ (((|#1|) . T)) (|has| |#1| (-550)) ((((-406 |#2|)) . T) (((-406 (-558))) . T) (($) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) ((((-378)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2740,7 +2740,7 @@ (|has| |#1| (-550)) (|has| |#1| (-1087)) ((((-771 |#1| (-855 |#2|))) |has| (-771 |#1| (-855 |#2|)) (-308 (-771 |#1| (-855 |#2|))))) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2752,13 +2752,13 @@ (|has| |#2| (-362)) ((((-575 |#1|)) . T) (((-406 (-558))) . T) (($) . T) (((-558)) . T)) ((((-558)) . T) (((-406 (-558))) . T) (($) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 (-52)))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-558)) . T)) (((|#1|) -12 (|has| |#1| (-308 |#1|)) (|has| |#1| (-1087)))) ((((-853)) . T)) ((((-853)) . 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T)) +((((-1159 |#1|)) . T) (((-558)) . T) (($) -3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) (((-1069)) . T) ((|#1|) . T) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558)))))) +(-3994 (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-171)) (|has| |#1| (-550)) (|has| |#1| (-1039))) +((((-1112 |#1| (-1163))) . T) (((-558)) . T) (((-1075 (-1163))) . T) (($) -3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) -3994 (|has| |#1| (-38 (-406 (-558)))) (|has| |#1| (-1028 (-406 (-558))))) (((-1163)) . T)) (((#0=(-575 |#1|) #0#) . T) (($ $) . T) ((#1=(-406 (-558)) #1#) . T)) ((($ $) . T) ((#0=(-406 (-558)) #0#) . T)) (((|#1|) |has| |#1| (-171))) @@ -2788,7 +2788,7 @@ (((|#1|) . T)) ((((-853)) . T)) ((((-293 |#3|)) . T)) -(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3996 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +(((#0=(-406 (-558)) #0#) |has| |#2| (-38 (-406 (-558)))) ((|#2| |#2|) . T) (($ $) -3994 (|has| |#2| (-171)) (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T)) @@ -2796,21 +2796,21 @@ (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) (((|#1|) . T) (((-406 (-558))) . T) (($) . T)) -((($ $) -3996 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) -((($ $) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . 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T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) +((($ $) -3994 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1| |#1|) . T) ((#0=(-406 (-558)) #0#) |has| |#1| (-38 (-406 (-558))))) ((((-853)) . T)) -((($) -3996 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) -((($) -3996 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-171)) (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) (|has| |#2| (-899)) (|has| |#1| (-899)) -((($) -3996 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-171)) (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) . T) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-853)) . T)) (((|#1|) . T)) -((((-2 (|:| -2055 (-1145)) (|:| -3528 |#1|))) . T)) +((((-2 (|:| -2176 (-1145)) (|:| -1925 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2825,10 +2825,10 @@ (((|#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087)))) (((#0=(-406 (-558)) #0#) . T)) ((((-406 (-558))) . 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T)) (((|#2| |#2|) . T) ((#0=(-406 (-558)) #0#) . T) (($ $) . T)) ((((-558)) . T)) @@ -3245,17 +3245,17 @@ ((((-129)) . T)) ((((-853)) . T)) ((((-1238 |#1| |#2| |#3|)) |has| |#1| (-362))) -((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) +((((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) |has| |#2| (-171)) (($) -3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-406 (-558))) |has| |#2| (-38 (-406 (-558)))) ((|#2|) . T)) (|has| |#1| (-362)) -((($) -3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) +((($) -3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((|#1|) |has| |#1| (-171)) (((-406 (-558))) |has| |#1| (-38 (-406 (-558))))) ((((-1091)) . T)) ((((-853)) . 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T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-1168)) . T)) (((|#1|) |has| |#1| (-171))) ((((-1168)) . T)) @@ -3277,13 +3277,13 @@ ((((-1168)) . T)) ((((-1168)) . T)) ((((-1168)) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-348))) ((((-1168)) . T)) ((((-1168)) . T)) (|has| |#1| (-362)) (|has| |#1| (-362)) -(-3996 (|has| |#1| (-171)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-171)) (|has| |#1| (-550))) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) (((|#1| (-762)) . T)) @@ -3298,16 +3298,16 @@ ((((-882 (-378))) . T) (((-882 (-558))) . T) (((-1163)) . T) (((-534)) . T)) (((|#1|) . T)) ((((-853)) . 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T)) -(-3996 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) +(-3994 (|has| |#2| (-171)) (|has| |#2| (-717)) (|has| |#2| (-839)) (|has| |#2| (-1039))) ((((-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) -(-3996 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) +(-3994 (-12 (|has| |#1| (-471)) (|has| |#2| (-471))) (-12 (|has| |#1| (-717)) (|has| |#2| (-717)))) (|has| |#1| (-144)) (|has| |#1| (-146)) (|has| |#1| (-362)) @@ -3333,7 +3333,7 @@ (((|#1| |#2|) . T)) ((((-558)) . T) ((|#2|) |has| |#2| (-171))) ((((-114)) . T) ((|#1|) . T) (((-558)) . T)) -(-3996 (|has| |#1| (-348)) (|has| |#1| (-367))) +(-3994 (|has| |#1| (-348)) (|has| |#1| (-367))) (((|#1| |#2|) . T)) ((((-224)) . T)) ((((-406 (-558))) . T) (($) . T) (((-558)) . T)) @@ -3345,7 +3345,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-534)) |has| |#1| (-606 (-534)))) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-841)) (|has| |#1| (-1087)))) ((($) . T) (((-406 (-558))) . T)) (|has| |#1| (-899)) (|has| |#1| (-899)) @@ -3356,14 +3356,14 @@ (((|#1| |#1|) |has| |#1| (-171))) (((|#1|) . T) (((-558)) . T)) ((((-1168)) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-550))) -(-3996 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-550))) +(-3994 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#2|) . T)) -(-3996 (|has| |#1| (-21)) (|has| |#1| (-839))) +(-3994 (|has| |#1| (-21)) (|has| |#1| (-839))) (((|#1|) |has| |#1| (-171))) (((|#1|) . T)) (((|#1|) . T)) -((((-853)) -3996 (-12 (|has| |#1| (-605 (-853))) (|has| |#2| (-605 (-853)))) (-12 (|has| |#1| (-1087)) (|has| |#2| (-1087))))) +((((-853)) -3994 (-12 (|has| |#1| (-605 (-853))) (|has| |#2| (-605 (-853)))) (-12 (|has| |#1| (-1087)) (|has| |#2| (-1087))))) ((((-406 |#2|) |#3|) . T)) ((((-406 (-558))) . T) (($) . T)) (|has| |#1| (-38 (-406 (-558)))) @@ -3375,19 +3375,19 @@ (((|#1|) . T) (((-406 (-558))) . T) (((-558)) . T) (($) . T)) (((#0=(-558) #0#) . T)) ((($) . T) (((-406 (-558))) . T)) -(-3996 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) -(-3996 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) +(-3994 (|has| |#4| (-171)) (|has| |#4| (-717)) (|has| |#4| (-839)) (|has| |#4| (-1039))) +(-3994 (|has| |#3| (-171)) (|has| |#3| (-717)) (|has| |#3| (-839)) (|has| |#3| (-1039))) ((((-853)) . T) (((-1168)) . 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T)) ((((-1161 |#1| |#2| |#3|)) |has| |#1| (-362))) -(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1012)) -(((|#2|) . T) (((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) ((((-853)) . T)) ((((-534)) |has| |#2| (-606 (-534))) (((-882 (-558))) |has| |#2| (-606 (-882 (-558)))) (((-882 (-378))) |has| |#2| (-606 (-882 (-378)))) (((-378)) . #0=(|has| |#2| (-1012))) (((-224)) . #0#)) ((((-293 |#3|)) . T)) @@ -3421,15 +3421,15 @@ ((((-1161 |#1| |#2| |#3|)) . T)) ((((-1161 |#1| |#2| |#3|)) . T) (((-1154 |#1| |#2| |#3|)) . T)) ((((-853)) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-558) |#1|) . 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T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) ((((-129)) . T) (((-853)) . T)) ((((-558) |#1|) . T)) ((((-129)) . T)) @@ -3453,13 +3453,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-362)) (|has| |#2| (-285 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3996 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) -(-3996 (|has| |#1| (-841)) (|has| |#1| (-1087))) +(-3994 (|has| |#1| (-362)) (|has| |#1| (-450)) (|has| |#1| (-899))) +(-3994 (|has| |#1| (-841)) (|has| |#1| (-1087))) ((((-853)) . T)) ((((-853)) . T)) ((((-853)) . T)) (((|#1| (-529 |#2|)) . T)) -((((-2 (|:| -2055 (-1163)) (|:| -3528 (-52)))) . T)) +((((-2 (|:| -2176 (-1163)) (|:| -1925 (-52)))) . T)) ((((-558) (-129)) . T)) (((|#1| (-558)) . T)) (((|#1| (-406 (-558))) . T)) @@ -3473,8 +3473,8 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) -(-3996 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) -(-3996 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) +(-3994 (|has| |#2| (-450)) (|has| |#2| (-550)) (|has| |#2| (-899))) +(-3994 (|has| |#1| (-450)) (|has| |#1| (-550)) (|has| |#1| (-899))) ((($) . T)) (((|#2| (-529 (-855 |#1|))) . T)) ((((-1168)) . T)) @@ -3489,13 +3489,13 @@ ((((-1168)) . T)) ((((-853)) . T) (((-1168)) . T)) ((((-1168)) . T)) -((((-853)) -3996 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) +((((-853)) -3994 (|has| |#1| (-605 (-853))) (|has| |#1| (-1087)))) (((|#1|) . T)) (((|#2| (-762)) . T)) (((|#1| |#2|) . T)) ((((-1145) |#1|) . T)) ((((-406 |#2|)) . T)) -((((-2 (|:| -2055 |#1|) (|:| -3528 |#2|))) . T)) +((((-2 (|:| -2176 |#1|) (|:| -1925 |#2|))) . T)) (|has| |#1| (-550)) (|has| |#1| (-550)) ((($) . T) ((|#2|) . T)) @@ -3504,14 +3504,14 @@ ((((-558)) . T) (($) . 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((-217 . -608) 151123) ((-318 . -23) T) ((-67 . -1200) T) ((-990 . -605) 151055) ((-684 . -230) 151037) ((-705 . -111) 151002) ((-635 . -34) T) ((-244 . -487) 150986) ((-1089 . -1085) 150970) ((-170 . -1087) T) ((-942 . -899) 150949) ((-513 . -608) 150933) ((-1274 . -1138) T) ((-1270 . -21) T) ((-479 . -899) 150912) ((-1270 . -25) T) ((-1268 . -130) T) ((-1266 . -130) T) ((-1259 . -102) T) ((-1242 . -605) 150878) ((-1231 . -1028) 150813) ((-1074 . -708) 150662) ((-1050 . -638) 150649) ((-942 . -638) 150574) ((-773 . -708) 150403) ((-534 . -605) 150385) ((-534 . -606) 150366) ((-771 . -708) 150215) ((-1210 . -1200) 150194) ((-1064 . -102) T) ((-380 . -25) T) ((-380 . -21) T) ((-479 . -638) 150119) ((-459 . -708) 150090) ((-452 . -708) 149939) ((-977 . -102) T) ((-1210 . -876) NIL) ((-1210 . -874) 149891) ((-1173 . -606) NIL) ((-728 . -102) T) ((-1173 . -605) 149873) ((-597 . -608) 149855) ((-1129 . -1110) 149800) ((-1036 . -1193) 149729) ((-529 . -25) T) ((-891 . -308) 149667) ((-705 . -608) 149621) ((-342 . -1046) T) ((-636 . -488) 149602) ((-140 . -102) T) ((-44 . -130) T) ((-288 . -1099) T) ((-671 . -93) T) ((-666 . -93) T) ((-654 . -605) 149584) ((-636 . -605) 149537) ((-476 . -93) T) ((-354 . -605) 149519) ((-351 . -605) 149501) ((-343 . -605) 149483) ((-263 . -606) 149231) ((-263 . -605) 149213) ((-246 . -605) 149195) ((-246 . -606) 149056) ((-132 . -93) T) ((-137 . -93) T) ((-136 . -93) T) ((-1210 . -1028) 149022) ((-1194 . -512) 148989) ((-1128 . -605) 148971) ((-810 . -848) T) ((-810 . -717) T) ((-594 . -287) 148948) ((-575 . -708) 148913) ((-477 . -606) NIL) ((-477 . -605) 148895) ((-516 . -708) 148840) ((-315 . -102) T) ((-312 . -102) T) ((-288 . -23) T) ((-151 . -130) T) ((-900 . -605) 148822) ((-385 . -717) T) ((-862 . -1045) 148774) ((-900 . -606) 148756) ((-862 . -111) 148694) ((-705 . -1039) T) ((-703 . -1222) 148678) ((-138 . -102) T) ((-135 . -102) T) ((-114 . -102) T) ((-684 . -348) NIL) ((-517 . -605) 148610) ((-378 . -786) T) ((-222 . -1087) T) 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146764) ((-1230 . -1045) 146599) ((-1210 . -890) 146432) ((-1209 . -1045) 146240) ((-1194 . -289) 146219) ((-1133 . -150) 146203) ((-1107 . -102) T) ((-1105 . -1087) T) ((-1067 . -23) T) ((-1062 . -102) T) ((-917 . -945) T) ((-728 . -308) 146141) ((-75 . -1200) T) ((-30 . -945) T) ((-168 . -899) 146094) ((-654 . -381) 146066) ((-112 . -835) T) ((-1 . -605) 146048) ((-1067 . -1099) T) ((-128 . -641) 146030) ((-50 . -612) 146014) ((-993 . -408) 145986) ((-588 . -890) 145899) ((-437 . -102) T) ((-140 . -308) NIL) ((-128 . -372) 145881) ((-862 . -1039) T) ((-824 . -841) 145860) ((-81 . -1200) T) ((-702 . -289) T) ((-40 . -1046) T) ((-575 . -171) T) ((-516 . -171) T) ((-509 . -605) 145842) ((-168 . -638) 145752) ((-505 . -605) 145734) ((-350 . -146) 145716) ((-350 . -144) T) ((-358 . -1099) T) ((-352 . -1099) T) ((-344 . -1099) T) ((-994 . -306) T) ((-904 . -306) T) ((-862 . -242) T) ((-108 . -1099) T) ((-862 . -232) 145695) ((-1230 . -111) 145516) ((-1209 . -111) 145305) ((-244 . -1234) 145289) ((-558 . -839) T) ((-358 . -23) T) ((-353 . -348) T) ((-315 . -308) 145276) ((-312 . -308) 145217) ((-352 . -23) T) ((-318 . -130) T) ((-344 . -23) T) ((-994 . -1012) T) ((-31 . -608) 145198) ((-108 . -23) T) ((-244 . -596) 145175) ((-1232 . -38) 145067) ((-1219 . -899) 145046) ((-112 . -1087) T) ((-1025 . -102) T) ((-1219 . -638) 144971) ((-861 . -785) NIL) ((-846 . -638) 144945) ((-861 . -782) NIL) ((-807 . -876) NIL) ((-861 . -717) T) ((-1074 . -512) 144818) ((-773 . -512) 144765) ((-771 . -512) 144717) ((-565 . -638) 144704) ((-807 . -1028) 144532) ((-452 . -512) 144475) ((-387 . -388) T) ((-1230 . -608) 144288) ((-1209 . -608) 144036) ((-60 . -1200) T) ((-613 . -841) 144015) ((-498 . -651) T) ((-1133 . -966) 143984) ((-993 . -450) T) ((-689 . -839) T) ((-508 . -783) T) ((-472 . -1045) 143819) ((-342 . -1087) T) ((-312 . -1138) NIL) ((-288 . -130) T) ((-393 . -1087) T) ((-684 . -369) 143786) ((-860 . -1046) T) ((-222 . -612) 143763) ((-326 . -285) 143740) ((-472 . -111) 143561) ((-1230 . -1039) T) ((-1209 . -1039) T) ((-807 . -376) 143545) ((-168 . -717) T) ((-644 . -102) T) ((-1230 . -242) 143524) ((-1230 . -232) 143476) ((-1209 . -232) 143381) ((-1209 . -242) 143360) ((-993 . -401) NIL) ((-660 . -631) 143308) ((-315 . -38) 143218) ((-312 . -38) 143147) ((-69 . -605) 143129) ((-318 . -491) 143095) ((-1173 . -287) 143074) ((-1100 . -1099) 142984) ((-83 . -1200) T) ((-61 . -605) 142966) ((-477 . -287) 142945) ((-1261 . -1028) 142922) ((-1151 . -1087) T) ((-1100 . -23) 142792) ((-807 . -890) 142728) ((-1219 . -717) T) ((-1089 . -1200) T) ((-472 . -608) 142554) ((-1074 . -289) 142485) ((-956 . -1087) T) ((-883 . -102) T) ((-773 . -289) 142396) ((-326 . -19) 142380) ((-59 . -287) 142357) ((-771 . -289) 142288) ((-846 . -717) T) ((-117 . -839) NIL) ((-514 . -287) 142265) ((-326 . -596) 142242) ((-494 . -287) 142219) ((-452 . -289) 142150) ((-1025 . -308) 142001) ((-671 . -488) 141982) ((-565 . -717) T) ((-666 . -488) 141963) ((-671 . -605) 141913) ((-666 . -605) 141879) ((-652 . -605) 141861) ((-476 . -488) 141842) ((-476 . -605) 141808) ((-244 . -606) 141769) ((-244 . -488) 141746) ((-137 . -488) 141727) ((-136 . -488) 141708) ((-132 . -488) 141689) ((-244 . -605) 141581) ((-212 . -102) T) ((-137 . -605) 141547) ((-136 . -605) 141513) ((-132 . -605) 141479) ((-1134 . -34) T) ((-933 . -1200) T) ((-342 . -708) 141424) ((-660 . -25) T) ((-660 . -21) T) ((-1163 . -608) 141405) ((-472 . -1039) T) ((-627 . -416) 141370) ((-599 . -416) 141335) ((-1107 . -1138) T) ((-575 . -289) T) ((-516 . -289) T) ((-1231 . -306) 141314) ((-472 . -232) 141266) ((-472 . -242) 141245) ((-1210 . -306) 141224) ((-1210 . -1012) NIL) ((-1067 . -130) T) ((-862 . -786) 141203) ((-143 . -102) T) ((-40 . -1087) T) ((-862 . -783) 141182) ((-635 . -1000) 141166) ((-574 . -1046) T) ((-558 . -1046) T) ((-493 . -1046) T) ((-406 . -450) T) ((-358 . -130) T) ((-315 . -399) 141150) ((-312 . -399) 141111) ((-352 . -130) T) ((-344 . -130) T) ((-1168 . -1087) T) ((-1107 . -38) 141098) ((-1081 . -605) 141065) ((-108 . -130) T) ((-944 . -1087) T) ((-911 . -1087) T) ((-762 . -1087) T) ((-662 . -1087) T) ((-691 . -146) T) ((-116 . -146) T) ((-1268 . -21) T) ((-1268 . -25) T) ((-1266 . -21) T) ((-1266 . -25) T) ((-654 . -1045) 141049) ((-529 . -841) T) ((-498 . -841) T) ((-354 . -1045) 141001) ((-351 . -1045) 140953) ((-343 . -1045) 140905) ((-250 . -1200) T) ((-249 . -1200) T) ((-263 . -1045) 140748) ((-246 . -1045) 140591) ((-654 . -111) 140570) ((-354 . -111) 140508) ((-351 . -111) 140446) ((-343 . -111) 140384) ((-263 . -111) 140213) ((-246 . -111) 140042) ((-808 . -1204) 140021) ((-615 . -410) 140005) ((-44 . -21) T) ((-44 . -25) T) ((-806 . -631) 139911) ((-808 . -550) 139890) ((-250 . -1028) 139717) ((-249 . -1028) 139544) ((-126 . -119) 139528) ((-900 . -1045) 139493) ((-703 . -102) T) ((-689 . -1046) T) ((-534 . -610) 139396) ((-342 . -171) T) ((-151 . -21) T) ((-151 . -25) T) ((-88 . -605) 139378) ((-900 . -111) 139334) ((-40 . -708) 139279) ((-860 . -1087) T) ((-654 . -608) 139256) ((-636 . -608) 139237) ((-354 . -608) 139174) ((-351 . -608) 139111) ((-343 . -608) 139048) ((-326 . -606) 139009) ((-326 . -605) 138921) ((-263 . -608) 138674) ((-246 . -608) 138459) ((-1209 . -783) 138412) ((-1209 . -786) 138365) ((-250 . -376) 138334) ((-249 . -376) 138303) ((-644 . -38) 138273) ((-600 . -34) T) ((-480 . -1099) 138183) ((-473 . -34) T) ((-1100 . -130) 138053) ((-954 . -25) 137864) ((-900 . -608) 137814) ((-864 . -605) 137796) ((-954 . -21) 137751) ((-806 . -21) 137661) ((-806 . -25) 137512) ((-615 . -1046) T) ((-1165 . -550) 137491) ((-1159 . -47) 137468) ((-354 . -1039) T) ((-351 . -1039) T) ((-480 . -23) 137338) ((-343 . -1039) T) ((-246 . -1039) T) ((-263 . -1039) T) ((-1112 . -47) 137310) ((-117 . -1046) T) ((-1024 . -638) 137284) ((-948 . -34) T) ((-354 . -232) 137263) ((-354 . -242) T) ((-351 . -232) 137242) ((-351 . -242) T) ((-343 . -232) 137221) ((-343 . -242) T) ((-246 . -325) 137178) ((-263 . -325) 137150) ((-263 . -232) 137129) ((-1143 . -150) 137113) ((-250 . -890) 137045) ((-249 . -890) 136977) ((-1069 . -841) T) ((-413 . -1099) T) ((-1043 . -23) T) ((-900 . -1039) T) ((-321 . -638) 136959) ((-1014 . -839) T) ((-1194 . -992) 136925) ((-1160 . -910) 136904) ((-1154 . -910) 136883) ((-1154 . -811) NIL) ((-900 . -242) T) ((-808 . -362) 136862) ((-384 . -23) T) ((-127 . -1087) 136840) ((-121 . -1087) 136818) ((-900 . -232) T) ((-128 . -34) T) ((-378 . -638) 136783) ((-860 . -708) 136770) ((-1036 . -150) 136735) ((-40 . -171) T) ((-684 . -410) 136717) ((-703 . -308) 136704) ((-827 . -638) 136664) ((-818 . -638) 136638) ((-318 . -25) T) ((-318 . -21) T) ((-648 . -285) 136617) ((-574 . -1087) T) ((-558 . -1087) T) ((-493 . -1087) T) ((-244 . -287) 136594) ((-312 . -230) 136555) ((-1159 . -876) NIL) ((-55 . -1087) T) ((-1112 . -876) 136414) ((-129 . -841) T) ((-1159 . -1028) 136294) ((-1112 . -1028) 136177) ((-182 . -605) 136159) ((-845 . -1028) 136055) ((-773 . -285) 135982) ((-808 . -1099) T) ((-1024 . -717) T) ((-594 . -641) 135966) ((-1036 . -966) 135895) ((-989 . -102) T) ((-808 . -23) T) ((-703 . -1138) 135873) ((-684 . -1046) T) ((-594 . -372) 135857) ((-350 . -450) T) ((-342 . -289) T) ((-1247 . -1087) T) ((-247 . -1087) T) ((-398 . -102) T) ((-288 . -21) T) ((-288 . -25) T) ((-360 . -717) T) ((-701 . -1087) T) ((-689 . -1087) T) ((-360 . -471) T) ((-1194 . -605) 135839) ((-1159 . -376) 135823) ((-1112 . -376) 135807) ((-1014 . -410) 135769) ((-140 . -228) 135751) ((-378 . -785) T) ((-378 . -782) T) ((-860 . -171) T) ((-378 . -717) T) ((-702 . -605) 135733) ((-703 . -38) 135562) ((-1246 . -1244) 135546) ((-350 . -401) T) ((-1246 . -1087) 135496) ((-574 . -708) 135483) ((-558 . -708) 135470) ((-493 . -708) 135435) ((-315 . -621) 135414) ((-827 . -717) T) ((-818 . -717) T) ((-635 . -1200) T) ((-1067 . -631) 135362) ((-1159 . -890) 135305) ((-1112 . -890) 135289) ((-652 . -1045) 135273) ((-108 . -631) 135255) ((-480 . -130) 135125) ((-1165 . -1099) T) ((-942 . -47) 135094) ((-615 . -1087) T) ((-652 . -111) 135073) ((-489 . -605) 135039) ((-326 . -287) 135016) ((-479 . -47) 134973) ((-1165 . -23) T) ((-117 . -1087) T) ((-103 . -102) 134951) ((-1258 . -1099) T) ((-1043 . -130) T) ((-1014 . -1046) T) ((-810 . -1028) 134935) ((-993 . -715) 134907) ((-1258 . -23) T) ((-689 . -708) 134872) ((-579 . -605) 134854) ((-385 . -1028) 134838) ((-353 . -1046) T) ((-384 . -130) T) ((-323 . -1028) 134822) ((-224 . -876) 134804) ((-994 . -910) T) ((-91 . -34) T) ((-994 . -811) T) ((-904 . -910) T) ((-1180 . -605) 134786) ((-1107 . -819) T) ((-485 . -1204) T) ((-1092 . -1087) T) ((-1067 . -21) T) ((-1067 . -25) T) ((-216 . -1204) T) ((-989 . -308) 134751) ((-224 . -1028) 134711) ((-40 . -289) T) ((-705 . -638) 134671) ((-671 . -608) 134652) ((-666 . -608) 134633) ((-485 . -550) T) ((-476 . -608) 134614) ((-358 . -25) T) ((-358 . -21) T) ((-352 . -25) T) ((-216 . -550) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-244 . -608) 134591) ((-137 . -608) 134572) ((-136 . -608) 134553) ((-132 . -608) 134534) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1046) T) ((-574 . -171) T) ((-558 . -171) T) ((-493 . -171) T) ((-648 . -605) 134516) ((-728 . -727) 134500) ((-335 . -605) 134482) ((-68 . -382) T) ((-68 . -394) T) ((-1089 . -107) 134466) ((-1050 . -876) 134448) ((-942 . -876) 134373) ((-643 . -1099) T) ((-615 . -708) 134360) ((-479 . -876) NIL) ((-1133 . -102) T) ((-1081 . -610) 134344) ((-1050 . -1028) 134326) ((-97 . -605) 134308) ((-475 . -146) T) ((-942 . -1028) 134188) ((-117 . -708) 134133) ((-643 . -23) T) ((-479 . -1028) 134009) ((-1074 . -606) NIL) ((-1074 . -605) 133991) ((-773 . -606) NIL) ((-773 . -605) 133952) ((-771 . -606) 133586) ((-771 . -605) 133500) ((-1100 . -631) 133406) ((-459 . -605) 133388) ((-452 . -605) 133370) ((-452 . -606) 133231) ((-1025 . -228) 133177) ((-862 . -899) 133156) ((-126 . -34) T) ((-808 . -130) T) ((-639 . -605) 133138) ((-572 . -102) T) ((-354 . -1265) 133122) ((-351 . -1265) 133106) ((-343 . -1265) 133090) 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. -394) T) ((-216 . -23) T) ((-1270 . -1263) 130940) ((-574 . -289) T) ((-558 . -289) T) ((-667 . -1028) 130924) ((-493 . -289) T) ((-135 . -468) 130879) ((-48 . -1087) T) ((-703 . -230) 130863) ((-861 . -890) NIL) ((-1219 . -876) NIL) ((-879 . -102) T) ((-875 . -102) T) ((-387 . -1087) T) ((-168 . -376) 130847) ((-168 . -337) 130831) ((-1219 . -1028) 130711) ((-846 . -1028) 130607) ((-1129 . -102) T) ((-643 . -130) T) ((-117 . -512) 130515) ((-652 . -783) 130494) ((-652 . -786) 130473) ((-565 . -1028) 130455) ((-293 . -1253) 130425) ((-856 . -102) T) ((-953 . -550) 130404) ((-1194 . -1045) 130287) ((-480 . -631) 130193) ((-894 . -1087) T) ((-1014 . -708) 130130) ((-702 . -1045) 130095) ((-609 . -102) T) ((-594 . -34) T) ((-1134 . -1200) T) ((-1194 . -111) 129964) ((-472 . -638) 129861) ((-353 . -708) 129806) ((-168 . -890) 129765) ((-689 . -289) T) ((-684 . -171) T) ((-702 . -111) 129721) ((-1274 . -1046) T) ((-1219 . -376) 129705) ((-417 . -1204) 129683) ((-1105 . -605) 129665) 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. -778) T) ((-493 . -992) T) ((-273 . -830) T) ((-272 . -830) T) ((-271 . -830) T) ((-270 . -830) T) ((-48 . -289) T) ((-269 . -830) T) ((-268 . -830) T) ((-267 . -830) T) ((-192 . -778) T) ((-604 . -841) T) ((-644 . -410) 123574) ((-222 . -608) 123536) ((-110 . -841) T) ((-643 . -21) T) ((-643 . -25) T) ((-1269 . -38) 123506) ((-117 . -285) 123457) ((-1246 . -19) 123441) ((-1246 . -596) 123418) ((-1259 . -1087) T) ((-1064 . -1087) T) ((-977 . -1087) T) ((-953 . -130) T) ((-728 . -1087) T) ((-726 . -130) T) ((-706 . -130) T) ((-509 . -784) T) ((-406 . -1138) 123396) ((-451 . -130) T) ((-509 . -785) T) ((-222 . -1039) T) ((-293 . -102) 123178) ((-140 . -1087) T) ((-689 . -992) T) ((-91 . -1200) T) ((-127 . -605) 123110) ((-121 . -605) 123042) ((-1274 . -171) T) ((-1160 . -362) 123021) ((-1154 . -362) 123000) ((-315 . -1087) T) ((-417 . -130) T) ((-312 . -1087) T) ((-406 . -38) 122952) ((-1120 . -102) T) ((-1232 . -708) 122844) ((-644 . -1046) T) ((-1122 . -1241) T) ((-318 . -144) 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. -1046) T) ((-684 . -992) NIL) ((-3 . |UnionCategory|) T) ((-1230 . -47) 121198) ((-1209 . -47) 121175) ((-1128 . -1000) 121146) ((-224 . -910) T) ((-40 . -111) 121075) ((-862 . -1028) 120939) ((-1107 . -708) 120926) ((-1092 . -605) 120908) ((-1067 . -146) 120887) ((-1067 . -144) 120838) ((-994 . -362) T) ((-318 . -1188) 120804) ((-378 . -306) T) ((-318 . -1185) 120770) ((-315 . -171) 120749) ((-312 . -171) T) ((-993 . -230) 120726) ((-904 . -362) T) ((-575 . -1265) 120713) ((-516 . -1265) 120690) ((-358 . -146) 120669) ((-358 . -144) 120620) ((-352 . -146) 120599) ((-352 . -144) 120550) ((-600 . -1176) 120526) ((-344 . -146) 120505) ((-344 . -144) 120456) ((-318 . -35) 120422) ((-473 . -1176) 120401) ((0 . |EnumerationCategory|) T) ((-318 . -95) 120367) ((-378 . -1012) T) ((-108 . -146) T) ((-108 . -144) NIL) ((-45 . -234) 120317) ((-644 . -1087) T) ((-600 . -107) 120264) ((-483 . -130) T) ((-473 . -107) 120214) ((-239 . -1099) 120124) ((-862 . -376) 120108) ((-862 . -337) 120092) 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-1265) 107069) ((-1266 . -102) T) ((-1232 . -111) 106961) ((-143 . -605) 106943) ((-983 . -130) T) ((-44 . -102) T) ((-239 . -841) 106894) ((-1219 . -1204) 106873) ((-103 . -487) 106857) ((-1269 . -708) 106827) ((-1074 . -47) 106788) ((-1050 . -1099) T) ((-942 . -1099) T) ((-127 . -34) T) ((-121 . -34) T) ((-773 . -47) 106765) ((-771 . -47) 106737) ((-1219 . -550) 106648) ((-353 . -367) T) ((-479 . -1099) T) ((-1159 . -130) T) ((-1112 . -130) T) ((-452 . -47) 106627) ((-861 . -362) T) ((-845 . -130) T) ((-151 . -102) T) ((-1050 . -23) T) ((-942 . -23) T) ((-565 . -550) T) ((-807 . -25) T) ((-807 . -21) T) ((-1129 . -512) 106560) ((-585 . -1070) T) ((-579 . -1028) 106544) ((-1232 . -608) 106418) ((-479 . -23) T) ((-350 . -1046) T) ((-1194 . -890) 106399) ((-660 . -308) 106337) ((-1100 . -1253) 106307) ((-689 . -638) 106272) ((-993 . -171) T) ((-953 . -144) 106251) ((-627 . -1087) T) ((-599 . -1087) T) ((-953 . -146) 106230) ((-994 . -841) T) ((-726 . -146) 106209) ((-726 . -144) 106188) 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. -1028) 103799) ((-619 . -102) T) ((-221 . -487) 103783) ((-1246 . -34) T) ((-135 . -608) 103767) ((-627 . -708) 103751) ((-599 . -708) 103735) ((-660 . -38) 103695) ((-318 . -102) T) ((-85 . -605) 103677) ((-50 . -1028) 103661) ((-1107 . -1045) 103648) ((-1074 . -376) 103632) ((-773 . -376) 103616) ((-60 . -57) 103578) ((-689 . -785) T) ((-689 . -782) T) ((-575 . -1028) 103565) ((-516 . -1028) 103542) ((-689 . -717) T) ((-323 . -130) T) ((-315 . -1039) 103432) ((-312 . -1039) T) ((-168 . -1099) T) ((-771 . -376) 103416) ((-45 . -150) 103366) ((-994 . -982) 103348) ((-452 . -376) 103332) ((-406 . -171) T) ((-315 . -242) 103311) ((-312 . -242) T) ((-312 . -232) NIL) ((-293 . -1087) 103093) ((-224 . -130) T) ((-1107 . -111) 103078) ((-168 . -23) T) ((-790 . -146) 103057) ((-790 . -144) 103036) ((-250 . -631) 102942) ((-249 . -631) 102848) ((-318 . -283) 102814) ((-1143 . -512) 102747) ((-1120 . -1087) T) ((-224 . -1048) T) ((-806 . -308) 102685) ((-1074 . -890) 102620) ((-773 . -890) 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-306) T) ((-506 . -23) T) ((-321 . -130) T) ((-3 . -1087) T) ((-993 . -606) 95499) ((-989 . -242) 95478) ((-989 . -232) 95457) ((-1274 . -717) T) ((-1238 . -144) 95436) ((-824 . -1087) T) ((-1238 . -146) 95415) ((-1231 . -146) 95394) ((-1231 . -144) 95373) ((-1230 . -1204) 95352) ((-1210 . -144) 95259) ((-1210 . -146) 95166) ((-1209 . -1204) 95145) ((-378 . -130) T) ((-558 . -876) 95127) ((0 . -1087) T) ((-173 . -171) T) ((-168 . -21) T) ((-168 . -25) T) ((-49 . -1087) T) ((-1232 . -638) 95032) ((-1230 . -550) 94983) ((-705 . -1099) T) ((-1209 . -550) 94934) ((-558 . -1028) 94916) ((-588 . -146) 94895) ((-588 . -144) 94874) ((-493 . -1028) 94817) ((-1122 . -1124) T) ((-87 . -383) T) ((-87 . -394) T) ((-862 . -362) T) ((-827 . -130) T) ((-818 . -130) T) ((-705 . -23) T) ((-504 . -605) 94783) ((-500 . -605) 94765) ((-1270 . -1046) T) ((-378 . -1048) T) ((-1016 . -1087) 94743) ((-55 . -1028) 94725) ((-891 . -34) T) ((-480 . -308) 94663) ((-585 . -102) T) ((-1143 . -606) 94624) ((-1143 . 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-963) 89455) ((-76 . -605) 89437) ((-689 . -306) T) ((-168 . -841) 89416) ((-900 . -362) T) ((-378 . -25) T) ((-378 . -21) T) ((-900 . -328) 89403) ((-86 . -605) 89385) ((-689 . -1012) T) ((-667 . -841) T) ((-1230 . -130) T) ((-1209 . -130) T) ((-891 . -1000) 89369) ((-827 . -21) T) ((-48 . -1028) 89312) ((-827 . -25) T) ((-818 . -25) T) ((-818 . -21) T) ((-1268 . -1046) T) ((-1266 . -1046) T) ((-644 . -717) T) ((-1091 . -610) 89215) ((-993 . -608) 89145) ((-1269 . -1045) 89129) ((-1219 . -841) 89108) ((-806 . -410) 89077) ((-103 . -119) 89061) ((-129 . -1087) T) ((-52 . -1087) T) ((-916 . -605) 89043) ((-861 . -982) 89020) ((-814 . -102) T) ((-1269 . -111) 88999) ((-643 . -38) 88969) ((-565 . -841) T) ((-354 . -1099) T) ((-351 . -1099) T) ((-343 . -1099) T) ((-263 . -1099) T) ((-246 . -1099) T) ((-615 . -306) 88948) ((-1137 . -308) 88752) ((-522 . -1070) T) ((-310 . -1087) T) ((-654 . -23) T) ((-480 . -230) 88721) ((-151 . -1046) T) ((-354 . -23) T) ((-351 . -23) T) ((-343 . -23) T) 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-367) NIL) ((-661 . -102) T) ((-179 . -102) T) ((-160 . -102) T) ((-155 . -102) T) ((-153 . -102) T) ((-103 . -34) T) ((-728 . -1200) T) ((-44 . -752) T) ((-586 . -102) T) ((-77 . -395) T) ((-77 . -394) T) ((-643 . -646) 84794) ((-140 . -1200) T) ((-861 . -146) T) ((-861 . -144) NIL) ((-1199 . -93) T) ((-350 . -1039) T) ((-70 . -382) T) ((-70 . -394) T) ((-1152 . -102) T) ((-660 . -512) 84727) ((-679 . -308) 84665) ((-953 . -38) 84562) ((-726 . -38) 84532) ((-544 . -308) 84336) ((-315 . -1200) T) ((-350 . -232) T) ((-350 . -242) T) ((-312 . -1200) T) ((-288 . -1087) T) ((-1167 . -605) 84318) ((-702 . -1204) T) ((-1143 . -641) 84302) ((-1194 . -550) 84281) ((-702 . -550) T) ((-315 . -874) 84265) ((-315 . -876) 84190) ((-312 . -874) 84151) ((-312 . -876) NIL) ((-790 . -308) 84116) ((-318 . -708) 83957) ((-323 . -322) 83934) ((-483 . -102) T) ((-472 . -25) T) ((-472 . -21) T) ((-417 . -38) 83908) ((-315 . -1028) 83571) ((-224 . -1185) T) ((-224 . -1188) T) ((-3 . -605) 83553) ((-312 . -1028) 83483) ((-2 . -1087) T) ((-2 . |RecordCategory|) T) ((-824 . -605) 83465) ((-1100 . -1046) 83395) ((-574 . -910) T) ((-558 . -811) T) ((-558 . -910) T) ((-493 . -910) T) ((-135 . -1028) 83379) ((-224 . -95) T) ((-75 . -439) T) ((-75 . -394) T) ((0 . -605) 83361) ((-168 . -146) 83340) ((-168 . -144) 83291) ((-224 . -35) T) ((-49 . -605) 83273) ((-475 . -1046) T) ((-485 . -230) 83255) ((-482 . -958) 83239) ((-480 . -839) 83218) ((-216 . -230) 83200) ((-81 . -439) T) ((-81 . -394) T) ((-1133 . -34) T) ((-806 . -171) 83179) ((-722 . -102) T) ((-1016 . -605) 83146) ((-498 . -285) 83121) ((-315 . -376) 83090) ((-312 . -376) 83051) ((-312 . -337) 83012) ((-1072 . -605) 82994) ((-807 . -939) 82941) ((-652 . -130) T) ((-1219 . -144) 82920) ((-1219 . -146) 82899) ((-1161 . -102) T) ((-1160 . -102) T) ((-1154 . -102) T) ((-1146 . -1087) T) ((-1113 . -102) T) ((-221 . -34) T) ((-288 . -708) 82886) ((-1146 . -602) 82862) ((-586 . -308) NIL) ((-482 . -1087) 82840) ((-389 . -605) 82822) ((-508 . -841) T) ((-1137 . -228) 82772) ((-1238 . -1237) 82756) ((-1238 . -1224) 82733) ((-1231 . -1229) 82694) ((-1231 . -1224) 82664) ((-1231 . -1227) 82648) ((-1210 . -1208) 82609) ((-1210 . -1224) 82586) ((-613 . -605) 82568) ((-1210 . -1206) 82552) ((-689 . -910) T) ((-1161 . -283) 82518) ((-1160 . -283) 82484) ((-1154 . -283) 82450) ((-1067 . -1087) T) ((-1049 . -1087) T) ((-48 . -301) T) ((-315 . -890) 82416) ((-312 . -890) NIL) ((-1049 . -1056) 82395) ((-1107 . -876) 82377) ((-790 . -38) 82361) ((-263 . -631) 82309) ((-246 . -631) 82257) ((-691 . -1045) 82244) ((-588 . -1224) 82221) ((-1113 . -283) 82187) ((-318 . -171) 82118) ((-358 . -1087) T) ((-352 . -1087) T) ((-344 . -1087) T) ((-498 . -19) 82100) ((-1107 . -1028) 82082) ((-1089 . -150) 82066) ((-108 . -1087) T) ((-116 . -1045) 82053) ((-702 . -362) T) ((-498 . -596) 82028) ((-691 . -111) 82013) ((-435 . -102) T) ((-45 . -1136) 81963) ((-116 . -111) 81948) ((-627 . -711) T) ((-599 . -711) T) ((-806 . -512) 81881) ((-1025 . -1200) T) ((-933 . -150) 81865) ((-1159 . -450) 81796) ((-1153 . -1087) T) ((-1145 . -1087) T) ((-523 . -102) T) ((-518 . -102) 81746) ((-1129 . -638) 81720) ((-1112 . -450) 81671) ((-1074 . -1204) 81650) ((-773 . -1204) 81629) ((-771 . -1204) 81608) ((-62 . -1200) T) ((-475 . -605) 81560) ((-475 . -606) 81482) ((-1074 . -550) 81413) ((-984 . -1087) T) ((-773 . -550) 81324) ((-771 . -550) 81255) ((-480 . -410) 81224) ((-615 . -910) 81203) ((-452 . -1204) 81182) ((-722 . -308) 81169) ((-691 . -608) 81141) ((-397 . -605) 81123) ((-665 . -512) 81056) ((-654 . -25) T) ((-654 . -21) T) ((-452 . -550) 80987) ((-354 . -25) T) ((-354 . -21) T) ((-117 . -910) T) ((-117 . -811) 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 . -608) 80969) ((-116 . -608) 80941) ((-1248 . -605) 80923) ((-1194 . -1099) T) ((-1194 . -23) T) ((-1154 . -308) 80808) ((-1113 . -308) 80795) ((-1067 . -708) 80663) ((-856 . -638) 80623) ((-933 . -970) 80607) ((-900 . -21) T) ((-288 . -171) T) ((-900 . -25) T) ((-310 . -93) T) ((-862 . -841) 80558) ((-702 . -1099) T) ((-702 . -23) T) ((-691 . -1039) T) ((-637 . -1087) 80536) ((-624 . -1087) T) ((-575 . -1204) T) ((-516 . -1204) T) ((-624 . -602) 80511) ((-575 . -550) T) ((-516 . -550) T) ((-358 . -708) 80463) ((-352 . -708) 80415) ((-338 . -1045) 80399) ((-344 . -708) 80351) ((-173 . -111) 80262) ((-173 . -1045) 80194) ((-108 . -708) 80144) ((-338 . -111) 80123) ((-273 . -1087) T) ((-272 . -1087) T) ((-271 . -1087) T) ((-270 . -1087) T) ((-269 . -1087) T) ((-268 . -1087) T) ((-267 . -1087) T) ((-211 . -1087) T) ((-210 . -1087) T) ((-208 . -1087) T) ((-168 . -1188) 80101) ((-168 . -1185) 80079) ((-207 . -1087) T) ((-206 . -1087) T) ((-116 . -1039) T) ((-205 . -1087) T) ((-202 . -1087) T) ((-691 . -232) T) ((-201 . -1087) T) ((-200 . -1087) T) ((-199 . -1087) T) ((-198 . -1087) T) ((-197 . -1087) T) ((-196 . -1087) T) 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T) ((-808 . -1046) T) ((-773 . -23) T) ((-771 . -23) T) ((-479 . -450) 77509) ((-1146 . -512) 77292) ((-380 . -381) 77271) ((-1165 . -410) 77255) ((-459 . -23) T) ((-452 . -23) T) ((-96 . -1087) T) ((-482 . -512) 77188) ((-288 . -289) T) ((-1069 . -605) 77170) ((-1069 . -606) 77151) ((-406 . -899) 77130) ((-50 . -1099) T) ((-1014 . -910) T) ((-993 . -717) T) ((-703 . -876) NIL) ((-575 . -1099) T) ((-516 . -1099) T) ((-834 . -638) 77103) ((-1194 . -130) T) ((-1154 . -399) 77055) ((-994 . -308) NIL) ((-806 . -487) 77039) ((-353 . -910) T) ((-1143 . -34) T) ((-406 . -638) 76991) ((-50 . -23) T) ((-702 . -130) T) ((-703 . -1028) 76871) ((-575 . -23) T) ((-108 . -512) NIL) ((-516 . -23) T) ((-168 . -408) 76842) ((-1127 . -1087) T) ((-1261 . -1260) 76826) ((-691 . -786) T) ((-691 . -783) T) ((-1107 . -306) T) ((-378 . -146) T) ((-279 . -605) 76808) ((-1209 . -982) 76778) ((-48 . -910) T) ((-665 . -487) 76762) ((-250 . -1253) 76732) ((-249 . -1253) 76702) ((-1163 . -841) T) ((-1100 . -171) 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-605) 75833) ((-226 . -1087) 75811) ((-637 . -512) 75744) ((-624 . -512) 75588) ((-824 . -1039) 75567) ((-635 . -150) 75551) ((-342 . -550) T) ((-703 . -890) 75494) ((-544 . -228) 75444) ((-1238 . -283) 75410) ((-1067 . -289) 75361) ((-485 . -839) T) ((-222 . -1099) T) ((-1231 . -283) 75327) ((-1210 . -283) 75293) ((-994 . -38) 75243) ((-216 . -839) T) ((-1194 . -491) 75209) ((-904 . -38) 75161) ((-834 . -785) 75140) ((-834 . -782) 75119) ((-834 . -717) 75098) ((-358 . -289) T) ((-352 . -289) T) ((-344 . -289) T) ((-168 . -450) 75029) ((-426 . -38) 75013) ((-108 . -289) T) ((-222 . -23) T) ((-406 . -785) 74992) ((-406 . -782) 74971) ((-406 . -717) T) ((-498 . -287) 74946) ((-475 . -1045) 74911) ((-648 . -130) T) ((-613 . -608) 74880) ((-1100 . -512) 74813) ((-335 . -130) T) ((-168 . -401) 74792) ((-480 . -708) 74734) ((-806 . -285) 74711) ((-475 . -111) 74667) ((-643 . -1046) T) ((-1219 . -450) 74598) ((-1257 . -1070) T) ((-1256 . -1070) T) ((-1074 . -130) T) ((-1043 . -708) 74540) 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-512) 70802) ((-613 . -786) 70781) ((-613 . -783) 70760) ((-1197 . -605) 70672) ((-221 . -1200) T) ((-665 . -605) 70604) ((-1143 . -1000) 70588) ((-933 . -102) 70538) ((-350 . -717) T) ((-852 . -605) 70520) ((-1210 . -399) 70472) ((-1100 . -487) 70456) ((-60 . -308) 70394) ((-330 . -102) T) ((-1194 . -21) T) ((-1194 . -25) T) ((-40 . -1099) T) ((-702 . -21) T) ((-619 . -605) 70376) ((-513 . -322) 70355) ((-702 . -25) T) ((-108 . -285) NIL) ((-911 . -1099) T) ((-40 . -23) T) ((-762 . -1099) T) ((-558 . -1204) T) ((-493 . -1204) T) ((-318 . -605) 70337) ((-994 . -230) 70319) ((-168 . -165) 70303) ((-574 . -550) T) ((-558 . -550) T) ((-493 . -550) T) ((-762 . -23) T) ((-1230 . -146) 70282) ((-1146 . -596) 70258) ((-1230 . -144) 70237) ((-1017 . -487) 70221) ((-1209 . -144) 70146) ((-1209 . -146) 70071) ((-1261 . -1267) 70050) ((-474 . -487) 70034) ((-461 . -487) 70018) ((-521 . -34) T) ((-643 . -708) 69988) ((-112 . -957) T) ((-652 . -841) 69967) ((-1165 . -171) 69918) ((-364 . -102) T) 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-376) 67934) ((-1107 . -811) T) ((-1107 . -910) T) ((-1100 . -596) 67911) ((-1067 . -606) 67895) ((-482 . -605) 67827) ((-806 . -287) 67804) ((-600 . -150) 67751) ((-417 . -1046) T) ((-485 . -708) 67701) ((-480 . -487) 67685) ((-326 . -841) 67664) ((-338 . -638) 67638) ((-50 . -21) T) ((-50 . -25) T) ((-216 . -708) 67588) ((-168 . -715) 67559) ((-173 . -638) 67491) ((-575 . -21) T) ((-575 . -25) T) ((-516 . -25) T) ((-516 . -21) T) ((-473 . -150) 67441) ((-1067 . -605) 67423) ((-1049 . -605) 67405) ((-983 . -102) T) ((-853 . -102) T) ((-790 . -410) 67369) ((-40 . -130) T) ((-689 . -362) T) ((-691 . -717) T) ((-211 . -885) T) ((-691 . -785) T) ((-691 . -782) T) ((-574 . -1099) T) ((-558 . -1099) T) ((-493 . -1099) T) ((-358 . -605) 67351) ((-352 . -605) 67333) ((-344 . -605) 67315) ((-66 . -395) T) ((-66 . -394) T) ((-108 . -606) 67245) ((-108 . -605) 67188) ((-210 . -885) T) ((-948 . -150) 67172) ((-762 . -130) T) ((-660 . -608) 67090) ((-133 . -717) T) ((-116 . -717) T) ((-1230 . -35) 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1008) ((-807 . -899) 987) ((-1270 . -1099) T) ((-1219 . -1045) 810) ((-846 . -1045) 794) ((-861 . -242) T) ((-861 . -232) NIL) ((-679 . -1200) T) ((-1270 . -23) T) ((-807 . -638) 719) ((-544 . -1200) T) ((-417 . -337) 703) ((-565 . -1045) 690) ((-1219 . -111) 499) ((-691 . -631) 481) ((-846 . -111) 460) ((-380 . -23) T) ((-168 . -608) 238) ((-1173 . -512) 30) ((-652 . -1087) T) ((-671 . -1087) T) ((-666 . -1087) T)) \ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 79c16bfa..e16e998e 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3440285144) +(30 . 3440300496) (4386 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -474,660 +474,658 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |table| |leviCivitaSymbol| |byte| |d01gbf| - |viewport2D| |tanhIfCan| |df2st| |symbolIfCan| |inrootof| |largest| - |new| |expandPower| |script| |retractable?| |overset?| |po| - |algebraicOf| |numberOfMonomials| |zero?| |getConstant| |ksec| - |moebius| |numberOfComposites| |decompose| |midpoint| |traverse| - |inputBinaryFile| |indicialEquation| |basisOfNucleus| |thenBranch| - |any| |leftRemainder| |OMencodingUnknown| - |semiSubResultantGcdEuclidean2| |doubleDisc| |arguments| - |nextsousResultant2| |realZeros| |stoseIntegralLastSubResultant| - |printStatement| |primeFrobenius| |infLex?| |subspace| |tex| |vspace| - |mesh?| |graeffe| |subQuasiComponent?| |taylorQuoByVar| |d01alf| - |cycleRagits| |makeViewport2D| |wholeRadix| |moduleSum| - |rightMinimalPolynomial| |physicalLength!| |lowerPolynomial| - |musserTrials| |OMcloseConn| |nthr| |coleman| |BumInSepFFE| - |OMreceive| |pmComplexintegrate| |complete| |sn| |leadingExponent| - |maxColIndex| |Frobenius| |basisOfMiddleNucleus| - |conditionsForIdempotents| |dimensions| |convergents| - |commutativeEquality| |minPoints| |lazyResidueClass| |minimumExponent| - |meatAxe| |createMultiplicationMatrix| |exQuo| |rightOne| |expPot| - |nil| |lcm| |lazyIrreducibleFactors| |insertMatch| |output| - |shrinkable| |subNodeOf?| |setTex!| |imagJ| |getExplanations| - |sizeMultiplication| |principal?| |removeRedundantFactors| |cosIfCan| - |clearTheSymbolTable| |iiexp| |uniform| |s18def| |determinant| - |append| |alternatingGroup| |subCase?| |putGraph| |numeric| |rename!| - |birth| |mainVariable?| |primitivePart| |ipow| |realEigenvalues| - |goto| |gcdcofact| |left| |radical| |approximate| |mantissa| |conjug| - |gcd| UP2UTS |readIfCan!| |rotate| |callForm?| |traceMatrix| |right| - |complex| |strongGenerators| |belong?| |OMParseError?| - |useEisensteinCriterion| |false| |center| |setlast!| |shellSort| - |semiResultantEuclideannaif| |unitNormal| |outputArgs| |f02xef| - |exponential| |cyclicEqual?| |randomLC| |prinb| |e02bcf| |chiSquare1| - |OMopenString| |setfirst!| |qinterval| |makeTerm| |normalized?| - |eulerE| |prologue| |close| |capacity| |getProperty| |charthRoot| - |preprocess| |numberOfDivisors| |conjugate| |inc| |f04faf| |revert| - |duplicates?| |rootOf| |cAcosh| |nextPartition| - |selectIntegrationRoutines| |doubleFloatFormat| |remove| |divideIfCan| - |logGamma| |#| |sinhcosh| |display| |setButtonValue| |putColorInfo| BY - |solveRetract| |symmetric?| |eyeDistance| |transform| |mr| - |removeCosSq| |rightRank| |cSec| |coHeight| |viewDeltaYDefault| - |mkIntegral| |bernoulliB| |kmax| |cAcsc| |seed| |last| |tableau| - |linearlyDependent?| |showSummary| |testModulus| |qqq| |iiacsch| |sum| - |assoc| |entries| |normInvertible?| |cartesian| |stack| - |transcendent?| |nthFlag| |monomial?| |rangePascalTriangle| - |dimensionsOf| |e02aef| |length| |permanent| |mainSquareFreePart| - |SturmHabichtCoefficients| |hexDigit| |phiCoord| |subResultantChain| - |eq?| |pointColor| |showAttributes| |c02aff| |scripts| - |partialQuotients| |zerosOf| |rotate!| |input| |OMconnOutDevice| - |skewSFunction| |rk4| |palgint0| |nthExpon| |systemCommand| - |orOperands| |arbitrary| |positiveRemainder| |library| |lp| |assign| - |rightFactorCandidate| |fullPartialFraction| |nsqfree| |number?| - |symbol| |sqfrFactor| |reducedSystem| |f02abf| |factorials| |comp| - |integralMatrix| |e04dgf| |droot| |iisinh| |dioSolve| |expression| - |euclideanSize| |f01qdf| |trapezoidalo| |insertTop!| |minGbasis| - |rightRankPolynomial| |multinomial| |rdregime| |digits| |normal| - |integer| |curveColor| |rightUnit| |bumprow| |computeBasis| - |halfExtendedResultant1| |row| |simplifyLog| |lieAdmissible?| - |updateStatus!| |deepExpand| |exponent| |set| |setErrorBound| |maxdeg| - |OMReadError?| |showArrayValues| |symmetricSquare| |viewDeltaXDefault| - |semiResultantEuclidean1| |list| |unitVector| |label| - |numberOfFactors| |bracket| |setTopPredicate| |minimumDegree| |trim| - |shanksDiscLogAlgorithm| |slash| |addMatch| |car| - |setScreenResolution| |commutator| |outputGeneral| - |generalInfiniteProduct| |makeSeries| |removeCoshSq| |initials| - |bivariateSLPEBR| |endOfFile?| |cdr| |algDsolve| |d02raf| |initTable!| - |e02adf| |numberOfChildren| |setDifference| |adaptive3D?| |pushucoef| - |odd?| |lSpaceBasis| |factorsOfCyclicGroupSize| |swap!| - |toseSquareFreePart| |totalfract| |e02bef| |setIntersection| - |minRowIndex| |interpolate| |zeroSetSplitIntoTriangularSystems| - |cosSinInfo| |curryLeft| |powers| |f07fef| |red| |unaryFunction| - |PDESolve| |extract!| |tracePowMod| |genericRightNorm| |setUnion| - |inR?| |or?| |areEquivalent?| |argscript| |OMgetBVar| |subscript| - |stFuncN| |rotatex| |f01rdf| |complexNormalize| |apply| |pr2dmp| - |equiv?| |critMTonD1| |selectAndPolynomials| |null?| - |nextPrimitivePoly| |ptFunc| |outputFixed| |palglimint0| - |squareFreeFactors| |internal?| |dec| |cycleTail| |increment| - |appendPoint| |axesColorDefault| |univcase| |bsolve| |constructor| - |numberOfOperations| |cSech| |size| |mapSolve| |setMinPoints3D| - |generalizedContinuumHypothesisAssumed| |sturmSequence| - |primitiveElement| |hash| |deepCopy| |tanAn| |rowEch| - |radicalEigenvector| |clearTable!| |coordinates| |option| - |tableForDiscreteLogarithm| |count| |show| |choosemon| |meshFun2Var| - |removeRedundantFactorsInContents| |currentScope| |addPoint| |build| - |bandedHessian| |digamma| = |setClosed| |coefChoose| |monic?| - |toseInvertibleSet| |unrankImproperPartitions1| |first| - |viewThetaDefault| |deepestInitial| |points| |leader| |space| |trace| - |cyclicParents| |rightRecip| |OMgetEndAtp| |bfEntry| |isOpen?| - |setImagSteps| |raisePolynomial| |d02bhf| |rest| |elRow1!| < - |numberOfPrimitivePoly| |consnewpol| |norm| |torsion?| |ceiling| - |datalist| |drawToScale| |substitute| |complexNumericIfCan| - |OMgetEndAttr| |ReduceOrder| > |midpoints| |firstNumer| |cyclicCopy| - |setStatus!| |compound?| |removeDuplicates| |plot| - |irreducibleRepresentation| |setrest!| |getOperands| <= |contract| - |mainDefiningPolynomial| |setEpilogue!| |fortran| |insertRoot!| - |stiffnessAndStabilityFactor| |chiSquare| |rightTrim| |fibonacci| - |shufflein| |schwerpunkt| >= |clip| |ratDsolve| - |algebraicCoefficients?| |magnitude| |listYoungTableaus| |bumptab| - |OMwrite| |leftTrim| |att2Result| |setOfMinN| - |selectOptimizationRoutines| |clipParametric| |setProperties!| - |prepareDecompose| |setLegalFortranSourceExtensions| |mainVariable| - |totalLex| |finiteBasis| |palgRDE0| |jacobiIdentity?| |extractBottom!| - |exponentialOrder| |e01bgf| |antisymmetric?| |identification| |sort| - |reset| |augment| |someBasis| |bounds| |iicoth| + |zeroDim?| - |cardinality| |maxIndex| |bottom!| |lquo| |sub| |sturmVariationsOf| - |cyclicEntries| |branchIfCan| - |basis| |host| |permutations| - |systemSizeIF| |idealiser| |write| |singRicDE| |localUnquote| - |leadingSupport| |reduction| / |e01bef| |readByteIfCan!| - |removeDuplicates!| |iiasin| |particularSolution| - |showFortranOutputStack| |save| |cotIfCan| |indiceSubResultant| - |roughSubIdeal?| |applyRules| |zero| |inspect| |deleteRoutine!| - |tanintegrate| |high| |realEigenvectors| |random| |e04jaf| - |checkPrecision| |stoseInternalLastSubResultant| |max| |monomRDE| - |insertionSort!| |factorSFBRlcUnit| |pattern| |radicalRoots| |cAtan| - |pushNewContour| |iibinom| |colorDef| |primitivePart!| |linGenPos| - |f04axf| |inGroundField?| |And| |returnTypeOf| |OMgetString| - |dimension| |leftScalarTimes!| |infix| |prepareSubResAlgo| |recip| - |sincos| |ramified?| |Or| |enqueue!| |write!| |SturmHabicht| |ffactor| - |xCoord| |edf2ef| |basisOfRightNucleus| |recolor| - |createPrimitivePoly| |Not| |iiatan| |s14aaf| |buildSyntax| |cSin| - |degree| |addmod| |repeatUntilLoop| |leftMult| |modifyPoint| |message| - |elColumn2!| |zag| |laguerreL| |deriv| |retract| |squareFree| |f04maf| - |makeSketch| |characteristicSet| |lieAlgebra?| |toScale| |/\\| |ran| - |ODESolve| |complexEigenvectors| |discriminantEuclidean| - |basisOfCenter| |coordinate| |flatten| |rquo| |Beta| |pmintegrate| - |\\/| |collect| |pointData| |mainVariables| |prem| - |subresultantSequence| |decimal| |aLinear| |leastAffineMultiple| - |removeIrreducibleRedundantFactors| |distance| |generic| - |lflimitedint| |f2st| |swapColumns!| |binaryTree| |mightHaveRoots| - LODO2FUN |univariate?| |hMonic| |nonSingularModel| |complexIntegrate| - |constantIfCan| |linearAssociatedLog| |f04asf| |shade| |gradient| - |repeating| |collectUpper| |dmp2rfi| |subMatrix| |e02ahf| - |getMultiplicationTable| |low| |cons| |useNagFunctions| |log2| - |normalDenom| |lastSubResultant| |possiblyInfinite?| |iifact| - |LiePolyIfCan| |float?| |argumentListOf| |triangularSystems| |llprop| - |mapdiv| |factorial| |root?| |pToHdmp| |mainCharacterization| |one?| - |hasHi| |retractIfCan| |makeFR| |Lazard2| |inverse| |cAsec| |zeroOf| - |lepol| |opeval| |df2fi| |gbasis| |invertibleSet| |cap| - |leftFactorIfCan| |iisqrt3| |check| |d01anf| - |permutationRepresentation| |totalDifferential| |setPoly| |lprop| - |iicosh| |expint| |top!| |changeMeasure| |ldf2vmf| |parametersOf| - |addPoint2| |graphStates| |euclideanGroebner| |harmonic| |OMputEndAtp| - |outerProduct| |innerSolve| |e04mbf| |ScanFloatIgnoreSpaces| - |primPartElseUnitCanonical| |innerint| |solveLinear| - |fortranCarriageReturn| |normalizeAtInfinity| |LyndonWordsList1| - |andOperands| |henselFact| |monomRDEsys| |concat!| |continuedFraction| - |linear?| |empty?| |solveid| |lexico| |doubleRank| |simpleBounds?| - |writeBytes!| |sec2cos| |vark| |generateIrredPoly| - |internalZeroSetSplit| |bitLength| |trapezoidal| |lifting| |f07adf| - |exptMod| |reduced?| |interReduce| |rischDE| |rightRemainder| - |palgRDE| |floor| |shuffle| |optional?| |showClipRegion| - |lfinfieldint| |s21baf| |node| |obj| |complexForm| |outputMeasure| - |lazyPremWithDefault| |rootOfIrreduciblePoly| |iFTable| - |setAdaptive3D| |nonLinearPart| |c06gsf| |map| |alphabetic?| - |compiledFunction| |coerceS| |cache| |hitherPlane| |quadraticForm| - |subset?| |f2df| |setEmpty!| |rationalPoints| |complexEigenvalues| - |setMaxPoints3D| |basisOfRightAnnihilator| |power| |karatsubaDivide| - |notelem| |internalSubQuasiComponent?| |block| |bandedJacobian| - |delete!| |adjoint| |pointColorDefault| |e01saf| |unexpand| |e01sef| - |genericRightTrace| |supersub| |infinite?| |iisec| |trivialIdeal?| - |sayLength| |countRealRoots| |rspace| |bit?| |fixedDivisor| |fill!| - |d01ajf| |finite?| |createPrimitiveNormalPoly| |symmetricRemainder| - |OMgetAttr| |convert| |comparison| |dequeue!| |splitDenominator| |key| - |mvar| |initiallyReduce| |computeCycleLength| |s13acf| |s21bbf| - |decrease| |shallowExpand| |makeop| |polyRicDE| - |rewriteIdealWithQuasiMonicGenerators| |primlimintfrac| |stop| - |laplace| |coefficient| |leadingCoefficientRicDE| |filename| - |connectTo| |acosIfCan| |bipolarCylindrical| |errorInfo| |s18adf| - |sup| |isTimes| |setleaves!| |char| |not?| |prefixRagits| - |complexElementary| |asinIfCan| |connect| |createGenericMatrix| - |stronglyReduce| |parse| |weakBiRank| |totolex| |algSplitSimple| - |clearTheIFTable| |null| |factorSquareFreeByRecursion| |FormatRoman| - |definingPolynomial| |numberOfIrreduciblePoly| |unit?| |whitePoint| - |PollardSmallFactor| |leaves| |integers| |headRemainder| |not| - |gcdprim| |palgint| |c06gbf| |basisOfCentroid| |pushdown| - |monicRightDivide| |cycleSplit!| |expIfCan| |and| - |removeSuperfluousQuasiComponents| |lowerCase| |children| - |commonDenominator| |OMputVariable| |bivariate?| |distribute| - |equation| |createNormalElement| |or| |explogs2trigs| |selectfirst| - |hypergeometric0F1| |float| |createPrimitiveElement| |algebraicSort| - |genericRightMinimalPolynomial| |findCycle| |xor| |makingStats?| - |bindings| |factorSquareFreePolynomial| |laurentRep| - |stiffnessAndStabilityOfODEIF| |karatsuba| |pomopo!| |lexTriangular| - |lazyPseudoQuotient| |makeMulti| |case| |var2Steps| - |unprotectedRemoveRedundantFactors| |padicFraction| |charpol| - |directSum| |setFieldInfo| |outputAsScript| |trailingCoefficient| - |Zero| |edf2efi| |characteristicSerie| |OMbindTCP| |moduloP| - |tubePoints| |bat1| |oneDimensionalArray| |mapDown!| |One| |coord| - |listLoops| |numer| |subSet| |rootsOf| |cExp| |split| |module| - |prindINFO| |leftRankPolynomial| |viewport3D| |ip4Address| |stFunc2| - |checkRur| |denom| |brillhartIrreducible?| |leftUnits| - |cyclicSubmodule| |hyperelliptic| |diff| |coercePreimagesImages| - |psolve| |resultant| |zeroVector| |scalarMatrix| |changeNameToObjf| - |swapRows!| |adaptive| |nullary| |mergeFactors| |primes| - |matrixConcat3D| |expandTrigProducts| |acoshIfCan| |pi| |index| - |btwFact| |divisors| |makeUnit| - |solveLinearPolynomialEquationByRecursion| |weights| |declare| - |internalAugment| |varselect| |infinity| |hermiteH| |integral| - |c06ekf| |randomR| |inverseIntegralMatrixAtInfinity| - |nextNormalPrimitivePoly| |linearPart| |weighted| |elt| |numFunEvals| - |atanhIfCan| |internalIntegrate| |union| - |leftCharacteristicPolynomial| |processTemplate| - |subscriptedVariables| |fortranLiteralLine| |limitPlus| |separant| - |terms| |iiacsc| |s19adf| |pair| |size?| |getSyntaxFormsFromFile| - |d01bbf| |f02wef| |iiacosh| |subst| |edf2fi| |factorsOfDegree| |lfunc| - |kernel| |squareTop| |leastPower| |nthRootIfCan| |groebner?| |imagk| - |mapUp!| |draw| |operation| |saturate| |getPickedPoints| |ldf2lst| - |minimalPolynomial| |movedPoints| |lyndon| |irreducibleFactors| |dn| - |internalDecompose| |ellipticCylindrical| |sumOfDivisors| - |solveLinearPolynomialEquationByFractions| |relerror| |lookup| - |bitCoef| |differentialVariables| |li| |asechIfCan| |mdeg| |member?| - |leftDivide| |value| |physicalLength| |OMreadFile| |numerators| - |fractRagits| |evaluate| |orbit| |box| |lyndonIfCan| |color| - |resultantEuclideannaif| |discreteLog| |minPoints3D| |multiEuclidean| - |stopTableGcd!| |equiv| |triangular?| |chebyshevT| |contours| - |numberOfHues| |infRittWu?| |pascalTriangle| |algebraic?| |makeObject| - |An| |nand| |limit| |ef2edf| |merge| |nil?| - |lastSubResultantEuclidean| |quotedOperators| |mathieu22| |dot| - |stirling1| |duplicates| |zCoord| |startTable!| |currentEnv| - |socf2socdf| |unparse| |mapUnivariateIfCan| |squareFreeLexTriangular| - |linears| |coef| |OMserve| |nthRoot| |vedf2vef| |s14baf| - |clearTheFTable| |OMputError| |order| |modularFactor| |enterPointData| - |radicalEigenvalues| |gramschmidt| |e01baf| |torsionIfCan| - |rationalPoint?| |backOldPos| |quoByVar| |s17akf| |leftFactor| - |bipolar| |LowTriBddDenomInv| |semiSubResultantGcdEuclidean1| - |karatsubaOnce| |mkAnswer| |binomThmExpt| |outputFloating| - |separateFactors| |hasTopPredicate?| |powerSum| |surface| |Aleph| - |splitNodeOf!| |normalizedAssociate| |OMgetEndObject| |implies?| - |divisor| |coerceListOfPairs| |d01asf| |hclf| |updatF| - |rationalFunction| |OMsend| |tValues| |internalLastSubResultant| - |associates?| |cAtanh| |escape| |OMputApp| |quartic| |UnVectorise| - |loadNativeModule| |divideIfCan!| |objectOf| |nrows| - |degreeSubResultant| |decomposeFunc| |OMopenFile| |taylorIfCan| - |wordsForStrongGenerators| |prolateSpheroidal| |atom?| |leadingIndex| - |numericalOptimization| |computeCycleEntry| |e02baf| |ncols| - |cyclePartition| |shallowCopy| |failed?| |setvalue!| |binomial| - |OMencodingBinary| |diagonal| |getBadValues| |poisson| - |intermediateResultsIF| |normalDeriv| |s17aef| - |functionIsFracPolynomial?| |lineColorDefault| |rootRadius| |cycleElt| - |leftOne| |Hausdorff| |reverse!| |factorByRecursion| |conditionP| - |rightCharacteristicPolynomial| |e04ycf| |distdfact| |closedCurve| - |square?| |makeViewport3D| |tower| |writeByteIfCan!| |wholeRagits| - |nativeModuleExtension| |OMsetEncoding| |selectsecond| |makeEq| - |e01daf| |rank| |iicsc| |beauzamyBound| |condition| |point| |quote| - |univariatePolynomialsGcds| |transcendenceDegree| |roughBasicSet| - |stoseInvertibleSetsqfreg| |enumerate| |smith| |lfextlimint| - |asimpson| |quadratic?| |critpOrder| |level| |subPolSet?| |Gamma| - |resetVariableOrder| |probablyZeroDim?| |positiveSolve| - |simplifyPower| |viewWriteAvailable| |iisech| |scopes| |makeCos| - |generators| |eq| |remove!| |associatedSystem| |mesh| - |genericLeftTraceForm| |rightDivide| |divisorCascade| - |highCommonTerms| |inHallBasis?| |search| |partition| |series| - |tanIfCan| |prinpolINFO| |iter| |reduceBasisAtInfinity| - |leftRegularRepresentation| |element?| |monicLeftDivide| - |leadingMonomial| |complexNumeric| |arity| |perspective| - |viewDefaults| |members| |roughBase?| |binaryFunction| |printInfo!| - |halfExtendedResultant2| |rightLcm| |root| |postfix| - |leadingCoefficient| |rules| |exteriorDifferential| |hcrf| - |optAttributes| |sts2stst| |symmetricTensors| |relativeApprox| - |unknown| |firstUncouplingMatrix| |branchPoint?| |trueEqual| |push!| - |badNum| |primitiveMonomials| |kernels| |extendedEuclidean| - |printCode| |complexRoots| |pushuconst| |prod| |homogeneous?| |inf| - |lists| |subResultantGcdEuclidean| |dihedralGroup| |reductum| - |univariate| |constantKernel| |eigenMatrix| |min| |mapmult| |exprex| - |merge!| |schema| |completeHermite| |OMUnknownSymbol?| |addiag| - |fractionPart| |pdf2df| |plotPolar| |head| |SturmHabichtMultiple| - |comment| |curveColorPalette| |frobenius| |zeroDimensional?| - |stoseInvertible?| |modulus| |maxint| |exactQuotient| |iisqrt2| - |anfactor| |binary| |pushdterm| |rightGcd| |localIntegralBasis| - |factor| |expintegrate| |cLog| |quoted?| |true| |isList| |maxrow| - |exp| |kovacic| |scanOneDimSubspaces| |iidsum| |regularRepresentation| - |sqrt| |primitive?| |safeCeiling| |extendedIntegrate| |alphanumeric| - |symbol?| ~= |maximumExponent| |maxPoints3D| |zeroMatrix| |untab| - |real| |legendreP| |degreeSubResultantEuclidean| |cos2sec| |iiperm| - |screenResolution3D| |coerce| |printStats!| |stronglyReduced?| - |d03eef| |f02aaf| |imag| |elliptic?| |multiset| |resultantEuclidean| - |mainKernel| |OMencodingXML| |digit| |iflist2Result| |clipWithRanges| - |s21bdf| |directProduct| |compile| |edf2df| - |unrankImproperPartitions0| |sample| |pquo| |signatureAst| |mat| - |critBonD| |pol| |indicialEquations| |normalElement| |extractTop!| - |iiacot| |csubst| |cosh2sech| |perfectSqrt| |constDsolve| - |flexibleArray| |listOfMonoms| |brace| |forLoop| |padicallyExpand| - |read!| |difference| |setOrder| |second| |list?| |oddInfiniteProduct| - |imports| |rCoord| |destruct| |stopMusserTrials| |critB| |e02bdf| - |userOrdered?| |third| |unitCanonical| |selectFiniteRoutines| - |inputOutputBinaryFile| |addBadValue| |allRootsOf| - |internalIntegrate0| |numerator| |generalPosition| |asecIfCan| - |cschIfCan| |getMeasure| |twist| |extend| |primintfldpoly| |sign| - |lagrange| |reducedContinuedFraction| |compdegd| |normFactors| - |LazardQuotient| |gethi| |algebraicVariables| |s20acf| - |constantOperator| |quadratic| |jordanAlgebra?| |selectPDERoutines| - |stoseInvertible?reg| |nilFactor| |blue| |monomial| |integralBasis| - |resetAttributeButtons| |solid?| |leadingBasisTerm| |e04gcf| - |cycleLength| |approxSqrt| |medialSet| |index?| |OMputInteger| - |multivariate| |maxPoints| |pdf2ef| |f01mcf| |iterationVar| - |extractSplittingLeaf| |listexp| |listRepresentation| |child?| - |gcdcofactprim| |algintegrate| |variables| |basisOfLeftAnnihilator| - |doublyTransitive?| |flexible?| |rightNorm| |cyclotomic| - |nextPrimitiveNormalPoly| |charClass| |characteristic| |laplacian| - |imagE| |xn| |measure2Result| |bitTruth| GF2FG |c06eaf| |composite| - |SFunction| |headReduce| |yellow| |denominators| |decreasePrecision| - |cyclic| |generalizedEigenvector| |predicate| |idealiserMatrix| - |genericRightDiscriminant| |isExpt| |mapExpon| |presuper| |create| - |writable?| |sinh2csch| |sort!| |generalizedInverse| - |unitsColorDefault| |elem?| |antiCommutator| |pToDmp| |showAll?| - |initial| |writeLine!| |rootPower| |quasiMonicPolynomials| |coerceP| - |trace2PowMod| |f01rcf| F2FG |normal01| |taylor| 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|iicos| |laguerre| |getIdentifier| |gderiv| |e02dcf| - |getlo| |cAcoth| |match| |cRationalPower| |variable?| - |SturmHabichtSequence| |extractIndex| |factorset| |expintfldpoly| - |relationsIdeal| |usingTable?| |bombieriNorm| - |numberOfFractionalTerms| |deref| |genus| |log10| |oddlambert| - |numberOfCycles| |generalLambert| |diag| |unmakeSUP| |minimize| - |submod| |bytes| |e04ucf| |tubeRadiusDefault| |fortranDoubleComplex| - |bitand| |integralAtInfinity?| |regime| - |semiLastSubResultantEuclidean| |rootBound| |denomRicDE| |d01fcf| |Is| - |term| |compBound| |implies| |dmpToP| |rootProduct| |equality| - |redmat| |bitior| |rational| |aQuartic| |linear| |formula| - |OMputFloat| |denomLODE| |negative?| |explicitEntries?| |subTriSet?| - |iomode| |debug| |ricDsolve| |splitLinear| |optpair| |OMputEndBind| - |transpose| |viewSizeDefault| |imaginary| |critT| |linearMatrix| - |d01amf| |changeVar| |result| D |arrayStack| |B1solve| |reopen!| - |intPatternMatch| |hasoln| |polynomial| |linSolve| 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|f01qcf| |nothing| |factorFraction| - |genericRightTraceForm| |lintgcd| |c06ecf| |linearlyDependentOverZ?| - |extractProperty| |round| |enterInCache| |integerIfCan| |s17agf| |say| - |pushFortranOutputStack| |cTan| |linearDependence| |create3Space| - |pointColorPalette| |fortranLiteral| |rule| |newSubProgram| - |stirling2| |OMputSymbol| |close!| |integralLastSubResultant| - |listConjugateBases| |entry| |nextNormalPoly| |completeEchelonBasis| - |derivative| |evenInfiniteProduct| |iicot| |balancedFactorisation| - |plenaryPower| |heapSort| |imagI| |sizeLess?| |sumSquares| - |fixedPointExquo| |setnext!| |pseudoQuotient| |ParCondList| - |complexZeros| |lazyPseudoDivide| |getStream| |less?| |Ei| - |nextSublist| |rangeIsFinite| |c06frf| |width| |startTableGcd!| - |sdf2lst| |d01apf| |explimitedint| |reverse| |outputSpacing| - |setPosition| |mapCoef| |OMgetEndApp| |multisect| |zeroDimPrimary?| - |increasePrecision| |reduceLODE| |dmpToHdmp| |lo| - |popFortranOutputStack| |safeFloor| |credPol| |baseRDEsys| - |lfintegrate| |outputBinaryFile| |tab1| |associatedEquations| |hspace| - |palgextint| |integralCoordinates| |pleskenSplit| |stopTable!| - |permutation| |e01sbf| |evenlambert| |extractIfCan| |extendIfCan| - |associative?| |void| |setRealSteps| |antiAssociative?| - |nextSubsetGray| |outputAsFortran| |createMultiplicationTable| - |f04atf| |dictionary| |factorAndSplit| |fortranLinkerArgs| UTS2UP - |removeRoughlyRedundantFactorsInContents| |primaryDecomp| |cothIfCan| - |expressIdealMember| |quasiRegular| |lyndon?| |s18aff| - |showTheRoutinesTable| |iidprod| |reify| |secIfCan| |insertBottom!| - |chebyshevU| |plusInfinity| |addPointLast| |latex| |OMputBind| - |viewPhiDefault| |noLinearFactor?| |removeZeroes| |summation| - |twoFactor| |rightExactQuotient| |qualifier| |doubleComplex?| - |minusInfinity| |expenseOfEvaluationIF| |exponents| |optional| - |e01sff| |polyred| |symmetricProduct| |double| |pointPlot| |isobaric?| - |lighting| |spherical| |companionBlocks| |init| |dihedral| - |fortranCharacter| |generic?| |s19acf| |nthFractionalTerm| - |OMputEndApp| |scripted?| |exprToUPS| |genericPosition| |repeating?| - |bag| |univariatePolynomials| |OMclose| |realSolve| |OMlistSymbols| - |tanh2trigh| |character?| |bumptab1| |antisymmetricTensors| |ranges| - |e02gaf| |monomials| |measure| |palgintegrate| |rowEchelon| |rootSimp| - |c05nbf| |monicDivide| |showTypeInOutput| - |halfExtendedSubResultantGcd1| |limitedIntegrate| |printingInfo?| - |f04adf| |besselJ| |semiIndiceSubResultantEuclidean| |diagonalMatrix| - |setPrologue!| |LyndonCoordinates| |closeComponent| - |jordanAdmissible?| |type| |getRef| |janko2| - |removeRedundantFactorsInPols| |permutationGroup| |routines| - |getOperator| |readBytes!| |is?| |stoseSquareFreePart| |coefficients| - |numericalIntegration| |rischDEsys| |cCosh| - |rewriteIdealWithRemainder| |toseLastSubResultant| - |purelyAlgebraicLeadingMonomial?| |generalTwoFactor| |OMconnInDevice| - |declare!| |rewriteSetByReducingWithParticularGenerators| SEGMENT - |setright!| |reduceByQuasiMonic| |complex?| |initiallyReduced?| - |generalizedContinuumHypothesisAssumed?| |leftMinimalPolynomial| - |squareMatrix| |bubbleSort!| |conical| |generalSqFr| |fixedPoint| - |constant| |operator| |makeSUP| |FormatArabic| |distFact| |mathieu11| - |leftZero| |clipPointsDefault| |f04arf| |ListOfTerms| |every?| - |drawCurves| |createZechTable| |palgextint0| |upperCase!| |insert!| - |defineProperty| |polynomialZeros| |factorSquareFree| - |partialNumerators| |extendedResultant| |super| |firstSubsetGray| - |extendedint| |roughEqualIdeals?| |rightTraceMatrix| |updatD| - |createLowComplexityTable| |cfirst| |graphImage| |structuralConstants| - |returnType!| |integralBasisAtInfinity| |elements| |integer?| |s17acf| - |validExponential| |sinIfCan| |indices| |plus!| |clipSurface| - |simplify| |mindegTerm| |matrixDimensions| |elseBranch| - |OMputEndError| |externalList| |factorPolynomial| |baseRDE| |concat| - |loopPoints| |noncommutativeJordanAlgebra?| 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|source| |matrix| |palgLODE| |iteratedInitials| |partitions| - |viewPosDefault| |inverseLaplace| |gcdPolynomial| |normDeriv2| - |stoseInvertibleSet| |bits| |curve| |open| |d03faf| - |innerEigenvectors| |listOfLists| |parent| |patternVariable| |hconcat| - |string?| |rightFactorIfCan| |makeGraphImage| |interval| - |zeroSquareMatrix| |compactFraction| |ptree| |interpretString| |keys| - |complexExpand| |rootPoly| |UP2ifCan| |OMgetEndError| |nor| - |OMsupportsCD?| |OMencodingSGML| |explicitlyEmpty?| |denominator| - |vectorise| |c05pbf| |construct| |stopTableInvSet!| |lllp| |coth2tanh| - |solid| |and?| |radix| |upDateBranches| |tan2trig| |uniform01| - |monicDecomposeIfCan| |localReal?| |d03edf| |ode| |graphState| - |OMgetAtp| |bright| |target| |erf| |csch2sinh| |setFormula!| - |mapBivariate| |wordInGenerators| |leftTrace| |groebSolve| - |closedCurve?| |explicitlyFinite?| |child| |lfextendedint| |pushup| - |contains?| |dimensionOfIrreducibleRepresentation| |rotatez| |returns| - |startPolynomial| |Si| |parts| |diophantineSystem| |rightMult| - |viewWriteDefault| |primintegrate| |testDim| |f02bjf| |showTheIFTable| - |ddFact| |trunc| |dilog| |vconcat| |vertConcat| |mix| |lazyIntegrate| - |OMmakeConn| |rdHack1| |plus| |s13adf| |setref| |corrPoly| |delay| - |mapMatrixIfCan| |sin| |principalAncestors| |youngGroup| |getCurve| - |pureLex| |sh| |mathieu12| |simplifyExp| |cos| |messagePrint| - |nullSpace| |discriminant| |indiceSubResultantEuclidean| |more?| - |front| |findBinding| |e01bff| |e02zaf| |ravel| |tan| - |transcendentalDecompose| |reflect| |coshIfCan| |leftDiscriminant| - |chvar| |reducedForm| |modularGcd| |copyInto!| |rename| - |powerAssociative?| |reshape| |cot| |linearAssociatedOrder| |back| - |irreducibleFactor| |setProperty!| |radicalSimplify| |monicModulo| - |setValue!| |split!| |times| |sec| |LagrangeInterpolation| |e02agf| - |isQuotient| |lazyVariations| |setColumn!| |scaleRoots| |drawComplex| - |inverseIntegralMatrix| |delete| |any?| |csc| |c06fuf| |removeSinSq| - NOT |getProperties| |range| |antiCommutative?| |laurentIfCan| - |singularAtInfinity?| |frst| |lhs| |asin| |badValues| |eigenvalues| - |cAcos| OR |OMunhandledSymbol| |squareFreePolynomial| |setelt| - |mindeg| |Vectorise| |tanNa| |lazyEvaluate| |prevPrime| |rhs| |acos| - |even?| |simpson| |roman| AND |setprevious!| |epilogue| |continue| - |mainMonomials| |sizePascalTriangle| |cyclicGroup| |monom| |atan| - |supDimElseRittWu?| |update| |reverseLex| |bivariatePolynomials| - |cycles| |simpsono| |copy| |splitSquarefree| |linearPolynomials| - |oblateSpheroidal| |f01brf| |acot| |sech2cosh| |minrank| |noKaratsuba| - |height| |truncate| |diagonalProduct| |df2ef| |completeEval| - |divergence| |axes| |ratPoly| |asec| |mapUnivariate| |f02axf| |resize| - |yCoordinates| |s17ajf| |selectOrPolynomials| - |generalizedEigenvectors| |s01eaf| |common| |accuracyIF| |acsc| - |c06fqf| |octon| |power!| |characteristicPolynomial| |autoCoerce| - |createThreeSpace| |cot2tan| |tree| |rewriteSetWithReduction| - |tryFunctionalDecomposition| |rowEchelonLocal| |sinh| |e02def| |qelt| - |RittWuCompare| |basisOfLeftNucloid| |topPredicate| |multiple?| - |ramifiedAtInfinity?| |getGraph| |qsetelt| |cosh| |match?| - |rationalIfCan| |position| |complexSolve| |times!| |sylvesterMatrix| - |makeVariable| |principalIdeal| |aCubic| |expr| |tanSum| - |addMatchRestricted| |purelyTranscendental?| |increase| |iitanh| - |tanh| |innerSolve1| |xRange| |sorted?| |virtualDegree| |cPower| - |curryRight| |tanh2coth| |quickSort| |d02gbf| |weight| |tail| |coth| - |OMconnectTCP| |sncndn| |yRange| |definingEquations| |leftQuotient| - |constantRight| |coerceL| |algint| |ref| |categoryFrame| |sech| - |legendre| |tablePow| |zRange| |f02aff| * |mathieu23| |errorKind| - |tRange| |exprToXXP| |term?| |outputList| |map!| |complexLimit| - |fortranCompilerName| |csch| |e02bbf| |printInfo| GE - |univariatePolynomial| |cSinh| |generator| |c05adf| |d02gaf| - |substring?| |variable| |OMUnknownCD?| |hermite| |qsetelt!| - |degreePartition| |asinh| |meshPar1Var| |overbar| |makeSin| GT - |npcoef| |delta| |geometric| |constant?| |iterators| |computeInt| - |besselY| |acosh| |getMatch| |elementary| |leadingTerm| |iiasinh| LE - |LazardQuotient2| |minordet| |removeZero| |suffix?| - |clearFortranOutputStack| |definingInequation| |infieldIntegrate| - |atanh| |iicsch| |se2rfi| |cAsin| LT |deepestTail| |setLength!| - |multiplyExponents| |leftRecip| |radicalSolve| |acoth| |Lazard| - |bringDown| |eof?| |currentCategoryFrame| |realRoots| |mulmod| - |e04fdf| |prefix?| |associatorDependence| |superHeight| |jacobi| - |anticoord| |abelianGroup| |zeroSetSplit| |hasPredicate?| - |normalizeIfCan| |replace| |ratDenom| |quasiRegular?| |f02aef| - |leftLcm| |resultantnaif| |acsch| |fmecg| |key?| |setRow!| - |symbolTableOf| |fracPart| |viewpoint| |call| |double?| |getCode| - |parametric?| |next| |rur| |bezoutResultant| |squareFreePart| - |mappingAst| |precision| |moebiusMu| |nextPrime| |screenResolution| - |toseInvertible?| |int| |iExquo| |lambda| |crest| |setelt!| |e02akf| - |complementaryBasis| |selectSumOfSquaresRoutines| |objects| |failed| - |column| |linkToFortran| |f01ref| |polygon| |d02ejf| |refine| - |pseudoDivide| |represents| |derivationCoordinates| |base| - |numberOfComputedEntries| |s18aef| |froot| |monomialIntPoly| - |headReduced?| |cyclotomicDecomposition| |monicRightFactorIfCan| - |LiePoly| |newReduc| |computePowers| |tanQ| |quotient| |isPlus| - |groebnerFactorize| |indicialEquationAtInfinity| |cycle| |factorList| - |monicCompleteDecompose| |parents| |representationType| |irreducible?| - |lambert| |f04mbf| |ScanArabic| |modTree| |hostPlatform| - |constantOpIfCan| |nextItem| |critM| |horizConcat| |tube| - |lazyPseudoRemainder| |port| |tryFunctionalDecomposition?| - |rightUnits| |integralMatrixAtInfinity| |UpTriBddDenomInv| - |extractPoint| |combineFeatureCompatibility| |numberOfVariables| - |trigs2explogs| |acscIfCan| |e01bhf| |OMgetBind| |unit| - |constantCoefficientRicDE| |linearAssociatedExp| |dequeue| |mapGen| - |aromberg| |exp1| |nthExponent| |factorGroebnerBasis| - |expenseOfEvaluation| |dark| |outputForm| |alphanumeric?| |makeCrit| - |genericLeftMinimalPolynomial| |qroot| |solve1| |f01bsf| - |isConnected?| |cubic| |test| |omError| |approxNthRoot| - |inconsistent?| |groebner| |incr| |maxRowIndex| |s15aef| |composites| - |parabolicCylindrical| |RemainderList| |clearCache| |iroot| - |seriesSolve| |d01gaf| |function| |divideExponents| - |leftExactQuotient| |parseString| |adaptive?| |iiGamma| - |internalInfRittWu?| |removeSinhSq| |morphism| |quotientByP| - |KrullNumber| |hi| |reciprocalPolynomial| |prefix| |rightScalarTimes!| - |besselK| |kroneckerDelta| |subHeight| |id| |iiacoth| - |fillPascalTriangle| |s13aaf| |log| |setStatus| |eval| |mainContent| - |upperCase?| |ParCond| |push| |imagK| |dim| |previous| |insert| - |rationalApproximation| |tubePlot| |OMsupportsSymbol?| - |modularGcdPrimitive| |nodeOf?| |normal?| |triangulate| - |leftTraceMatrix| |e02daf| |nil| |infinite| |arbitraryExponent| + |Record| |Union| |cSech| |removeSquaresIfCan| |incr| |suffix?| + |initializeGroupForWordProblem| |newTypeLists| |unmakeSUP| + |createLowComplexityTable| |completeHermite| |cyclicEqual?| + |fortranLiteralLine| |OMputSymbol| |composites| + |rightCharacteristicPolynomial| |roughSubIdeal?| |hi| |gramschmidt| + |symbolIfCan| |expint| |decreasePrecision| |toseInvertible?| |shuffle| + |qPot| |iisinh| |monicLeftDivide| |countable?| |localAbs| |const| + |prefix?| |s21bdf| |pushNewContour| |jacobiIdentity?| + |semiResultantEuclidean1| |diagonal?| |divergence| + |constantToUnaryFunction| |radicalSolve| |sncndn| |wholeRagits| + |simpson| |polyred| |smith| |exprToGenUPS| |redPo| |jordanAdmissible?| + |showTheSymbolTable| |trailingCoefficient| |listLoops| + |indicialEquationAtInfinity| |coth2trigh| |getProperty| |acscIfCan| + |region| |matrixConcat3D| |taylorIfCan| |sign| |float?| |splitLinear| + |integrate| |algSplitSimple| |cSec| |unary?| |function| |c05adf| + |pr2dmp| |binarySearchTree| |e02def| |rightScalarTimes!| + |basisOfLeftAnnihilator| |iiasec| |id| |setValue!| |debug3D| |nodes| + |alphabetic?| |relerror| |normInvertible?| |c05pbf| |f04mcf| |points| + |brillhartTrials| |leftZero| |heapSort| |product| |insert| + |whitePoint| |stop| |cCosh| |lazy?| |slex| |eval| LODO2FUN |putGraph| + |GospersMethod| |applyRules| |formula| |pushucoef| |repeatUntilLoop| + |characteristicSet| |rightZero| |table| |nil| |infix?| + |stoseInvertible?reg| |minimize| |children| |OMUnknownSymbol?| + |bernoulli| |squareFreeLexTriangular| |close!| |interpret| |eulerE| + |limitPlus| |subResultantsChain| |postfix| |mapSolve| |new| + |rationalApproximation| |mask| |rightRegularRepresentation| |pureLex| + |dmpToHdmp| |initiallyReduce| |obj| |frst| |invmultisect| |arity| + |infLex?| |e04ycf| |nativeModuleExtension| |subCase?| |top!| + |componentUpperBound| |cyclic| |pmComplexintegrate| |cache| |graphs| + |balancedBinaryTree| |safetyMargin| |parabolicCylindrical| |Lazard| + |goodnessOfFit| |cycle| |approximate| |norm| |inrootof| |edf2df| |int| + |cfirst| |randomLC| |setAdaptive3D| |nrows| |axes| |dioSolve| + |edf2efi| |definingEquations| |coHeight| |complex| |e01baf| |iibinom| + |symmetricProduct| |extractBottom!| |unitVector| |singleFactorBound| + |leviCivitaSymbol| |ncols| |gcdPrimitive| |subSet| + |PollardSmallFactor| |multiplyCoefficients| |acotIfCan| + |functionIsOscillatory| |e01bhf| |useSingleFactorBound?| |outputAsTex| + |optional?| |status| |argumentListOf| |constantLeft| |readLineIfCan!| + |biRank| |OMlistCDs| |lfextlimint| |roman| |equiv?| |close| + |wordsForStrongGenerators| |expandTrigProducts| |getRef| + |doublyTransitive?| |just| |dim| |optpair| |knownInfBasis| + |BasicMethod| |var2StepsDefault| |leftAlternative?| |d02gaf| |s15adf| + |minColIndex| |lagrange| |clipPointsDefault| |leftMult| |split!| + |useEisensteinCriterion?| |setMinPoints3D| |cartesian| |lookup| + |charthRoot| |remove| |rank| |display| |RittWuCompare| + |stopTableInvSet!| |besselK| BY |odd?| |exteriorDifferential| + |integralLastSubResultant| |inspect| |distdfact| |lcm| + |compiledFunction| |submod| |rroot| |univariate?| |rename!| |space| + |separant| |lieAlgebra?| |perspective| |infieldint| |OMsetEncoding| + |computeCycleLength| |symmetricDifference| |last| |commonDenominator| + |sh| |safeFloor| |categories| |linears| |bringDown| |invmod| + |removeRoughlyRedundantFactorsInPol| |imagI| |left| |nextColeman| + |assoc| |nilFactor| |critMonD1| |append| |changeMeasure| + |countRealRootsMultiple| |addiag| |idealSimplify| |ratPoly| + |checkForZero| |univariateSolve| |factorList| |subspace| + |leftQuotient| |right| |OMputObject| |rewriteIdealWithRemainder| + |pointPlot| |gcd| |generalizedEigenvector| |iExquo| |constantOperator| + |remainder| |characteristicSerie| |RemainderList| |cCsch| + |viewDeltaYDefault| |dfRange| |tubePlot| |graphImage| |false| + |unrankImproperPartitions0| |input| |complete| |byte| |hexDigit?| + |euclideanSize| |f01qef| |monomRDEsys| |exponentialOrder| |OMgetBind| + |colorDef| |numberOfFactors| |library| |triangularSystems| |rootsOf| + |taylorRep| |drawComplexVectorField| |integers| |critMTonD1| |lists| + |largest| |prolateSpheroidal| |f01maf| |lSpaceBasis| + |listConjugateBases| |rk4f| |iCompose| |makeFloatFunction| |bitCoef| + |asimpson| |cAsinh| |acoshIfCan| |superscript| |toScale| + |viewDefaults| |generalizedContinuumHypothesisAssumed| + |mainCoefficients| |OMUnknownCD?| |nextsubResultant2| |#| + |basisOfLeftNucloid| |mainValue| |sizeLess?| |eof?| |second| + |aspFilename| |queue| |bytes| FG2F |transcendent?| |set| |lllp| + |cyclic?| |inc| |third| |hcrf| |OMbindTCP| |deleteRoutine!| + |closedCurve| |OMputVariable| |mathieu12| |hMonic| |s13acf| + |makeYoungTableau| |showSummary| |vspace| |rationalPower| |cAcsch| + |selectsecond| |ldf2vmf| |pop!| |credPol| |semicolonSeparate| |power| + |iroot| |iilog| |constantRight| |monicCompleteDecompose| + |idealiserMatrix| |fractionPart| |leftMinimalPolynomial| + |showAttributes| |swap| |viewZoomDefault| |mkIntegral| |bothWays| + |ldf2lst| |structuralConstants| |crest| |OMputInteger| |f01qdf| + |s20adf| |setrest!| |symbol| |concat!| |OMmakeConn| |e01bgf| |bracket| + |plot| |sn| |bits| |expextendedint| |headRemainder| |expression| + |usingTable?| |createLowComplexityNormalBasis| |btwFact| + |binomThmExpt| |OMgetInteger| |atoms| |integer| |f02aaf| |wholePart| + |atom?| |solveLinearPolynomialEquation| |definingInequation| + |rational| |sturmSequence| |setVariableOrder| |leftFactorIfCan| + |copy!| |s17dlf| |d02cjf| |skewSFunction| |read!| |makeEq| + |setsubMatrix!| |e02ddf| |removeZeroes| |topPredicate| |coth2tanh| + |hash| |linearPolynomials| |lazyPseudoQuotient| |OMlistSymbols| + |tanintegrate| |square?| |lazyPseudoRemainder| |badValues| |label| + |show| |count| |selectMultiDimensionalRoutines| |leftRemainder| + |cscIfCan| |limitedint| |orthonormalBasis| |prinb| |explimitedint| + |c06fqf| |or?| = |rem| |karatsubaDivide| |freeOf?| |isConnected?| + |coerceL| |bernoulliB| |minimalPolynomial| |stosePrepareSubResAlgo| + |minPoints| |subResultantGcdEuclidean| |trace| |maxPoints| |number?| + |quadraticNorm| |cn| |fortranReal| |s17adf| |recur| |getVariableOrder| + < |BumInSepFFE| |squareMatrix| |basisOfRightNucleus| |separateDegrees| + |compdegd| |bombieriNorm| |d01ajf| |showClipRegion| > |parametric?| + |irreducibleRepresentation| |highCommonTerms| |equiv| |cLog| + |permutations| |removeRedundantFactorsInPols| + |reducedContinuedFraction| |zeroVector| |rdHack1| |bitTruth| <= + |getZechTable| |s17agf| |rename| |cyclotomicDecomposition| + |lineColorDefault| |summation| |deepExpand| >= |factorSquareFree| + |constructor| |outputFloating| |infieldIntegrate| |aQuartic| + |virtualDegree| |sinhcosh| |iisqrt3| |clipParametric| |UP2ifCan| + |oblateSpheroidal| |rk4| |modifyPoint| |processTemplate| |eulerPhi| + |elliptic?| |option| |euclideanNormalForm| |ideal| |shellSort| + |minus!| |makeMulti| |difference| |trace2PowMod| |palglimint| + |tryFunctionalDecomposition?| |shrinkable| + |OMputApp| |meatAxe| + |notelem| |nothing| |inverseColeman| |tanh2trigh| |imagj| + |semiDiscriminantEuclidean| |leftPower| |areEquivalent?| - |trigs| + |reduced?| |sylvesterSequence| |hasSolution?| |OMencodingUnknown| + |prefixRagits| |closedCurve?| |readable?| / |octon| + |removeIrreducibleRedundantFactors| |asecIfCan| |pdf2ef| |presub| + |cubic| |e01bef| |loopPoints| |movedPoints| |outputSpacing| |s17aff| + |besselJ| |recolor| |bubbleSort!| |createMultiplicationTable| + |sqfrFactor| |uniform| |init| |s13adf| |finite?| |dihedralGroup| + |internalInfRittWu?| |systemSizeIF| |say| |mkPrim| |powerAssociative?| + |inHallBasis?| |quoted?| |rule| |rightTrim| |numberOfFractionalTerms| + |partialNumerators| |OMreceive| |exprHasAlgebraicWeight| + |separateFactors| |cTan| |whatInfinity| |rootRadius| + |monicRightFactorIfCan| |leftTrim| |check| GF2FG |rur| |coefChoose| + |f01brf| |iicsch| |triangular?| |setButtonValue| |typeList| |multiset| + |setProperties!| |exponent| |duplicates| |f02bbf| |var2Steps| + |OMputFloat| |subscriptedVariables| |cPower| |twoFactor| |s17ahf| + |scalarMatrix| |B1solve| |subtractIfCan| |palgint0| |elColumn2!| + |removeRoughlyRedundantFactorsInPols| |rootDirectory| |rightUnits| + |quartic| |outlineRender| |removeSinSq| |conical| |character?| |pack!| + |ignore?| |incrementKthElement| |argscript| |basisOfCommutingElements| + |power!| |createMultiplicationMatrix| |internalSubQuasiComponent?| + |symmetricPower| |setOrder| |noncommutativeJordanAlgebra?| + |explicitlyFinite?| |lyndon| |overlap| |OMgetEndError| |void| + |semiResultantEuclideannaif| |f01mcf| |c06gqf| + |semiSubResultantGcdEuclidean2| |f04atf| |complexElementary| + |createPrimitiveNormalPoly| |ridHack1| |pattern| |distance| + |primextendedint| |bivariateSLPEBR| |createPrimitivePoly| |omError| + |f01rcf| |isList| |reverse| |setref| |setPosition| |d02bbf| + |interReduce| |exportedOperators| |linearDependence| |reducedSystem| + |LiePoly| |s18def| |deref| |constantKernel| |c06eaf| + |semiIndiceSubResultantEuclidean| |entry| |hasTopPredicate?| + |eigenvector| |partition| |cycleElt| |putColorInfo| |d01anf| + |bezoutResultant| |extendedResultant| |keys| |cschIfCan| |middle| + |linearAssociatedOrder| |se2rfi| |genericLeftDiscriminant| |idealiser| + |rightExactQuotient| |nor| |prepareDecompose| |removeSinhSq| + |sech2cosh| |nthExpon| |chebyshevT| |lastSubResultantElseSplit| + |child| |resultantEuclidean| |setErrorBound| |fTable| |monic?| |block| + |denomLODE| |pade| |curryRight| |removeDuplicates!| + |integralMatrixAtInfinity| |changeNameToObjf| |UnVectorise| |isOp| + |fullDisplay| |zag| |unprotectedRemoveRedundantFactors| |dictionary| + |reseed| |OMgetBVar| |characteristicPolynomial| |makeprod| |zCoord| + |iterationVar| |lexGroebner| |list?| |perfectNthRoot| |maxrow| + |external?| |sequences| |pdct| |getProperties| |generalSqFr| + |bumptab1| RF2UTS |newReduc| F2FG |irreducibleFactors| |colorFunction| + |generic| |reopen!| |endOfFile?| |iiatan| |doubleDisc| |asinIfCan| + |solveRetract| |genus| |mapCoef| |symmetricRemainder| + |sizeMultiplication| |top| |powerSum| |approxNthRoot| |tanIfCan| + |clearTheIFTable| |collectQuasiMonic| |corrPoly| |firstSubsetGray| + |eigenMatrix| |unitNormal| |generate| |constant| + |stoseInvertibleSetreg| |f02abf| |create3Space| |singRicDE| + |invertibleElseSplit?| |permutationRepresentation| |composite| + |squareFreePart| |qfactor| |var1Steps| |cAsin| |back| |leftOne| + |lfextendedint| |mainKernel| |toroidal| |maxdeg| |rischDE| + |incrementBy| |minrank| |orOperands| |negative?| |normalize| + |triangSolve| |setLegalFortranSourceExtensions| |qualifier| + |swapRows!| |acsch| |getMeasure| |expand| |infinityNorm| |s17dcf| + |laguerreL| |iiasin| |shiftRoots| |UpTriBddDenomInv| |divideIfCan!| + |s14abf| |diagonalMatrix| |filterWhile| |bandedJacobian| + |padicFraction| |antisymmetricTensors| |factorAndSplit| |tanh2coth| + |subscript| |prinshINFO| |paren| |morphism| |cylindrical| + |filterUntil| |cCot| |fixedPoint| |point| |oddInfiniteProduct| + |kovacic| |erf| |dn| |OMsupportsCD?| |createThreeSpace| + |toseInvertibleSet| |select| |extractSplittingLeaf| |pow| + |nextsousResultant2| |computePowers| |connect| |genericLeftTrace| + |lflimitedint| |minPol| |resultantReduitEuclidean| |algDsolve| + |s14aaf| |inconsistent?| |LyndonBasis| |symmetric?| |delay| + |OMgetAttr| |OMgetEndApp| |startTable!| |byteBuffer| |factorials| + |central?| |pointColorPalette| |series| |varList| |dilog| |normal01| + |SFunction| |oddlambert| |mapmult| |subHeight| |range| |localUnquote| + |surface| |sumOfSquares| |prinpolINFO| |factorSquareFreeByRecursion| + |sin| |totalDifferential| |extendedint| |mappingAst| |rightRecip| + |intPatternMatch| |deepestTail| |withPredicates| |bat1| + |wronskianMatrix| |mainForm| |cos| |objectOf| |doubleComplex?| + |deleteProperty!| |adaptive| |principal?| |arbitrary| + |irreducibleFactor| |noKaratsuba| |null| |pushup| |tan| |Hausdorff| + |OMReadError?| |OMencodingXML| |mainVariable| |nthRoot| |quickSort| + |outputArgs| |charpol| |explicitEntries?| |listexp| |min| |not| + |matrix| |particularSolution| |cot| |cAcos| |extractPoint| |entry?| + |OMencodingSGML| |cAsech| |elRow2!| |fortranLinkerArgs| |operator| + |rk4qc| |deriv| |and| |sec| |removeSuperfluousCases| |stFuncN| + |components| |resultantReduit| |rightRemainder| |arguments| |ranges| + |c06fpf| |sin2csc| |or| |scanOneDimSubspaces| |csc| |cot2tan| |ptree| + |mpsode| |internalDecompose| |chiSquare1| |key| |twist| |curry| |tanQ| + |imports| |tubePointsDefault| |xor| |createGenericMatrix| |asin| + |comparison| |shiftRight| |f2st| |s21baf| |setPrologue!| |leftFactor| + |reduceBasisAtInfinity| |minIndex| |realZeros| |case| |acos| + |eyeDistance| |newLine| |filename| |mapMatrixIfCan| |exprex| |node?| + |quotientByP| |supDimElseRittWu?| |identitySquareMatrix| |groebner| + |buildSyntax| |Zero| |leftExtendedGcd| |atan| |normFactors| + |roughEqualIdeals?| |multisect| |not?| |setAttributeButtonStep| + |readLine!| |integralMatrix| |fortranLiteral| |leadingSupport| + |FormatRoman| |One| |acot| |exists?| |moebiusMu| |headReduce| + |permutationGroup| |parse| |unrankImproperPartitions1| |setright!| + |oneDimensionalArray| |setLength!| |HenselLift| |contains?| |asec| + |red| |basisOfRightNucloid| |iiacoth| |showArrayValues| |socf2socdf| + |duplicates?| |reverse!| |endSubProgram| |dimensions| |changeBase| + |acsc| |ddFact| |alphabetic| |totalLex| |OMgetEndAtp| + |antiCommutative?| |reducedQPowers| |leftUnit| |plus| + |showFortranOutputStack| |sinh| |nthRootIfCan| |select!| |nullary| + |degreeSubResultant| |hasoln| |setEmpty!| |lintgcd| |perfectSqrt| + |quotient| |d02gbf| |cosh| |variable?| |vedf2vef| |explicitlyEmpty?| + |showAllElements| |f02xef| |e04gcf| |generators| |midpoint| + |alternative?| |transform| |elt| |tanh| |lepol| |tubeRadius| + |setScreenResolution3D| |max| |rewriteSetWithReduction| |powmod| + |leftTraceMatrix| |alphanumeric?| |leadingTerm| |jacobian| |rational?| + |coth| |chebyshevU| |OMunhandledSymbol| |palgRDE| |bipolar| + |pointColor| |univcase| |times| |definingPolynomial| |sech| + |stronglyReduce| |kind| |cos2sec| |charClass| |interval| + |OMopenString| |isQuotient| |LyndonCoordinates| |midpoints| |hex| + |setPredicates| |polarCoordinates| |mainMonomial| |csch| + |createZechTable| |op| |hostPlatform| |rarrow| |variable| |tab| + |extend| |isMult| |factorSquareFreePolynomial| |color| + |dimensionOfIrreducibleRepresentation| |OMgetObject| |asinh| + |unaryFunction| |mainVariables| |iterators| |listYoungTableaus| + |complexForm| |KrullNumber| |lazyPquo| |integralRepresents| |implies| + |groebner?| |rangeIsFinite| |useSingleFactorBound| |routines| + |viewThetaDefault| |goto| |reverseLex| |coshIfCan| |airyBi| + |evenlambert| |monom| |equivOperands| |complexRoots| |OMsend| |index| + |LazardQuotient| |unparse| |rationalPoints| |fortranCarriageReturn| + |enqueue!| |derivationCoordinates| |sub| |SturmHabichtSequence| + |lowerPolynomial| |s17ajf| |fillPascalTriangle| |height| |argument| + |rootOf| |c06ecf| |constDsolve| |logpart| |initials| |trunc| + |OMgetFloat| |symbolTableOf| |bfEntry| |lhs| |linearPart| + |squareFreePrim| |remove!| |repeating?| |common| |getBadValues| + |bezoutDiscriminant| |operators| |opeval| |union| |sin?| |pair| |rhs| + |addBadValue| |iiasinh| |reduceByQuasiMonic| |traverse| |tree| + |finiteBound| |rightDiscriminant| |iiperm| |halfExtendedResultant1| + |countRealRoots| |s14baf| |divideExponents| |cycleLength| |makeCrit| + |c02aff| |addMatchRestricted| |collectUnder| |addPointLast| + |hyperelliptic| |palgextint0| |partialDenominators| |addPoint| + |leftDiscriminant| |e02daf| |heap| |list| |bipolarCylindrical| + |csch2sinh| |constantOpIfCan| |df2mf| |fortranLogical| + |characteristic| |squareFreePolynomial| |lastSubResultantEuclidean| + |cCsc| |resultantEuclideannaif| |laurentRep| |car| |matrixDimensions| + |low| |value| |tail| |zeroSquareMatrix| |PDESolve| |lfinfieldint| + |bumptab| |writeByte!| |hue| |fortranDouble| |subNodeOf?| |bsolve| + |cdr| |binary| |OMputString| |imagk| |OMputBVar| |prem| |scaleRoots| + |setfirst!| |setDifference| |c06gcf| |firstNumer| |loadNativeModule| + |pToDmp| |printTypes| |extractIfCan| |outputList| |argumentList!| + |pushuconst| |tValues| |outputMeasure| |critT| |write!| + |setIntersection| |infiniteProduct| |generator| |dmpToP| + |numberOfComputedEntries| |sturmVariationsOf| |vconcat| |packageCall| + |c06frf| |whileLoop| |HermiteIntegrate| |associatedSystem| + |LowTriBddDenomInv| |bag| |setUnion| |component| |ratpart| + |extractIndex| |fracPart| |selectOrPolynomials| |gethi| |belong?| + |normalizeAtInfinity| |bivariatePolynomials| |linearlyDependentOverZ?| + |apply| |weighted| |poisson| |df2fi| |musserTrials| |exQuo| + |getOperator| |imagJ| |flexibleArray| |chineseRemainder| + |LazardQuotient2| |dominantTerm| |iitan| |purelyTranscendental?| + |screenResolution3D| |seriesToOutputForm| |row| |s13aaf| |po| + |partialQuotients| |eigenvalues| |cAcosh| |inputBinaryFile| |size| + |setFormula!| |stFunc1| |latex| |diff| |rspace| |isOpen?| + |trapezoidal| |li| |complexEigenvalues| |stiffnessAndStabilityOfODEIF| + |genericLeftMinimalPolynomial| |expPot| |errorInfo| |nextItem| + |laplacian| |conjugates| |clearTheFTable| + |halfExtendedSubResultantGcd1| |rootProduct| |complex?| + |zeroDimPrime?| |removeRedundantFactors| |double| |subResultantGcd| + |order| |extract!| |retractable?| |upperCase!| |associator| + |allRootsOf| |radPoly| |approxSqrt| |chvar| |useNagFunctions| + |elseBranch| |tanNa| |mapUp!| |compactFraction| + |internalLastSubResultant| |OMgetApp| |leftExactQuotient| |setTex!| + |minPoly| |discreteLog| |pushdterm| |showAll?| + |isAbsolutelyIrreducible?| |OMwrite| |nullity| |drawComplex| + |cyclicCopy| |cyclicEntries| |chainSubResultants| |SturmHabicht| + |extendIfCan| |linear| |subst| |vertConcat| |subresultantSequence| + |pseudoRemainder| |call| |build| |inRadical?| |listOfMonoms| |mesh| + |intermediateResultsIF| |s18aef| |factorset| |prod| |lazyResidueClass| + |crushedSet| |redPol| |semiSubResultantGcdEuclidean1| + |LyndonWordsList1| |extractProperty| |selectIntegrationRoutines| + |polynomial| |gbasis| |generalizedEigenvectors| |startTableGcd!| + |quotedOperators| |OMgetError| |univariatePolynomials| |minordet| + |increase| |reindex| |OMputBind| |OMcloseConn| |redpps| |linearMatrix| + |zerosOf| |cycles| |indicialEquation| |declare!| |cCos| |numFunEvals| + |printStats!| |rightOne| |viewpoint| |factor1| |nextPartition| + |e04naf| |qroot| |figureUnits| |s18adf| |critM| |approximants| + |nextIrreduciblePoly| |parents| |lifting| |setMaxPoints3D| + |rightFactorCandidate| |karatsuba| |mapBivariate| |OMputEndError| + |search| |objects| |tracePowMod| |bit?| |simplifyLog| |mindeg| + |OMParseError?| |lowerCase!| |binding| |fortranInteger| |coerceImages| + |lazyIrreducibleFactors| |test| |base| |saturate| |box| |imagE| + |coercePreimagesImages| |qinterval| |algebraicOf| |initiallyReduced?| + |equality| |matrixGcd| |cosIfCan| |writeLine!| |OMgetEndBVar| + |overset?| |insert!| |getExplanations| |medialSet| |reducedForm| + |ffactor| |normalDeriv| |log2| |readBytes!| |expintfldpoly| + |precision| |att2Result| |commaSeparate| |internalIntegrate0| |prefix| + |setStatus!| |genericLeftTraceForm| |minPoints3D| |associative?| + |branchIfCan| |algebraicVariables| |mix| |associates?| + |interpretString| |limitedIntegrate| |basisOfNucleus| |orbits| |round| + |segment| |rightGcd| |setMinPoints| |decimal| |invertibleSet| + |minimumExponent| |concat| |parseString| |karatsubaOnce| |andOperands| + |removeZero| |iitanh| |froot| |stronglyReduced?| |homogeneous?| + |solve| |inverseIntegralMatrix| |simpsono| |forLoop| |rotate!| + |leftGcd| |doubleFloatFormat| |viewPhiDefault| |bfKeys| |sdf2lst| + |bandedHessian| |setAdaptive| |pomopo!| |OMclose| |rightAlternative?| + |sup| |true| |horizConcat| |double?| |s01eaf| |polCase| + |basisOfRightAnnihilator| |solve1| |boundOfCauchy| |atanhIfCan| + |unvectorise| |genericRightNorm| |fixedDivisor| |nthr| |mathieu22| + |generalizedContinuumHypothesisAssumed?| |fullPartialFraction| + |recoverAfterFail| |rootPower| |wordInGenerators| |OMputEndBVar| + |lieAdmissible?| |contractSolve| |d01amf| |pastel| |multiEuclidean| + |weierstrass| |airyAi| |externalList| |getPickedPoints| |iiacos| |xn| + |useEisensteinCriterion| |index?| |modularGcd| |xCoord| |basis| + |normalDenom| |previous| |relationsIdeal| |psolve| |defineProperty| + |f07adf| |setRealSteps| |signature| |LyndonWordsList| |compound?| + |rightDivide| |printInfo| |s17aef| |sum| |lazyIntegrate| + |complexExpand| |setOfMinN| |setMaxPoints| |iprint| |symbolTable| + |redmat| |enterInCache| |reducedDiscriminant| |localIntegralBasis| + |cap| |cAtanh| |output| |compose| |numerator| |mkAnswer| + |clearFortranOutputStack| |thenBranch| |mapExponents| + |monomialIntPoly| |noLinearFactor?| |aLinear| |scale| |printingInfo?| + |splitSquarefree| |OMconnOutDevice| |henselFact| |innerSolve1| + |divideIfCan| |any| |d03eef| |accuracyIF| |inf| |adaptive?| |lp| + |setleft!| |padicallyExpand| |internalIntegrate| |factorPolynomial| + |raisePolynomial| |upperCase?| |tube| |factorOfDegree| |d01apf| + |digamma| |torsion?| |lexTriangular| |realSolve| |OMreadStr| + |symmetricGroup| |open?| |neglist| |inR?| |getCode| + |commutativeEquality| |iiatanh| |center| |leftNorm| |doubleResultant| + |f01bsf| |leftTrace| |isTimes| |find| |extension| |coleman| |dot| + |torsionIfCan| |dAndcExp| |nsqfree| |quasiMonicPolynomials| |point?| + |rootPoly| |fill!| |any?| |setprevious!| |edf2ef| |copyInto!| + |antiAssociative?| |host| |lyndon?| |polynomialZeros| |updateStatus!| + |node| |changeVar| |createNormalPrimitivePoly| |uncouplingMatrices| + |divisorCascade| |stopTableGcd!| |pushFortranOutputStack| + |expintegrate| |symbol?| |measure2Result| |wordInStrongGenerators| + |setlast!| |preprocess| |functionIsFracPolynomial?| |integerIfCan| + |separate| |popFortranOutputStack| |headReduced?| |continue| + |interpolate| |bezoutMatrix| |exquo| |resultant| |exptMod| |coerceS| + |logGamma| |style| |iiacosh| |variationOfParameters| |div| + |selectOptimizationRoutines| |cond| |firstDenom| |exp1| |mathieu24| + |Not| |empty| |ocf2ocdf| |sorted?| |closed?| |escape| |quo| + |insertMatch| |stack| |generalPosition| |blue| |squareFreeFactors| + |dimension| |setleaves!| |leftCharacteristicPolynomial| + |getIdentifier| |option?| |leastAffineMultiple| |f04adf| + |toseLastSubResultant| |setClipValue| |groebnerIdeal| |lowerCase?| + |groebSolve| |rightMult| |optimize| |iiGamma| |OMsupportsSymbol?| + |OMreadFile| |positiveSolve| |coerceP| |solveLinearlyOverQ| + |systemCommand| |hasHi| |totalDegree| |cycleRagits| |setClosed| + |ceiling| |rootBound| |geometric| |reduction| |baseRDE| |parts| + |maximumExponent| |ip4Address| |unexpand| |stirling1| |rationalPoint?| + |front| |mainSquareFreePart| |nextSubsetGray| + |semiResultantEuclidean2| |log10| |s18aff| |normDeriv2| |rdregime| + |resetBadValues| |scalarTypeOf| |createPrimitiveElement| |innerSolve| + |normal| |bitand| |representationType| |rombergo| |htrigs| + |arrayStack| |tensorProduct| |normalElement| |rightPower| + |primlimintfrac| |gradient| |bitior| + |zeroSetSplitIntoTriangularSystems| |fibonacci| |s17dgf| |c06fuf| + |epilogue| |s19acf| |part?| |palgextint| |sinIfCan| |edf2fi| + |signAround| |length| |patternVariable| |integral?| |numberOfDivisors| + |nthExponent| |graphCurves| |zeroDimensional?| |sinh2csch| |comp| + |trueEqual| |minset| |scripts| |implies?| |aQuadratic| + |leftScalarTimes!| |internal?| |zeroDim?| |f01ref| |gderiv| + |abelianGroup| |rquo| |coordinates| |equation| |hitherPlane| + |numerators| |simplifyPower| |showIntensityFunctions| + |setScreenResolution| |viewWriteDefault| |numberOfMonomials| |e01sef| + |An| |purelyAlgebraicLeadingMonomial?| |position!| |prime?| |hermiteH| + |failed?| |makeFR| |lazyPseudoDivide| |curve?| |mathieu23| + |integralBasis| |constant?| |denomRicDE| |sylvesterMatrix| + |fortranTypeOf| |maxPoints3D| |exprHasWeightCosWXorSinWX| + |makeViewport2D| |lazyGintegrate| |modularGcdPrimitive| |findBinding| + |SturmHabichtCoefficients| |myDegree| |content| |showTheRoutinesTable| + |leftLcm| |stoseInvertibleSet| UP2UTS |drawToScale| |e04mbf| |s19aaf| + |laplace| |monicDecomposeIfCan| |irreducible?| |setLabelValue| + |shufflein| |writeBytes!| |extractTop!| |backOldPos| |algebraicSort| + |debug| |showScalarValues| |repeating| |arg1| |factorsOfDegree| + |divisor| |digits| |quasiMonic?| |integralCoordinates| |s19abf| + |evaluateInverse| |nthFractionalTerm| |sort!| D |arg2| |cosSinInfo| + |light| |stFunc2| |palgintegrate| |exponential1| |factorGroebnerBasis| + |modifyPointData| |indices| |stoseInvertible?| |primintegrate| + |hconcat| |zeroSetSplit| |e02bdf| |mainMonomials| |palginfieldint| + |infix| |basisOfMiddleNucleus| |polygon| |conditions| + |genericRightTrace| |nlde| |janko2| |primPartElseUnitCanonical!| + |tableForDiscreteLogarithm| |conjugate| |sPol| |cycleTail| + |cardinality| |commutator| |match| |kroneckerDelta| |e02dcf| + |getStream| |f04qaf| |nand| |logical?| |fractRagits| + |viewWriteAvailable| |integral| |setvalue!| |iidprod| |schwerpunkt| + |cyclicParents| |Beta| |palgLODE0| |quadraticForm| |computeInt| + |d01fcf| |getOrder| |zoom| |sequence| |Lazard2| |OMserve| |wholeRadix| + |readIfCan!| |resetAttributeButtons| |hexDigit| |e01bff| + |makeVariable| |localReal?| |zeroMatrix| |coerceListOfPairs| |push!| + |sec2cos| |generalTwoFactor| |iiacot| |genericRightMinimalPolynomial| + |OMputAtp| |rightQuotient| |lambert| |hasPredicate?| |resultantnaif| + |cross| |nodeOf?| |ScanFloatIgnoreSpaces| |purelyAlgebraic?| + |sparsityIF| |collectUpper| |curryLeft| |pointLists| |zero?| + |rowEchelon| |pleskenSplit| |complexNumericIfCan| |moebius| + |fixedPoints| |print| |logIfCan| |directory| |reset| |lfunc| + |curveColor| |supersub| |userOrdered?| |clipBoolean| |resolve| + |OMputEndApp| |acschIfCan| |modulus| |coefficient| |identityMatrix| + |flexible?| |reorder| |choosemon| |quoByVar| |expenseOfEvaluation| + |prepareSubResAlgo| |generalizedInverse| |d02ejf| |write| + |outputAsFortran| |getlo| |first| |checkRur| |f04arf| |limit| + |sizePascalTriangle| Y |iisech| |increment| |outputGeneral| |plus!| + |save| |testDim| |rest| |clip| |cAcot| |OMputEndBind| + |rectangularMatrix| |splitConstant| |f01qcf| + |conditionsForIdempotents| |c06ekf| |reify| |substitute| |name| + |d01asf| |string?| |linearDependenceOverZ| |solid?| |e02zaf| |besselY| + |maxIndex| |imagi| |removeDuplicates| F |body| |inverse| |pmintegrate| + |patternMatch| |LagrangeInterpolation| |f04faf| |evaluate| |phiCoord| + |d03edf| |primitivePart| |untab| |normalizeIfCan| |badNum| |rotate| + |subset?| |createIrreduciblePoly| |Is| |binomial| |pair?| ~ |f04mbf| + |cCoth| |less?| |Nul| |basicSet| |csubst| |findCycle| |dmp2rfi| + |birth| |powers| |moduleSum| |infinite?| |vark| + |topFortranOutputStack| |OMconnInDevice| |primPartElseUnitCanonical| + |retract| |maxint| |makeResult| |open| |squareTop| |rightNorm| |fmecg| + |rootSimp| |/\\| |normal?| |numberOfComponents| |scripted?| + |principalIdeal| |stopTable!| |flatten| |selectNonFiniteRoutines| + |brillhartIrreducible?| |ListOfTerms| |unitCanonical| |\\/| + |OMgetEndAttr| |numberOfComposites| |recip| |leadingCoefficientRicDE| + |refine| |cAcoth| |port| |goodPoint| |ratDsolve| |ef2edf| |iisin| + |scopes| |dark| |quatern| |generalInfiniteProduct| |f02bjf| + |rightUnit| |hclf| |meshFun2Var| |s17akf| |appendPoint| + |factorFraction| |randomR| |clipSurface| |cAsec| ** |checkPrecision| + |t| |f02adf| |clearDenominator| |absolutelyIrreducible?| |shift| + |perfectNthPower?| |getMatch| |orbit| |direction| |unitsColorDefault| + |legendreP| |replace| |rightFactorIfCan| |e02agf| |cyclicGroup| + |impliesOperands| |subResultantChain| |ipow| |shiftLeft| |secIfCan| + |iisec| |collect| |transpose| |rischNormalize| EQ |fglmIfCan| |term| + |clearTheSymbolTable| |ode| |retractIfCan| |ScanArabic| + |extendedEuclidean| |listBranches| |callForm?| |multiEuclideanTree| + |revert| |transcendentalDecompose| |makingStats?| |subMatrix| + |property| |specialTrigs| |every?| |Ei| |numer| |generateIrredPoly| + |clearCache| |f2df| |changeName| |innerint| |permutation| |bottom!| + |rightMinimalPolynomial| |f07fef| |cyclotomic| |denom| |c06ebf| + |leadingBasisTerm| |exprToUPS| |autoReduced?| |OMencodingBinary| + |exactQuotient| |leastPower| |outerProduct| |key?| + |algebraicCoefficients?| |c05nbf| |sincos| + |rewriteSetByReducingWithParticularGenerators| |cosh2sech| |aCubic| + |pseudoDivide| |units| |setProperty| |cRationalPower| |leftUnits| |pi| + |OMputError| |selectFiniteRoutines| |triangulate| |makeCos| + |decompose| |setProperties| |leaf?| |updatF| |showTheIFTable| + |bumprow| |infinity| |green| |removeRedundantFactorsInContents| + |ReduceOrder| |genericRightTraceForm| |outputForm| |makeSeries| + |intChoose| |category| |zeroOf| |trivialIdeal?| + |standardBasisOfCyclicSubmodule| |super| |lazyVariations| |elementary| + |reflect| |inverseIntegralMatrixAtInfinity| |connectTo| |domain| + |insertBottom!| |identity| |supRittWu?| |factors| |eq?| |compBound| + |elem?| |sqfree| |package| |nextPrimitiveNormalPoly| + |degreeSubResultantEuclidean| |makeGraphImage| |kernel| |merge| + |bindings| |code| |axesColorDefault| |simplify| |graphState| |map| + |modTree| |draw| |pointData| |drawCurves| |viewSizeDefault| + |fprindINFO| |lyndonIfCan| |iisqrt2| |iiexp| |printCode| |magnitude| + |traceMatrix| |d01aqf| |wrregime| |e02ahf| |realEigenvalues| |terms| + |lazyPremWithDefault| |satisfy?| |nextSublist| |mergeDifference| + |genericPosition| |clikeUniv| |e01sbf| |lquo| |mapUnivariate| |lex| + |setRow!| |rationalFunction| |internalZeroSetSplit| |dom| |ramified?| + |solveLinear| |represents| |totalGroebner| |f02agf| |makeObject| + |yCoordinates| |physicalLength!| |inputOutputBinaryFile| |numeric| + |diagonal| |removeCoshSq| |convert| |iidsum| |computeBasis| + |ScanRoman| |expr| |radical| |monicDivide| |isobaric?| |s17dhf| + |nextNormalPrimitivePoly| |startTableInvSet!| |d01gbf| |sayLength| + |cyclicSubmodule| |coef| |setColumn!| |sample| |changeWeightLevel| + |pole?| |tanSum| |llprop| |stripCommentsAndBlanks| |pointSizeDefault| + |imaginary| |quadratic?| |unit| |antiCommutator| |OMgetAtp| UTS2UP + |currentScope| |selectAndPolynomials| |primitivePart!| |title| + |patternMatchTimes| |acosIfCan| |factorsOfCyclicGroupSize| + |nextNormalPoly| |cExp| |options| |f07aef| |differentialVariables| + |expandPower| |getMultiplicationTable| |scan| |iiacsc| |members| + |s18acf| |nil?| |invertIfCan| |intersect| |anfactor| |mindegTerm| + |integralDerivationMatrix| |optAttributes| |currentCategoryFrame| + |mkcomm| |e04ucf| |hermite| |e| |ran| |f02axf| |overlabel| |string| + |strongGenerators| |nthFlag| |simplifyExp| |s21bbf| |maxColIndex| + |bat| |sumSquares| |moduloP| |bitLength| |nthCoef| |parametersOf| + |nonSingularModel| |cot2trig| |mapdiv| |copies| |readByte!| + |showTypeInOutput| |bivariate?| |pquo| |pdf2df| + |genericRightDiscriminant| |viewport2D| |mesh?| |polygon?| |polyRDE| + |lighting| |baseRDEsys| |returnType!| |next| |regularRepresentation| + |seriesSolve| |getOperands| |gcdprim| |continuedFraction| + |constantCoefficientRicDE| |lllip| |setelt!| |mainVariable?| + |removeRoughlyRedundantFactorsInContents| |leadingExponent| + |trapezoidalo| |iiabs| |completeHensel| |predicate| |linGenPos| + |null?| |setTopPredicate| |antisymmetric?| |swap!| + |ScanFloatIgnoreSpacesIfCan| |roughBase?| |rightExtendedGcd| + |semiResultantReduitEuclidean| |is?| |critpOrder| |asechIfCan| + |leadingIndex| |divisors| |makeTerm| |s19adf| |plusInfinity| + |completeEchelonBasis| |split| |primitiveElement| |high| |mainContent| + |normalise| |setCondition!| |nthFactor| |typeLists| + |rootOfIrreduciblePoly| |rk4a| |minusInfinity| |realRoots| + |internalSubPolSet?| |algint| |e01daf| |degreePartition| + |messagePrint| |solid| |multiple?| |tubePoints| + |sumOfKthPowerDivisors| |declare| |curve| |completeSmith| |resetNew| + |Vectorise| |width| |tubeRadiusDefault| |monomial?| |OMread| + |selectODEIVPRoutines| |integerBound| |resize| |ODESolve| + |rubiksGroup| |unknown| |errorKind| |f02ajf| |distribute| |addPoint2| + |decrease| |Frobenius| |factorial| |palgLODE| |fixedPointExquo| |kmax| + |linear?| |spherical| |roughUnitIdeal?| |complexIntegrate| + |OMgetEndBind| |primitive?| |intcompBasis| |sts2stst| |qelt| + |universe| |in?| |getButtonValue| |signatureAst| + |integralBasisAtInfinity| |lfintegrate| |graeffe| |qsetelt| + |primaryDecomp| |leader| |contract| |palgint| |isPower| |parameters| + |linearAssociatedExp| |createRandomElement| |isExpt| |plotPolar| + |derivative| |type| |toseSquareFreePart| |d01gaf| |xRange| |multMonom| + |deepCopy| |nextPrimitivePoly| |f04axf| |sort| |ramifiedAtInfinity?| + |e02akf| |size?| |insertTop!| |binaryFunction| |yRange| + |blankSeparate| |selectPolynomials| |paraboloidal| |subPolSet?| + |rootKerSimp| |identification| |fortran| |module| |over| |mulmod| + |zRange| |realEigenvectors| |contours| |optional| |mdeg| + |extensionDegree| |numericalOptimization| |minimumDegree| + |getConstant| |map!| |Ci| |OMputEndAttr| |iicsc| |thetaCoord| + |fortranDoubleComplex| |meshPar1Var| |makeUnit| |exactQuotient!| + |qsetelt!| |safeCeiling| |d03faf| |iteratedInitials| |ref| + |algebraicDecompose| |currentEnv| |rangePascalTriangle| |delta| + |random| |nullSpace| |and?| |real?| |root?| |setchildren!| + |mainDefiningPolynomial| |tRange| |lazyPrem| |quadratic| |mat| + |createNormalElement| |shallowExpand| |expandLog| |operation| + |tanhIfCan| |complexEigenvectors| |evenInfiniteProduct| |cAcsc| + |empty?| |coefficients| |repSq| |graphStates| |constantIfCan| |f02akf| + |cothIfCan| |setnext!| |printInfo!| |nullary?| |binaryTournament| + |unravel| |companionBlocks| |mapExpon| |outputBinaryFile| |datalist| + |totalfract| |e04fdf| |symmetricTensors| |realElementary| |c06gbf| + |dequeue| |complement| |head| |elements| |exprHasLogarithmicWeights| + |getSyntaxFormsFromFile| |delete!| |subQuasiComponent?| |singular?| + |tanAn| |ptFunc| |inGroundField?| |complementaryBasis| |augment| + SEGMENT |numberOfHues| |polygamma| |minGbasis| |besselI| |e02dff| + |depth| |eigenvectors| |elliptic| |computeCycleEntry| |trim| + |startPolynomial| |prindINFO| |partitions| |createNormalPoly| |e04jaf| + |lambda| |message| |member?| |Gamma| |singularitiesOf| |startStats!| + |vector| |categoryFrame| |moreAlgebraic?| |stoseInvertible?sqfreg| + |printHeader| |comment| |beauzamyBound| |integralAtInfinity?| |taylor| + |overbar| |parabolic| |solveLinearPolynomialEquationByRecursion| + |differentiate| |innerEigenvectors| |ksec| |leaves| |setEpilogue!| + |getGoodPrime| |replaceKthElement| |explogs2trigs| |laurent| + |discriminant| |atanIfCan| |getGraph| |script| |df2st| |iicot| + |acothIfCan| |exprToXXP| |solveid| |tower| |euclideanGroebner| + |dimensionsOf| |puiseux| |makeop| |radix| |extendedIntegrate| + |ratDenom| |halfExtendedResultant2| |seed| |radicalEigenvectors| + |dihedral| |s18dcf| |linearAssociatedLog| |padecf| |setStatus| + |condition| |mantissa| |pToHdmp| |associatorDependence| + |taylorQuoByVar| |basisOfCentroid| |numberOfNormalPoly| |setImagSteps| + |critBonD| |inv| |fintegrate| |presuper| |SturmHabichtMultiple| + |elRow1!| |tex| |cons| |adjoint| |expressIdealMember| |level| + |ParCond| |discriminantEuclidean| |hessian| |extendedSubResultantGcd| + |ground?| |mapGen| |nonQsign| |integer?| |tab1| |d02bhf| |determinant| + |e02bef| |relativeApprox| |eq| |upperCase| |domainOf| |rowEch| |lift| + |error| |outputFixed| |ground| |returnTypeOf| + |cyclotomicFactorization| |selectSumOfSquaresRoutines| + |sortConstraints| |modularFactor| |iter| |d01bbf| |euler| + |pseudoQuotient| |showTheFTable| |numberOfImproperPartitions| + |shanksDiscLogAlgorithm| |reduce| |leadingMonomial| |leftDivide| + |assert| |oddintegers| |someBasis| |complexNumeric| |enterPointData| + |OMputAttr| |bright| |wreath| |viewPosDefault| + |stoseInternalLastSubResultant| |infRittWu?| |weights| + |leadingCoefficient| |resetVariableOrder| |mirror| |e02baf| |rules| + |mr| |iicos| |insertRoot!| |rightRankPolynomial| |rightTrace| |quote| + |kernels| |makeSin| |primitiveMonomials| |regime| |quasiAlgebraicSet| + |randnum| |Si| |balancedFactorisation| |leftRankPolynomial| |legendre| + |divide| |leadingIdeal| |rationalIfCan| |reductum| + |indiceSubResultantEuclidean| |univariate| |upDateBranches| + |alphanumeric| |source| |rightLcm| |leastMonomial| |s21bcf| |term?| + |dec| |harmonic| |e02aef| |romberg| |extractClosed| + |mainCharacterization| |superHeight| |listOfLists| |lexico| |tableau| + |fortranCharacter| |primextintfrac| |f04asf| |polyRicDE| ~= + |quasiRegular| |basisOfCenter| |c02agf| |genericLeftNorm| + |radicalEigenvector| |associatedEquations| |pol| |s17acf| + |selectfirst| |factor| |coerce| |ParCondList| |minRowIndex| + |pointColorDefault| |exp| |pascalTriangle| |pushdown| + |curveColorPalette| |sqrt| |aromberg| |notOperand| |create| + |construct| |groebgen| |f02wef| |inverseLaplace| + |firstUncouplingMatrix| |normalForm| |subNode?| |physicalLength| + |fractionFreeGauss!| |OMgetString| |column| |real| |lazyEvaluate| + |d01alf| |move| |target| |showRegion| |tablePow| |mainPrimitivePart| + |palglimint0| |perfectSquare?| |slash| |bounds| |imag| |delete| + |laguerre| |stiffnessAndStabilityFactor| |quasiRegular?| |f02fjf| + |monomRDE| |directProduct| NOT |fixPredicate| |probablyZeroDim?| + |cyclePartition| |internalAugment| |compile| |diophantineSystem| + |multinomial| |jacobi| |gcdcofact| |univariatePolynomialsGcds| OR + |npcoef| |semiLastSubResultantEuclidean| |complexSolve| |drawStyle| + |one?| |iiasech| |e01saf| |doubleRank| |mainExpression| |polar| AND + |permanent| |more?| |brace| |cycleEntry| |atrapezoidal| |viewport3D| + |has?| |complexLimit| |hypergeometric0F1| + |rewriteIdealWithQuasiMonicGenerators| |OMputEndAtp| |destruct| + |tan2trig| |d02raf| |functionIsContinuousAtEndPoints| |gcdPolynomial| + |stopMusserTrials| |linearlyDependent?| |numericIfCan| + |indicialEquations| |shade| |sechIfCan| |Aleph| |ravel| + |partialFraction| |parent| |monicRightDivide| |monomials| |generic?| + |sinhIfCan| |validExponential| |frobenius| |dualSignature| |reshape| + |OMgetEndObject| |coordinate| |nextLatticePermutation| |clearTable!| + |writable?| |hspace| |rowEchLocal| |complexZeros| |cTanh| |chiSquare| + |meshPar2Var| |lo| |numberOfCycles| |positive?| |iicoth| + |linkToFortran| |monomial| |truncate| |digit?| |branchPoint?| + |predicates| |restorePrecision| |algebraic?| |char| |setPoly| + |factorSFBRlcUnit| |addMatch| |numFunEvals3D| |multivariate| + |lastSubResultant| |anticoord| |f02aef| |unitNormalize| + |insertionSort!| |digit| |roughBasicSet| |leftRank| |setelt| + |variables| |shallowCopy| |listRepresentation| |rotatey| |f02aff| + |expenseOfEvaluationIF| |stoseLastSubResultant| |nary?| |varselect| + |makeSUP| |setProperty!| |positiveRemainder| |conjug| + |transcendenceDegree| |update| |combineFeatureCompatibility| |e02bbf| + * |rootSplit| |times!| |copy| |initTable!| |directSum| |subTriSet?| + |simpleBounds?| |fortranCompilerName| |rotatex| |problemPoints| + |fortranComplex| |uniform01| |d02kef| |possiblyNewVariety?| + |squareFree| |testModulus| |headAst| |ellipticCylindrical| |float| + |qqq| |initial| |halfExtendedSubResultantGcd2| |alternating| |e02gaf| + |critB| |f02awf| |prevPrime| |OMgetVariable| |expIfCan| + |removeConstantTerm| |swapColumns!| |autoCoerce| |splitNodeOf!| + |rCoord| |asinhIfCan| |measure| |cycleSplit!| |prologue| + |principalAncestors| |csc2sin| |zeroDimPrimary?| |dequeue!| + |leftRegularRepresentation| |diagonalProduct| |makeRecord| + |stoseIntegralLastSubResultant| |dflist| |match?| |prime| |position| + |iipow| |s17def| |generalLambert| |yellow| |merge!| + |possiblyInfinite?| |cSin| |maxRowIndex| |nonLinearPart| + |radicalRoots| |lprop| |rightTraceMatrix| |nextPrime| |e04dgf| + |FormatArabic| |factorByRecursion| |newSubProgram| |cotIfCan| |acosh| + |jordanAlgebra?| |exponents| |getMultiplicationMatrix| |finiteBasis| + |mergeFactors| |mapDown!| |child?| |convergents| |weight| |flagFactor| + |atanh| |numericalIntegration| |iflist2Result| + |stoseInvertibleSetsqfreg| |symmetricSquare| |pile| |d01akf| |e02adf| + |f07fdf| |multiplyExponents| |acoth| |makeViewport3D| |push| + |numberOfVariables| |univariatePolynomial| |calcRanges| + |decomposeFunc| |weakBiRank| |ord| |iomode| |isPlus| |assign| |asech| + |failed| |iiacsch| |numberOfPrimitivePoly| |f01rdf| GE |rootNormalize| + |primlimitedint| |linSolve| |df2ef| |setFieldInfo| |radicalSimplify| + |eisensteinIrreducible?| |removeCosSq| |commutative?| |sumOfDivisors| + |radicalEigenvalues| |yCoord| |iFTable| GT + |tryFunctionalDecomposition| |denominator| |laurentIfCan| + |numberOfIrreduciblePoly| |normalizedAssociate| |f04maf| |tan2cot| + |multiple| |controlPanel| |monomialIntegrate| |e02bcf| |normalized?| + |changeThreshhold| |removeSuperfluousQuasiComponents| LE + |basisOfLeftNucleus| |binaryTree| |primintfldpoly| |printStatement| + |quasiComponent| |zero| |applyQuote| |lifting1| |normalizedDivide| + |abs| |diag| |OMgetSymbol| |solveInField| LT |increasePrecision| + |splitDenominator| |exponential| |iifact| |s15aef| |intensity| + |rotatez| |numberOfOperations| |even?| |youngGroup| + |rewriteIdealWithHeadRemainder| |denominators| |schema| |floor| + |gcdcofactprim| |And| |droot| |degree| |rst| |f04jgf| |capacity| + |iicosh| |cAtan| |e02ajf| |updatD| |screenResolution| |symFunc| + |stirling2| |distFact| |Or| |coord| |conditionP| |indiceSubResultant| + |ruleset| |clipWithRanges| |c06gsf| |s20acf| |enumerate| |palgRDE0| + |viewDeltaXDefault| |closeComponent| |numberOfChildren| |element?| + |ode2| |OMconnectTCP| |diagonals| |e01sff| |maxrank| |invertible?| + |currentSubProgram| |branchPointAtInfinity?| |polyPart| + |reciprocalPolynomial| |completeEval| |leftRecip| |ricDsolve| + |groebnerFactorize| |certainlySubVariety?| |cSinh| |rischDEsys| + |trigs2explogs| |stoseSquareFreePart| |OMopenFile| |primes| + |deepestInitial| |rightRank| |getDatabase| |monicModulo| + |outputAsScript| |totolex| |suchThat| |selectPDERoutines| |entries| + |complexNormalize| |rowEchelonLocal| |hdmpToDmp| |mapUnivariateIfCan| + |LiePolyIfCan| |makeSketch| |powern| |unit?| |expt| + |solveLinearPolynomialEquationByFractions| |imagK| + |semiDegreeSubResultantEuclidean| |lowerCase| |result| |vectorise| + |fractRadix| |algintegrate| |primeFactor| |plenaryPower| + |radicalOfLeftTraceForm| |subresultantVector| |consnewpol| + |substring?| |log| |OMgetType| |ode1| |mightHaveRoots| |mvar| + |properties| |singularAtInfinity?| |mathieu11| |root| |hdmpToP| |cup| + |returns| |alternatingGroup| |fi2df| |getCurve| |reduceLODE| + |var1StepsDefault| |OMputEndObject| |translate| |adaptive3D?| + |primeFrobenius| |addmod| |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index a2eeaf9c..7eb7d312 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5234 +1,5234 @@ -(3184356 . 3440285167) -((-4094 (((-112) (-1 (-112) |#2| |#2|) $) 63) (((-112) $) NIL)) (-2697 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3999 ((|#2| $ (-558) |#2|) NIL) ((|#2| $ (-1213 (-558)) |#2|) 34)) (-2397 (($ $) 59)) (-3023 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 40) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 38) ((|#2| (-1 |#2| |#2| |#2|) $) 37)) (-4078 (((-558) (-1 (-112) |#2|) $) 22) (((-558) |#2| $) NIL) (((-558) |#2| $ (-558)) 73)) (-3906 (((-635 |#2|) $) 13)) (-2297 (($ (-1 (-112) |#2| |#2|) $ $) 47) (($ $ $) NIL)) (-4126 (($ (-1 |#2| |#2|) $) 29)) (-2009 (($ (-1 |#2| |#2|) 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T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3996 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3996 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3996 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3996 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3996 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3996 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3996 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . T) ((-1253 |#2|) |has| |#2| (-362))) -((-3142 (((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 21)) (-3023 ((|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|) 23)) (-2009 (((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)) 18))) -(((-238 |#1| |#2| |#3|) (-10 -7 (-15 -3142 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3023 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -2009 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) (-762) (-1200) (-1200)) (T -238)) -((-2009 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *7 (-1200)) (-5 *2 (-239 *5 *7)) (-5 *1 (-238 *5 *6 *7)))) (-3023 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-239 *5 *6)) (-14 *5 (-762)) (-4 *6 (-1200)) (-4 *2 (-1200)) (-5 *1 (-238 *5 *6 *2)))) (-3142 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-239 *6 *7)) (-14 *6 (-762)) (-4 *7 (-1200)) (-4 *5 (-1200)) (-5 *2 (-239 *6 *5)) (-5 *1 (-238 *6 *7 *5))))) -(-10 -7 (-15 -3142 ((-239 |#1| |#3|) (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -3023 (|#3| (-1 |#3| |#2| |#3|) (-239 |#1| |#2|) |#3|)) (-15 -2009 ((-239 |#1| |#3|) (-1 |#3| |#2|) (-239 |#1| |#2|)))) -((-2549 (((-112) $ $) NIL (|has| |#2| (-1087)))) (-1297 (((-112) $) NIL (|has| |#2| (-130)))) (-1565 (($ (-911)) 56 (|has| |#2| (-1039)))) (-1597 (((-1251) $ (-558) (-558)) NIL (|has| $ (-6 -4384)))) (-2077 (($ $ $) 60 (|has| |#2| (-784)))) (-3097 (((-3 $ "failed") $ $) 49 (|has| |#2| (-130)))) (-2230 (((-112) $ (-762)) 17)) (-1648 (((-762)) NIL (|has| |#2| (-367)))) (-2626 (((-558) $) NIL (|has| |#2| (-839)))) (-3999 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4384)))) (-2579 (($) NIL T CONST)) (-1926 (((-3 (-558) "failed") $) NIL (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087)))) (((-3 (-406 (-558)) "failed") $) NIL (-12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) (((-3 |#2| "failed") $) 29 (|has| |#2| (-1087)))) (-1855 (((-558) $) NIL (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087)))) (((-406 (-558)) $) NIL (-12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) ((|#2| $) 27 (|has| |#2| (-1087)))) (-1524 (((-679 (-558)) (-679 $)) NIL (-12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) (((-2 (|:| -2582 (-679 (-558))) (|:| |vec| (-1246 (-558)))) (-679 $) (-1246 $)) NIL (-12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039)))) (((-2 (|:| -2582 (-679 |#2|)) (|:| |vec| (-1246 |#2|))) (-679 $) (-1246 $)) NIL (|has| |#2| (-1039))) (((-679 |#2|) (-679 $)) NIL (|has| |#2| (-1039)))) (-1827 (((-3 $ "failed") $) 53 (|has| |#2| (-717)))) (-1802 (($) NIL (|has| |#2| (-367)))) (-4142 ((|#2| $ (-558) |#2|) NIL (|has| $ (-6 -4384)))) (-4067 ((|#2| $ (-558)) 51)) (-2736 (((-112) $) NIL (|has| |#2| (-839)))) (-3906 (((-635 |#2|) $) 15 (|has| $ (-6 -4383)))) (-1924 (((-112) $) NIL (|has| |#2| (-717)))) (-2904 (((-112) $) NIL (|has| |#2| (-839)))) (-3942 (((-112) $ (-762)) NIL)) (-3765 (((-558) $) 20 (|has| (-558) (-841)))) (-2504 (($ $ $) NIL (-3996 (|has| |#2| 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(-1039))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1039)))) (-1663 (((-762) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4383))) (((-762) |#2| $) NIL (-12 (|has| $ (-6 -4383)) (|has| |#2| (-1087))))) (-4025 (($ $) NIL)) (-2560 (((-1246 |#2|) $) 10) (($ (-558)) NIL (-3996 (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-1039)))) (($ (-406 (-558))) NIL (-12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087)))) (($ |#2|) 13 (|has| |#2| (-1087))) (((-853) $) NIL (|has| |#2| (-605 (-853))))) (-2672 (((-762)) NIL (|has| |#2| (-1039)))) (-3980 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4383)))) (-3767 (($ $) NIL (|has| |#2| (-839)))) (-2152 (($) 35 (|has| |#2| (-130)) CONST)) (-2161 (($) 38 (|has| |#2| (-717)) CONST)) (-2921 (($ $) NIL (-12 (|has| |#2| (-232)) (|has| |#2| (-1039)))) (($ $ (-762)) NIL (-12 (|has| |#2| (-232)) (|has| |#2| (-1039)))) (($ $ (-1163)) NIL (-12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) (($ $ (-635 (-1163))) NIL (-12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) (($ $ (-1163) (-762)) NIL (-12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) (($ $ (-635 (-1163)) (-635 (-762))) NIL (-12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039)))) (($ $ (-1 |#2| |#2|) (-762)) NIL (|has| |#2| (-1039))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1039)))) (-1731 (((-112) $ $) NIL (-3996 (|has| |#2| (-784)) (|has| |#2| (-839))))) (-1708 (((-112) $ $) NIL (-3996 (|has| |#2| (-784)) (|has| |#2| (-839))))) (-1673 (((-112) $ $) 26 (|has| |#2| (-1087)))) (-1719 (((-112) $ $) NIL (-3996 (|has| |#2| (-784)) (|has| |#2| (-839))))) (-1696 (((-112) $ $) 58 (-3996 (|has| |#2| (-784)) (|has| |#2| (-839))))) (-1784 (($ $ |#2|) NIL (|has| |#2| (-362)))) (-1773 (($ $ $) NIL (|has| |#2| (-1039))) (($ $) NIL (|has| |#2| (-1039)))) (-1763 (($ $ $) 33 (|has| |#2| (-25)))) (** (($ $ (-762)) NIL (|has| |#2| (-717))) (($ $ (-911)) NIL (|has| |#2| (-717)))) (* (($ (-558) $) NIL (|has| |#2| (-1039))) (($ $ $) 44 (|has| |#2| (-717))) (($ $ |#2|) 42 (|has| |#2| (-717))) (($ |#2| $) 43 (|has| |#2| (-717))) (($ (-762) $) NIL (|has| |#2| (-130))) (($ (-911) $) NIL (|has| |#2| (-25)))) (-1450 (((-762) $) NIL (|has| $ (-6 -4383))))) +((-3982 (*1 *1 *2) (-12 (-5 *2 (-1246 *4)) (-4 *4 (-1200)) (-4 *1 (-237 *3 *4)))) (-1441 (*1 *1 *2) (-12 (-5 *2 (-911)) (-4 *1 (-237 *3 *4)) (-4 *4 (-1039)) (-4 *4 (-1200)))) (-2823 (*1 *2 *1 *1) (-12 (-4 *1 (-237 *3 *2)) (-4 *2 (-1200)) (-4 *2 (-1039)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-237 *3 *2)) (-4 *2 (-1200)) (-4 *2 (-717)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-237 *3 *2)) (-4 *2 (-1200)) (-4 *2 (-717))))) +(-13 (-596 (-558) |t#2|) (-605 (-1246 |t#2|)) (-10 -8 (-6 -4383) (-15 -3982 ($ (-1246 |t#2|))) (IF (|has| |t#2| (-1087)) (-6 (-410 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1039)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-230 |t#2|)) (-6 (-376 |t#2|)) (-15 -1441 ($ (-911))) (-15 -2823 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-130)) (-6 (-130)) |%noBranch|) (IF (|has| |t#2| (-717)) (PROGN (-6 (-717)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-367)) (-6 (-367)) |%noBranch|) (IF (|has| |t#2| (-171)) (PROGN (-6 (-38 |t#2|)) (-6 (-171))) |%noBranch|) (IF (|has| |t#2| (-6 -4380)) (-6 -4380) |%noBranch|) (IF (|has| |t#2| (-839)) (-6 (-839)) |%noBranch|) (IF (|has| |t#2| (-784)) (-6 (-784)) |%noBranch|) (IF (|has| |t#2| (-362)) (-6 (-1253 |t#2|)) |%noBranch|))) +(((-21) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-23) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-25) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-171)) ((-102) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-111 $ $) |has| |#2| (-171)) ((-130) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130))) ((-608 #0=(-406 (-558))) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-608 (-558)) -3994 (|has| |#2| (-1039)) (-12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-608 |#2|) -3994 (|has| |#2| (-1087)) (|has| |#2| (-171))) ((-605 (-853)) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-605 (-853))) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-605 (-1246 |#2|)) . T) ((-171) |has| |#2| (-171)) ((-230 |#2|) |has| |#2| (-1039)) ((-232) -12 (|has| |#2| (-232)) (|has| |#2| (-1039))) ((-285 #1=(-558) |#2|) . T) ((-287 #1# |#2|) . T) ((-308 |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-367) |has| |#2| (-367)) ((-376 |#2|) |has| |#2| (-1039)) ((-410 |#2|) |has| |#2| (-1087)) ((-487 |#2|) . T) ((-596 #1# |#2|) . T) ((-512 |#2| |#2|) -12 (|has| |#2| (-308 |#2|)) (|has| |#2| (-1087))) ((-638 |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-638 $) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-631 (-558)) -12 (|has| |#2| (-631 (-558))) (|has| |#2| (-1039))) ((-631 |#2|) |has| |#2| (-1039)) ((-708 |#2|) -3994 (|has| |#2| (-362)) (|has| |#2| (-171))) ((-717) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-782) |has| |#2| (-839)) ((-783) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-784) |has| |#2| (-784)) ((-785) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-786) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-839) |has| |#2| (-839)) ((-841) -3994 (|has| |#2| (-839)) (|has| |#2| (-784))) ((-890 (-1163)) -12 (|has| |#2| (-890 (-1163))) (|has| |#2| (-1039))) ((-1028 #0#) -12 (|has| |#2| (-1028 (-406 (-558)))) (|has| |#2| (-1087))) ((-1028 (-558)) -12 (|has| |#2| (-1028 (-558))) (|has| |#2| (-1087))) ((-1028 |#2|) |has| |#2| (-1087)) ((-1045 |#2|) -3994 (|has| |#2| (-1039)) (|has| |#2| (-362)) (|has| |#2| (-171))) ((-1045 $) |has| |#2| (-171)) ((-1039) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1046) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-171))) ((-1099) -3994 (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-717)) (|has| |#2| (-171))) ((-1087) -3994 (|has| |#2| (-1087)) (|has| |#2| (-1039)) (|has| |#2| (-839)) (|has| |#2| (-784)) (|has| |#2| (-717)) (|has| |#2| (-367)) (|has| |#2| (-362)) (|has| |#2| (-171)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1200) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) -3994 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) . T) ((-608 |#2|) . T) ((-608 |#3|) . T) ((-608 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450))) ((-605 (-853)) . 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T) ((-638 |#2|) |has| |#1| (-362)) ((-638 $) . T) ((-631 (-558)) -12 (|has| |#1| (-362)) (|has| |#2| (-631 (-558)))) ((-631 |#2|) |has| |#1| (-362)) ((-708 #1#) -3994 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-708 |#1|) |has| |#1| (-171)) ((-708 |#2|) |has| |#1| (-362)) ((-708 $) -3994 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3996 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3996 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . 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T) ((-23) . T) ((-47 |#1| #0=(-762)) . T) ((-25) . T) ((-38 #1=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3994 (|has| |#1| (-1028 (-406 (-558)))) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 #2=(-1069)) . T) ((-608 |#1|) . T) ((-608 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-605 (-853)) . T) ((-171) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-606 (-534)) -12 (|has| (-1069) (-606 (-534))) (|has| |#1| (-606 (-534)))) ((-606 (-882 (-378))) -12 (|has| (-1069) (-606 (-882 (-378)))) (|has| |#1| (-606 (-882 (-378))))) ((-606 (-882 (-558))) -12 (|has| (-1069) (-606 (-882 (-558)))) (|has| |#1| (-606 (-882 (-558))))) ((-230 |#1|) . T) ((-232) . T) ((-285 (-406 $) (-406 $)) |has| |#1| (-550)) ((-285 |#1| |#1|) . T) ((-285 $ $) . T) ((-289) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-306) |has| |#1| (-362)) ((-308 $) . T) ((-325 |#1| #0#) . T) ((-376 |#1|) . T) ((-410 |#1|) . T) ((-450) -3994 (|has| |#1| (-899)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-512 #2# |#1|) . T) ((-512 #2# $) . T) ((-512 $ $) . T) ((-550) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-638 #1#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-631 (-558)) |has| |#1| (-631 (-558))) ((-631 |#1|) . T) ((-708 #1#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362))) ((-717) . T) ((-841) |has| |#1| (-841)) ((-890 #2#) . T) ((-890 (-1163)) |has| |#1| (-890 (-1163))) ((-876 (-378)) -12 (|has| (-1069) (-876 (-378))) (|has| |#1| (-876 (-378)))) ((-876 (-558)) -12 (|has| (-1069) (-876 (-558))) (|has| |#1| (-876 (-558)))) ((-939 |#1| #0# #2#) . T) ((-899) |has| |#1| (-899)) ((-910) |has| |#1| (-362)) ((-1028 (-406 (-558))) |has| |#1| (-1028 (-406 (-558)))) ((-1028 (-558)) |has| |#1| (-1028 (-558))) ((-1028 #2#) . T) ((-1028 |#1|) . T) ((-1045 #1#) |has| |#1| (-38 (-406 (-558)))) ((-1045 |#1|) . T) ((-1045 $) -3994 (|has| |#1| (-899)) (|has| |#1| (-550)) (|has| |#1| (-450)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-1039) . T) ((-1046) . T) ((-1099) . T) ((-1087) . T) ((-1138) |has| |#1| (-1138)) ((-1204) |has| |#1| (-899))) +((-4078 (((-635 (-1069)) $) 28)) (-3905 (($ $) 25)) (-4056 (($ |#2| |#3|) NIL) (($ $ (-1069) |#3|) 22) (($ $ (-635 (-1069)) (-635 |#3|)) 21)) (-3867 (($ $) 14)) (-3881 ((|#2| $) 12)) (-4263 ((|#3| $) 10))) +(((-1223 |#1| |#2| |#3|) (-10 -8 (-15 -4078 ((-635 (-1069)) |#1|)) (-15 -4056 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -4056 (|#1| |#1| (-1069) |#3|)) (-15 -3905 (|#1| |#1|)) (-15 -4056 (|#1| |#2| |#3|)) (-15 -4263 (|#3| |#1|)) (-15 -3867 (|#1| |#1|)) (-15 -3881 (|#2| |#1|))) (-1224 |#2| |#3|) (-1039) (-783)) (T -1223)) +NIL +(-10 -8 (-15 -4078 ((-635 (-1069)) |#1|)) (-15 -4056 (|#1| |#1| (-635 (-1069)) (-635 |#3|))) (-15 -4056 (|#1| |#1| (-1069) |#3|)) (-15 -3905 (|#1| |#1|)) (-15 -4056 (|#1| |#2| |#3|)) (-15 -4263 (|#3| |#1|)) (-15 -3867 (|#1| |#1|)) (-15 -3881 (|#2| |#1|))) +((-3929 (((-112) $ $) 7)) (-3124 (((-112) $) 16)) (-4078 (((-635 (-1069)) $) 77)) (-2317 (((-1163) $) 106)) (-2008 (((-2 (|:| -3466 $) (|:| 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 #0=(-406 (-558))) |has| |#1| (-38 (-406 (-558)))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) |has| |#1| (-550)) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-406 (-558)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3996 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #0#) |has| |#1| (-38 (-406 (-558)))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) |has| |#1| (-550)) ((-605 (-853)) . T) ((-171) -3996 (|has| |#1| (-550)) (|has| |#1| (-171))) ((-232) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-285 $ $) |has| |#2| (-1099)) ((-289) |has| |#1| (-550)) ((-550) |has| |#1| (-550)) ((-638 #0#) |has| |#1| (-38 (-406 (-558)))) ((-638 |#1|) . T) ((-638 $) . T) ((-708 #0#) |has| |#1| (-38 (-406 (-558)))) ((-708 |#1|) |has| |#1| (-171)) ((-708 $) |has| |#1| (-550)) ((-717) . 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T) ((-23) . T) ((-47 |#1| #0=(-406 (-558))) . T) ((-25) . T) ((-38 #1=(-406 (-558))) -3994 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-38 |#1|) |has| |#1| (-171)) ((-38 $) -3994 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-35) |has| |#1| (-38 (-406 (-558)))) ((-95) |has| |#1| (-38 (-406 (-558)))) ((-102) . T) ((-111 #1# #1#) -3994 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -3994 (|has| |#1| (-550)) (|has| |#1| (-362)) (|has| |#1| (-171))) ((-130) . T) ((-144) |has| |#1| (-144)) ((-146) |has| |#1| (-146)) ((-608 #1#) -3994 (|has| |#1| (-362)) (|has| |#1| (-38 (-406 (-558))))) ((-608 (-558)) . T) ((-608 |#1|) |has| |#1| (-171)) ((-608 $) -3994 (|has| |#1| (-550)) (|has| |#1| (-362))) ((-605 (-853)) . 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"TRANFUN-" 2871292 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1183 2870620 2870652 2870713 "TOPSP" 2870777 T TOPSP (NIL) -7 NIL NIL NIL) (-1182 2869968 2870083 2870237 "TOOLSIGN" 2870501 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1181 2868629 2869145 2869384 "TEXTFILE" 2869751 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1180 2866568 2867082 2867511 "TEX" 2868222 T TEX (NIL) -8 NIL NIL NIL) (-1179 2866349 2866380 2866452 "TEX1" 2866531 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1178 2865997 2866060 2866150 "TEMUTL" 2866281 T TEMUTL (NIL) -7 NIL NIL NIL) (-1177 2864151 2864431 2864756 "TBCMPPK" 2865720 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1176 2856039 2862311 2862367 "TBAGG" 2862767 NIL TBAGG (NIL T T) -9 NIL 2862978 NIL) (-1175 2851109 2852597 2854351 "TBAGG-" 2854356 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1174 2850493 2850600 2850745 "TANEXP" 2850998 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1173 2843994 2850350 2850443 "TABLE" 2850448 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1172 2843406 2843505 2843643 "TABLEAU" 2843891 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1171 2838014 2839234 2840482 "TABLBUMP" 2842192 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1170 2837442 2837542 2837670 "SYSTEM" 2837908 T SYSTEM (NIL) -7 NIL NIL NIL) (-1169 2833905 2834600 2835383 "SYSSOLP" 2836693 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1168 2830239 2831166 2831882 "SYNTAX" 2833211 T SYNTAX (NIL) -8 NIL NIL NIL) (-1167 2827397 2827999 2828631 "SYMTAB" 2829629 T SYMTAB (NIL) -8 NIL NIL NIL) (-1166 2822646 2823548 2824531 "SYMS" 2826436 T SYMS (NIL) -8 NIL NIL NIL) (-1165 2819918 2822104 2822334 "SYMPOLY" 2822451 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1164 2819435 2819510 2819633 "SYMFUNC" 2819830 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1163 2815487 2816747 2817560 "SYMBOL" 2818644 T SYMBOL (NIL) -8 NIL NIL NIL) (-1162 2809026 2810715 2812435 "SWITCH" 2813789 T SWITCH (NIL) -8 NIL NIL NIL) (-1161 2802296 2807847 2808150 "SUTS" 2808781 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2794397 2801543 2801816 "SUPXS" 2802081 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2785927 2794015 2794141 "SUP" 2794306 NIL SUP (NIL T) -8 NIL NIL NIL) (-1158 2785086 2785213 2785430 "SUPFRACF" 2785795 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1157 2784707 2784766 2784879 "SUP2" 2785021 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1156 2783120 2783394 2783757 "SUMRF" 2784406 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1155 2782434 2782500 2782699 "SUMFS" 2783041 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1154 2766441 2781611 2781862 "SULS" 2782241 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1153 2766070 2766263 2766333 "SUCHTAST" 2766393 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1152 2765392 2765595 2765735 "SUCH" 2765978 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1151 2759286 2760298 2761257 "SUBSPACE" 2764480 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1150 2758716 2758806 2758970 "SUBRESP" 2759174 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1149 2752085 2753381 2754692 "STTF" 2757452 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746258 2747378 2748525 "STTFNC" 2750985 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737573 2739440 2741234 "STTAYLOR" 2744499 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730817 2737437 2737520 "STRTBL" 2737525 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726208 2730772 2730803 "STRING" 2730808 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721096 2725581 2725611 "STRICAT" 2725670 T STRICAT (NIL) -9 NIL 2725732 NIL) (-1143 2713906 2718715 2719326 "STREAM" 2720520 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713416 2713493 2713637 "STREAM3" 2713823 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712398 2712581 2712816 "STREAM2" 2713229 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712086 2712138 2712231 "STREAM1" 2712340 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711102 2711283 2711514 "STINPROD" 2711902 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710680 2710864 2710894 "STEP" 2710974 T STEP (NIL) -9 NIL 2711052 NIL) (-1137 2704223 2710579 2710656 "STBL" 2710661 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699397 2703444 2703487 "STAGG" 2703640 NIL STAGG (NIL T) -9 NIL 2703729 NIL) (-1135 2697099 2697701 2698573 "STAGG-" 2698578 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695294 2696869 2696961 "STACK" 2697042 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688019 2693435 2693891 "SREGSET" 2694924 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680445 2681813 2683326 "SRDCMPK" 2686625 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673412 2677885 2677915 "SRAGG" 2679218 T SRAGG (NIL) -9 NIL 2679826 NIL) (-1130 2672429 2672684 2673063 "SRAGG-" 2673068 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2666924 2671376 2671797 "SQMATRIX" 2672055 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660673 2663642 2664369 "SPLTREE" 2666269 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656663 2657329 2657975 "SPLNODE" 2660099 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655710 2655943 2655973 "SPFCAT" 2656417 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654447 2654657 2654921 "SPECOUT" 2655468 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646099 2647843 2647873 "SPADXPT" 2652265 T SPADXPT (NIL) -9 NIL 2654299 NIL) (-1123 2645860 2645900 2645969 "SPADPRSR" 2646052 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644043 2645815 2645846 "SPADAST" 2645851 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636014 2637761 2637804 "SPACEC" 2642177 NIL SPACEC (NIL T) -9 NIL 2643993 NIL) (-1120 2634185 2635946 2635995 "SPACE3" 2636000 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2632937 2633108 2633399 "SORTPAK" 2633990 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2630987 2631290 2631709 "SOLVETRA" 2632601 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2629998 2630220 2630494 "SOLVESER" 2630760 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625218 2626099 2627101 "SOLVERAD" 2629050 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621033 2621642 2622371 "SOLVEFOR" 2624585 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615330 2620382 2620479 "SNTSCAT" 2620484 NIL SNTSCAT (NIL T T T T) -9 NIL 2620554 NIL) (-1113 2609473 2613653 2614044 "SMTS" 2615020 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2603924 2609361 2609438 "SMP" 2609443 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602083 2602384 2602782 "SMITH" 2603621 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2594978 2599134 2599237 "SMATCAT" 2600588 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601138 NIL) (-1109 2591918 2592741 2593919 "SMATCAT-" 2593924 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589631 2591154 2591197 "SKAGG" 2591458 NIL SKAGG (NIL T) -9 NIL 2591593 NIL) (-1107 2585973 2589047 2589242 "SINT" 2589429 T SINT (NIL) -8 NIL NIL 2589602) (-1106 2585745 2585783 2585849 "SIMPAN" 2585929 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585052 2585280 2585420 "SIG" 2585627 T SIG (NIL) -8 NIL NIL NIL) (-1104 2583890 2584111 2584386 "SIGNRF" 2584811 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582695 2582846 2583137 "SIGNEF" 2583719 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582028 2582278 2582402 "SIGAST" 2582593 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579718 2580172 2580678 "SHP" 2581569 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573624 2579619 2579695 "SHDP" 2579700 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573223 2573389 2573419 "SGROUP" 2573512 T SGROUP (NIL) -9 NIL 2573574 NIL) (-1098 2573081 2573107 2573180 "SGROUP-" 2573185 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2569917 2570614 2571337 "SGCF" 2572380 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564312 2569364 2569461 "SFRTCAT" 2569466 NIL SFRTCAT (NIL T T T T) -9 NIL 2569505 NIL) (-1095 2557736 2558751 2559887 "SFRGCD" 2563295 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2550864 2551935 2553121 "SFQCMPK" 2556669 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550486 2550575 2550685 "SFORT" 2550805 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549631 2550326 2550447 "SEXOF" 2550452 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548765 2549512 2549580 "SEX" 2549585 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544304 2544993 2545088 "SEXCAT" 2548025 NIL SEXCAT (NIL T T T T T) -9 NIL 2548603 NIL) (-1089 2541484 2544238 2544286 "SET" 2544291 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539735 2540197 2540502 "SETMN" 2541225 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539341 2539467 2539497 "SETCAT" 2539614 T SETCAT (NIL) -9 NIL 2539699 NIL) (-1086 2539121 2539173 2539272 "SETCAT-" 2539277 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535508 2537582 2537625 "SETAGG" 2538495 NIL SETAGG (NIL T) -9 NIL 2538835 NIL) (-1084 2534966 2535082 2535319 "SETAGG-" 2535324 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534436 2534662 2534763 "SEQAST" 2534887 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533635 2533929 2533990 "SEGXCAT" 2534276 NIL SEGXCAT (NIL T T) -9 NIL 2534396 NIL) (-1081 2532691 2533301 2533483 "SEG" 2533488 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531670 2531884 2531927 "SEGCAT" 2532449 NIL SEGCAT (NIL T) -9 NIL 2532670 NIL) (-1079 2530719 2531049 2531249 "SEGBIND" 2531505 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530340 2530399 2530512 "SEGBIND2" 2530654 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2529941 2530141 2530218 "SEGAST" 2530285 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529160 2529286 2529490 "SEG2" 2529785 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528597 2529095 2529142 "SDVAR" 2529147 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2520887 2528367 2528497 "SDPOL" 2528502 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519480 2519746 2520065 "SCPKG" 2520602 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518616 2518796 2518996 "SCOPE" 2519302 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2517837 2517970 2518149 "SCACHE" 2518471 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517509 2517669 2517699 "SASTCAT" 2517704 T SASTCAT (NIL) -9 NIL 2517717 NIL) (-1069 2517023 2517344 2517420 "SAOS" 2517455 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516588 2516623 2516796 "SAERFFC" 2516982 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510562 2516485 2516565 "SAE" 2516570 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510155 2510190 2510349 "SAEFACT" 2510521 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508476 2508790 2509191 "RURPK" 2509821 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507112 2507391 2507703 "RULESET" 2508310 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504299 2504802 2505267 "RULE" 2506793 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2503938 2504093 2504176 "RULECOLD" 2504251 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503436 2503655 2503749 "RSTRCAST" 2503866 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498285 2499079 2499999 "RSETGCD" 2502635 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487542 2492594 2492691 "RSETCAT" 2496810 NIL RSETCAT (NIL T T T T) -9 NIL 2497907 NIL) (-1058 2485469 2486008 2486832 "RSETCAT-" 2486837 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2477856 2479231 2480751 "RSDCMPK" 2484068 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2475861 2476302 2476376 "RRCC" 2477462 NIL RRCC (NIL T T) -9 NIL 2477806 NIL) (-1055 2475212 2475386 2475665 "RRCC-" 2475670 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474682 2474908 2475009 "RPTAST" 2475133 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448688 2458275 2458342 "RPOLCAT" 2469006 NIL RPOLCAT (NIL T T T) -9 NIL 2472165 NIL) (-1052 2440188 2442526 2445648 "RPOLCAT-" 2445653 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431235 2438399 2438881 "ROUTINE" 2439728 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428068 2430861 2431001 "ROMAN" 2431117 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426343 2426928 2427188 "ROIRC" 2427873 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422736 2424979 2425009 "RNS" 2425313 T RNS (NIL) -9 NIL 2425586 NIL) (-1047 2421245 2421628 2422162 "RNS-" 2422237 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420694 2421076 2421106 "RNG" 2421111 T RNG (NIL) -9 NIL 2421132 NIL) (-1045 2420086 2420448 2420491 "RMODULE" 2420553 NIL RMODULE (NIL T) -9 NIL 2420595 NIL) (-1044 2418922 2419016 2419352 "RMCAT2" 2419987 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415799 2418268 2418565 "RMATRIX" 2418684 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408741 2410975 2411090 "RMATCAT" 2414449 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415431 NIL) (-1041 2408116 2408263 2408570 "RMATCAT-" 2408575 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407683 2407758 2407886 "RINTERP" 2408035 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406816 2407336 2407366 "RING" 2407422 T RING (NIL) -9 NIL 2407508 NIL) (-1038 2406608 2406652 2406749 "RING-" 2406754 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405449 2405686 2405944 "RIDIST" 2406372 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396765 2404917 2405123 "RGCHAIN" 2405297 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396141 2396521 2396562 "RGBCSPC" 2396620 NIL RGBCSPC (NIL T) -9 NIL 2396672 NIL) (-1034 2395325 2395680 2395721 "RGBCMDL" 2395953 NIL RGBCMDL (NIL T) -9 NIL 2396067 NIL) (-1033 2392319 2392933 2393603 "RF" 2394689 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2391965 2392028 2392131 "RFFACTOR" 2392250 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391690 2391725 2391822 "RFFACT" 2391924 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389807 2390171 2390553 "RFDIST" 2391330 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389260 2389352 2389515 "RETSOL" 2389709 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2388896 2388976 2389019 "RETRACT" 2389152 NIL RETRACT (NIL T) -9 NIL 2389239 NIL) (-1027 2388745 2388770 2388857 "RETRACT-" 2388862 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388374 2388567 2388637 "RETAST" 2388697 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381228 2388027 2388154 "RESULT" 2388269 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2379854 2380497 2380696 "RESRING" 2381131 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379490 2379539 2379637 "RESLATC" 2379791 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379196 2379230 2379337 "REPSQ" 2379449 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376618 2377198 2377800 "REP" 2378616 T REP (NIL) -7 NIL NIL NIL) (-1020 2376316 2376350 2376461 "REPDB" 2376577 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370226 2371605 2372828 "REP2" 2375128 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366603 2367284 2368092 "REP1" 2369453 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359329 2364744 2365200 "REGSET" 2366233 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358142 2358477 2358727 "REF" 2359114 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357519 2357622 2357789 "REDORDER" 2358026 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353524 2356732 2356959 "RECLOS" 2357347 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352576 2352757 2352972 "REALSOLV" 2353331 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352422 2352463 2352493 "REAL" 2352498 T REAL (NIL) -9 NIL 2352533 NIL) (-1011 2348905 2349707 2350591 "REAL0Q" 2351587 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344506 2345494 2346555 "REAL0" 2347886 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344004 2344223 2344317 "RDUCEAST" 2344434 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343409 2343481 2343688 "RDIV" 2343926 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342477 2342651 2342864 "RDIST" 2343231 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341074 2341361 2341733 "RDETRS" 2342185 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2338886 2339340 2339878 "RDETR" 2340616 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337497 2337775 2338179 "RDEEFS" 2338602 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2335992 2336298 2336730 "RDEEF" 2337185 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330253 2333128 2333158 "RCFIELD" 2334453 T RCFIELD (NIL) -9 NIL 2335183 NIL) (-1001 2328317 2328821 2329517 "RCFIELD-" 2329592 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324633 2326418 2326461 "RCAGG" 2327545 NIL RCAGG (NIL T) -9 NIL 2328010 NIL) (-999 2324263 2324357 2324518 "RCAGG-" 2324523 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323603 2323715 2323878 "RATRET" 2324147 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323160 2323227 2323346 "RATFACT" 2323531 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322475 2322595 2322745 "RANDSRC" 2323030 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322212 2322256 2322327 "RADUTIL" 2322424 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315374 2321054 2321362 "RADIX" 2321936 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307031 2315218 2315346 "RADFF" 2315351 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306683 2306758 2306786 "RADCAT" 2306943 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306468 2306516 2306613 "RADCAT-" 2306618 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304619 2306243 2306332 "QUEUE" 2306412 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301195 2304556 2304601 "QUAT" 2304606 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2300833 2300876 2301003 "QUATCT2" 2301146 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294580 2297882 2297922 "QUATCAT" 2298702 NIL QUATCAT (NIL T) -9 NIL 2299468 NIL) (-986 2290724 2291761 2293148 "QUATCAT-" 2293242 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288244 2289808 2289849 "QUAGG" 2290224 NIL QUAGG (NIL T) -9 NIL 2290399 NIL) (-984 2287876 2288069 2288137 "QQUTAST" 2288196 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286801 2287274 2287446 "QFORM" 2287748 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278013 2283218 2283258 "QFCAT" 2283916 NIL QFCAT (NIL T) -9 NIL 2284917 NIL) (-981 2273585 2274786 2276377 "QFCAT-" 2276471 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273223 2273266 2273393 "QFCAT2" 2273536 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272683 2272793 2272923 "QEQUAT" 2273113 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265831 2266902 2268086 "QCMPACK" 2271616 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263407 2263828 2264256 "QALGSET" 2265486 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262652 2262826 2263058 "QALGSET2" 2263227 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261343 2261566 2261883 "PWFFINTB" 2262425 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259525 2259693 2260047 "PUSHVAR" 2261157 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255443 2256497 2256538 "PTRANFN" 2258422 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2253845 2254136 2254458 "PTPACK" 2255154 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253477 2253534 2253643 "PTFUNC2" 2253782 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248004 2252349 2252390 "PTCAT" 2252686 NIL PTCAT (NIL T) -9 NIL 2252839 NIL) (-969 2247662 2247697 2247821 "PSQFR" 2247963 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246257 2246555 2246889 "PSEUDLIN" 2247360 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233027 2235391 2237715 "PSETPK" 2244017 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226071 2228785 2228881 "PSETCAT" 2231902 NIL PSETCAT (NIL T T T T) -9 NIL 2232716 NIL) (-965 2223907 2224541 2225362 "PSETCAT-" 2225367 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223256 2223421 2223449 "PSCURVE" 2223717 T PSCURVE (NIL) -9 NIL 2223884 NIL) (-963 2219612 2221094 2221159 "PSCAT" 2222003 NIL PSCAT (NIL T T T) -9 NIL 2222243 NIL) (-962 2218675 2218891 2219291 "PSCAT-" 2219296 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217407 2218040 2218245 "PRTITION" 2218490 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2216909 2217128 2217220 "PRTDAST" 2217335 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206007 2208213 2210401 "PRS" 2214771 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2203865 2205357 2205397 "PRQAGG" 2205580 NIL PRQAGG (NIL T) -9 NIL 2205682 NIL) (-957 2203251 2203480 2203508 "PROPLOG" 2203693 T PROPLOG (NIL) -9 NIL 2203815 NIL) (-956 2200421 2201065 2201529 "PROPFRML" 2202819 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2199881 2199991 2200121 "PROPERTY" 2200311 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2193966 2198047 2198867 "PRODUCT" 2199107 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191279 2193424 2193658 "PR" 2193777 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191075 2191107 2191166 "PRINT" 2191240 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190415 2190532 2190684 "PRIMES" 2190955 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188480 2188881 2189347 "PRIMELT" 2189994 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188209 2188258 2188286 "PRIMCAT" 2188410 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184370 2188147 2188192 "PRIMARR" 2188197 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183377 2183555 2183783 "PRIMARR2" 2184188 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183020 2183076 2183187 "PREASSOC" 2183315 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182495 2182628 2182656 "PPCURVE" 2182861 T PPCURVE (NIL) -9 NIL 2182997 NIL) (-944 2182117 2182290 2182373 "PORTNUM" 2182432 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179476 2179875 2180467 "POLYROOT" 2181698 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173421 2179080 2179240 "POLY" 2179349 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172804 2172862 2173096 "POLYLIFT" 2173357 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169079 2169528 2170157 "POLYCATQ" 2172349 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2155896 2161254 2161319 "POLYCAT" 2164833 NIL POLYCAT (NIL T T T) -9 NIL 2166761 NIL) (-938 2149346 2151207 2153591 "POLYCAT-" 2153596 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2148933 2149001 2149121 "POLY2UP" 2149272 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-936 2148565 2148622 2148731 "POLY2" 2148870 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-935 2147250 2147489 2147765 "POLUTIL" 2148339 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-934 2145605 2145882 2146213 "POLTOPOL" 2146972 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-933 2141123 2145541 2145587 "POINT" 2145592 NIL POINT (NIL T) -8 NIL NIL NIL) (-932 2139310 2139667 2140042 "PNTHEORY" 2140768 T PNTHEORY (NIL) -7 NIL NIL NIL) (-931 2137729 2138026 2138438 "PMTOOLS" 2139008 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-930 2137322 2137400 2137517 "PMSYM" 2137645 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-929 2136832 2136901 2137075 "PMQFCAT" 2137247 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-928 2136187 2136297 2136453 "PMPRED" 2136709 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-927 2135583 2135669 2135830 "PMPREDFS" 2136088 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-926 2134226 2134434 2134819 "PMPLCAT" 2135345 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-925 2133758 2133837 2133989 "PMLSAGG" 2134141 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133233 2133309 2133490 "PMKERNEL" 2133676 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2132850 2132925 2133038 "PMINS" 2133152 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132278 2132347 2132563 "PMFS" 2132775 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131506 2131624 2131829 "PMDOWN" 2132155 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130669 2130828 2131010 "PMASS" 2131344 T PMASS (NIL) -7 NIL NIL NIL) (-919 2129943 2130054 2130217 "PMASSFS" 2130555 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129598 2129666 2129760 "PLOTTOOL" 2129869 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124220 2125409 2126557 "PLOT" 2128470 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120034 2121068 2121989 "PLOT3D" 2123319 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2118946 2119123 2119358 "PLOT1" 2119838 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094340 2099012 2103863 "PLEQN" 2114212 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093658 2093780 2093960 "PINTERP" 2094205 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093351 2093398 2093501 "PINTERPA" 2093605 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092599 2093120 2093207 "PI" 2093247 T PI (NIL) -8 NIL NIL 2093314) (-910 2090996 2091937 2091965 "PID" 2092147 T PID (NIL) -9 NIL 2092281 NIL) (-909 2090721 2090758 2090846 "PICOERCE" 2090953 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090041 2090180 2090356 "PGROEB" 2090577 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085628 2086442 2087347 "PGE" 2089156 T PGE (NIL) -7 NIL NIL NIL) (-906 2083752 2083998 2084364 "PGCD" 2085345 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083090 2083193 2083354 "PFRPAC" 2083636 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079770 2081638 2081991 "PFR" 2082769 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078159 2078403 2078728 "PFOTOOLS" 2079517 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076692 2076931 2077282 "PFOQ" 2077916 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075165 2075377 2075740 "PFO" 2076476 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071753 2075054 2075123 "PF" 2075128 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069187 2070424 2070452 "PFECAT" 2071037 T PFECAT (NIL) -9 NIL 2071421 NIL) (-898 2068632 2068786 2069000 "PFECAT-" 2069005 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067236 2067487 2067788 "PFBRU" 2068381 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065103 2065454 2065886 "PFBR" 2066887 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061019 2062479 2063155 "PERM" 2064460 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056285 2057226 2058096 "PERMGRP" 2060182 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054417 2055348 2055389 "PERMCAT" 2055835 NIL PERMCAT (NIL T) -9 NIL 2056140 NIL) (-892 2054070 2054111 2054235 "PERMAN" 2054370 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051606 2053735 2053857 "PENDTREE" 2053981 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049699 2050433 2050474 "PDRING" 2051131 NIL PDRING (NIL T) -9 NIL 2051417 NIL) (-889 2048802 2049020 2049382 "PDRING-" 2049387 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046044 2046795 2047463 "PDEPROB" 2048154 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043591 2044093 2044648 "PDEPACK" 2045509 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042503 2042693 2042944 "PDECOMP" 2043390 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040108 2040925 2040953 "PDECAT" 2041740 T PDECAT (NIL) -9 NIL 2042453 NIL) (-884 2039859 2039892 2039982 "PCOMP" 2040069 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038064 2038660 2038957 "PBWLB" 2039588 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030569 2032137 2033475 "PATTERN" 2036747 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030201 2030258 2030367 "PATTERN2" 2030506 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2027958 2028346 2028803 "PATTERN1" 2029790 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025353 2025907 2026388 "PATRES" 2027523 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2024917 2024984 2025116 "PATRES2" 2025280 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022800 2023205 2023612 "PATMATCH" 2024584 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022336 2022519 2022560 "PATMAB" 2022667 NIL PATMAB (NIL T) -9 NIL 2022750 NIL) (-875 2020881 2021190 2021448 "PATLRES" 2022141 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020427 2020550 2020591 "PATAB" 2020596 NIL PATAB (NIL T) -9 NIL 2020768 NIL) (-873 2017908 2018440 2019013 "PARTPERM" 2019874 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017529 2017592 2017694 "PARSURF" 2017839 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017161 2017218 2017327 "PARSU2" 2017466 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2016925 2016965 2017032 "PARSER" 2017114 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016546 2016609 2016711 "PARSCURV" 2016856 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016178 2016235 2016344 "PARSC2" 2016483 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015817 2015875 2015972 "PARPCURV" 2016114 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015449 2015506 2015615 "PARPC2" 2015754 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2014969 2015055 2015174 "PAN2EXPR" 2015350 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013775 2014090 2014318 "PALETTE" 2014761 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012243 2012780 2013140 "PAIR" 2013461 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006149 2011502 2011696 "PADICRC" 2012098 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999413 2005495 2005679 "PADICRAT" 2005997 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997763 1999350 1999395 "PADIC" 1999400 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1994973 1996503 1996543 "PADICCT" 1997124 NIL PADICCT (NIL NIL) -9 NIL 1997406 NIL) (-858 1993930 1994130 1994398 "PADEPAC" 1994760 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993142 1993275 1993481 "PADE" 1993792 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991564 1992350 1992630 "OWP" 1992946 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990637 1991169 1991341 "OVAR" 1991432 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1989901 1990022 1990183 "OUT" 1990496 T OUT (NIL) -7 NIL NIL NIL) (-853 1978808 1981010 1983210 "OUTFORM" 1987721 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978229 1978405 1978532 "OUTBFILE" 1978701 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1977866 1977949 1977977 "OUTBCON" 1978128 T OUTBCON (NIL) -9 NIL 1978213 NIL) (-850 1977706 1977741 1977817 "OUTBCON-" 1977822 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977114 1977435 1977524 "OSI" 1977637 T OSI (NIL) -8 NIL NIL NIL) (-848 1976670 1976982 1977010 "OSGROUP" 1977015 T OSGROUP (NIL) -9 NIL 1977037 NIL) (-847 1975415 1975642 1975927 "ORTHPOL" 1976417 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973001 1975250 1975371 "OREUP" 1975376 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970439 1972692 1972819 "ORESUP" 1972943 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1967967 1968467 1969028 "OREPCTO" 1969928 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961791 1963958 1963999 "OREPCAT" 1966347 NIL OREPCAT (NIL T) -9 NIL 1967451 NIL) (-842 1958938 1959720 1960778 "OREPCAT-" 1960783 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958115 1958387 1958415 "ORDSET" 1958724 T ORDSET (NIL) -9 NIL 1958888 NIL) (-840 1957634 1957756 1957949 "ORDSET-" 1957954 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956268 1957025 1957053 "ORDRING" 1957255 T ORDRING (NIL) -9 NIL 1957380 NIL) (-838 1955913 1956007 1956151 "ORDRING-" 1956156 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955319 1955756 1955784 "ORDMON" 1955789 T ORDMON (NIL) -9 NIL 1955810 NIL) (-836 1954481 1954628 1954823 "ORDFUNS" 1955168 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1953845 1954238 1954266 "ORDFIN" 1954331 T ORDFIN (NIL) -9 NIL 1954405 NIL) (-834 1950437 1952431 1952840 "ORDCOMP" 1953469 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949703 1949830 1950016 "ORDCOMP2" 1950297 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946311 1947194 1948008 "OPTPROB" 1948909 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943113 1943752 1944456 "OPTPACK" 1945627 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940826 1941566 1941594 "OPTCAT" 1942413 T OPTCAT (NIL) -9 NIL 1943063 NIL) (-829 1940269 1940503 1940608 "OPSIG" 1940741 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940037 1940076 1940142 "OPQUERY" 1940223 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937203 1938348 1938852 "OP" 1939566 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936738 1936909 1936950 "OPERCAT" 1937085 NIL OPERCAT (NIL T) -9 NIL 1937153 NIL) (-825 1936584 1936611 1936697 "OPERCAT-" 1936702 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933429 1935381 1935750 "ONECOMP" 1936248 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932734 1932849 1933023 "ONECOMP2" 1933301 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932153 1932259 1932389 "OMSERVER" 1932624 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929041 1931593 1931633 "OMSAGG" 1931694 NIL OMSAGG (NIL T) -9 NIL 1931758 NIL) (-820 1927664 1927927 1928209 "OMPKG" 1928779 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927094 1927197 1927225 "OM" 1927524 T OM (NIL) -9 NIL NIL NIL) (-818 1925676 1926643 1926812 "OMLO" 1926975 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924601 1924748 1924975 "OMEXPR" 1925502 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1923919 1924147 1924283 "OMERR" 1924485 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923097 1923340 1923500 "OMERRK" 1923779 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922575 1922774 1922882 "OMENC" 1923009 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916470 1917655 1918826 "OMDEV" 1921424 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915539 1915710 1915904 "OMCONN" 1916296 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914160 1915102 1915130 "OINTDOM" 1915135 T OINTDOM (NIL) -9 NIL 1915156 NIL) (-810 1909966 1911150 1911866 "OFMONOID" 1913476 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909404 1909903 1909948 "ODVAR" 1909953 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1906862 1909149 1909304 "ODR" 1909309 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899206 1906638 1906764 "ODPOL" 1906769 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893082 1899078 1899183 "ODP" 1899188 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1891848 1892063 1892338 "ODETOOLS" 1892856 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888817 1889473 1890189 "ODESYS" 1891181 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883699 1884607 1885632 "ODERTRIC" 1887892 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883125 1883207 1883401 "ODERED" 1883611 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880013 1880561 1881238 "ODERAT" 1882548 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1876973 1877437 1878034 "ODEPRRIC" 1879542 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1874943 1875512 1875998 "ODEPROB" 1876507 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871465 1871948 1872595 "ODEPRIM" 1874422 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870714 1870816 1871076 "ODEPAL" 1871357 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1866876 1867667 1868531 "ODEPACK" 1869870 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1865909 1866016 1866245 "ODEINT" 1866765 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860010 1861435 1862882 "ODEIFTBL" 1864482 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855345 1856131 1857090 "ODEEF" 1859169 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854680 1854769 1854999 "ODECONST" 1855250 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852831 1853466 1853494 "ODECAT" 1854099 T ODECAT (NIL) -9 NIL 1854630 NIL) (-790 1849738 1852543 1852662 "OCT" 1852744 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849376 1849419 1849546 "OCTCT2" 1849689 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844150 1846550 1846590 "OC" 1847687 NIL OC (NIL T) -9 NIL 1848545 NIL) (-787 1841377 1842125 1843115 "OC-" 1843209 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840755 1841197 1841225 "OCAMON" 1841230 T OCAMON (NIL) -9 NIL 1841251 NIL) (-785 1840312 1840627 1840655 "OASGP" 1840660 T OASGP (NIL) -9 NIL 1840680 NIL) (-784 1839599 1840062 1840090 "OAMONS" 1840130 T OAMONS (NIL) -9 NIL 1840173 NIL) (-783 1839039 1839446 1839474 "OAMON" 1839479 T OAMON (NIL) -9 NIL 1839499 NIL) (-782 1838343 1838835 1838863 "OAGROUP" 1838868 T OAGROUP (NIL) -9 NIL 1838888 NIL) (-781 1838033 1838083 1838171 "NUMTUBE" 1838287 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831606 1833124 1834660 "NUMQUAD" 1836517 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827362 1828350 1829375 "NUMODE" 1830601 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824743 1825597 1825625 "NUMINT" 1826548 T NUMINT (NIL) -9 NIL 1827312 NIL) (-777 1823691 1823888 1824106 "NUMFMT" 1824545 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810050 1812995 1815527 "NUMERIC" 1821198 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804447 1809499 1809594 "NTSCAT" 1809599 NIL NTSCAT (NIL T T T T) -9 NIL 1809638 NIL) (-774 1803641 1803806 1803999 "NTPOLFN" 1804286 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791481 1800466 1801278 "NSUP" 1802862 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791113 1791170 1791279 "NSUP2" 1791418 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781110 1790887 1791020 "NSMP" 1791025 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779542 1779843 1780200 "NREP" 1780798 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778133 1778385 1778743 "NPCOEF" 1779285 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777199 1777314 1777530 "NORMRETR" 1778014 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775240 1775530 1775939 "NORMPK" 1776907 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1774925 1774953 1775077 "NORMMA" 1775206 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774752 1774882 1774911 "NONE" 1774916 T NONE (NIL) -8 NIL NIL NIL) (-764 1774541 1774570 1774639 "NONE1" 1774716 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774024 1774086 1774272 "NODE1" 1774473 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772295 1773118 1773373 "NNI" 1773720 T NNI (NIL) -8 NIL NIL 1773955) (-761 1770715 1771028 1771392 "NLINSOL" 1771963 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1766983 1767951 1768850 "NIPROB" 1769836 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765740 1765974 1766276 "NFINTBAS" 1766745 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765190 1765390 1765431 "NETCLT" 1765603 NIL NETCLT (NIL T) -9 NIL 1765685 NIL) (-757 1763898 1764129 1764410 "NCODIV" 1764958 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763660 1763697 1763772 "NCNTFRAC" 1763855 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1761840 1762204 1762624 "NCEP" 1763285 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760751 1761490 1761518 "NASRING" 1761628 T NASRING (NIL) -9 NIL 1761702 NIL) (-753 1760546 1760590 1760684 "NASRING-" 1760689 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759699 1760198 1760226 "NARNG" 1760343 T NARNG (NIL) -9 NIL 1760434 NIL) (-751 1759391 1759458 1759592 "NARNG-" 1759597 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758270 1758477 1758712 "NAGSP" 1759176 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749542 1751226 1752899 "NAGS" 1756617 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748090 1748398 1748729 "NAGF07" 1749231 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742628 1743919 1745226 "NAGF04" 1746803 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735596 1737210 1738843 "NAGF02" 1741015 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730820 1731920 1733037 "NAGF01" 1734499 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724448 1726014 1727599 "NAGE04" 1729255 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715617 1717738 1719868 "NAGE02" 1722338 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711570 1712517 1713481 "NAGE01" 1714673 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709365 1709899 1710457 "NAGD03" 1711032 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701115 1703043 1704997 "NAGD02" 1707431 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1694926 1696351 1697791 "NAGD01" 1699695 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691135 1691957 1692794 "NAGC06" 1694109 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689600 1689932 1690288 "NAGC05" 1690799 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1688976 1689095 1689239 "NAGC02" 1689476 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688036 1688593 1688633 "NAALG" 1688712 NIL NAALG (NIL T) -9 NIL 1688773 NIL) (-734 1687871 1687900 1687990 "NAALG-" 1687995 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681821 1682929 1684116 "MULTSQFR" 1686767 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681140 1681215 1681399 "MULTFACT" 1681733 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674233 1678103 1678156 "MTSCAT" 1679226 NIL MTSCAT (NIL T T) -9 NIL 1679740 NIL) (-730 1673945 1673999 1674091 "MTHING" 1674173 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673737 1673770 1673830 "MSYSCMD" 1673905 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1669849 1672492 1672812 "MSET" 1673450 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1666944 1669410 1669451 "MSETAGG" 1669456 NIL MSETAGG (NIL T) -9 NIL 1669490 NIL) (-726 1662827 1664323 1665068 "MRING" 1666244 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662393 1662460 1662591 "MRF2" 1662754 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662011 1662046 1662190 "MRATFAC" 1662352 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659623 1659918 1660349 "MPRFF" 1661716 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653683 1659477 1659574 "MPOLY" 1659579 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653173 1653208 1653416 "MPCPF" 1653642 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652687 1652730 1652914 "MPC3" 1653124 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1651882 1651963 1652184 "MPC2" 1652602 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650183 1650520 1650910 "MONOTOOL" 1651542 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649434 1649725 1649753 "MONOID" 1649972 T MONOID (NIL) -9 NIL 1650119 NIL) (-716 1648980 1649099 1649280 "MONOID-" 1649285 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1639839 1645747 1645806 "MONOGEN" 1646480 NIL MONOGEN (NIL T T) -9 NIL 1646936 NIL) (-714 1637057 1637792 1638792 "MONOGEN-" 1638911 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1635916 1636336 1636364 "MONADWU" 1636756 T MONADWU (NIL) -9 NIL 1636994 NIL) (-712 1635288 1635447 1635695 "MONADWU-" 1635700 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634673 1634891 1634919 "MONAD" 1635126 T MONAD (NIL) -9 NIL 1635238 NIL) (-710 1634358 1634436 1634568 "MONAD-" 1634573 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632674 1633271 1633550 "MOEBIUS" 1634111 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632066 1632444 1632484 "MODULE" 1632489 NIL MODULE (NIL T) -9 NIL 1632515 NIL) (-707 1631634 1631730 1631920 "MODULE-" 1631925 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629349 1629998 1630325 "MODRING" 1631458 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626335 1627454 1627975 "MODOP" 1628878 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1624950 1625402 1625679 "MODMONOM" 1626198 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614757 1623241 1623655 "MODMON" 1624587 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1611948 1613601 1613877 "MODFIELD" 1614632 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1610952 1611229 1611419 "MMLFORM" 1611778 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610478 1610521 1610700 "MMAP" 1610903 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608695 1609428 1609469 "MLO" 1609892 NIL MLO (NIL T) -9 NIL 1610134 NIL) (-698 1606062 1606577 1607179 "MLIFT" 1608176 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605453 1605537 1605691 "MKUCFUNC" 1605973 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605052 1605122 1605245 "MKRECORD" 1605376 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604100 1604261 1604489 "MKFUNC" 1604863 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603488 1603592 1603748 "MKFLCFN" 1603983 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603031 1603398 1603457 "MKCHSET" 1603462 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602308 1602410 1602595 "MKBCFUNC" 1602924 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599050 1601862 1601998 "MINT" 1602192 T MINT (NIL) -8 NIL NIL NIL) (-690 1597862 1598105 1598382 "MHROWRED" 1598805 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593288 1596397 1596802 "MFLOAT" 1597477 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592645 1592721 1592892 "MFINFACT" 1593200 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1588960 1589808 1590692 "MESH" 1591781 T MESH (NIL) -7 NIL NIL NIL) (-686 1587350 1587662 1588015 "MDDFACT" 1588647 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584192 1586509 1586550 "MDAGG" 1586805 NIL MDAGG (NIL T) -9 NIL 1586948 NIL) (-684 1573970 1583485 1583692 "MCMPLX" 1584005 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573111 1573257 1573457 "MCDEN" 1573819 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571001 1571271 1571651 "MCALCFN" 1572841 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1569926 1570166 1570399 "MAYBE" 1570807 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567538 1568061 1568623 "MATSTOR" 1569397 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563544 1566910 1567158 "MATRIX" 1567323 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559313 1560017 1560753 "MATLIN" 1562901 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549467 1552605 1552682 "MATCAT" 1557562 NIL MATCAT (NIL T T T) -9 NIL 1558979 NIL) (-676 1545831 1546844 1548200 "MATCAT-" 1548205 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544425 1544578 1544911 "MATCAT2" 1545666 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542537 1542861 1543245 "MAPPKG3" 1544100 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541518 1541691 1541913 "MAPPKG2" 1542361 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540017 1540301 1540628 "MAPPKG1" 1541224 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539123 1539423 1539600 "MAPPAST" 1539860 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538734 1538792 1538915 "MAPHACK3" 1539059 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538326 1538387 1538501 "MAPHACK2" 1538666 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537764 1537867 1538009 "MAPHACK1" 1538217 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1535870 1536464 1536768 "MAGMA" 1537492 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535376 1535594 1535685 "MACROAST" 1535799 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531843 1533615 1534076 "M3D" 1534948 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1525997 1530212 1530253 "LZSTAGG" 1531035 NIL LZSTAGG (NIL T) -9 NIL 1531330 NIL) (-663 1521971 1523128 1524585 "LZSTAGG-" 1524590 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519085 1519862 1520349 "LWORD" 1521516 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518688 1518889 1518964 "LSTAST" 1519030 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1511889 1518459 1518593 "LSQM" 1518598 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511113 1511252 1511480 "LSPP" 1511744 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1508925 1509226 1509682 "LSMP" 1510802 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505704 1506378 1507108 "LSMP1" 1508227 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499629 1504871 1504912 "LSAGG" 1504974 NIL LSAGG (NIL T) -9 NIL 1505052 NIL) (-655 1496324 1497248 1498461 "LSAGG-" 1498466 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1493950 1495468 1495717 "LPOLY" 1496119 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493532 1493617 1493740 "LPEFRAC" 1493859 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1491879 1492626 1492879 "LO" 1493364 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491531 1491643 1491671 "LOGIC" 1491782 T LOGIC (NIL) -9 NIL 1491863 NIL) (-650 1491393 1491416 1491487 "LOGIC-" 1491492 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490586 1490726 1490919 "LODOOPS" 1491249 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488044 1490502 1490568 "LODO" 1490573 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486582 1486817 1487170 "LODOF" 1487791 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1482938 1485335 1485376 "LODOCAT" 1485814 NIL LODOCAT (NIL T) -9 NIL 1486025 NIL) (-645 1482671 1482729 1482856 "LODOCAT-" 1482861 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480026 1482512 1482630 "LODO2" 1482635 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477496 1479963 1480008 "LODO1" 1480013 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476356 1476521 1476833 "LODEEF" 1477319 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471642 1474486 1474527 "LNAGG" 1475474 NIL LNAGG (NIL T) -9 NIL 1475918 NIL) (-640 1470789 1471003 1471345 "LNAGG-" 1471350 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1466952 1467714 1468353 "LMOPS" 1470204 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466347 1466709 1466750 "LMODULE" 1466811 NIL LMODULE (NIL T) -9 NIL 1466853 NIL) (-637 1463593 1465992 1466115 "LMDICT" 1466257 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463319 1463501 1463561 "LITERAL" 1463566 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456546 1462265 1462563 "LIST" 1463054 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456071 1456145 1456284 "LIST3" 1456466 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455078 1455256 1455484 "LIST2" 1455889 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453212 1453524 1453923 "LIST2MAP" 1454725 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1451942 1452578 1452619 "LINEXP" 1452874 NIL LINEXP (NIL T) -9 NIL 1453023 NIL) (-630 1450589 1450849 1451146 "LINDEP" 1451694 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447356 1448075 1448852 "LIMITRF" 1449844 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445632 1445927 1446343 "LIMITPS" 1447051 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440087 1445143 1445371 "LIE" 1445453 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439136 1439579 1439619 "LIECAT" 1439759 NIL LIECAT (NIL T) -9 NIL 1439910 NIL) (-625 1438977 1439004 1439092 "LIECAT-" 1439097 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431589 1438426 1438591 "LIB" 1438832 T LIB (NIL) -8 NIL NIL NIL) (-623 1427226 1428107 1429042 "LGROBP" 1430706 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425092 1425366 1425728 "LF" 1426947 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1423932 1424624 1424652 "LFCAT" 1424859 T LFCAT (NIL) -9 NIL 1424998 NIL) (-620 1420836 1421464 1422152 "LEXTRIPK" 1423296 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417607 1418406 1418909 "LEXP" 1420416 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417110 1417328 1417420 "LETAST" 1417535 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415508 1415821 1416222 "LEADCDET" 1416792 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414698 1414772 1415001 "LAZM3PK" 1415429 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409653 1412775 1413313 "LAUPOL" 1414210 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409218 1409262 1409430 "LAPLACE" 1409603 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407192 1408319 1408570 "LA" 1409051 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406273 1406823 1406864 "LALG" 1406926 NIL LALG (NIL T) -9 NIL 1406985 NIL) (-611 1405987 1406046 1406182 "LALG-" 1406187 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405822 1405846 1405887 "KVTFROM" 1405949 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404625 1405039 1405268 "KTVLOGIC" 1405613 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404460 1404484 1404525 "KRCFROM" 1404587 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403364 1403551 1403850 "KOVACIC" 1404260 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403199 1403223 1403264 "KONVERT" 1403326 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403034 1403058 1403099 "KOERCE" 1403161 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400768 1401528 1401921 "KERNEL" 1402673 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400270 1400351 1400481 "KERNEL2" 1400682 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394121 1398809 1398863 "KDAGG" 1399240 NIL KDAGG (NIL T T) -9 NIL 1399446 NIL) (-601 1393650 1393774 1393979 "KDAGG-" 1393984 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386825 1393311 1393466 "KAFILE" 1393528 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381280 1386336 1386564 "JORDAN" 1386646 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380686 1380929 1381050 "JOINAST" 1381179 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380532 1380591 1380646 "JAVACODE" 1380651 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376831 1378737 1378791 "IXAGG" 1379720 NIL IXAGG (NIL T T) -9 NIL 1380179 NIL) (-595 1375750 1376056 1376475 "IXAGG-" 1376480 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371330 1375672 1375731 "IVECTOR" 1375736 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370096 1370333 1370599 "ITUPLE" 1371097 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368532 1368709 1369015 "ITRIGMNP" 1369918 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367277 1367481 1367764 "ITFUN3" 1368308 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1366909 1366966 1367075 "ITFUN2" 1367214 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364746 1365771 1366070 "ITAYLOR" 1366643 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353729 1358883 1360046 "ISUPS" 1363616 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352833 1352973 1353209 "ISUMP" 1353576 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348097 1352634 1352713 "ISTRING" 1352786 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347600 1347818 1347910 "ISAST" 1348025 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346810 1346891 1347107 "IRURPK" 1347514 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345746 1345947 1346187 "IRSN" 1346590 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343775 1344130 1344566 "IRRF2F" 1345384 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343522 1343560 1343636 "IRREDFFX" 1343731 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342137 1342396 1342695 "IROOT" 1343255 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338769 1339821 1340513 "IR" 1341477 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336382 1336877 1337443 "IR2" 1338247 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335454 1335567 1335788 "IR2F" 1336265 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335245 1335279 1335339 "IPRNTPK" 1335414 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1331864 1335134 1335203 "IPF" 1335208 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330227 1331789 1331846 "IPADIC" 1331851 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329567 1329787 1329917 "IP4ADDR" 1330117 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329067 1329271 1329381 "IOMODE" 1329477 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328425 1328664 1328791 "IOBFILE" 1328960 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328189 1328329 1328357 "IOBCON" 1328362 T IOBCON (NIL) -9 NIL 1328383 NIL) (-569 1327686 1327744 1327934 "INVLAPLA" 1328125 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317335 1319688 1322074 "INTTR" 1325350 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313679 1314421 1315285 "INTTOOLS" 1316520 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313265 1313356 1313473 "INTSLPE" 1313582 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311260 1313188 1313247 "INTRVL" 1313252 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308862 1309374 1309949 "INTRF" 1310745 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308273 1308370 1308512 "INTRET" 1308760 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306270 1306659 1307129 "INTRAT" 1307881 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303498 1304081 1304707 "INTPM" 1305755 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300201 1300800 1301545 "INTPAF" 1302884 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295380 1296342 1297393 "INTPACK" 1299170 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292292 1295109 1295236 "INT" 1295273 T INT (NIL) -8 NIL NIL NIL) (-557 1291544 1291696 1291904 "INTHERTR" 1292134 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1290983 1291063 1291251 "INTHERAL" 1291458 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288829 1289272 1289729 "INTHEORY" 1290546 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280137 1281758 1283537 "INTG0" 1287181 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260710 1265500 1270310 "INTFTBL" 1275347 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1259959 1260097 1260270 "INTFACT" 1260569 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257344 1257790 1258354 "INTEF" 1259513 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255811 1256516 1256544 "INTDOM" 1256845 T INTDOM (NIL) -9 NIL 1257052 NIL) (-549 1255180 1255354 1255596 "INTDOM-" 1255601 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251675 1253564 1253618 "INTCAT" 1254417 NIL INTCAT (NIL T) -9 NIL 1254737 NIL) (-547 1251148 1251250 1251378 "INTBIT" 1251567 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249819 1249973 1250287 "INTALG" 1250993 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249276 1249366 1249536 "INTAF" 1249723 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242730 1249086 1249226 "INTABL" 1249231 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237745 1240419 1240447 "INS" 1241381 T INS (NIL) -9 NIL 1242046 NIL) (-542 1234985 1235756 1236730 "INS-" 1236803 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233760 1233987 1234285 "INPSIGN" 1234738 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1232878 1232995 1233192 "INPRODPF" 1233640 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231772 1231889 1232126 "INPRODFF" 1232758 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230772 1230924 1231184 "INNMFACT" 1231608 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1229969 1230066 1230254 "INMODGCD" 1230671 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228478 1228722 1229046 "INFSP" 1229714 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227662 1227779 1227962 "INFPROD0" 1228358 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224544 1225727 1226242 "INFORM" 1227155 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224154 1224214 1224312 "INFORM1" 1224479 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223677 1223766 1223880 "INFINITY" 1224060 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223138 1223397 1223498 "INETCLTS" 1223596 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221755 1222004 1222325 "INEP" 1222886 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221031 1221652 1221717 "INDE" 1221722 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220595 1220663 1220780 "INCRMAPS" 1220958 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219613 1219864 1220070 "INBFILE" 1220409 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1214924 1215849 1216793 "INBFF" 1218701 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214593 1214669 1214697 "INBCON" 1214830 T INBCON (NIL) -9 NIL 1214908 NIL) (-524 1214433 1214468 1214544 "INBCON-" 1214549 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1213935 1214154 1214246 "INAST" 1214361 T INAST (NIL) -8 NIL NIL NIL) (-522 1213389 1213614 1213720 "IMPTAST" 1213849 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1209883 1213233 1213337 "IMATRIX" 1213342 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208595 1208718 1209033 "IMATQF" 1209739 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206815 1207042 1207379 "IMATLIN" 1208351 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201441 1206739 1206797 "ILIST" 1206802 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199394 1201301 1201414 "IIARRAY2" 1201419 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194827 1199305 1199369 "IFF" 1199374 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194201 1194444 1194560 "IFAST" 1194731 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189244 1193493 1193681 "IFARRAY" 1194058 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188451 1189148 1189221 "IFAMON" 1189226 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188035 1188100 1188154 "IEVALAB" 1188361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187710 1187778 1187938 "IEVALAB-" 1187943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187368 1187624 1187687 "IDPO" 1187692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186645 1187257 1187332 "IDPOAMS" 1187337 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1185979 1186534 1186609 "IDPOAM" 1186614 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185064 1185314 1185367 "IDPC" 1185780 NIL IDPC (NIL T T) -9 NIL 1185929 NIL) (-506 1184560 1184956 1185029 "IDPAM" 1185034 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1183963 1184452 1184525 "IDPAG" 1184530 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183731 1183878 1183928 "IDENT" 1183933 T IDENT (NIL) -8 NIL NIL NIL) (-503 1179986 1180834 1181729 "IDECOMP" 1182888 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172860 1173909 1174956 "IDEAL" 1179022 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172024 1172136 1172335 "ICDEN" 1172744 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171123 1171504 1171651 "ICARD" 1171897 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169183 1169496 1169901 "IBPTOOLS" 1170800 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164817 1168803 1168916 "IBITS" 1169102 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161540 1162116 1162811 "IBATOOL" 1164234 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159320 1159781 1160314 "IBACHIN" 1161075 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157197 1159166 1159269 "IARRAY2" 1159274 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153350 1157123 1157180 "IARRAY1" 1157185 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147344 1151762 1152243 "IAN" 1152889 T IAN (NIL) -8 NIL NIL NIL) (-492 1146855 1146912 1147085 "IALGFACT" 1147281 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146383 1146496 1146524 "HYPCAT" 1146731 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1145921 1146038 1146224 "HYPCAT-" 1146229 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145543 1145716 1145799 "HOSTNAME" 1145858 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145388 1145425 1145466 "HOMOTOP" 1145471 NIL HOMOTOP (NIL T) -9 NIL 1145504 NIL) (-487 1142067 1143398 1143439 "HOAGG" 1144420 NIL HOAGG (NIL T) -9 NIL 1145099 NIL) (-486 1140661 1141060 1141586 "HOAGG-" 1141591 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134703 1140258 1140406 "HEXADEC" 1140533 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133451 1133673 1133936 "HEUGCD" 1134480 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132554 1133288 1133418 "HELLFDIV" 1133423 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130782 1132331 1132419 "HEAP" 1132498 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130073 1130334 1130468 "HEADAST" 1130668 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1123993 1129988 1130050 "HDP" 1130055 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117744 1123628 1123780 "HDMP" 1123894 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117069 1117208 1117372 "HB" 1117600 T HB (NIL) -7 NIL NIL NIL) (-477 1110566 1116915 1117019 "HASHTBL" 1117024 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110069 1110287 1110379 "HASAST" 1110494 T HASAST (NIL) -8 NIL NIL NIL) (-475 1107881 1109691 1109873 "HACKPI" 1109907 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103576 1107734 1107847 "GTSET" 1107852 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097102 1103454 1103552 "GSTBL" 1103557 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089415 1096133 1096398 "GSERIES" 1096893 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088582 1088973 1089001 "GROUP" 1089204 T GROUP (NIL) -9 NIL 1089338 NIL) (-470 1087948 1088107 1088358 "GROUP-" 1088363 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086317 1086636 1087023 "GROEBSOL" 1087625 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085257 1085519 1085570 "GRMOD" 1086099 NIL GRMOD (NIL T T) -9 NIL 1086267 NIL) (-467 1085025 1085061 1085189 "GRMOD-" 1085194 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080351 1081379 1082379 "GRIMAGE" 1084045 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078818 1079078 1079402 "GRDEF" 1080047 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078262 1078378 1078519 "GRAY" 1078697 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077475 1077855 1077906 "GRALG" 1078059 NIL GRALG (NIL T T) -9 NIL 1078152 NIL) (-462 1077136 1077209 1077372 "GRALG-" 1077377 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1073940 1076721 1076899 "GPOLSET" 1077043 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073294 1073351 1073609 "GOSPER" 1073877 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069053 1069732 1070258 "GMODPOL" 1072993 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068058 1068242 1068480 "GHENSEL" 1068865 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062109 1062952 1063979 "GENUPS" 1067142 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061806 1061857 1061946 "GENUFACT" 1062052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061218 1061295 1061460 "GENPGCD" 1061724 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060692 1060727 1060940 "GENMFACT" 1061177 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059260 1059515 1059822 "GENEEZ" 1060435 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053173 1058871 1059033 "GDMP" 1059183 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042550 1046944 1048050 "GCNAALG" 1052156 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1040977 1041805 1041833 "GCDDOM" 1042088 T GCDDOM (NIL) -9 NIL 1042245 NIL) (-449 1040447 1040574 1040789 "GCDDOM-" 1040794 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039119 1039304 1039608 "GB" 1040226 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027739 1030065 1032457 "GBINTERN" 1036810 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025576 1025868 1026289 "GBF" 1027414 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024357 1024522 1024789 "GBEUCLID" 1025392 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023706 1023831 1023980 "GAUSSFAC" 1024228 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022073 1022375 1022689 "GALUTIL" 1023425 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020381 1020655 1020979 "GALPOLYU" 1021800 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017746 1018036 1018443 "GALFACTU" 1020078 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009552 1011051 1012659 "GALFACT" 1016178 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1006940 1007598 1007626 "FVFUN" 1008782 T FVFUN (NIL) -9 NIL 1009502 NIL) (-438 1006206 1006388 1006416 "FVC" 1006707 T FVC (NIL) -9 NIL 1006890 NIL) (-437 1005848 1006003 1006084 "FUNCTION" 1006158 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003619 1004170 1004636 "FT" 1005402 T FT (NIL) -8 NIL NIL NIL) (-435 1002437 1002920 1003123 "FTEM" 1003436 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000693 1000982 1001386 "FSUPFACT" 1002128 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999090 999379 999711 "FST" 1000381 T FST (NIL) -8 NIL NIL NIL) (-432 998261 998367 998562 "FSRED" 998972 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 996940 997195 997549 "FSPRMELT" 997976 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994025 994463 994962 "FSPECF" 996503 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976085 984528 984568 "FS" 988416 NIL FS (NIL T) -9 NIL 990705 NIL) (-428 964735 967725 971781 "FS-" 972078 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964249 964303 964480 "FSINT" 964676 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962576 963242 963545 "FSERIES" 964028 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961590 961706 961937 "FSCINT" 962456 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957824 960534 960575 "FSAGG" 960945 NIL FSAGG (NIL T) -9 NIL 961204 NIL) (-423 955586 956187 956983 "FSAGG-" 957078 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954628 954771 954998 "FSAGG2" 955439 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952283 952562 953116 "FS2UPS" 954346 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951865 951908 952063 "FS2" 952234 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950722 950893 951202 "FS2EXPXP" 951690 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950148 950263 950415 "FRUTIL" 950602 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941603 945643 947001 "FR" 948822 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936678 939321 939361 "FRNAALG" 940757 NIL FRNAALG (NIL T) -9 NIL 941364 NIL) (-415 932356 933427 934702 "FRNAALG-" 935452 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 931994 932037 932164 "FRNAAF2" 932307 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930401 930848 931143 "FRMOD" 931806 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928180 928784 929101 "FRIDEAL" 930192 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927375 927462 927751 "FRIDEAL2" 928087 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926508 926922 926963 "FRETRCT" 926968 NIL FRETRCT (NIL T) -9 NIL 927144 NIL) (-409 925620 925851 926202 "FRETRCT-" 926207 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922832 924008 924067 "FRAMALG" 924949 NIL FRAMALG (NIL T T) -9 NIL 925241 NIL) (-407 920966 921421 922051 "FRAMALG-" 922274 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 914924 920441 920717 "FRAC" 920722 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914560 914617 914724 "FRAC2" 914861 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914196 914253 914360 "FR2" 914497 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908869 911721 911749 "FPS" 912868 T FPS (NIL) -9 NIL 913425 NIL) (-402 908318 908427 908591 "FPS-" 908737 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905772 907407 907435 "FPC" 907660 T FPC (NIL) -9 NIL 907802 NIL) (-400 905565 905605 905702 "FPC-" 905707 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904443 905053 905094 "FPATMAB" 905099 NIL FPATMAB (NIL T) -9 NIL 905251 NIL) (-398 902143 902619 903045 "FPARFRAC" 904080 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897537 898035 898717 "FORTRAN" 901575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895253 895753 896292 "FORT" 897018 T FORT (NIL) -7 NIL NIL NIL) (-395 892929 893491 893519 "FORTFN" 894579 T FORTFN (NIL) -9 NIL 895203 NIL) (-394 892693 892743 892771 "FORTCAT" 892830 T FORTCAT (NIL) -9 NIL 892892 NIL) (-393 890826 891309 891699 "FORMULA" 892323 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890614 890644 890713 "FORMULA1" 890790 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890137 890189 890362 "FORDER" 890556 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889233 889397 889590 "FOP" 889964 T FOP (NIL) -7 NIL NIL NIL) (-389 887841 888513 888687 "FNLA" 889115 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886596 886985 887013 "FNCAT" 887473 T FNCAT (NIL) -9 NIL 887733 NIL) (-387 886162 886555 886583 "FNAME" 886588 T FNAME (NIL) -8 NIL NIL NIL) (-386 884825 885754 885782 "FMTC" 885787 T FMTC (NIL) -9 NIL 885823 NIL) (-385 881187 882348 882977 "FMONOID" 884229 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880406 880929 881078 "FM" 881083 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877830 878476 878504 "FMFUN" 879648 T FMFUN (NIL) -9 NIL 880356 NIL) (-382 877099 877280 877308 "FMC" 877598 T FMC (NIL) -9 NIL 877780 NIL) (-381 874293 875127 875181 "FMCAT" 876376 NIL FMCAT (NIL T T) -9 NIL 876871 NIL) (-380 873186 874059 874159 "FM1" 874238 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 870960 871376 871870 "FLOATRP" 872737 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864584 868689 869310 "FLOAT" 870359 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862022 862522 863100 "FLOATCP" 864051 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860831 861635 861676 "FLINEXP" 861681 NIL FLINEXP (NIL T) -9 NIL 861774 NIL) (-375 859985 860220 860548 "FLINEXP-" 860553 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859061 859205 859429 "FLASORT" 859837 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856278 857120 857172 "FLALG" 858399 NIL FLALG (NIL T T) -9 NIL 858866 NIL) (-372 850062 853764 853805 "FLAGG" 855067 NIL FLAGG (NIL T) -9 NIL 855719 NIL) (-371 848788 849127 849617 "FLAGG-" 849622 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847830 847973 848200 "FLAGG2" 848641 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844805 845779 845838 "FINRALG" 846966 NIL FINRALG (NIL T T) -9 NIL 847474 NIL) (-368 843965 844194 844533 "FINRALG-" 844538 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843371 843584 843612 "FINITE" 843808 T FINITE (NIL) -9 NIL 843915 NIL) (-366 835829 837990 838030 "FINAALG" 841697 NIL FINAALG (NIL T) -9 NIL 843150 NIL) (-365 831170 832211 833355 "FINAALG-" 834734 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830565 830925 831028 "FILE" 831100 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829249 829561 829615 "FILECAT" 830299 NIL FILECAT (NIL T T) -9 NIL 830515 NIL) (-362 827117 828611 828639 "FIELD" 828679 T FIELD (NIL) -9 NIL 828759 NIL) (-361 825737 826122 826633 "FIELD-" 826638 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823615 824372 824719 "FGROUP" 825423 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822705 822869 823089 "FGLMICPK" 823447 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818572 822630 822687 "FFX" 822692 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818173 818234 818369 "FFSLPE" 818505 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814166 814945 815741 "FFPOLY" 817409 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813670 813706 813915 "FFPOLY2" 814124 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809556 813589 813652 "FFP" 813657 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 804989 809467 809531 "FF" 809536 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800150 804332 804522 "FFNBX" 804843 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795124 799285 799543 "FFNBP" 800004 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789792 794408 794619 "FFNB" 794957 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788624 788822 789137 "FFINTBAS" 789589 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784852 787031 787059 "FFIELDC" 787679 T FFIELDC (NIL) -9 NIL 788055 NIL) (-347 783515 783885 784382 "FFIELDC-" 784387 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783085 783130 783254 "FFHOM" 783457 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780783 781267 781784 "FFF" 782600 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776436 780525 780626 "FFCGX" 780726 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772103 776168 776275 "FFCGP" 776379 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767321 771830 771938 "FFCG" 772039 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749154 758192 758278 "FFCAT" 763443 NIL FFCAT (NIL T T T) -9 NIL 764894 NIL) (-340 744352 745399 746713 "FFCAT-" 747943 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743763 743806 744041 "FFCAT2" 744303 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 732975 736735 737955 "FEXPR" 742615 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 731975 732410 732451 "FEVALAB" 732535 NIL FEVALAB (NIL T) -9 NIL 732796 NIL) (-336 731134 731344 731682 "FEVALAB-" 731687 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729727 730517 730720 "FDIV" 731033 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726793 727508 727623 "FDIVCAT" 729191 NIL FDIVCAT (NIL T T T T) -9 NIL 729628 NIL) (-333 726555 726582 726752 "FDIVCAT-" 726757 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725775 725862 726139 "FDIV2" 726462 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724461 724720 725009 "FCPAK1" 725506 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723589 723961 724102 "FCOMP" 724352 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707326 710739 714277 "FC" 720071 T FC (NIL) -8 NIL NIL NIL) (-328 699905 703890 703930 "FAXF" 705732 NIL FAXF (NIL T) -9 NIL 706424 NIL) (-327 697184 697839 698664 "FAXF-" 699129 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692284 696560 696736 "FARRAY" 697041 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687537 689569 689622 "FAMR" 690645 NIL FAMR (NIL T T) -9 NIL 691105 NIL) (-324 686427 686729 687164 "FAMR-" 687169 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685623 686349 686402 "FAMONOID" 686407 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683435 684119 684172 "FAMONC" 685113 NIL FAMONC (NIL T T) -9 NIL 685499 NIL) (-321 682127 683189 683326 "FAGROUP" 683331 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 679922 680241 680644 "FACUTIL" 681808 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679021 679206 679428 "FACTFUNC" 679732 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671426 678272 678484 "EXPUPXS" 678877 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 668909 669449 670035 "EXPRTUBE" 670860 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665103 665695 666432 "EXPRODE" 668248 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650477 663758 664186 "EXPR" 664707 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 644884 645471 646284 "EXPR2UPS" 649775 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644520 644577 644684 "EXPR2" 644821 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 635925 643652 643949 "EXPEXPAN" 644357 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635752 635882 635911 "EXIT" 635916 T EXIT (NIL) -8 NIL NIL NIL) (-310 635259 635476 635567 "EXITAST" 635681 T EXITAST (NIL) -8 NIL NIL NIL) (-309 634886 634948 635061 "EVALCYC" 635191 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634427 634545 634586 "EVALAB" 634756 NIL EVALAB (NIL T) -9 NIL 634860 NIL) (-307 633908 634030 634251 "EVALAB-" 634256 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631376 632644 632672 "EUCDOM" 633227 T EUCDOM (NIL) -9 NIL 633577 NIL) (-305 629781 630223 630813 "EUCDOM-" 630818 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617321 620079 622829 "ESTOOLS" 627051 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 616953 617010 617119 "ESTOOLS2" 617258 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616704 616746 616826 "ESTOOLS1" 616905 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610609 612337 612365 "ES" 615133 T ES (NIL) -9 NIL 616542 NIL) (-300 605557 606843 608660 "ES-" 608824 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 601932 602692 603472 "ESCONT" 604797 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601677 601709 601791 "ESCONT1" 601894 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601352 601402 601502 "ES2" 601621 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 600982 601040 601149 "ES1" 601288 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600198 600327 600503 "ERROR" 600826 T ERROR (NIL) -7 NIL NIL NIL) (-294 593701 600057 600148 "EQTBL" 600153 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586258 589015 590464 "EQ" 592285 NIL -3318 (NIL T) -8 NIL NIL NIL) (-292 585890 585947 586056 "EQ2" 586195 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581182 582228 583321 "EP" 584829 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579764 580065 580382 "ENV" 580885 T ENV (NIL) -8 NIL NIL NIL) (-289 578943 579463 579491 "ENTIRER" 579496 T ENTIRER (NIL) -9 NIL 579542 NIL) (-288 575445 576898 577268 "EMR" 578742 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574589 574774 574828 "ELTAGG" 575208 NIL ELTAGG (NIL T T) -9 NIL 575419 NIL) (-286 574308 574370 574511 "ELTAGG-" 574516 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574097 574126 574180 "ELTAB" 574264 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573223 573369 573568 "ELFUTS" 573948 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 572965 573021 573049 "ELEMFUN" 573154 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572835 572856 572924 "ELEMFUN-" 572929 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567726 570935 570976 "ELAGG" 571916 NIL ELAGG (NIL T) -9 NIL 572379 NIL) (-280 566011 566445 567108 "ELAGG-" 567113 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564668 564948 565243 "ELABEXPR" 565736 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557534 559335 560162 "EFUPXS" 563944 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 550984 552785 553595 "EFULS" 556810 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548406 548764 549243 "EFSTRUC" 550616 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537478 539043 540603 "EF" 546921 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536579 536963 537112 "EAB" 537349 T EAB (NIL) -8 NIL NIL NIL) (-273 535788 536538 536566 "E04UCFA" 536571 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 534997 535747 535775 "E04NAFA" 535780 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534206 534956 534984 "E04MBFA" 534989 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533415 534165 534193 "E04JAFA" 534198 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532626 533374 533402 "E04GCFA" 533407 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531837 532585 532613 "E04FDFA" 532618 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531046 531796 531824 "E04DGFA" 531829 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525224 526571 527935 "E04AGNT" 529702 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 523930 524410 524450 "DVARCAT" 524925 NIL DVARCAT (NIL T) -9 NIL 525124 NIL) (-264 523134 523346 523660 "DVARCAT-" 523665 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516034 522933 523062 "DSMP" 523067 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510844 511979 513047 "DROPT" 514986 T DROPT (NIL) -8 NIL NIL NIL) (-261 510509 510568 510666 "DROPT1" 510779 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505624 506750 507887 "DROPT0" 509392 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 503969 504294 504680 "DRAWPT" 505258 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498556 499479 500558 "DRAW" 502943 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498189 498242 498360 "DRAWHACK" 498497 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 496920 497189 497480 "DRAWCX" 497918 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496436 496504 496655 "DRAWCURV" 496846 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 486907 488866 490981 "DRAWCFUN" 494341 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483720 485602 485643 "DQAGG" 486272 NIL DQAGG (NIL T) -9 NIL 486545 NIL) (-252 471999 478698 478781 "DPOLCAT" 480633 NIL DPOLCAT (NIL T T T T) -9 NIL 481178 NIL) (-251 466838 468184 470142 "DPOLCAT-" 470147 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 459993 466699 466797 "DPMO" 466802 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453051 459773 459940 "DPMM" 459945 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452715 452970 453018 "DOMCTOR" 453023 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452010 452237 452374 "DOMAIN" 452598 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445761 451645 451797 "DMP" 451911 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445361 445417 445561 "DLP" 445699 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439231 444688 444878 "DLIST" 445203 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436075 438084 438125 "DLAGG" 438675 NIL DLAGG (NIL T) -9 NIL 438905 NIL) (-242 434888 435518 435546 "DIVRING" 435638 T DIVRING (NIL) -9 NIL 435721 NIL) (-241 434125 434315 434615 "DIVRING-" 434620 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432227 432584 432990 "DISPLAY" 433739 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426169 432141 432204 "DIRPROD" 432209 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425017 425220 425485 "DIRPROD2" 425962 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414280 420232 420285 "DIRPCAT" 420695 NIL DIRPCAT (NIL NIL T) -9 NIL 421535 NIL) (-236 411606 412248 413129 "DIRPCAT-" 413466 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 410893 411053 411239 "DIOSP" 411440 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407595 409805 409846 "DIOPS" 410280 NIL DIOPS (NIL T) -9 NIL 410509 NIL) (-233 407144 407258 407449 "DIOPS-" 407454 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406036 406630 406658 "DIFRING" 406845 T DIFRING (NIL) -9 NIL 406955 NIL) (-231 405682 405759 405911 "DIFRING-" 405916 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403487 404725 404766 "DIFEXT" 405129 NIL DIFEXT (NIL T) -9 NIL 405423 NIL) (-229 401772 402200 402866 "DIFEXT-" 402871 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399094 401304 401345 "DIAGG" 401350 NIL DIAGG (NIL T) -9 NIL 401370 NIL) (-227 398478 398635 398887 "DIAGG-" 398892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 393943 397437 397714 "DHMATRIX" 398247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389555 390464 391474 "DFSFUN" 392953 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384671 388486 388798 "DFLOAT" 389263 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 382899 383180 383576 "DFINTTLS" 384379 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 379964 380920 381320 "DERHAM" 382565 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377813 379739 379828 "DEQUEUE" 379908 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377028 377161 377357 "DEGRED" 377675 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373423 374168 375021 "DEFINTRF" 376256 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 370950 371419 372018 "DEFINTEF" 372942 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370327 370570 370685 "DEFAST" 370855 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364369 369924 370072 "DECIMAL" 370199 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 361881 362339 362845 "DDFACT" 363913 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361477 361520 361671 "DBLRESP" 361832 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359376 359710 360070 "DBASE" 361244 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358645 358856 359002 "DATAARY" 359275 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357778 358604 358632 "D03FAFA" 358637 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 356912 357737 357765 "D03EEFA" 357770 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354862 355328 355817 "D03AGNT" 356443 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354178 354821 354849 "D02EJFA" 354854 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353494 354137 354165 "D02CJFA" 354170 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352810 353453 353481 "D02BHFA" 353486 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352126 352769 352797 "D02BBFA" 352802 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345324 346912 348518 "D02AGNT" 350540 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343093 343615 344161 "D01WGTS" 344798 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342188 343052 343080 "D01TRNS" 343085 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341283 342147 342175 "D01GBFA" 342180 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340378 341242 341270 "D01FCFA" 341275 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339473 340337 340365 "D01ASFA" 340370 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338568 339432 339460 "D01AQFA" 339465 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337663 338527 338555 "D01APFA" 338560 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336758 337622 337650 "D01ANFA" 337655 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335853 336717 336745 "D01AMFA" 336750 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 334948 335812 335840 "D01ALFA" 335845 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334043 334907 334935 "D01AKFA" 334940 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333138 334002 334030 "D01AJFA" 334035 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326435 327986 329547 "D01AGNT" 331597 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325772 325900 326052 "CYCLOTOM" 326303 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322507 323220 323947 "CYCLES" 325065 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321819 321953 322124 "CVMP" 322368 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319590 319848 320224 "CTRIGMNP" 321547 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319313 319549 319577 "CTOR" 319582 T CTOR (NIL) -8 NIL NIL NIL) (-185 318849 319044 319145 "CTORKIND" 319232 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318320 318548 318576 "CTORCAT" 318696 T CTORCAT (NIL) -9 NIL 318779 NIL) (-183 318015 318095 318221 "CTORCAT-" 318226 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317531 317718 317816 "CTORCALL" 317937 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 316905 317004 317157 "CSTTOOLS" 317428 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312704 313361 314119 "CRFP" 316217 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312206 312425 312517 "CRCEAST" 312632 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311253 311438 311666 "CRAPACK" 312010 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310637 310738 310942 "CPMATCH" 311129 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310362 310390 310496 "CPIMA" 310603 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306726 307398 308116 "COORDSYS" 309697 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306110 306239 306389 "CONTOUR" 306596 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302036 304113 304605 "CONTFRAC" 305650 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 301916 301937 301965 "CONDUIT" 302002 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301089 301609 301637 "COMRING" 301642 T COMRING (NIL) -9 NIL 301694 NIL) (-170 300170 300447 300631 "COMPPROP" 300925 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299831 299866 299994 "COMPLPAT" 300129 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 289888 299640 299749 "COMPLEX" 299754 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289524 289581 289688 "COMPLEX2" 289825 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289242 289277 289375 "COMPFACT" 289483 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273415 283635 283675 "COMPCAT" 284679 NIL COMPCAT (NIL T) -9 NIL 286064 NIL) (-164 262931 265854 269481 "COMPCAT-" 269837 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262660 262688 262791 "COMMUPC" 262897 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262455 262488 262547 "COMMONOP" 262621 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262038 262206 262293 "COMM" 262388 T COMM (NIL) -8 NIL NIL NIL) (-160 261642 261842 261917 "COMMAAST" 261983 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 260891 261085 261113 "COMBOPC" 261451 T COMBOPC (NIL) -9 NIL 261626 NIL) (-158 259787 259997 260239 "COMBINAT" 260681 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 255985 256558 257198 "COMBF" 259209 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254771 255101 255336 "COLOR" 255770 T COLOR (NIL) -8 NIL NIL NIL) (-155 254274 254492 254584 "COLONAST" 254699 T COLONAST (NIL) -8 NIL NIL NIL) (-154 253914 253961 254086 "CMPLXRT" 254221 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253389 253614 253713 "CLLCTAST" 253835 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 248891 249919 250999 "CLIP" 252329 T CLIP (NIL) -7 NIL NIL NIL) (-151 247273 247997 248236 "CLIF" 248718 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243495 245419 245460 "CLAGG" 246389 NIL CLAGG (NIL T) -9 NIL 246925 NIL) (-149 241917 242374 242957 "CLAGG-" 242962 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241461 241546 241686 "CINTSLPE" 241826 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 238962 239433 239981 "CHVAR" 240989 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238205 238725 238753 "CHARZ" 238758 T CHARZ (NIL) -9 NIL 238773 NIL) (-145 237959 237999 238077 "CHARPOL" 238159 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237086 237639 237667 "CHARNZ" 237714 T CHARNZ (NIL) -9 NIL 237770 NIL) (-143 235075 235776 236111 "CHAR" 236771 T CHAR (NIL) -8 NIL NIL NIL) (-142 234801 234862 234890 "CFCAT" 235001 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234046 234157 234339 "CDEN" 234685 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230038 233199 233479 "CCLASS" 233786 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229345 229488 229651 "CATEGORY" 229895 T -10 (NIL) -8 NIL NIL NIL) (-138 229009 229264 229312 "CATCTOR" 229317 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228483 228709 228808 "CATAST" 228930 T CATAST (NIL) -8 NIL NIL NIL) (-136 227986 228204 228296 "CASEAST" 228411 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223038 224015 224768 "CARTEN" 227289 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222146 222294 222515 "CARTEN2" 222885 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220488 221296 221553 "CARD" 221909 T CARD (NIL) -8 NIL NIL NIL) (-132 220091 220292 220367 "CAPSLAST" 220433 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219463 219791 219819 "CACHSET" 219951 T CACHSET (NIL) -9 NIL 220028 NIL) (-130 218959 219255 219283 "CABMON" 219333 T CABMON (NIL) -9 NIL 219389 NIL) (-129 218107 218505 218641 "BYTE" 218804 T BYTE (NIL) -8 NIL NIL 218920) (-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 3184428 3184433 3184438 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3184413 3184418 3184423 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3184398 3184403 3184408 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3184383 3184388 3184393 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1274 3183559 3184258 3184335 "ZMOD" 3184340 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1273 3182669 3182833 3183042 "ZLINDEP" 3183391 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1272 3171973 3173737 3175709 "ZDSOLVE" 3180799 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1271 3171219 3171360 3171549 "YSTREAM" 3171819 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1270 3169030 3170520 3170724 "XRPOLY" 3171062 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1269 3165618 3166901 3167476 "XPR" 3168502 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1268 3163374 3164949 3165153 "XPOLY" 3165449 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1267 3161165 3162499 3162554 "XPOLYC" 3162842 NIL XPOLYC (NIL T T) -9 NIL 3162955 NIL) (-1266 3157583 3159682 3160070 "XPBWPOLY" 3160823 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1265 3153494 3155746 3155788 "XF" 3156409 NIL XF (NIL T) -9 NIL 3156809 NIL) (-1264 3153115 3153203 3153372 "XF-" 3153377 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1263 3148449 3149704 3149759 "XFALG" 3151931 NIL XFALG (NIL T T) -9 NIL 3152720 NIL) (-1262 3147582 3147686 3147891 "XEXPPKG" 3148341 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1261 3145726 3147432 3147528 "XDPOLY" 3147533 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1260 3144671 3145237 3145280 "XALG" 3145285 NIL XALG (NIL T) -9 NIL 3145396 NIL) (-1259 3138140 3142648 3143142 "WUTSET" 3144263 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1258 3136431 3137192 3137515 "WP" 3137951 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1257 3136060 3136253 3136323 "WHILEAST" 3136383 T WHILEAST (NIL) -8 NIL NIL NIL) (-1256 3135559 3135777 3135871 "WHEREAST" 3135988 T WHEREAST (NIL) -8 NIL NIL NIL) (-1255 3134445 3134643 3134938 "WFFINTBS" 3135356 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1254 3132349 3132776 3133238 "WEIER" 3134017 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1253 3131496 3131920 3131962 "VSPACE" 3132098 NIL VSPACE (NIL T) -9 NIL 3132172 NIL) (-1252 3131334 3131361 3131452 "VSPACE-" 3131457 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1251 3131142 3131185 3131253 "VOID" 3131288 T VOID (NIL) -8 NIL NIL NIL) (-1250 3129278 3129637 3130043 "VIEW" 3130758 T VIEW (NIL) -7 NIL NIL NIL) (-1249 3125703 3126341 3127078 "VIEWDEF" 3128563 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1248 3115039 3117251 3119424 "VIEW3D" 3123552 T VIEW3D (NIL) -8 NIL NIL NIL) (-1247 3107321 3108950 3110529 "VIEW2D" 3113482 T VIEW2D (NIL) -8 NIL NIL NIL) (-1246 3102725 3107091 3107183 "VECTOR" 3107264 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1245 3101302 3101561 3101879 "VECTOR2" 3102455 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1244 3094829 3099086 3099129 "VECTCAT" 3100122 NIL VECTCAT (NIL T) -9 NIL 3100708 NIL) (-1243 3093843 3094097 3094487 "VECTCAT-" 3094492 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1242 3093324 3093494 3093614 "VARIABLE" 3093758 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1241 3093257 3093262 3093292 "UTYPE" 3093297 T UTYPE (NIL) -9 NIL NIL NIL) (-1240 3092087 3092241 3092503 "UTSODETL" 3093083 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1239 3089527 3089987 3090511 "UTSODE" 3091628 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1238 3081403 3087153 3087642 "UTS" 3089096 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1237 3072646 3077970 3078013 "UTSCAT" 3079125 NIL UTSCAT (NIL T) -9 NIL 3079882 NIL) (-1236 3070001 3070716 3071705 "UTSCAT-" 3071710 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1235 3069628 3069671 3069804 "UTS2" 3069952 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1234 3063901 3066466 3066509 "URAGG" 3068579 NIL URAGG (NIL T) -9 NIL 3069302 NIL) (-1233 3060840 3061703 3062826 "URAGG-" 3062831 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1232 3056564 3059454 3059926 "UPXSSING" 3060504 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1231 3048666 3055811 3056084 "UPXS" 3056349 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1230 3041779 3048570 3048642 "UPXSCONS" 3048647 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1229 3032024 3038774 3038836 "UPXSCCA" 3039410 NIL UPXSCCA (NIL T T) -9 NIL 3039643 NIL) (-1228 3031662 3031747 3031921 "UPXSCCA-" 3031926 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1227 3021760 3028283 3028326 "UPXSCAT" 3028974 NIL UPXSCAT (NIL T) -9 NIL 3029582 NIL) (-1226 3021190 3021269 3021448 "UPXS2" 3021675 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1225 3019844 3020097 3020448 "UPSQFREE" 3020933 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1224 3013632 3016646 3016701 "UPSCAT" 3017862 NIL UPSCAT (NIL T T) -9 NIL 3018636 NIL) (-1223 3012836 3013043 3013370 "UPSCAT-" 3013375 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1222 2998686 3006684 3006727 "UPOLYC" 3008828 NIL UPOLYC (NIL T) -9 NIL 3010049 NIL) (-1221 2990015 2992440 2995587 "UPOLYC-" 2995592 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1220 2989642 2989685 2989818 "UPOLYC2" 2989966 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1219 2981216 2989325 2989454 "UP" 2989561 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1218 2980555 2980662 2980826 "UPMP" 2981105 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1217 2980108 2980189 2980328 "UPDIVP" 2980468 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1216 2978676 2978925 2979241 "UPDECOMP" 2979857 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1215 2977911 2978023 2978208 "UPCDEN" 2978560 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1214 2977430 2977499 2977648 "UP2" 2977836 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1213 2975947 2976634 2976911 "UNISEG" 2977188 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1212 2975162 2975289 2975494 "UNISEG2" 2975790 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1211 2974222 2974402 2974628 "UNIFACT" 2974978 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1210 2958189 2973399 2973650 "ULS" 2974029 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1209 2946229 2958093 2958165 "ULSCONS" 2958170 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1208 2928845 2940787 2940849 "ULSCCAT" 2941487 NIL ULSCCAT (NIL T T) -9 NIL 2941775 NIL) (-1207 2927895 2928140 2928528 "ULSCCAT-" 2928533 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1206 2917770 2924207 2924250 "ULSCAT" 2925113 NIL ULSCAT (NIL T) -9 NIL 2925843 NIL) (-1205 2917200 2917279 2917458 "ULS2" 2917685 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1204 2915603 2916526 2916556 "UFD" 2916768 T UFD (NIL) -9 NIL 2916882 NIL) (-1203 2915397 2915443 2915538 "UFD-" 2915543 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1202 2914479 2914662 2914878 "UDVO" 2915203 T UDVO (NIL) -7 NIL NIL NIL) (-1201 2912295 2912704 2913175 "UDPO" 2914043 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1200 2912228 2912233 2912263 "TYPE" 2912268 T TYPE (NIL) -9 NIL NIL NIL) (-1199 2912015 2912183 2912214 "TYPEAST" 2912219 T TYPEAST (NIL) -8 NIL NIL NIL) (-1198 2910986 2911188 2911428 "TWOFACT" 2911809 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1197 2910058 2910395 2910630 "TUPLE" 2910786 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1196 2907749 2908268 2908807 "TUBETOOL" 2909541 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1195 2906598 2906803 2907044 "TUBE" 2907542 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1194 2901362 2905570 2905853 "TS" 2906350 NIL TS (NIL T) -8 NIL NIL NIL) (-1193 2890029 2894121 2894218 "TSETCAT" 2899487 NIL TSETCAT (NIL T T T T) -9 NIL 2901018 NIL) (-1192 2884764 2886361 2888252 "TSETCAT-" 2888257 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1191 2879027 2879873 2880815 "TRMANIP" 2883900 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1190 2878468 2878531 2878694 "TRIMAT" 2878959 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1189 2876264 2876501 2876865 "TRIGMNIP" 2878217 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1188 2875784 2875897 2875927 "TRIGCAT" 2876140 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1187 2875453 2875532 2875673 "TRIGCAT-" 2875678 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1186 2872350 2874311 2874592 "TREE" 2875207 NIL TREE (NIL T) -8 NIL NIL NIL) (-1185 2871624 2872152 2872182 "TRANFUN" 2872217 T TRANFUN (NIL) -9 NIL 2872283 NIL) (-1184 2870903 2871094 2871374 "TRANFUN-" 2871379 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1183 2870707 2870739 2870800 "TOPSP" 2870864 T TOPSP (NIL) -7 NIL NIL NIL) (-1182 2870055 2870170 2870324 "TOOLSIGN" 2870588 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1181 2868716 2869232 2869471 "TEXTFILE" 2869838 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1180 2866655 2867169 2867598 "TEX" 2868309 T TEX (NIL) -8 NIL NIL NIL) (-1179 2866436 2866467 2866539 "TEX1" 2866618 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1178 2866084 2866147 2866237 "TEMUTL" 2866368 T TEMUTL (NIL) -7 NIL NIL NIL) (-1177 2864238 2864518 2864843 "TBCMPPK" 2865807 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1176 2856126 2862398 2862454 "TBAGG" 2862854 NIL TBAGG (NIL T T) -9 NIL 2863065 NIL) (-1175 2851196 2852684 2854438 "TBAGG-" 2854443 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1174 2850580 2850687 2850832 "TANEXP" 2851085 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1173 2844081 2850437 2850530 "TABLE" 2850535 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1172 2843493 2843592 2843730 "TABLEAU" 2843978 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1171 2838101 2839321 2840569 "TABLBUMP" 2842279 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1170 2837529 2837629 2837757 "SYSTEM" 2837995 T SYSTEM (NIL) -7 NIL NIL NIL) (-1169 2833992 2834687 2835470 "SYSSOLP" 2836780 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1168 2830326 2831253 2831969 "SYNTAX" 2833298 T SYNTAX (NIL) -8 NIL NIL NIL) (-1167 2827484 2828086 2828718 "SYMTAB" 2829716 T SYMTAB (NIL) -8 NIL NIL NIL) (-1166 2822733 2823635 2824618 "SYMS" 2826523 T SYMS (NIL) -8 NIL NIL NIL) (-1165 2820005 2822191 2822421 "SYMPOLY" 2822538 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1164 2819522 2819597 2819720 "SYMFUNC" 2819917 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1163 2815574 2816834 2817647 "SYMBOL" 2818731 T SYMBOL (NIL) -8 NIL NIL NIL) (-1162 2809113 2810802 2812522 "SWITCH" 2813876 T SWITCH (NIL) -8 NIL NIL NIL) (-1161 2802383 2807934 2808237 "SUTS" 2808868 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2794484 2801630 2801903 "SUPXS" 2802168 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1159 2786014 2794102 2794228 "SUP" 2794393 NIL SUP (NIL T) -8 NIL NIL NIL) (-1158 2785173 2785300 2785517 "SUPFRACF" 2785882 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1157 2784794 2784853 2784966 "SUP2" 2785108 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1156 2783207 2783481 2783844 "SUMRF" 2784493 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1155 2782521 2782587 2782786 "SUMFS" 2783128 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1154 2766528 2781698 2781949 "SULS" 2782328 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1153 2766157 2766350 2766420 "SUCHTAST" 2766480 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1152 2765479 2765682 2765822 "SUCH" 2766065 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1151 2759373 2760385 2761344 "SUBSPACE" 2764567 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1150 2758803 2758893 2759057 "SUBRESP" 2759261 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1149 2752172 2753468 2754779 "STTF" 2757539 NIL STTF (NIL T) -7 NIL NIL NIL) (-1148 2746345 2747465 2748612 "STTFNC" 2751072 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1147 2737660 2739527 2741321 "STTAYLOR" 2744586 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1146 2730904 2737524 2737607 "STRTBL" 2737612 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1145 2726295 2730859 2730890 "STRING" 2730895 T STRING (NIL) -8 NIL NIL NIL) (-1144 2721183 2725668 2725698 "STRICAT" 2725757 T STRICAT (NIL) -9 NIL 2725819 NIL) (-1143 2713993 2718802 2719413 "STREAM" 2720607 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1142 2713503 2713580 2713724 "STREAM3" 2713910 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1141 2712485 2712668 2712903 "STREAM2" 2713316 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1140 2712173 2712225 2712318 "STREAM1" 2712427 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1139 2711189 2711370 2711601 "STINPROD" 2711989 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1138 2710767 2710951 2710981 "STEP" 2711061 T STEP (NIL) -9 NIL 2711139 NIL) (-1137 2704310 2710666 2710743 "STBL" 2710748 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1136 2699484 2703531 2703574 "STAGG" 2703727 NIL STAGG (NIL T) -9 NIL 2703816 NIL) (-1135 2697186 2697788 2698660 "STAGG-" 2698665 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1134 2695381 2696956 2697048 "STACK" 2697129 NIL STACK (NIL T) -8 NIL NIL NIL) (-1133 2688106 2693522 2693978 "SREGSET" 2695011 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1132 2680532 2681900 2683413 "SRDCMPK" 2686712 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1131 2673499 2677972 2678002 "SRAGG" 2679305 T SRAGG (NIL) -9 NIL 2679913 NIL) (-1130 2672516 2672771 2673150 "SRAGG-" 2673155 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1129 2667011 2671463 2671884 "SQMATRIX" 2672142 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1128 2660760 2663729 2664456 "SPLTREE" 2666356 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1127 2656750 2657416 2658062 "SPLNODE" 2660186 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1126 2655797 2656030 2656060 "SPFCAT" 2656504 T SPFCAT (NIL) -9 NIL NIL NIL) (-1125 2654534 2654744 2655008 "SPECOUT" 2655555 T SPECOUT (NIL) -7 NIL NIL NIL) (-1124 2646186 2647930 2647960 "SPADXPT" 2652352 T SPADXPT (NIL) -9 NIL 2654386 NIL) (-1123 2645947 2645987 2646056 "SPADPRSR" 2646139 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1122 2644130 2645902 2645933 "SPADAST" 2645938 T SPADAST (NIL) -8 NIL NIL NIL) (-1121 2636101 2637848 2637891 "SPACEC" 2642264 NIL SPACEC (NIL T) -9 NIL 2644080 NIL) (-1120 2634272 2636033 2636082 "SPACE3" 2636087 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1119 2633024 2633195 2633486 "SORTPAK" 2634077 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1118 2631074 2631377 2631796 "SOLVETRA" 2632688 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1117 2630085 2630307 2630581 "SOLVESER" 2630847 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1116 2625305 2626186 2627188 "SOLVERAD" 2629137 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1115 2621120 2621729 2622458 "SOLVEFOR" 2624672 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1114 2615417 2620469 2620566 "SNTSCAT" 2620571 NIL SNTSCAT (NIL T T T T) -9 NIL 2620641 NIL) (-1113 2609560 2613740 2614131 "SMTS" 2615107 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1112 2604011 2609448 2609525 "SMP" 2609530 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1111 2602170 2602471 2602869 "SMITH" 2603708 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1110 2595065 2599221 2599324 "SMATCAT" 2600675 NIL SMATCAT (NIL NIL T T T) -9 NIL 2601225 NIL) (-1109 2592005 2592828 2594006 "SMATCAT-" 2594011 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1108 2589718 2591241 2591284 "SKAGG" 2591545 NIL SKAGG (NIL T) -9 NIL 2591680 NIL) (-1107 2586060 2589134 2589329 "SINT" 2589516 T SINT (NIL) -8 NIL NIL 2589689) (-1106 2585832 2585870 2585936 "SIMPAN" 2586016 T SIMPAN (NIL) -7 NIL NIL NIL) (-1105 2585139 2585367 2585507 "SIG" 2585714 T SIG (NIL) -8 NIL NIL NIL) (-1104 2583977 2584198 2584473 "SIGNRF" 2584898 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1103 2582782 2582933 2583224 "SIGNEF" 2583806 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1102 2582115 2582365 2582489 "SIGAST" 2582680 T SIGAST (NIL) -8 NIL NIL NIL) (-1101 2579805 2580259 2580765 "SHP" 2581656 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1100 2573711 2579706 2579782 "SHDP" 2579787 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1099 2573310 2573476 2573506 "SGROUP" 2573599 T SGROUP (NIL) -9 NIL 2573661 NIL) (-1098 2573168 2573194 2573267 "SGROUP-" 2573272 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1097 2570004 2570701 2571424 "SGCF" 2572467 T SGCF (NIL) -7 NIL NIL NIL) (-1096 2564399 2569451 2569548 "SFRTCAT" 2569553 NIL SFRTCAT (NIL T T T T) -9 NIL 2569592 NIL) (-1095 2557823 2558838 2559974 "SFRGCD" 2563382 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1094 2550951 2552022 2553208 "SFQCMPK" 2556756 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1093 2550573 2550662 2550772 "SFORT" 2550892 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1092 2549718 2550413 2550534 "SEXOF" 2550539 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1091 2548852 2549599 2549667 "SEX" 2549672 T SEX (NIL) -8 NIL NIL NIL) (-1090 2544391 2545080 2545175 "SEXCAT" 2548112 NIL SEXCAT (NIL T T T T T) -9 NIL 2548690 NIL) (-1089 2541571 2544325 2544373 "SET" 2544378 NIL SET (NIL T) -8 NIL NIL NIL) (-1088 2539822 2540284 2540589 "SETMN" 2541312 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1087 2539428 2539554 2539584 "SETCAT" 2539701 T SETCAT (NIL) -9 NIL 2539786 NIL) (-1086 2539208 2539260 2539359 "SETCAT-" 2539364 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1085 2535595 2537669 2537712 "SETAGG" 2538582 NIL SETAGG (NIL T) -9 NIL 2538922 NIL) (-1084 2535053 2535169 2535406 "SETAGG-" 2535411 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1083 2534523 2534749 2534850 "SEQAST" 2534974 T SEQAST (NIL) -8 NIL NIL NIL) (-1082 2533722 2534016 2534077 "SEGXCAT" 2534363 NIL SEGXCAT (NIL T T) -9 NIL 2534483 NIL) (-1081 2532778 2533388 2533570 "SEG" 2533575 NIL SEG (NIL T) -8 NIL NIL NIL) (-1080 2531757 2531971 2532014 "SEGCAT" 2532536 NIL SEGCAT (NIL T) -9 NIL 2532757 NIL) (-1079 2530806 2531136 2531336 "SEGBIND" 2531592 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1078 2530427 2530486 2530599 "SEGBIND2" 2530741 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1077 2530028 2530228 2530305 "SEGAST" 2530372 T SEGAST (NIL) -8 NIL NIL NIL) (-1076 2529247 2529373 2529577 "SEG2" 2529872 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1075 2528684 2529182 2529229 "SDVAR" 2529234 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1074 2520974 2528454 2528584 "SDPOL" 2528589 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1073 2519567 2519833 2520152 "SCPKG" 2520689 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1072 2518703 2518883 2519083 "SCOPE" 2519389 T SCOPE (NIL) -8 NIL NIL NIL) (-1071 2517924 2518057 2518236 "SCACHE" 2518558 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1070 2517596 2517756 2517786 "SASTCAT" 2517791 T SASTCAT (NIL) -9 NIL 2517804 NIL) (-1069 2517110 2517431 2517507 "SAOS" 2517542 T SAOS (NIL) -8 NIL NIL NIL) (-1068 2516675 2516710 2516883 "SAERFFC" 2517069 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1067 2510649 2516572 2516652 "SAE" 2516657 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1066 2510242 2510277 2510436 "SAEFACT" 2510608 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1065 2508563 2508877 2509278 "RURPK" 2509908 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1064 2507199 2507478 2507790 "RULESET" 2508397 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1063 2504386 2504889 2505354 "RULE" 2506880 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1062 2504025 2504180 2504263 "RULECOLD" 2504338 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1061 2503523 2503742 2503836 "RSTRCAST" 2503953 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1060 2498372 2499166 2500086 "RSETGCD" 2502722 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1059 2487629 2492681 2492778 "RSETCAT" 2496897 NIL RSETCAT (NIL T T T T) -9 NIL 2497994 NIL) (-1058 2485556 2486095 2486919 "RSETCAT-" 2486924 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1057 2477943 2479318 2480838 "RSDCMPK" 2484155 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1056 2475948 2476389 2476463 "RRCC" 2477549 NIL RRCC (NIL T T) -9 NIL 2477893 NIL) (-1055 2475299 2475473 2475752 "RRCC-" 2475757 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1054 2474769 2474995 2475096 "RPTAST" 2475220 T RPTAST (NIL) -8 NIL NIL NIL) (-1053 2448775 2458362 2458429 "RPOLCAT" 2469093 NIL RPOLCAT (NIL T T T) -9 NIL 2472252 NIL) (-1052 2440275 2442613 2445735 "RPOLCAT-" 2445740 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1051 2431322 2438486 2438968 "ROUTINE" 2439815 T ROUTINE (NIL) -8 NIL NIL NIL) (-1050 2428155 2430948 2431088 "ROMAN" 2431204 T ROMAN (NIL) -8 NIL NIL NIL) (-1049 2426430 2427015 2427275 "ROIRC" 2427960 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1048 2422823 2425066 2425096 "RNS" 2425400 T RNS (NIL) -9 NIL 2425673 NIL) (-1047 2421332 2421715 2422249 "RNS-" 2422324 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1046 2420781 2421163 2421193 "RNG" 2421198 T RNG (NIL) -9 NIL 2421219 NIL) (-1045 2420173 2420535 2420578 "RMODULE" 2420640 NIL RMODULE (NIL T) -9 NIL 2420682 NIL) (-1044 2419009 2419103 2419439 "RMCAT2" 2420074 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1043 2415886 2418355 2418652 "RMATRIX" 2418771 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1042 2408828 2411062 2411177 "RMATCAT" 2414536 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2415518 NIL) (-1041 2408203 2408350 2408657 "RMATCAT-" 2408662 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1040 2407770 2407845 2407973 "RINTERP" 2408122 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1039 2406903 2407423 2407453 "RING" 2407509 T RING (NIL) -9 NIL 2407595 NIL) (-1038 2406695 2406739 2406836 "RING-" 2406841 NIL RING- (NIL T) -8 NIL NIL NIL) (-1037 2405536 2405773 2406031 "RIDIST" 2406459 T RIDIST (NIL) -7 NIL NIL NIL) (-1036 2396852 2405004 2405210 "RGCHAIN" 2405384 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1035 2396228 2396608 2396649 "RGBCSPC" 2396707 NIL RGBCSPC (NIL T) -9 NIL 2396759 NIL) (-1034 2395412 2395767 2395808 "RGBCMDL" 2396040 NIL RGBCMDL (NIL T) -9 NIL 2396154 NIL) (-1033 2392406 2393020 2393690 "RF" 2394776 NIL RF (NIL T) -7 NIL NIL NIL) (-1032 2392052 2392115 2392218 "RFFACTOR" 2392337 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1031 2391777 2391812 2391909 "RFFACT" 2392011 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1030 2389894 2390258 2390640 "RFDIST" 2391417 T RFDIST (NIL) -7 NIL NIL NIL) (-1029 2389347 2389439 2389602 "RETSOL" 2389796 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1028 2388983 2389063 2389106 "RETRACT" 2389239 NIL RETRACT (NIL T) -9 NIL 2389326 NIL) (-1027 2388832 2388857 2388944 "RETRACT-" 2388949 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1026 2388461 2388654 2388724 "RETAST" 2388784 T RETAST (NIL) -8 NIL NIL NIL) (-1025 2381315 2388114 2388241 "RESULT" 2388356 T RESULT (NIL) -8 NIL NIL NIL) (-1024 2379941 2380584 2380783 "RESRING" 2381218 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1023 2379577 2379626 2379724 "RESLATC" 2379878 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1022 2379283 2379317 2379424 "REPSQ" 2379536 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1021 2376705 2377285 2377887 "REP" 2378703 T REP (NIL) -7 NIL NIL NIL) (-1020 2376403 2376437 2376548 "REPDB" 2376664 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1019 2370313 2371692 2372915 "REP2" 2375215 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1018 2366690 2367371 2368179 "REP1" 2369540 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1017 2359416 2364831 2365287 "REGSET" 2366320 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2358229 2358564 2358814 "REF" 2359201 NIL REF (NIL T) -8 NIL NIL NIL) (-1015 2357606 2357709 2357876 "REDORDER" 2358113 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1014 2353611 2356819 2357046 "RECLOS" 2357434 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1013 2352663 2352844 2353059 "REALSOLV" 2353418 T REALSOLV (NIL) -7 NIL NIL NIL) (-1012 2352509 2352550 2352580 "REAL" 2352585 T REAL (NIL) -9 NIL 2352620 NIL) (-1011 2348992 2349794 2350678 "REAL0Q" 2351674 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1010 2344593 2345581 2346642 "REAL0" 2347973 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1009 2344091 2344310 2344404 "RDUCEAST" 2344521 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1008 2343496 2343568 2343775 "RDIV" 2344013 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1007 2342564 2342738 2342951 "RDIST" 2343318 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1006 2341161 2341448 2341820 "RDETRS" 2342272 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1005 2338973 2339427 2339965 "RDETR" 2340703 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1004 2337584 2337862 2338266 "RDEEFS" 2338689 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1003 2336079 2336385 2336817 "RDEEF" 2337272 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1002 2330340 2333215 2333245 "RCFIELD" 2334540 T RCFIELD (NIL) -9 NIL 2335270 NIL) (-1001 2328404 2328908 2329604 "RCFIELD-" 2329679 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1000 2324720 2326505 2326548 "RCAGG" 2327632 NIL RCAGG (NIL T) -9 NIL 2328097 NIL) (-999 2324350 2324444 2324605 "RCAGG-" 2324610 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-998 2323690 2323802 2323965 "RATRET" 2324234 NIL RATRET (NIL T) -7 NIL NIL NIL) (-997 2323247 2323314 2323433 "RATFACT" 2323618 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-996 2322562 2322682 2322832 "RANDSRC" 2323117 T RANDSRC (NIL) -7 NIL NIL NIL) (-995 2322299 2322343 2322414 "RADUTIL" 2322511 T RADUTIL (NIL) -7 NIL NIL NIL) (-994 2315461 2321141 2321449 "RADIX" 2322023 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-993 2307118 2315305 2315433 "RADFF" 2315438 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-992 2306770 2306845 2306873 "RADCAT" 2307030 T RADCAT (NIL) -9 NIL NIL NIL) (-991 2306555 2306603 2306700 "RADCAT-" 2306705 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-990 2304706 2306330 2306419 "QUEUE" 2306499 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-989 2301282 2304643 2304688 "QUAT" 2304693 NIL QUAT (NIL T) -8 NIL NIL NIL) (-988 2300920 2300963 2301090 "QUATCT2" 2301233 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-987 2294667 2297969 2298009 "QUATCAT" 2298789 NIL QUATCAT (NIL T) -9 NIL 2299555 NIL) (-986 2290811 2291848 2293235 "QUATCAT-" 2293329 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-985 2288331 2289895 2289936 "QUAGG" 2290311 NIL QUAGG (NIL T) -9 NIL 2290486 NIL) (-984 2287963 2288156 2288224 "QQUTAST" 2288283 T QQUTAST (NIL) -8 NIL NIL NIL) (-983 2286888 2287361 2287533 "QFORM" 2287835 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-982 2278100 2283305 2283345 "QFCAT" 2284003 NIL QFCAT (NIL T) -9 NIL 2285004 NIL) (-981 2273672 2274873 2276464 "QFCAT-" 2276558 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-980 2273310 2273353 2273480 "QFCAT2" 2273623 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-979 2272770 2272880 2273010 "QEQUAT" 2273200 T QEQUAT (NIL) -8 NIL NIL NIL) (-978 2265918 2266989 2268173 "QCMPACK" 2271703 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-977 2263494 2263915 2264343 "QALGSET" 2265573 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-976 2262739 2262913 2263145 "QALGSET2" 2263314 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-975 2261430 2261653 2261970 "PWFFINTB" 2262512 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-974 2259612 2259780 2260134 "PUSHVAR" 2261244 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-973 2255530 2256584 2256625 "PTRANFN" 2258509 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-972 2253932 2254223 2254545 "PTPACK" 2255241 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-971 2253564 2253621 2253730 "PTFUNC2" 2253869 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-970 2248091 2252436 2252477 "PTCAT" 2252773 NIL PTCAT (NIL T) -9 NIL 2252926 NIL) (-969 2247749 2247784 2247908 "PSQFR" 2248050 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-968 2246344 2246642 2246976 "PSEUDLIN" 2247447 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-967 2233114 2235478 2237802 "PSETPK" 2244104 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-966 2226158 2228872 2228968 "PSETCAT" 2231989 NIL PSETCAT (NIL T T T T) -9 NIL 2232803 NIL) (-965 2223994 2224628 2225449 "PSETCAT-" 2225454 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-964 2223343 2223508 2223536 "PSCURVE" 2223804 T PSCURVE (NIL) -9 NIL 2223971 NIL) (-963 2219699 2221181 2221246 "PSCAT" 2222090 NIL PSCAT (NIL T T T) -9 NIL 2222330 NIL) (-962 2218762 2218978 2219378 "PSCAT-" 2219383 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-961 2217494 2218127 2218332 "PRTITION" 2218577 T PRTITION (NIL) -8 NIL NIL NIL) (-960 2216996 2217215 2217307 "PRTDAST" 2217422 T PRTDAST (NIL) -8 NIL NIL NIL) (-959 2206094 2208300 2210488 "PRS" 2214858 NIL PRS (NIL T T) -7 NIL NIL NIL) (-958 2203952 2205444 2205484 "PRQAGG" 2205667 NIL PRQAGG (NIL T) -9 NIL 2205769 NIL) (-957 2203338 2203567 2203595 "PROPLOG" 2203780 T PROPLOG (NIL) -9 NIL 2203902 NIL) (-956 2200508 2201152 2201616 "PROPFRML" 2202906 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-955 2199968 2200078 2200208 "PROPERTY" 2200398 T PROPERTY (NIL) -8 NIL NIL NIL) (-954 2194053 2198134 2198954 "PRODUCT" 2199194 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-953 2191366 2193511 2193745 "PR" 2193864 NIL PR (NIL T T) -8 NIL NIL NIL) (-952 2191162 2191194 2191253 "PRINT" 2191327 T PRINT (NIL) -7 NIL NIL NIL) (-951 2190502 2190619 2190771 "PRIMES" 2191042 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-950 2188567 2188968 2189434 "PRIMELT" 2190081 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-949 2188296 2188345 2188373 "PRIMCAT" 2188497 T PRIMCAT (NIL) -9 NIL NIL NIL) (-948 2184457 2188234 2188279 "PRIMARR" 2188284 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-947 2183464 2183642 2183870 "PRIMARR2" 2184275 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-946 2183107 2183163 2183274 "PREASSOC" 2183402 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-945 2182582 2182715 2182743 "PPCURVE" 2182948 T PPCURVE (NIL) -9 NIL 2183084 NIL) (-944 2182204 2182377 2182460 "PORTNUM" 2182519 T PORTNUM (NIL) -8 NIL NIL NIL) (-943 2179563 2179962 2180554 "POLYROOT" 2181785 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-942 2173508 2179167 2179327 "POLY" 2179436 NIL POLY (NIL T) -8 NIL NIL NIL) (-941 2172891 2172949 2173183 "POLYLIFT" 2173444 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-940 2169166 2169615 2170244 "POLYCATQ" 2172436 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-939 2155983 2161341 2161406 "POLYCAT" 2164920 NIL POLYCAT (NIL T T T) -9 NIL 2166848 NIL) (-938 2149433 2151294 2153678 "POLYCAT-" 2153683 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-937 2149020 2149088 2149208 "POLY2UP" 2149359 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-936 2148652 2148709 2148818 "POLY2" 2148957 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-935 2147337 2147576 2147852 "POLUTIL" 2148426 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-934 2145692 2145969 2146300 "POLTOPOL" 2147059 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-933 2141210 2145628 2145674 "POINT" 2145679 NIL POINT (NIL T) -8 NIL NIL NIL) (-932 2139397 2139754 2140129 "PNTHEORY" 2140855 T PNTHEORY (NIL) -7 NIL NIL NIL) (-931 2137816 2138113 2138525 "PMTOOLS" 2139095 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-930 2137409 2137487 2137604 "PMSYM" 2137732 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-929 2136919 2136988 2137162 "PMQFCAT" 2137334 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-928 2136274 2136384 2136540 "PMPRED" 2136796 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-927 2135670 2135756 2135917 "PMPREDFS" 2136175 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-926 2134313 2134521 2134906 "PMPLCAT" 2135432 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-925 2133845 2133924 2134076 "PMLSAGG" 2134228 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-924 2133320 2133396 2133577 "PMKERNEL" 2133763 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-923 2132937 2133012 2133125 "PMINS" 2133239 NIL PMINS (NIL T) -7 NIL NIL NIL) (-922 2132365 2132434 2132650 "PMFS" 2132862 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-921 2131593 2131711 2131916 "PMDOWN" 2132242 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-920 2130756 2130915 2131097 "PMASS" 2131431 T PMASS (NIL) -7 NIL NIL NIL) (-919 2130030 2130141 2130304 "PMASSFS" 2130642 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-918 2129685 2129753 2129847 "PLOTTOOL" 2129956 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-917 2124307 2125496 2126644 "PLOT" 2128557 T PLOT (NIL) -8 NIL NIL NIL) (-916 2120121 2121155 2122076 "PLOT3D" 2123406 T PLOT3D (NIL) -8 NIL NIL NIL) (-915 2119033 2119210 2119445 "PLOT1" 2119925 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-914 2094427 2099099 2103950 "PLEQN" 2114299 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-913 2093745 2093867 2094047 "PINTERP" 2094292 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-912 2093438 2093485 2093588 "PINTERPA" 2093692 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-911 2092686 2093207 2093294 "PI" 2093334 T PI (NIL) -8 NIL NIL 2093401) (-910 2091083 2092024 2092052 "PID" 2092234 T PID (NIL) -9 NIL 2092368 NIL) (-909 2090808 2090845 2090933 "PICOERCE" 2091040 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-908 2090128 2090267 2090443 "PGROEB" 2090664 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-907 2085715 2086529 2087434 "PGE" 2089243 T PGE (NIL) -7 NIL NIL NIL) (-906 2083839 2084085 2084451 "PGCD" 2085432 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-905 2083177 2083280 2083441 "PFRPAC" 2083723 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-904 2079857 2081725 2082078 "PFR" 2082856 NIL PFR (NIL T) -8 NIL NIL NIL) (-903 2078246 2078490 2078815 "PFOTOOLS" 2079604 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-902 2076779 2077018 2077369 "PFOQ" 2078003 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-901 2075252 2075464 2075827 "PFO" 2076563 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-900 2071840 2075141 2075210 "PF" 2075215 NIL PF (NIL NIL) -8 NIL NIL NIL) (-899 2069274 2070511 2070539 "PFECAT" 2071124 T PFECAT (NIL) -9 NIL 2071508 NIL) (-898 2068719 2068873 2069087 "PFECAT-" 2069092 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-897 2067323 2067574 2067875 "PFBRU" 2068468 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-896 2065190 2065541 2065973 "PFBR" 2066974 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-895 2061106 2062566 2063242 "PERM" 2064547 NIL PERM (NIL T) -8 NIL NIL NIL) (-894 2056372 2057313 2058183 "PERMGRP" 2060269 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-893 2054504 2055435 2055476 "PERMCAT" 2055922 NIL PERMCAT (NIL T) -9 NIL 2056227 NIL) (-892 2054157 2054198 2054322 "PERMAN" 2054457 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-891 2051693 2053822 2053944 "PENDTREE" 2054068 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-890 2049786 2050520 2050561 "PDRING" 2051218 NIL PDRING (NIL T) -9 NIL 2051504 NIL) (-889 2048889 2049107 2049469 "PDRING-" 2049474 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-888 2046131 2046882 2047550 "PDEPROB" 2048241 T PDEPROB (NIL) -8 NIL NIL NIL) (-887 2043678 2044180 2044735 "PDEPACK" 2045596 T PDEPACK (NIL) -7 NIL NIL NIL) (-886 2042590 2042780 2043031 "PDECOMP" 2043477 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-885 2040195 2041012 2041040 "PDECAT" 2041827 T PDECAT (NIL) -9 NIL 2042540 NIL) (-884 2039946 2039979 2040069 "PCOMP" 2040156 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-883 2038151 2038747 2039044 "PBWLB" 2039675 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-882 2030656 2032224 2033562 "PATTERN" 2036834 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-881 2030288 2030345 2030454 "PATTERN2" 2030593 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-880 2028045 2028433 2028890 "PATTERN1" 2029877 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-879 2025440 2025994 2026475 "PATRES" 2027610 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-878 2025004 2025071 2025203 "PATRES2" 2025367 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-877 2022887 2023292 2023699 "PATMATCH" 2024671 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-876 2022423 2022606 2022647 "PATMAB" 2022754 NIL PATMAB (NIL T) -9 NIL 2022837 NIL) (-875 2020968 2021277 2021535 "PATLRES" 2022228 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-874 2020514 2020637 2020678 "PATAB" 2020683 NIL PATAB (NIL T) -9 NIL 2020855 NIL) (-873 2017995 2018527 2019100 "PARTPERM" 2019961 T PARTPERM (NIL) -7 NIL NIL NIL) (-872 2017616 2017679 2017781 "PARSURF" 2017926 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-871 2017248 2017305 2017414 "PARSU2" 2017553 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-870 2017012 2017052 2017119 "PARSER" 2017201 T PARSER (NIL) -7 NIL NIL NIL) (-869 2016633 2016696 2016798 "PARSCURV" 2016943 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-868 2016265 2016322 2016431 "PARSC2" 2016570 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-867 2015904 2015962 2016059 "PARPCURV" 2016201 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-866 2015536 2015593 2015702 "PARPC2" 2015841 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-865 2015056 2015142 2015261 "PAN2EXPR" 2015437 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-864 2013862 2014177 2014405 "PALETTE" 2014848 T PALETTE (NIL) -8 NIL NIL NIL) (-863 2012330 2012867 2013227 "PAIR" 2013548 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-862 2006236 2011589 2011783 "PADICRC" 2012185 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-861 1999500 2005582 2005766 "PADICRAT" 2006084 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-860 1997850 1999437 1999482 "PADIC" 1999487 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-859 1995060 1996590 1996630 "PADICCT" 1997211 NIL PADICCT (NIL NIL) -9 NIL 1997493 NIL) (-858 1994017 1994217 1994485 "PADEPAC" 1994847 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-857 1993229 1993362 1993568 "PADE" 1993879 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-856 1991651 1992437 1992717 "OWP" 1993033 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-855 1990724 1991256 1991428 "OVAR" 1991519 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-854 1989988 1990109 1990270 "OUT" 1990583 T OUT (NIL) -7 NIL NIL NIL) (-853 1978895 1981097 1983297 "OUTFORM" 1987808 T OUTFORM (NIL) -8 NIL NIL NIL) (-852 1978311 1978492 1978619 "OUTBFILE" 1978788 T OUTBFILE (NIL) -8 NIL NIL NIL) (-851 1977933 1978021 1978049 "OUTBCON" 1978205 T OUTBCON (NIL) -9 NIL 1978295 NIL) (-850 1977776 1977810 1977885 "OUTBCON-" 1977890 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-849 1977184 1977505 1977594 "OSI" 1977707 T OSI (NIL) -8 NIL NIL NIL) (-848 1976740 1977052 1977080 "OSGROUP" 1977085 T OSGROUP (NIL) -9 NIL 1977107 NIL) (-847 1975485 1975712 1975997 "ORTHPOL" 1976487 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-846 1973071 1975320 1975441 "OREUP" 1975446 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-845 1970509 1972762 1972889 "ORESUP" 1973013 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-844 1968037 1968537 1969098 "OREPCTO" 1969998 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-843 1961861 1964028 1964069 "OREPCAT" 1966417 NIL OREPCAT (NIL T) -9 NIL 1967521 NIL) (-842 1959008 1959790 1960848 "OREPCAT-" 1960853 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-841 1958185 1958457 1958485 "ORDSET" 1958794 T ORDSET (NIL) -9 NIL 1958958 NIL) (-840 1957704 1957826 1958019 "ORDSET-" 1958024 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-839 1956338 1957095 1957123 "ORDRING" 1957325 T ORDRING (NIL) -9 NIL 1957450 NIL) (-838 1955983 1956077 1956221 "ORDRING-" 1956226 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-837 1955389 1955826 1955854 "ORDMON" 1955859 T ORDMON (NIL) -9 NIL 1955880 NIL) (-836 1954551 1954698 1954893 "ORDFUNS" 1955238 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-835 1953915 1954308 1954336 "ORDFIN" 1954401 T ORDFIN (NIL) -9 NIL 1954475 NIL) (-834 1950507 1952501 1952910 "ORDCOMP" 1953539 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-833 1949773 1949900 1950086 "ORDCOMP2" 1950367 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-832 1946381 1947264 1948078 "OPTPROB" 1948979 T OPTPROB (NIL) -8 NIL NIL NIL) (-831 1943183 1943822 1944526 "OPTPACK" 1945697 T OPTPACK (NIL) -7 NIL NIL NIL) (-830 1940896 1941636 1941664 "OPTCAT" 1942483 T OPTCAT (NIL) -9 NIL 1943133 NIL) (-829 1940339 1940573 1940678 "OPSIG" 1940811 T OPSIG (NIL) -8 NIL NIL NIL) (-828 1940107 1940146 1940212 "OPQUERY" 1940293 T OPQUERY (NIL) -7 NIL NIL NIL) (-827 1937273 1938418 1938922 "OP" 1939636 NIL OP (NIL T) -8 NIL NIL NIL) (-826 1936808 1936979 1937020 "OPERCAT" 1937155 NIL OPERCAT (NIL T) -9 NIL 1937223 NIL) (-825 1936654 1936681 1936767 "OPERCAT-" 1936772 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-824 1933499 1935451 1935820 "ONECOMP" 1936318 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-823 1932804 1932919 1933093 "ONECOMP2" 1933371 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-822 1932223 1932329 1932459 "OMSERVER" 1932694 T OMSERVER (NIL) -7 NIL NIL NIL) (-821 1929111 1931663 1931703 "OMSAGG" 1931764 NIL OMSAGG (NIL T) -9 NIL 1931828 NIL) (-820 1927734 1927997 1928279 "OMPKG" 1928849 T OMPKG (NIL) -7 NIL NIL NIL) (-819 1927164 1927267 1927295 "OM" 1927594 T OM (NIL) -9 NIL NIL NIL) (-818 1925746 1926713 1926882 "OMLO" 1927045 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-817 1924671 1924818 1925045 "OMEXPR" 1925572 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-816 1923989 1924217 1924353 "OMERR" 1924555 T OMERR (NIL) -8 NIL NIL NIL) (-815 1923167 1923410 1923570 "OMERRK" 1923849 T OMERRK (NIL) -8 NIL NIL NIL) (-814 1922645 1922844 1922952 "OMENC" 1923079 T OMENC (NIL) -8 NIL NIL NIL) (-813 1916540 1917725 1918896 "OMDEV" 1921494 T OMDEV (NIL) -8 NIL NIL NIL) (-812 1915609 1915780 1915974 "OMCONN" 1916366 T OMCONN (NIL) -8 NIL NIL NIL) (-811 1914230 1915172 1915200 "OINTDOM" 1915205 T OINTDOM (NIL) -9 NIL 1915226 NIL) (-810 1910036 1911220 1911936 "OFMONOID" 1913546 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-809 1909474 1909973 1910018 "ODVAR" 1910023 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-808 1906932 1909219 1909374 "ODR" 1909379 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-807 1899276 1906708 1906834 "ODPOL" 1906839 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-806 1893152 1899148 1899253 "ODP" 1899258 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-805 1891918 1892133 1892408 "ODETOOLS" 1892926 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-804 1888887 1889543 1890259 "ODESYS" 1891251 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-803 1883769 1884677 1885702 "ODERTRIC" 1887962 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-802 1883195 1883277 1883471 "ODERED" 1883681 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-801 1880083 1880631 1881308 "ODERAT" 1882618 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-800 1877043 1877507 1878104 "ODEPRRIC" 1879612 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-799 1875013 1875582 1876068 "ODEPROB" 1876577 T ODEPROB (NIL) -8 NIL NIL NIL) (-798 1871535 1872018 1872665 "ODEPRIM" 1874492 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-797 1870784 1870886 1871146 "ODEPAL" 1871427 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-796 1866946 1867737 1868601 "ODEPACK" 1869940 T ODEPACK (NIL) -7 NIL NIL NIL) (-795 1865979 1866086 1866315 "ODEINT" 1866835 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-794 1860080 1861505 1862952 "ODEIFTBL" 1864552 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-793 1855415 1856201 1857160 "ODEEF" 1859239 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-792 1854750 1854839 1855069 "ODECONST" 1855320 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-791 1852901 1853536 1853564 "ODECAT" 1854169 T ODECAT (NIL) -9 NIL 1854700 NIL) (-790 1849808 1852613 1852732 "OCT" 1852814 NIL OCT (NIL T) -8 NIL NIL NIL) (-789 1849446 1849489 1849616 "OCTCT2" 1849759 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-788 1844220 1846620 1846660 "OC" 1847757 NIL OC (NIL T) -9 NIL 1848615 NIL) (-787 1841447 1842195 1843185 "OC-" 1843279 NIL OC- (NIL T T) -8 NIL NIL NIL) (-786 1840825 1841267 1841295 "OCAMON" 1841300 T OCAMON (NIL) -9 NIL 1841321 NIL) (-785 1840382 1840697 1840725 "OASGP" 1840730 T OASGP (NIL) -9 NIL 1840750 NIL) (-784 1839669 1840132 1840160 "OAMONS" 1840200 T OAMONS (NIL) -9 NIL 1840243 NIL) (-783 1839109 1839516 1839544 "OAMON" 1839549 T OAMON (NIL) -9 NIL 1839569 NIL) (-782 1838413 1838905 1838933 "OAGROUP" 1838938 T OAGROUP (NIL) -9 NIL 1838958 NIL) (-781 1838103 1838153 1838241 "NUMTUBE" 1838357 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-780 1831676 1833194 1834730 "NUMQUAD" 1836587 T NUMQUAD (NIL) -7 NIL NIL NIL) (-779 1827432 1828420 1829445 "NUMODE" 1830671 T NUMODE (NIL) -7 NIL NIL NIL) (-778 1824813 1825667 1825695 "NUMINT" 1826618 T NUMINT (NIL) -9 NIL 1827382 NIL) (-777 1823761 1823958 1824176 "NUMFMT" 1824615 T NUMFMT (NIL) -7 NIL NIL NIL) (-776 1810120 1813065 1815597 "NUMERIC" 1821268 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-775 1804517 1809569 1809664 "NTSCAT" 1809669 NIL NTSCAT (NIL T T T T) -9 NIL 1809708 NIL) (-774 1803711 1803876 1804069 "NTPOLFN" 1804356 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-773 1791551 1800536 1801348 "NSUP" 1802932 NIL NSUP (NIL T) -8 NIL NIL NIL) (-772 1791183 1791240 1791349 "NSUP2" 1791488 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-771 1781180 1790957 1791090 "NSMP" 1791095 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-770 1779612 1779913 1780270 "NREP" 1780868 NIL NREP (NIL T) -7 NIL NIL NIL) (-769 1778203 1778455 1778813 "NPCOEF" 1779355 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-768 1777269 1777384 1777600 "NORMRETR" 1778084 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-767 1775310 1775600 1776009 "NORMPK" 1776977 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-766 1774995 1775023 1775147 "NORMMA" 1775276 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-765 1774822 1774952 1774981 "NONE" 1774986 T NONE (NIL) -8 NIL NIL NIL) (-764 1774611 1774640 1774709 "NONE1" 1774786 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-763 1774094 1774156 1774342 "NODE1" 1774543 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-762 1772365 1773188 1773443 "NNI" 1773790 T NNI (NIL) -8 NIL NIL 1774025) (-761 1770785 1771098 1771462 "NLINSOL" 1772033 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-760 1767053 1768021 1768920 "NIPROB" 1769906 T NIPROB (NIL) -8 NIL NIL NIL) (-759 1765810 1766044 1766346 "NFINTBAS" 1766815 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-758 1765250 1765460 1765501 "NETCLT" 1765673 NIL NETCLT (NIL T) -9 NIL 1765755 NIL) (-757 1763958 1764189 1764470 "NCODIV" 1765018 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-756 1763720 1763757 1763832 "NCNTFRAC" 1763915 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-755 1761900 1762264 1762684 "NCEP" 1763345 NIL NCEP (NIL T) -7 NIL NIL NIL) (-754 1760811 1761550 1761578 "NASRING" 1761688 T NASRING (NIL) -9 NIL 1761762 NIL) (-753 1760606 1760650 1760744 "NASRING-" 1760749 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-752 1759759 1760258 1760286 "NARNG" 1760403 T NARNG (NIL) -9 NIL 1760494 NIL) (-751 1759451 1759518 1759652 "NARNG-" 1759657 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-750 1758330 1758537 1758772 "NAGSP" 1759236 T NAGSP (NIL) -7 NIL NIL NIL) (-749 1749602 1751286 1752959 "NAGS" 1756677 T NAGS (NIL) -7 NIL NIL NIL) (-748 1748150 1748458 1748789 "NAGF07" 1749291 T NAGF07 (NIL) -7 NIL NIL NIL) (-747 1742688 1743979 1745286 "NAGF04" 1746863 T NAGF04 (NIL) -7 NIL NIL NIL) (-746 1735656 1737270 1738903 "NAGF02" 1741075 T NAGF02 (NIL) -7 NIL NIL NIL) (-745 1730880 1731980 1733097 "NAGF01" 1734559 T NAGF01 (NIL) -7 NIL NIL NIL) (-744 1724508 1726074 1727659 "NAGE04" 1729315 T NAGE04 (NIL) -7 NIL NIL NIL) (-743 1715677 1717798 1719928 "NAGE02" 1722398 T NAGE02 (NIL) -7 NIL NIL NIL) (-742 1711630 1712577 1713541 "NAGE01" 1714733 T NAGE01 (NIL) -7 NIL NIL NIL) (-741 1709425 1709959 1710517 "NAGD03" 1711092 T NAGD03 (NIL) -7 NIL NIL NIL) (-740 1701175 1703103 1705057 "NAGD02" 1707491 T NAGD02 (NIL) -7 NIL NIL NIL) (-739 1694986 1696411 1697851 "NAGD01" 1699755 T NAGD01 (NIL) -7 NIL NIL NIL) (-738 1691195 1692017 1692854 "NAGC06" 1694169 T NAGC06 (NIL) -7 NIL NIL NIL) (-737 1689660 1689992 1690348 "NAGC05" 1690859 T NAGC05 (NIL) -7 NIL NIL NIL) (-736 1689036 1689155 1689299 "NAGC02" 1689536 T NAGC02 (NIL) -7 NIL NIL NIL) (-735 1688096 1688653 1688693 "NAALG" 1688772 NIL NAALG (NIL T) -9 NIL 1688833 NIL) (-734 1687931 1687960 1688050 "NAALG-" 1688055 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-733 1681881 1682989 1684176 "MULTSQFR" 1686827 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-732 1681200 1681275 1681459 "MULTFACT" 1681793 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-731 1674293 1678163 1678216 "MTSCAT" 1679286 NIL MTSCAT (NIL T T) -9 NIL 1679800 NIL) (-730 1674005 1674059 1674151 "MTHING" 1674233 NIL MTHING (NIL T) -7 NIL NIL NIL) (-729 1673797 1673830 1673890 "MSYSCMD" 1673965 T MSYSCMD (NIL) -7 NIL NIL NIL) (-728 1669909 1672552 1672872 "MSET" 1673510 NIL MSET (NIL T) -8 NIL NIL NIL) (-727 1667004 1669470 1669511 "MSETAGG" 1669516 NIL MSETAGG (NIL T) -9 NIL 1669550 NIL) (-726 1662887 1664383 1665128 "MRING" 1666304 NIL MRING (NIL T T) -8 NIL NIL NIL) (-725 1662453 1662520 1662651 "MRF2" 1662814 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-724 1662071 1662106 1662250 "MRATFAC" 1662412 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-723 1659683 1659978 1660409 "MPRFF" 1661776 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-722 1653743 1659537 1659634 "MPOLY" 1659639 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-721 1653233 1653268 1653476 "MPCPF" 1653702 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-720 1652747 1652790 1652974 "MPC3" 1653184 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-719 1651942 1652023 1652244 "MPC2" 1652662 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-718 1650243 1650580 1650970 "MONOTOOL" 1651602 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-717 1649494 1649785 1649813 "MONOID" 1650032 T MONOID (NIL) -9 NIL 1650179 NIL) (-716 1649040 1649159 1649340 "MONOID-" 1649345 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-715 1639899 1645807 1645866 "MONOGEN" 1646540 NIL MONOGEN (NIL T T) -9 NIL 1646996 NIL) (-714 1637117 1637852 1638852 "MONOGEN-" 1638971 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-713 1635976 1636396 1636424 "MONADWU" 1636816 T MONADWU (NIL) -9 NIL 1637054 NIL) (-712 1635348 1635507 1635755 "MONADWU-" 1635760 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-711 1634733 1634951 1634979 "MONAD" 1635186 T MONAD (NIL) -9 NIL 1635298 NIL) (-710 1634418 1634496 1634628 "MONAD-" 1634633 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-709 1632734 1633331 1633610 "MOEBIUS" 1634171 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-708 1632126 1632504 1632544 "MODULE" 1632549 NIL MODULE (NIL T) -9 NIL 1632575 NIL) (-707 1631694 1631790 1631980 "MODULE-" 1631985 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-706 1629409 1630058 1630385 "MODRING" 1631518 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-705 1626395 1627514 1628035 "MODOP" 1628938 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-704 1625010 1625462 1625739 "MODMONOM" 1626258 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-703 1614817 1623301 1623715 "MODMON" 1624647 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-702 1612008 1613661 1613937 "MODFIELD" 1614692 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-701 1611012 1611289 1611479 "MMLFORM" 1611838 T MMLFORM (NIL) -8 NIL NIL NIL) (-700 1610538 1610581 1610760 "MMAP" 1610963 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-699 1608755 1609488 1609529 "MLO" 1609952 NIL MLO (NIL T) -9 NIL 1610194 NIL) (-698 1606122 1606637 1607239 "MLIFT" 1608236 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-697 1605513 1605597 1605751 "MKUCFUNC" 1606033 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-696 1605112 1605182 1605305 "MKRECORD" 1605436 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-695 1604160 1604321 1604549 "MKFUNC" 1604923 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-694 1603548 1603652 1603808 "MKFLCFN" 1604043 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-693 1603091 1603458 1603517 "MKCHSET" 1603522 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-692 1602368 1602470 1602655 "MKBCFUNC" 1602984 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-691 1599110 1601922 1602058 "MINT" 1602252 T MINT (NIL) -8 NIL NIL NIL) (-690 1597922 1598165 1598442 "MHROWRED" 1598865 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-689 1593348 1596457 1596862 "MFLOAT" 1597537 T MFLOAT (NIL) -8 NIL NIL NIL) (-688 1592705 1592781 1592952 "MFINFACT" 1593260 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-687 1589020 1589868 1590752 "MESH" 1591841 T MESH (NIL) -7 NIL NIL NIL) (-686 1587410 1587722 1588075 "MDDFACT" 1588707 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-685 1584252 1586569 1586610 "MDAGG" 1586865 NIL MDAGG (NIL T) -9 NIL 1587008 NIL) (-684 1574030 1583545 1583752 "MCMPLX" 1584065 T MCMPLX (NIL) -8 NIL NIL NIL) (-683 1573171 1573317 1573517 "MCDEN" 1573879 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-682 1571061 1571331 1571711 "MCALCFN" 1572901 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-681 1569986 1570226 1570459 "MAYBE" 1570867 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-680 1567598 1568121 1568683 "MATSTOR" 1569457 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-679 1563604 1566970 1567218 "MATRIX" 1567383 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-678 1559373 1560077 1560813 "MATLIN" 1562961 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-677 1549527 1552665 1552742 "MATCAT" 1557622 NIL MATCAT (NIL T T T) -9 NIL 1559039 NIL) (-676 1545891 1546904 1548260 "MATCAT-" 1548265 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-675 1544485 1544638 1544971 "MATCAT2" 1545726 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-674 1542597 1542921 1543305 "MAPPKG3" 1544160 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-673 1541578 1541751 1541973 "MAPPKG2" 1542421 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-672 1540077 1540361 1540688 "MAPPKG1" 1541284 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-671 1539183 1539483 1539660 "MAPPAST" 1539920 T MAPPAST (NIL) -8 NIL NIL NIL) (-670 1538794 1538852 1538975 "MAPHACK3" 1539119 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-669 1538386 1538447 1538561 "MAPHACK2" 1538726 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-668 1537824 1537927 1538069 "MAPHACK1" 1538277 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-667 1535930 1536524 1536828 "MAGMA" 1537552 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-666 1535436 1535654 1535745 "MACROAST" 1535859 T MACROAST (NIL) -8 NIL NIL NIL) (-665 1531903 1533675 1534136 "M3D" 1535008 NIL M3D (NIL T) -8 NIL NIL NIL) (-664 1526057 1530272 1530313 "LZSTAGG" 1531095 NIL LZSTAGG (NIL T) -9 NIL 1531390 NIL) (-663 1522031 1523188 1524645 "LZSTAGG-" 1524650 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-662 1519145 1519922 1520409 "LWORD" 1521576 NIL LWORD (NIL T) -8 NIL NIL NIL) (-661 1518748 1518949 1519024 "LSTAST" 1519090 T LSTAST (NIL) -8 NIL NIL NIL) (-660 1511949 1518519 1518653 "LSQM" 1518658 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-659 1511173 1511312 1511540 "LSPP" 1511804 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-658 1508985 1509286 1509742 "LSMP" 1510862 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-657 1505764 1506438 1507168 "LSMP1" 1508287 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-656 1499689 1504931 1504972 "LSAGG" 1505034 NIL LSAGG (NIL T) -9 NIL 1505112 NIL) (-655 1496384 1497308 1498521 "LSAGG-" 1498526 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-654 1494010 1495528 1495777 "LPOLY" 1496179 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-653 1493592 1493677 1493800 "LPEFRAC" 1493919 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-652 1491939 1492686 1492939 "LO" 1493424 NIL LO (NIL T T T) -8 NIL NIL NIL) (-651 1491591 1491703 1491731 "LOGIC" 1491842 T LOGIC (NIL) -9 NIL 1491923 NIL) (-650 1491453 1491476 1491547 "LOGIC-" 1491552 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-649 1490646 1490786 1490979 "LODOOPS" 1491309 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-648 1488104 1490562 1490628 "LODO" 1490633 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-647 1486642 1486877 1487230 "LODOF" 1487851 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-646 1482998 1485395 1485436 "LODOCAT" 1485874 NIL LODOCAT (NIL T) -9 NIL 1486085 NIL) (-645 1482731 1482789 1482916 "LODOCAT-" 1482921 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-644 1480086 1482572 1482690 "LODO2" 1482695 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-643 1477556 1480023 1480068 "LODO1" 1480073 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-642 1476416 1476581 1476893 "LODEEF" 1477379 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-641 1471702 1474546 1474587 "LNAGG" 1475534 NIL LNAGG (NIL T) -9 NIL 1475978 NIL) (-640 1470849 1471063 1471405 "LNAGG-" 1471410 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-639 1467012 1467774 1468413 "LMOPS" 1470264 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-638 1466407 1466769 1466810 "LMODULE" 1466871 NIL LMODULE (NIL T) -9 NIL 1466913 NIL) (-637 1463653 1466052 1466175 "LMDICT" 1466317 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-636 1463379 1463561 1463621 "LITERAL" 1463626 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-635 1456606 1462325 1462623 "LIST" 1463114 NIL LIST (NIL T) -8 NIL NIL NIL) (-634 1456131 1456205 1456344 "LIST3" 1456526 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-633 1455138 1455316 1455544 "LIST2" 1455949 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-632 1453272 1453584 1453983 "LIST2MAP" 1454785 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-631 1452002 1452638 1452679 "LINEXP" 1452934 NIL LINEXP (NIL T) -9 NIL 1453083 NIL) (-630 1450649 1450909 1451206 "LINDEP" 1451754 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-629 1447416 1448135 1448912 "LIMITRF" 1449904 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-628 1445692 1445987 1446403 "LIMITPS" 1447111 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-627 1440147 1445203 1445431 "LIE" 1445513 NIL LIE (NIL T T) -8 NIL NIL NIL) (-626 1439196 1439639 1439679 "LIECAT" 1439819 NIL LIECAT (NIL T) -9 NIL 1439970 NIL) (-625 1439037 1439064 1439152 "LIECAT-" 1439157 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-624 1431649 1438486 1438651 "LIB" 1438892 T LIB (NIL) -8 NIL NIL NIL) (-623 1427286 1428167 1429102 "LGROBP" 1430766 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-622 1425152 1425426 1425788 "LF" 1427007 NIL LF (NIL T T) -7 NIL NIL NIL) (-621 1423992 1424684 1424712 "LFCAT" 1424919 T LFCAT (NIL) -9 NIL 1425058 NIL) (-620 1420896 1421524 1422212 "LEXTRIPK" 1423356 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-619 1417667 1418466 1418969 "LEXP" 1420476 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-618 1417170 1417388 1417480 "LETAST" 1417595 T LETAST (NIL) -8 NIL NIL NIL) (-617 1415568 1415881 1416282 "LEADCDET" 1416852 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-616 1414758 1414832 1415061 "LAZM3PK" 1415489 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-615 1409713 1412835 1413373 "LAUPOL" 1414270 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-614 1409278 1409322 1409490 "LAPLACE" 1409663 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-613 1407252 1408379 1408630 "LA" 1409111 NIL LA (NIL T T T) -8 NIL NIL NIL) (-612 1406333 1406883 1406924 "LALG" 1406986 NIL LALG (NIL T) -9 NIL 1407045 NIL) (-611 1406047 1406106 1406242 "LALG-" 1406247 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-610 1405882 1405906 1405947 "KVTFROM" 1406009 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-609 1404685 1405099 1405328 "KTVLOGIC" 1405673 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-608 1404520 1404544 1404585 "KRCFROM" 1404647 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-607 1403424 1403611 1403910 "KOVACIC" 1404320 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-606 1403259 1403283 1403324 "KONVERT" 1403386 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-605 1403094 1403118 1403159 "KOERCE" 1403221 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-604 1400828 1401588 1401981 "KERNEL" 1402733 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-603 1400330 1400411 1400541 "KERNEL2" 1400742 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-602 1394181 1398869 1398923 "KDAGG" 1399300 NIL KDAGG (NIL T T) -9 NIL 1399506 NIL) (-601 1393710 1393834 1394039 "KDAGG-" 1394044 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1386885 1393371 1393526 "KAFILE" 1393588 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-599 1381340 1386396 1386624 "JORDAN" 1386706 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-598 1380746 1380989 1381110 "JOINAST" 1381239 T JOINAST (NIL) -8 NIL NIL NIL) (-597 1380592 1380651 1380706 "JAVACODE" 1380711 T JAVACODE (NIL) -8 NIL NIL NIL) (-596 1376891 1378797 1378851 "IXAGG" 1379780 NIL IXAGG (NIL T T) -9 NIL 1380239 NIL) (-595 1375810 1376116 1376535 "IXAGG-" 1376540 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-594 1371390 1375732 1375791 "IVECTOR" 1375796 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-593 1370156 1370393 1370659 "ITUPLE" 1371157 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-592 1368592 1368769 1369075 "ITRIGMNP" 1369978 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-591 1367337 1367541 1367824 "ITFUN3" 1368368 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-590 1366969 1367026 1367135 "ITFUN2" 1367274 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-589 1364806 1365831 1366130 "ITAYLOR" 1366703 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-588 1353789 1358943 1360106 "ISUPS" 1363676 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-587 1352893 1353033 1353269 "ISUMP" 1353636 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-586 1348157 1352694 1352773 "ISTRING" 1352846 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-585 1347660 1347878 1347970 "ISAST" 1348085 T ISAST (NIL) -8 NIL NIL NIL) (-584 1346870 1346951 1347167 "IRURPK" 1347574 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-583 1345806 1346007 1346247 "IRSN" 1346650 T IRSN (NIL) -7 NIL NIL NIL) (-582 1343835 1344190 1344626 "IRRF2F" 1345444 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-581 1343582 1343620 1343696 "IRREDFFX" 1343791 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-580 1342197 1342456 1342755 "IROOT" 1343315 NIL IROOT (NIL T) -7 NIL NIL NIL) (-579 1338829 1339881 1340573 "IR" 1341537 NIL IR (NIL T) -8 NIL NIL NIL) (-578 1336442 1336937 1337503 "IR2" 1338307 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-577 1335514 1335627 1335848 "IR2F" 1336325 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-576 1335305 1335339 1335399 "IPRNTPK" 1335474 T IPRNTPK (NIL) -7 NIL NIL NIL) (-575 1331924 1335194 1335263 "IPF" 1335268 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-574 1330287 1331849 1331906 "IPADIC" 1331911 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-573 1329627 1329847 1329977 "IP4ADDR" 1330177 T IP4ADDR (NIL) -8 NIL NIL NIL) (-572 1329127 1329331 1329441 "IOMODE" 1329537 T IOMODE (NIL) -8 NIL NIL NIL) (-571 1328475 1328724 1328851 "IOBFILE" 1329020 T IOBFILE (NIL) -8 NIL NIL NIL) (-570 1328216 1328379 1328407 "IOBCON" 1328412 T IOBCON (NIL) -9 NIL 1328433 NIL) (-569 1327713 1327771 1327961 "INVLAPLA" 1328152 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-568 1317362 1319715 1322101 "INTTR" 1325377 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-567 1313706 1314448 1315312 "INTTOOLS" 1316547 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-566 1313292 1313383 1313500 "INTSLPE" 1313609 T INTSLPE (NIL) -7 NIL NIL NIL) (-565 1311287 1313215 1313274 "INTRVL" 1313279 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-564 1308889 1309401 1309976 "INTRF" 1310772 NIL INTRF (NIL T) -7 NIL NIL NIL) (-563 1308300 1308397 1308539 "INTRET" 1308787 NIL INTRET (NIL T) -7 NIL NIL NIL) (-562 1306297 1306686 1307156 "INTRAT" 1307908 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-561 1303525 1304108 1304734 "INTPM" 1305782 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-560 1300228 1300827 1301572 "INTPAF" 1302911 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-559 1295407 1296369 1297420 "INTPACK" 1299197 T INTPACK (NIL) -7 NIL NIL NIL) (-558 1292319 1295136 1295263 "INT" 1295300 T INT (NIL) -8 NIL NIL NIL) (-557 1291571 1291723 1291931 "INTHERTR" 1292161 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-556 1291010 1291090 1291278 "INTHERAL" 1291485 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-555 1288856 1289299 1289756 "INTHEORY" 1290573 T INTHEORY (NIL) -7 NIL NIL NIL) (-554 1280164 1281785 1283564 "INTG0" 1287208 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-553 1260737 1265527 1270337 "INTFTBL" 1275374 T INTFTBL (NIL) -8 NIL NIL NIL) (-552 1259986 1260124 1260297 "INTFACT" 1260596 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-551 1257371 1257817 1258381 "INTEF" 1259540 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-550 1255838 1256543 1256571 "INTDOM" 1256872 T INTDOM (NIL) -9 NIL 1257079 NIL) (-549 1255207 1255381 1255623 "INTDOM-" 1255628 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-548 1251702 1253591 1253645 "INTCAT" 1254444 NIL INTCAT (NIL T) -9 NIL 1254764 NIL) (-547 1251175 1251277 1251405 "INTBIT" 1251594 T INTBIT (NIL) -7 NIL NIL NIL) (-546 1249846 1250000 1250314 "INTALG" 1251020 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-545 1249303 1249393 1249563 "INTAF" 1249750 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-544 1242757 1249113 1249253 "INTABL" 1249258 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-543 1237772 1240446 1240474 "INS" 1241408 T INS (NIL) -9 NIL 1242073 NIL) (-542 1235012 1235783 1236757 "INS-" 1236830 NIL INS- (NIL T) -8 NIL NIL NIL) (-541 1233787 1234014 1234312 "INPSIGN" 1234765 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-540 1232905 1233022 1233219 "INPRODPF" 1233667 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-539 1231799 1231916 1232153 "INPRODFF" 1232785 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-538 1230799 1230951 1231211 "INNMFACT" 1231635 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-537 1229996 1230093 1230281 "INMODGCD" 1230698 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-536 1228505 1228749 1229073 "INFSP" 1229741 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-535 1227689 1227806 1227989 "INFPROD0" 1228385 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-534 1224571 1225754 1226269 "INFORM" 1227182 T INFORM (NIL) -8 NIL NIL NIL) (-533 1224181 1224241 1224339 "INFORM1" 1224506 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-532 1223704 1223793 1223907 "INFINITY" 1224087 T INFINITY (NIL) -7 NIL NIL NIL) (-531 1223155 1223424 1223525 "INETCLTS" 1223623 T INETCLTS (NIL) -8 NIL NIL NIL) (-530 1221772 1222021 1222342 "INEP" 1222903 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-529 1221048 1221669 1221734 "INDE" 1221739 NIL INDE (NIL T) -8 NIL NIL NIL) (-528 1220612 1220680 1220797 "INCRMAPS" 1220975 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-527 1219625 1219881 1220087 "INBFILE" 1220426 T INBFILE (NIL) -8 NIL NIL NIL) (-526 1214936 1215861 1216805 "INBFF" 1218713 NIL INBFF (NIL T) -7 NIL NIL NIL) (-525 1214590 1214671 1214699 "INBCON" 1214837 T INBCON (NIL) -9 NIL 1214920 NIL) (-524 1214433 1214467 1214542 "INBCON-" 1214547 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-523 1213935 1214154 1214246 "INAST" 1214361 T INAST (NIL) -8 NIL NIL NIL) (-522 1213389 1213614 1213720 "IMPTAST" 1213849 T IMPTAST (NIL) -8 NIL NIL NIL) (-521 1209883 1213233 1213337 "IMATRIX" 1213342 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-520 1208595 1208718 1209033 "IMATQF" 1209739 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-519 1206815 1207042 1207379 "IMATLIN" 1208351 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-518 1201441 1206739 1206797 "ILIST" 1206802 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-517 1199394 1201301 1201414 "IIARRAY2" 1201419 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-516 1194827 1199305 1199369 "IFF" 1199374 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-515 1194201 1194444 1194560 "IFAST" 1194731 T IFAST (NIL) -8 NIL NIL NIL) (-514 1189244 1193493 1193681 "IFARRAY" 1194058 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-513 1188451 1189148 1189221 "IFAMON" 1189226 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-512 1188035 1188100 1188154 "IEVALAB" 1188361 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-511 1187710 1187778 1187938 "IEVALAB-" 1187943 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-510 1187368 1187624 1187687 "IDPO" 1187692 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-509 1186645 1187257 1187332 "IDPOAMS" 1187337 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-508 1185979 1186534 1186609 "IDPOAM" 1186614 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-507 1185064 1185314 1185367 "IDPC" 1185780 NIL IDPC (NIL T T) -9 NIL 1185929 NIL) (-506 1184560 1184956 1185029 "IDPAM" 1185034 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-505 1183963 1184452 1184525 "IDPAG" 1184530 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-504 1183731 1183878 1183928 "IDENT" 1183933 T IDENT (NIL) -8 NIL NIL NIL) (-503 1179986 1180834 1181729 "IDECOMP" 1182888 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-502 1172860 1173909 1174956 "IDEAL" 1179022 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-501 1172024 1172136 1172335 "ICDEN" 1172744 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-500 1171123 1171504 1171651 "ICARD" 1171897 T ICARD (NIL) -8 NIL NIL NIL) (-499 1169183 1169496 1169901 "IBPTOOLS" 1170800 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-498 1164817 1168803 1168916 "IBITS" 1169102 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-497 1161540 1162116 1162811 "IBATOOL" 1164234 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-496 1159320 1159781 1160314 "IBACHIN" 1161075 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-495 1157197 1159166 1159269 "IARRAY2" 1159274 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-494 1153350 1157123 1157180 "IARRAY1" 1157185 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-493 1147344 1151762 1152243 "IAN" 1152889 T IAN (NIL) -8 NIL NIL NIL) (-492 1146855 1146912 1147085 "IALGFACT" 1147281 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-491 1146383 1146496 1146524 "HYPCAT" 1146731 T HYPCAT (NIL) -9 NIL NIL NIL) (-490 1145921 1146038 1146224 "HYPCAT-" 1146229 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-489 1145543 1145716 1145799 "HOSTNAME" 1145858 T HOSTNAME (NIL) -8 NIL NIL NIL) (-488 1145388 1145425 1145466 "HOMOTOP" 1145471 NIL HOMOTOP (NIL T) -9 NIL 1145504 NIL) (-487 1142067 1143398 1143439 "HOAGG" 1144420 NIL HOAGG (NIL T) -9 NIL 1145099 NIL) (-486 1140661 1141060 1141586 "HOAGG-" 1141591 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-485 1134703 1140258 1140406 "HEXADEC" 1140533 T HEXADEC (NIL) -8 NIL NIL NIL) (-484 1133451 1133673 1133936 "HEUGCD" 1134480 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-483 1132554 1133288 1133418 "HELLFDIV" 1133423 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-482 1130782 1132331 1132419 "HEAP" 1132498 NIL HEAP (NIL T) -8 NIL NIL NIL) (-481 1130073 1130334 1130468 "HEADAST" 1130668 T HEADAST (NIL) -8 NIL NIL NIL) (-480 1123993 1129988 1130050 "HDP" 1130055 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-479 1117744 1123628 1123780 "HDMP" 1123894 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-478 1117069 1117208 1117372 "HB" 1117600 T HB (NIL) -7 NIL NIL NIL) (-477 1110566 1116915 1117019 "HASHTBL" 1117024 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-476 1110069 1110287 1110379 "HASAST" 1110494 T HASAST (NIL) -8 NIL NIL NIL) (-475 1107881 1109691 1109873 "HACKPI" 1109907 T HACKPI (NIL) -8 NIL NIL NIL) (-474 1103576 1107734 1107847 "GTSET" 1107852 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-473 1097102 1103454 1103552 "GSTBL" 1103557 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-472 1089415 1096133 1096398 "GSERIES" 1096893 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-471 1088582 1088973 1089001 "GROUP" 1089204 T GROUP (NIL) -9 NIL 1089338 NIL) (-470 1087948 1088107 1088358 "GROUP-" 1088363 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-469 1086317 1086636 1087023 "GROEBSOL" 1087625 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-468 1085257 1085519 1085570 "GRMOD" 1086099 NIL GRMOD (NIL T T) -9 NIL 1086267 NIL) (-467 1085025 1085061 1085189 "GRMOD-" 1085194 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-466 1080351 1081379 1082379 "GRIMAGE" 1084045 T GRIMAGE (NIL) -8 NIL NIL NIL) (-465 1078818 1079078 1079402 "GRDEF" 1080047 T GRDEF (NIL) -7 NIL NIL NIL) (-464 1078262 1078378 1078519 "GRAY" 1078697 T GRAY (NIL) -7 NIL NIL NIL) (-463 1077475 1077855 1077906 "GRALG" 1078059 NIL GRALG (NIL T T) -9 NIL 1078152 NIL) (-462 1077136 1077209 1077372 "GRALG-" 1077377 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-461 1073940 1076721 1076899 "GPOLSET" 1077043 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-460 1073294 1073351 1073609 "GOSPER" 1073877 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-459 1069053 1069732 1070258 "GMODPOL" 1072993 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-458 1068058 1068242 1068480 "GHENSEL" 1068865 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-457 1062109 1062952 1063979 "GENUPS" 1067142 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-456 1061806 1061857 1061946 "GENUFACT" 1062052 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-455 1061218 1061295 1061460 "GENPGCD" 1061724 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-454 1060692 1060727 1060940 "GENMFACT" 1061177 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-453 1059260 1059515 1059822 "GENEEZ" 1060435 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-452 1053173 1058871 1059033 "GDMP" 1059183 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-451 1042550 1046944 1048050 "GCNAALG" 1052156 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-450 1040977 1041805 1041833 "GCDDOM" 1042088 T GCDDOM (NIL) -9 NIL 1042245 NIL) (-449 1040447 1040574 1040789 "GCDDOM-" 1040794 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-448 1039119 1039304 1039608 "GB" 1040226 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-447 1027739 1030065 1032457 "GBINTERN" 1036810 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-446 1025576 1025868 1026289 "GBF" 1027414 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-445 1024357 1024522 1024789 "GBEUCLID" 1025392 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-444 1023706 1023831 1023980 "GAUSSFAC" 1024228 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-443 1022073 1022375 1022689 "GALUTIL" 1023425 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-442 1020381 1020655 1020979 "GALPOLYU" 1021800 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-441 1017746 1018036 1018443 "GALFACTU" 1020078 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-440 1009552 1011051 1012659 "GALFACT" 1016178 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-439 1006940 1007598 1007626 "FVFUN" 1008782 T FVFUN (NIL) -9 NIL 1009502 NIL) (-438 1006206 1006388 1006416 "FVC" 1006707 T FVC (NIL) -9 NIL 1006890 NIL) (-437 1005848 1006003 1006084 "FUNCTION" 1006158 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-436 1003619 1004170 1004636 "FT" 1005402 T FT (NIL) -8 NIL NIL NIL) (-435 1002437 1002920 1003123 "FTEM" 1003436 T FTEM (NIL) -8 NIL NIL NIL) (-434 1000693 1000982 1001386 "FSUPFACT" 1002128 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-433 999090 999379 999711 "FST" 1000381 T FST (NIL) -8 NIL NIL NIL) (-432 998261 998367 998562 "FSRED" 998972 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-431 996940 997195 997549 "FSPRMELT" 997976 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-430 994025 994463 994962 "FSPECF" 996503 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-429 976085 984528 984568 "FS" 988416 NIL FS (NIL T) -9 NIL 990705 NIL) (-428 964735 967725 971781 "FS-" 972078 NIL FS- (NIL T T) -8 NIL NIL NIL) (-427 964249 964303 964480 "FSINT" 964676 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-426 962576 963242 963545 "FSERIES" 964028 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-425 961590 961706 961937 "FSCINT" 962456 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-424 957824 960534 960575 "FSAGG" 960945 NIL FSAGG (NIL T) -9 NIL 961204 NIL) (-423 955586 956187 956983 "FSAGG-" 957078 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-422 954628 954771 954998 "FSAGG2" 955439 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-421 952283 952562 953116 "FS2UPS" 954346 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-420 951865 951908 952063 "FS2" 952234 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-419 950722 950893 951202 "FS2EXPXP" 951690 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-418 950148 950263 950415 "FRUTIL" 950602 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-417 941603 945643 947001 "FR" 948822 NIL FR (NIL T) -8 NIL NIL NIL) (-416 936678 939321 939361 "FRNAALG" 940757 NIL FRNAALG (NIL T) -9 NIL 941364 NIL) (-415 932356 933427 934702 "FRNAALG-" 935452 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-414 931994 932037 932164 "FRNAAF2" 932307 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-413 930401 930848 931143 "FRMOD" 931806 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-412 928180 928784 929101 "FRIDEAL" 930192 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-411 927375 927462 927751 "FRIDEAL2" 928087 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-410 926508 926922 926963 "FRETRCT" 926968 NIL FRETRCT (NIL T) -9 NIL 927144 NIL) (-409 925620 925851 926202 "FRETRCT-" 926207 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-408 922832 924008 924067 "FRAMALG" 924949 NIL FRAMALG (NIL T T) -9 NIL 925241 NIL) (-407 920966 921421 922051 "FRAMALG-" 922274 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-406 914924 920441 920717 "FRAC" 920722 NIL FRAC (NIL T) -8 NIL NIL NIL) (-405 914560 914617 914724 "FRAC2" 914861 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-404 914196 914253 914360 "FR2" 914497 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-403 908869 911721 911749 "FPS" 912868 T FPS (NIL) -9 NIL 913425 NIL) (-402 908318 908427 908591 "FPS-" 908737 NIL FPS- (NIL T) -8 NIL NIL NIL) (-401 905772 907407 907435 "FPC" 907660 T FPC (NIL) -9 NIL 907802 NIL) (-400 905565 905605 905702 "FPC-" 905707 NIL FPC- (NIL T) -8 NIL NIL NIL) (-399 904443 905053 905094 "FPATMAB" 905099 NIL FPATMAB (NIL T) -9 NIL 905251 NIL) (-398 902143 902619 903045 "FPARFRAC" 904080 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-397 897537 898035 898717 "FORTRAN" 901575 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-396 895253 895753 896292 "FORT" 897018 T FORT (NIL) -7 NIL NIL NIL) (-395 892929 893491 893519 "FORTFN" 894579 T FORTFN (NIL) -9 NIL 895203 NIL) (-394 892693 892743 892771 "FORTCAT" 892830 T FORTCAT (NIL) -9 NIL 892892 NIL) (-393 890826 891309 891699 "FORMULA" 892323 T FORMULA (NIL) -8 NIL NIL NIL) (-392 890614 890644 890713 "FORMULA1" 890790 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-391 890137 890189 890362 "FORDER" 890556 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-390 889233 889397 889590 "FOP" 889964 T FOP (NIL) -7 NIL NIL NIL) (-389 887841 888513 888687 "FNLA" 889115 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-388 886596 886985 887013 "FNCAT" 887473 T FNCAT (NIL) -9 NIL 887733 NIL) (-387 886162 886555 886583 "FNAME" 886588 T FNAME (NIL) -8 NIL NIL NIL) (-386 884825 885754 885782 "FMTC" 885787 T FMTC (NIL) -9 NIL 885823 NIL) (-385 881187 882348 882977 "FMONOID" 884229 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-384 880406 880929 881078 "FM" 881083 NIL FM (NIL T T) -8 NIL NIL NIL) (-383 877830 878476 878504 "FMFUN" 879648 T FMFUN (NIL) -9 NIL 880356 NIL) (-382 877099 877280 877308 "FMC" 877598 T FMC (NIL) -9 NIL 877780 NIL) (-381 874293 875127 875181 "FMCAT" 876376 NIL FMCAT (NIL T T) -9 NIL 876871 NIL) (-380 873186 874059 874159 "FM1" 874238 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-379 870960 871376 871870 "FLOATRP" 872737 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-378 864584 868689 869310 "FLOAT" 870359 T FLOAT (NIL) -8 NIL NIL NIL) (-377 862022 862522 863100 "FLOATCP" 864051 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-376 860831 861635 861676 "FLINEXP" 861681 NIL FLINEXP (NIL T) -9 NIL 861774 NIL) (-375 859985 860220 860548 "FLINEXP-" 860553 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-374 859061 859205 859429 "FLASORT" 859837 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-373 856278 857120 857172 "FLALG" 858399 NIL FLALG (NIL T T) -9 NIL 858866 NIL) (-372 850062 853764 853805 "FLAGG" 855067 NIL FLAGG (NIL T) -9 NIL 855719 NIL) (-371 848788 849127 849617 "FLAGG-" 849622 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-370 847830 847973 848200 "FLAGG2" 848641 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 844805 845779 845838 "FINRALG" 846966 NIL FINRALG (NIL T T) -9 NIL 847474 NIL) (-368 843965 844194 844533 "FINRALG-" 844538 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-367 843371 843584 843612 "FINITE" 843808 T FINITE (NIL) -9 NIL 843915 NIL) (-366 835829 837990 838030 "FINAALG" 841697 NIL FINAALG (NIL T) -9 NIL 843150 NIL) (-365 831170 832211 833355 "FINAALG-" 834734 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-364 830565 830925 831028 "FILE" 831100 NIL FILE (NIL T) -8 NIL NIL NIL) (-363 829249 829561 829615 "FILECAT" 830299 NIL FILECAT (NIL T T) -9 NIL 830515 NIL) (-362 827117 828611 828639 "FIELD" 828679 T FIELD (NIL) -9 NIL 828759 NIL) (-361 825737 826122 826633 "FIELD-" 826638 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-360 823615 824372 824719 "FGROUP" 825423 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-359 822705 822869 823089 "FGLMICPK" 823447 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-358 818572 822630 822687 "FFX" 822692 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-357 818173 818234 818369 "FFSLPE" 818505 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-356 814166 814945 815741 "FFPOLY" 817409 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-355 813670 813706 813915 "FFPOLY2" 814124 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-354 809556 813589 813652 "FFP" 813657 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-353 804989 809467 809531 "FF" 809536 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 800150 804332 804522 "FFNBX" 804843 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-351 795124 799285 799543 "FFNBP" 800004 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-350 789792 794408 794619 "FFNB" 794957 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-349 788624 788822 789137 "FFINTBAS" 789589 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-348 784852 787031 787059 "FFIELDC" 787679 T FFIELDC (NIL) -9 NIL 788055 NIL) (-347 783515 783885 784382 "FFIELDC-" 784387 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-346 783085 783130 783254 "FFHOM" 783457 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-345 780783 781267 781784 "FFF" 782600 NIL FFF (NIL T) -7 NIL NIL NIL) (-344 776436 780525 780626 "FFCGX" 780726 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-343 772103 776168 776275 "FFCGP" 776379 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-342 767321 771830 771938 "FFCG" 772039 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-341 749154 758192 758278 "FFCAT" 763443 NIL FFCAT (NIL T T T) -9 NIL 764894 NIL) (-340 744352 745399 746713 "FFCAT-" 747943 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-339 743763 743806 744041 "FFCAT2" 744303 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-338 732975 736735 737955 "FEXPR" 742615 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-337 731975 732410 732451 "FEVALAB" 732535 NIL FEVALAB (NIL T) -9 NIL 732796 NIL) (-336 731134 731344 731682 "FEVALAB-" 731687 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-335 729727 730517 730720 "FDIV" 731033 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-334 726793 727508 727623 "FDIVCAT" 729191 NIL FDIVCAT (NIL T T T T) -9 NIL 729628 NIL) (-333 726555 726582 726752 "FDIVCAT-" 726757 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-332 725775 725862 726139 "FDIV2" 726462 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-331 724461 724720 725009 "FCPAK1" 725506 T FCPAK1 (NIL) -7 NIL NIL NIL) (-330 723589 723961 724102 "FCOMP" 724352 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-329 707326 710739 714277 "FC" 720071 T FC (NIL) -8 NIL NIL NIL) (-328 699905 703890 703930 "FAXF" 705732 NIL FAXF (NIL T) -9 NIL 706424 NIL) (-327 697184 697839 698664 "FAXF-" 699129 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-326 692284 696560 696736 "FARRAY" 697041 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-325 687537 689569 689622 "FAMR" 690645 NIL FAMR (NIL T T) -9 NIL 691105 NIL) (-324 686427 686729 687164 "FAMR-" 687169 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-323 685623 686349 686402 "FAMONOID" 686407 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-322 683435 684119 684172 "FAMONC" 685113 NIL FAMONC (NIL T T) -9 NIL 685499 NIL) (-321 682127 683189 683326 "FAGROUP" 683331 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-320 679922 680241 680644 "FACUTIL" 681808 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-319 679021 679206 679428 "FACTFUNC" 679732 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-318 671426 678272 678484 "EXPUPXS" 678877 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-317 668909 669449 670035 "EXPRTUBE" 670860 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-316 665103 665695 666432 "EXPRODE" 668248 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-315 650477 663758 664186 "EXPR" 664707 NIL EXPR (NIL T) -8 NIL NIL NIL) (-314 644884 645471 646284 "EXPR2UPS" 649775 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-313 644520 644577 644684 "EXPR2" 644821 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-312 635925 643652 643949 "EXPEXPAN" 644357 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-311 635752 635882 635911 "EXIT" 635916 T EXIT (NIL) -8 NIL NIL NIL) (-310 635259 635476 635567 "EXITAST" 635681 T EXITAST (NIL) -8 NIL NIL NIL) (-309 634886 634948 635061 "EVALCYC" 635191 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-308 634427 634545 634586 "EVALAB" 634756 NIL EVALAB (NIL T) -9 NIL 634860 NIL) (-307 633908 634030 634251 "EVALAB-" 634256 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-306 631376 632644 632672 "EUCDOM" 633227 T EUCDOM (NIL) -9 NIL 633577 NIL) (-305 629781 630223 630813 "EUCDOM-" 630818 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-304 617321 620079 622829 "ESTOOLS" 627051 T ESTOOLS (NIL) -7 NIL NIL NIL) (-303 616953 617010 617119 "ESTOOLS2" 617258 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-302 616704 616746 616826 "ESTOOLS1" 616905 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-301 610609 612337 612365 "ES" 615133 T ES (NIL) -9 NIL 616542 NIL) (-300 605557 606843 608660 "ES-" 608824 NIL ES- (NIL T) -8 NIL NIL NIL) (-299 601932 602692 603472 "ESCONT" 604797 T ESCONT (NIL) -7 NIL NIL NIL) (-298 601677 601709 601791 "ESCONT1" 601894 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-297 601352 601402 601502 "ES2" 601621 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-296 600982 601040 601149 "ES1" 601288 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-295 600198 600327 600503 "ERROR" 600826 T ERROR (NIL) -7 NIL NIL NIL) (-294 593701 600057 600148 "EQTBL" 600153 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-293 586258 589015 590464 "EQ" 592285 NIL -3297 (NIL T) -8 NIL NIL NIL) (-292 585890 585947 586056 "EQ2" 586195 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-291 581182 582228 583321 "EP" 584829 NIL EP (NIL T) -7 NIL NIL NIL) (-290 579764 580065 580382 "ENV" 580885 T ENV (NIL) -8 NIL NIL NIL) (-289 578943 579463 579491 "ENTIRER" 579496 T ENTIRER (NIL) -9 NIL 579542 NIL) (-288 575445 576898 577268 "EMR" 578742 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-287 574589 574774 574828 "ELTAGG" 575208 NIL ELTAGG (NIL T T) -9 NIL 575419 NIL) (-286 574308 574370 574511 "ELTAGG-" 574516 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-285 574097 574126 574180 "ELTAB" 574264 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-284 573223 573369 573568 "ELFUTS" 573948 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-283 572965 573021 573049 "ELEMFUN" 573154 T ELEMFUN (NIL) -9 NIL NIL NIL) (-282 572835 572856 572924 "ELEMFUN-" 572929 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-281 567726 570935 570976 "ELAGG" 571916 NIL ELAGG (NIL T) -9 NIL 572379 NIL) (-280 566011 566445 567108 "ELAGG-" 567113 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-279 564668 564948 565243 "ELABEXPR" 565736 T ELABEXPR (NIL) -8 NIL NIL NIL) (-278 557534 559335 560162 "EFUPXS" 563944 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-277 550984 552785 553595 "EFULS" 556810 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-276 548406 548764 549243 "EFSTRUC" 550616 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-275 537478 539043 540603 "EF" 546921 NIL EF (NIL T T) -7 NIL NIL NIL) (-274 536579 536963 537112 "EAB" 537349 T EAB (NIL) -8 NIL NIL NIL) (-273 535788 536538 536566 "E04UCFA" 536571 T E04UCFA (NIL) -8 NIL NIL NIL) (-272 534997 535747 535775 "E04NAFA" 535780 T E04NAFA (NIL) -8 NIL NIL NIL) (-271 534206 534956 534984 "E04MBFA" 534989 T E04MBFA (NIL) -8 NIL NIL NIL) (-270 533415 534165 534193 "E04JAFA" 534198 T E04JAFA (NIL) -8 NIL NIL NIL) (-269 532626 533374 533402 "E04GCFA" 533407 T E04GCFA (NIL) -8 NIL NIL NIL) (-268 531837 532585 532613 "E04FDFA" 532618 T E04FDFA (NIL) -8 NIL NIL NIL) (-267 531046 531796 531824 "E04DGFA" 531829 T E04DGFA (NIL) -8 NIL NIL NIL) (-266 525224 526571 527935 "E04AGNT" 529702 T E04AGNT (NIL) -7 NIL NIL NIL) (-265 523930 524410 524450 "DVARCAT" 524925 NIL DVARCAT (NIL T) -9 NIL 525124 NIL) (-264 523134 523346 523660 "DVARCAT-" 523665 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-263 516034 522933 523062 "DSMP" 523067 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-262 510844 511979 513047 "DROPT" 514986 T DROPT (NIL) -8 NIL NIL NIL) (-261 510509 510568 510666 "DROPT1" 510779 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-260 505624 506750 507887 "DROPT0" 509392 T DROPT0 (NIL) -7 NIL NIL NIL) (-259 503969 504294 504680 "DRAWPT" 505258 T DRAWPT (NIL) -7 NIL NIL NIL) (-258 498556 499479 500558 "DRAW" 502943 NIL DRAW (NIL T) -7 NIL NIL NIL) (-257 498189 498242 498360 "DRAWHACK" 498497 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-256 496920 497189 497480 "DRAWCX" 497918 T DRAWCX (NIL) -7 NIL NIL NIL) (-255 496436 496504 496655 "DRAWCURV" 496846 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-254 486907 488866 490981 "DRAWCFUN" 494341 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-253 483720 485602 485643 "DQAGG" 486272 NIL DQAGG (NIL T) -9 NIL 486545 NIL) (-252 471999 478698 478781 "DPOLCAT" 480633 NIL DPOLCAT (NIL T T T T) -9 NIL 481178 NIL) (-251 466838 468184 470142 "DPOLCAT-" 470147 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-250 459993 466699 466797 "DPMO" 466802 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-249 453051 459773 459940 "DPMM" 459945 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-248 452715 452970 453018 "DOMCTOR" 453023 T DOMCTOR (NIL) -8 NIL NIL NIL) (-247 452010 452237 452374 "DOMAIN" 452598 T DOMAIN (NIL) -8 NIL NIL NIL) (-246 445761 451645 451797 "DMP" 451911 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-245 445361 445417 445561 "DLP" 445699 NIL DLP (NIL T) -7 NIL NIL NIL) (-244 439231 444688 444878 "DLIST" 445203 NIL DLIST (NIL T) -8 NIL NIL NIL) (-243 436075 438084 438125 "DLAGG" 438675 NIL DLAGG (NIL T) -9 NIL 438905 NIL) (-242 434888 435518 435546 "DIVRING" 435638 T DIVRING (NIL) -9 NIL 435721 NIL) (-241 434125 434315 434615 "DIVRING-" 434620 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-240 432227 432584 432990 "DISPLAY" 433739 T DISPLAY (NIL) -7 NIL NIL NIL) (-239 426169 432141 432204 "DIRPROD" 432209 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-238 425017 425220 425485 "DIRPROD2" 425962 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-237 414280 420232 420285 "DIRPCAT" 420695 NIL DIRPCAT (NIL NIL T) -9 NIL 421535 NIL) (-236 411606 412248 413129 "DIRPCAT-" 413466 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-235 410893 411053 411239 "DIOSP" 411440 T DIOSP (NIL) -7 NIL NIL NIL) (-234 407595 409805 409846 "DIOPS" 410280 NIL DIOPS (NIL T) -9 NIL 410509 NIL) (-233 407144 407258 407449 "DIOPS-" 407454 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-232 406036 406630 406658 "DIFRING" 406845 T DIFRING (NIL) -9 NIL 406955 NIL) (-231 405682 405759 405911 "DIFRING-" 405916 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-230 403487 404725 404766 "DIFEXT" 405129 NIL DIFEXT (NIL T) -9 NIL 405423 NIL) (-229 401772 402200 402866 "DIFEXT-" 402871 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-228 399094 401304 401345 "DIAGG" 401350 NIL DIAGG (NIL T) -9 NIL 401370 NIL) (-227 398478 398635 398887 "DIAGG-" 398892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-226 393943 397437 397714 "DHMATRIX" 398247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-225 389555 390464 391474 "DFSFUN" 392953 T DFSFUN (NIL) -7 NIL NIL NIL) (-224 384671 388486 388798 "DFLOAT" 389263 T DFLOAT (NIL) -8 NIL NIL NIL) (-223 382899 383180 383576 "DFINTTLS" 384379 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-222 379964 380920 381320 "DERHAM" 382565 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-221 377813 379739 379828 "DEQUEUE" 379908 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-220 377028 377161 377357 "DEGRED" 377675 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-219 373423 374168 375021 "DEFINTRF" 376256 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-218 370950 371419 372018 "DEFINTEF" 372942 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-217 370327 370570 370685 "DEFAST" 370855 T DEFAST (NIL) -8 NIL NIL NIL) (-216 364369 369924 370072 "DECIMAL" 370199 T DECIMAL (NIL) -8 NIL NIL NIL) (-215 361881 362339 362845 "DDFACT" 363913 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-214 361477 361520 361671 "DBLRESP" 361832 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-213 359376 359710 360070 "DBASE" 361244 NIL DBASE (NIL T) -8 NIL NIL NIL) (-212 358645 358856 359002 "DATAARY" 359275 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-211 357778 358604 358632 "D03FAFA" 358637 T D03FAFA (NIL) -8 NIL NIL NIL) (-210 356912 357737 357765 "D03EEFA" 357770 T D03EEFA (NIL) -8 NIL NIL NIL) (-209 354862 355328 355817 "D03AGNT" 356443 T D03AGNT (NIL) -7 NIL NIL NIL) (-208 354178 354821 354849 "D02EJFA" 354854 T D02EJFA (NIL) -8 NIL NIL NIL) (-207 353494 354137 354165 "D02CJFA" 354170 T D02CJFA (NIL) -8 NIL NIL NIL) (-206 352810 353453 353481 "D02BHFA" 353486 T D02BHFA (NIL) -8 NIL NIL NIL) (-205 352126 352769 352797 "D02BBFA" 352802 T D02BBFA (NIL) -8 NIL NIL NIL) (-204 345324 346912 348518 "D02AGNT" 350540 T D02AGNT (NIL) -7 NIL NIL NIL) (-203 343093 343615 344161 "D01WGTS" 344798 T D01WGTS (NIL) -7 NIL NIL NIL) (-202 342188 343052 343080 "D01TRNS" 343085 T D01TRNS (NIL) -8 NIL NIL NIL) (-201 341283 342147 342175 "D01GBFA" 342180 T D01GBFA (NIL) -8 NIL NIL NIL) (-200 340378 341242 341270 "D01FCFA" 341275 T D01FCFA (NIL) -8 NIL NIL NIL) (-199 339473 340337 340365 "D01ASFA" 340370 T D01ASFA (NIL) -8 NIL NIL NIL) (-198 338568 339432 339460 "D01AQFA" 339465 T D01AQFA (NIL) -8 NIL NIL NIL) (-197 337663 338527 338555 "D01APFA" 338560 T D01APFA (NIL) -8 NIL NIL NIL) (-196 336758 337622 337650 "D01ANFA" 337655 T D01ANFA (NIL) -8 NIL NIL NIL) (-195 335853 336717 336745 "D01AMFA" 336750 T D01AMFA (NIL) -8 NIL NIL NIL) (-194 334948 335812 335840 "D01ALFA" 335845 T D01ALFA (NIL) -8 NIL NIL NIL) (-193 334043 334907 334935 "D01AKFA" 334940 T D01AKFA (NIL) -8 NIL NIL NIL) (-192 333138 334002 334030 "D01AJFA" 334035 T D01AJFA (NIL) -8 NIL NIL NIL) (-191 326435 327986 329547 "D01AGNT" 331597 T D01AGNT (NIL) -7 NIL NIL NIL) (-190 325772 325900 326052 "CYCLOTOM" 326303 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-189 322507 323220 323947 "CYCLES" 325065 T CYCLES (NIL) -7 NIL NIL NIL) (-188 321819 321953 322124 "CVMP" 322368 NIL CVMP (NIL T) -7 NIL NIL NIL) (-187 319590 319848 320224 "CTRIGMNP" 321547 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-186 319313 319549 319577 "CTOR" 319582 T CTOR (NIL) -8 NIL NIL NIL) (-185 318849 319044 319145 "CTORKIND" 319232 T CTORKIND (NIL) -8 NIL NIL NIL) (-184 318320 318548 318576 "CTORCAT" 318696 T CTORCAT (NIL) -9 NIL 318779 NIL) (-183 318015 318095 318221 "CTORCAT-" 318226 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-182 317531 317718 317816 "CTORCALL" 317937 T CTORCALL (NIL) -8 NIL NIL NIL) (-181 316905 317004 317157 "CSTTOOLS" 317428 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-180 312704 313361 314119 "CRFP" 316217 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-179 312206 312425 312517 "CRCEAST" 312632 T CRCEAST (NIL) -8 NIL NIL NIL) (-178 311253 311438 311666 "CRAPACK" 312010 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-177 310637 310738 310942 "CPMATCH" 311129 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-176 310362 310390 310496 "CPIMA" 310603 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-175 306726 307398 308116 "COORDSYS" 309697 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-174 306110 306239 306389 "CONTOUR" 306596 T CONTOUR (NIL) -8 NIL NIL NIL) (-173 302036 304113 304605 "CONTFRAC" 305650 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-172 301916 301937 301965 "CONDUIT" 302002 T CONDUIT (NIL) -9 NIL NIL NIL) (-171 301089 301609 301637 "COMRING" 301642 T COMRING (NIL) -9 NIL 301694 NIL) (-170 300170 300447 300631 "COMPPROP" 300925 T COMPPROP (NIL) -8 NIL NIL NIL) (-169 299831 299866 299994 "COMPLPAT" 300129 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-168 289888 299640 299749 "COMPLEX" 299754 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-167 289524 289581 289688 "COMPLEX2" 289825 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-166 289242 289277 289375 "COMPFACT" 289483 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-165 273415 283635 283675 "COMPCAT" 284679 NIL COMPCAT (NIL T) -9 NIL 286064 NIL) (-164 262931 265854 269481 "COMPCAT-" 269837 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-163 262660 262688 262791 "COMMUPC" 262897 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-162 262455 262488 262547 "COMMONOP" 262621 T COMMONOP (NIL) -7 NIL NIL NIL) (-161 262038 262206 262293 "COMM" 262388 T COMM (NIL) -8 NIL NIL NIL) (-160 261642 261842 261917 "COMMAAST" 261983 T COMMAAST (NIL) -8 NIL NIL NIL) (-159 260891 261085 261113 "COMBOPC" 261451 T COMBOPC (NIL) -9 NIL 261626 NIL) (-158 259787 259997 260239 "COMBINAT" 260681 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-157 255985 256558 257198 "COMBF" 259209 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-156 254771 255101 255336 "COLOR" 255770 T COLOR (NIL) -8 NIL NIL NIL) (-155 254274 254492 254584 "COLONAST" 254699 T COLONAST (NIL) -8 NIL NIL NIL) (-154 253914 253961 254086 "CMPLXRT" 254221 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-153 253389 253614 253713 "CLLCTAST" 253835 T CLLCTAST (NIL) -8 NIL NIL NIL) (-152 248891 249919 250999 "CLIP" 252329 T CLIP (NIL) -7 NIL NIL NIL) (-151 247273 247997 248236 "CLIF" 248718 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-150 243495 245419 245460 "CLAGG" 246389 NIL CLAGG (NIL T) -9 NIL 246925 NIL) (-149 241917 242374 242957 "CLAGG-" 242962 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-148 241461 241546 241686 "CINTSLPE" 241826 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-147 238962 239433 239981 "CHVAR" 240989 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-146 238205 238725 238753 "CHARZ" 238758 T CHARZ (NIL) -9 NIL 238773 NIL) (-145 237959 237999 238077 "CHARPOL" 238159 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-144 237086 237639 237667 "CHARNZ" 237714 T CHARNZ (NIL) -9 NIL 237770 NIL) (-143 235075 235776 236111 "CHAR" 236771 T CHAR (NIL) -8 NIL NIL NIL) (-142 234801 234862 234890 "CFCAT" 235001 T CFCAT (NIL) -9 NIL NIL NIL) (-141 234046 234157 234339 "CDEN" 234685 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-140 230038 233199 233479 "CCLASS" 233786 T CCLASS (NIL) -8 NIL NIL NIL) (-139 229345 229488 229651 "CATEGORY" 229895 T -10 (NIL) -8 NIL NIL NIL) (-138 229009 229264 229312 "CATCTOR" 229317 T CATCTOR (NIL) -8 NIL NIL NIL) (-137 228483 228709 228808 "CATAST" 228930 T CATAST (NIL) -8 NIL NIL NIL) (-136 227986 228204 228296 "CASEAST" 228411 T CASEAST (NIL) -8 NIL NIL NIL) (-135 223038 224015 224768 "CARTEN" 227289 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-134 222146 222294 222515 "CARTEN2" 222885 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-133 220488 221296 221553 "CARD" 221909 T CARD (NIL) -8 NIL NIL NIL) (-132 220091 220292 220367 "CAPSLAST" 220433 T CAPSLAST (NIL) -8 NIL NIL NIL) (-131 219463 219791 219819 "CACHSET" 219951 T CACHSET (NIL) -9 NIL 220028 NIL) (-130 218959 219255 219283 "CABMON" 219333 T CABMON (NIL) -9 NIL 219389 NIL) (-129 218107 218505 218641 "BYTE" 218804 T BYTE (NIL) -8 NIL NIL 218920) (-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 diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 10c78694..014a2181 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,192 +1,62 @@ -(734351 . 3440285147) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) - (-12 (-5 *4 (-679 (-224))) (-5 *5 (-679 (-558))) (-5 *6 (-224)) - (-5 *3 (-558)) (-5 *2 (-1025)) (-5 *1 (-743))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1246 *1)) (-4 *1 (-366 *4)) (-4 *4 (-171)) - (-5 *2 (-679 *4)))) - ((*1 *2) - (-12 (-4 *4 (-171)) (-5 *2 (-679 *4)) (-5 *1 (-415 *3 *4)) - (-4 *3 (-416 *4)))) - ((*1 *2) (-12 (-4 *1 (-416 *3)) (-4 *3 (-171)) (-5 *2 (-679 *3))))) +(734363 . 3440300499) +(((*1 *1 *1 *1 *1) (-4 *1 (-543)))) +(((*1 *1 *1 *2) (-12 (-4 *1 (-401)) (-5 *2 (-762)))) + ((*1 *1 *1) (-4 *1 (-401)))) +(((*1 *2) (-12 (-5 *2 (-112)) (-5 *1 (-916))))) +(((*1 *1 *2 *2 *2) + (-12 (-5 *1 (-226 *2)) (-4 *2 (-13 (-362) (-1185))))) + ((*1 *2 *1 *3 *4 *4) + (-12 (-5 *3 (-911)) (-5 *4 (-378)) (-5 *2 (-1251)) (-5 *1 (-1247)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-378)) (-5 *2 (-1251)) (-5 *1 (-1248))))) +(((*1 *2 *1) (-12 (-5 *2 (-1251)) (-5 *1 (-813))))) +(((*1 *2) (-12 (-5 *2 (-911)) (-5 *1 (-1249)))) + ((*1 *2 *2) (-12 (-5 *2 (-911)) (-5 *1 (-1249))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-362)) - (-5 *2 - (-2 (|:| A (-679 *5)) - (|:| |eqs| - (-635 - (-2 (|:| C (-679 *5)) (|:| |g| (-1246 *5)) (|:| -2442 *6) - (|:| |rh| *5)))))) - (-5 *1 (-804 *5 *6)) (-5 *3 (-679 *5)) (-5 *4 (-1246 *5)) - (-4 *6 (-646 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-362)) (-4 *6 (-646 *5)) - (-5 *2 (-2 (|:| -2582 (-679 *6)) (|:| |vec| (-1246 *5)))) - (-5 *1 (-804 *5 *6)) (-5 *3 (-679 *6)) (-5 *4 (-1246 *5))))) -(((*1 *2 *1) - (-12 (-4 *1 (-328 *3)) (-4 *3 (-362)) (-4 *3 (-367)) (-5 *2 (-112)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1159 *4)) (-4 *4 (-348)) (-5 *2 (-112)) - (-5 *1 (-356 *4)))) + (-12 (-4 *5 (-362)) (-4 *7 (-1222 *5)) (-4 *4 (-715 *5 *7)) + (-5 *2 (-2 (|:| -3702 (-679 *6)) (|:| |vec| (-1246 *5)))) + (-5 *1 (-802 *5 *6 *7 *4 *3)) (-4 *6 (-646 *5)) (-4 *3 (-646 *4))))) +(((*1 *2 *1) (-12 (-5 *1 (-1195 *2)) (-4 *2 (-964))))) +(((*1 *2 *3) (-12 (-5 *3 (-406 (-558))) (-5 *2 (-224)) (-5 *1 (-304))))) +(((*1 *2 *3) (-12 (-5 *3 (-911)) (-5 *2 (-894 (-558))) (-5 *1 (-907)))) ((*1 *2 *3) - (-12 (-5 *3 (-1246 *4)) (-4 *4 (-348)) (-5 *2 (-112)) - (-5 *1 (-526 *4))))) -(((*1 *2 *3 *1) - (-12 (-5 *3 (-1127 *4 *5)) (-4 *4 (-13 (-1087) (-34))) - (-4 *5 (-13 (-1087) (-34))) (-5 *2 (-112)) (-5 *1 (-1128 *4 *5))))) + (-12 (-5 *3 (-635 (-558))) (-5 *2 (-894 (-558))) (-5 *1 (-907))))) +(((*1 *1 *2) (-12 (-5 *2 (-315 (-168 (-378)))) (-5 *1 (-329)))) + ((*1 *1 *2) (-12 (-5 *2 (-315 (-558))) (-5 *1 (-329)))) + ((*1 *1 *2) (-12 (-5 *2 (-315 (-378))) (-5 *1 (-329)))) + ((*1 *1 *2) (-12 (-5 *2 (-315 (-684))) (-5 *1 (-329)))) + ((*1 *1 *2) (-12 (-5 *2 (-315 (-691))) (-5 *1 (-329)))) + ((*1 *1 *2) (-12 (-5 *2 (-315 (-689))) (-5 *1 (-329)))) + ((*1 *1) (-5 *1 (-329)))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-1165 (-406 (-558)))) (-5 *1 (-189))))) (((*1 *2 *3) - (-12 (-5 *3 (-635 *2)) (-4 *2 (-1222 *4)) (-5 *1 (-537 *4 *2 *5 *6)) - (-4 *4 (-306)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-762)))))) -(((*1 *2 *3 *3) (-12 (-5 *3 (-1145)) (-5 *2 (-112)) (-5 *1 (-820))))) -(((*1 *2 *3 *3 *3 *4 *5 *4 *6) - (-12 (-5 *3 (-315 (-558))) (-5 *4 (-1 (-224) (-224))) - (-5 *5 (-1081 (-224))) (-5 *6 (-558)) (-5 *2 (-1195 (-916))) - (-5 *1 (-317)))) - ((*1 *2 *3 *3 *3 *4 *5 *4 *6 *7) - (-12 (-5 *3 (-315 (-558))) (-5 *4 (-1 (-224) (-224))) - (-5 *5 (-1081 (-224))) (-5 *6 (-558)) (-5 *7 (-1145)) - (-5 *2 (-1195 (-916))) (-5 *1 (-317)))) - ((*1 *2 *3 *3 *3 *4 *5 *6 *7) - (-12 (-5 *3 (-315 (-558))) (-5 *4 (-1 (-224) (-224))) - (-5 *5 (-1081 (-224))) (-5 *6 (-224)) (-5 *7 (-558)) - (-5 *2 (-1195 (-916))) (-5 *1 (-317)))) - ((*1 *2 *3 *3 *3 *4 *5 *6 *7 *8) - (-12 (-5 *3 (-315 (-558))) (-5 *4 (-1 (-224) (-224))) - (-5 *5 (-1081 (-224))) (-5 *6 (-224)) (-5 *7 (-558)) (-5 *8 (-1145)) - (-5 *2 (-1195 (-916))) (-5 *1 (-317))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-762)) (-5 *2 (-406 (-558))) (-5 *1 (-224)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-762)) (-5 *2 (-406 (-558))) (-5 *1 (-224)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-762)) (-5 *2 (-406 (-558))) (-5 *1 (-378)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-762)) (-5 *2 (-406 (-558))) (-5 *1 (-378))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-558)) (-4 *1 (-641 *3)) (-4 *3 (-1200)))) - ((*1 *1 *2 *1 *3) - (-12 (-5 *3 (-558)) (-4 *1 (-641 *2)) (-4 *2 (-1200))))) -(((*1 *1 *1) (-12 (-4 *1 (-243 *2)) (-4 *2 (-1200))))) -(((*1 *1 *2) (-12 (-5 *2 (-156)) (-5 *1 (-864))))) -(((*1 *2 *1) (-12 (-4 *1 (-788 *2)) (-4 *2 (-171)))) - ((*1 *2 *1) (-12 (-4 *1 (-987 *2)) (-4 *2 (-171))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-174))))) + (-12 (-5 *3 (-479 *4 *5)) (-14 *4 (-635 (-1163))) (-4 *5 (-1039)) + (-5 *2 (-942 *5)) (-5 *1 (-934 *4 *5))))) +(((*1 *1 *1 *1) (-5 *1 (-853))) ((*1 *1 *1) (-5 *1 (-853))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1159 (-558))) (-5 *3 (-558)) (-4 *1 (-859 *4))))) +(((*1 *2 *3) + (-12 (-5 *3 (-635 (-558))) (-5 *2 (-894 (-558))) (-5 *1 (-907)))) + ((*1 *2) (-12 (-5 *2 (-894 (-558))) (-5 *1 (-907))))) +(((*1 *2) + (-12 (-4 *1 (-341 *3 *4 *5)) (-4 *3 (-1204)) (-4 *4 (-1222 *3)) + (-4 *5 (-1222 (-406 *4))) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-635 (-955))) (-5 *1 (-109)))) + ((*1 *2 *1) (-12 (-5 *2 (-45 (-1145) (-765))) (-5 *1 (-114))))) +(((*1 *2 *1) + (-12 (-4 *1 (-966 *3 *4 *2 *5)) (-4 *3 (-1039)) (-4 *4 (-784)) + (-4 *5 (-1053 *3 *4 *2)) (-4 *2 (-841)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1053 *3 *4 *2)) (-4 *3 (-1039)) (-4 *4 (-784)) + (-4 *2 (-841))))) +(((*1 *2 *3 *1) + (-12 (-4 *4 (-13 (-839) (-362))) (-5 *2 (-112)) (-5 *1 (-1049 *4 *3)) + (-4 *3 (-1222 *4))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-679 *8)) (-5 *4 (-762)) (-4 *8 (-939 *5 *7 *6)) - (-4 *5 (-13 (-306) (-146))) (-4 *6 (-13 (-841) (-606 (-1163)))) - (-4 *7 (-784)) - (-5 *2 - (-635 - (-2 (|:| |det| *8) (|:| |rows| (-635 (-558))) - (|:| |cols| (-635 (-558)))))) - (-5 *1 (-914 *5 *6 *7 *8))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-143))))) -(((*1 *1 *1) - (-12 (-4 *1 (-1053 *2 *3 *4)) (-4 *2 (-1039)) (-4 *3 (-784)) - (-4 *4 (-841)) (-4 *2 (-450))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *3 (-406 *5)) (-4 *4 (-1204)) (-4 *5 (-1222 *4)) - (-5 *1 (-147 *4 *5 *2)) (-4 *2 (-1222 *3)))) - ((*1 *2 *3) - (-12 (-5 *3 (-1165 (-406 (-558)))) (-5 *2 (-406 (-558))) - (-5 *1 (-189)))) - ((*1 *2 *2 *3 *4) - (-12 (-5 *2 (-679 (-315 (-224)))) (-5 *3 (-635 (-1163))) - (-5 *4 (-1246 (-315 (-224)))) (-5 *1 (-204)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-635 (-293 *3))) (-4 *3 (-308 *3)) (-4 *3 (-1087)) - (-4 *3 (-1200)) (-5 *1 (-293 *3)))) - ((*1 *1 *1 *1) - (-12 (-4 *2 (-308 *2)) (-4 *2 (-1087)) (-4 *2 (-1200)) - (-5 *1 (-293 *2)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-1 *1 *1)) (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-1 *1 (-635 *1))) (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 (-114))) (-5 *3 (-635 (-1 *1 (-635 *1)))) - (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 (-114))) (-5 *3 (-635 (-1 *1 *1))) (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-1163)) (-5 *3 (-1 *1 *1)) (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-1163)) (-5 *3 (-1 *1 (-635 *1))) (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 (-1163))) (-5 *3 (-635 (-1 *1 (-635 *1)))) - (-4 *1 (-301)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 (-1163))) (-5 *3 (-635 (-1 *1 *1))) (-4 *1 (-301)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-635 (-293 *3))) (-4 *1 (-308 *3)) (-4 *3 (-1087)))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-293 *3)) (-4 *1 (-308 *3)) (-4 *3 (-1087)))) - ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *2 (-558))) (-5 *4 (-1165 (-406 (-558)))) - (-5 *1 (-309 *2)) (-4 *2 (-38 (-406 (-558)))))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 *4)) (-5 *3 (-635 *1)) (-4 *1 (-373 *4 *5)) - (-4 *4 (-841)) (-4 *5 (-171)))) - ((*1 *1 *1 *2 *1) - (-12 (-4 *1 (-373 *2 *3)) (-4 *2 (-841)) (-4 *3 (-171)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-1163)) (-5 *3 (-762)) (-5 *4 (-1 *1 *1)) - (-4 *1 (-429 *5)) (-4 *5 (-841)) (-4 *5 (-1039)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-1163)) (-5 *3 (-762)) (-5 *4 (-1 *1 (-635 *1))) - (-4 *1 (-429 *5)) (-4 *5 (-841)) (-4 *5 (-1039)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-635 (-1163))) (-5 *3 (-635 (-762))) - (-5 *4 (-635 (-1 *1 (-635 *1)))) (-4 *1 (-429 *5)) (-4 *5 (-841)) - (-4 *5 (-1039)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-635 (-1163))) (-5 *3 (-635 (-762))) - (-5 *4 (-635 (-1 *1 *1))) (-4 *1 (-429 *5)) (-4 *5 (-841)) - (-4 *5 (-1039)))) - ((*1 *1 *1 *2 *3 *4) - (-12 (-5 *2 (-635 (-114))) (-5 *3 (-635 *1)) (-5 *4 (-1163)) - (-4 *1 (-429 *5)) (-4 *5 (-841)) (-4 *5 (-606 (-534))))) - ((*1 *1 *1 *2 *1 *3) - (-12 (-5 *2 (-114)) (-5 *3 (-1163)) (-4 *1 (-429 *4)) (-4 *4 (-841)) - (-4 *4 (-606 (-534))))) - ((*1 *1 *1) - (-12 (-4 *1 (-429 *2)) (-4 *2 (-841)) (-4 *2 (-606 (-534))))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-635 (-1163))) (-4 *1 (-429 *3)) (-4 *3 (-841)) - (-4 *3 (-606 (-534))))) - ((*1 *1 *1 *2) - (-12 (-5 *2 (-1163)) (-4 *1 (-429 *3)) (-4 *3 (-841)) - (-4 *3 (-606 (-534))))) - ((*1 *1 *1 *2 *3) - (-12 (-4 *1 (-512 *2 *3)) (-4 *2 (-1087)) (-4 *3 (-1200)))) - ((*1 *1 *1 *2 *3) - (-12 (-5 *2 (-635 *4)) (-5 *3 (-635 *5)) (-4 *1 (-512 *4 *5)) - (-4 *4 (-1087)) (-4 *5 (-1200)))) - ((*1 *2 *1 *2) - (-12 (-5 *2 (-824 *3)) (-4 *3 (-362)) (-5 *1 (-709 *3)))) - ((*1 *2 *1 *2) (-12 (-5 *1 (-709 *2)) (-4 *2 (-362)))) - ((*1 *2 *1 *2) (-12 (-4 *1 (-893 *2)) (-4 *2 (-1087)))) - ((*1 *2 *2 *3 *2) - (-12 (-5 *2 (-406 (-942 *4))) (-5 *3 (-1163)) (-4 *4 (-550)) - (-5 *1 (-1033 *4)))) - ((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-635 (-1163))) (-5 *4 (-635 (-406 (-942 *5)))) - (-5 *2 (-406 (-942 *5))) (-4 *5 (-550)) (-5 *1 (-1033 *5)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-293 (-406 (-942 *4)))) (-5 *2 (-406 (-942 *4))) - (-4 *4 (-550)) (-5 *1 (-1033 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-635 (-293 (-406 (-942 *4))))) (-5 *2 (-406 (-942 *4))) - (-4 *4 (-550)) (-5 *1 (-1033 *4)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-1143 *3)) (-4 *3 (-1039)) (-5 *1 (-1147 *3)))) - ((*1 *2 *1 *3) - (-12 (-4 *1 (-1224 *3 *4)) (-4 *3 (-1039)) (-4 *4 (-783)) - (|has| *3 (-15 ** (*3 *3 *4))) (-5 *2 (-1143 *3))))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-3 (-112) "failed")) (-4 *3 (-450)) (-4 *4 (-841)) - (-4 *5 (-784)) (-5 *1 (-977 *3 *4 *5 *6)) (-4 *6 (-939 *3 *5 *4))))) + (-12 (-5 *3 (-1 *2 *2)) (-4 *2 (-1237 *4)) (-5 *1 (-1239 *4 *2)) + 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singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1143 (-224))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -2103 + (-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 (-553)))) + ((*1 *2 *1) + (-12 (-4 *1 (-596 *3 *4)) (-4 *3 (-1087)) (-4 *4 (-1200)) + (-5 *2 (-635 *4))))) +(((*1 *1 *1) (-5 *1 (-1051)))) +(((*1 *2 *2 *3) + (-12 (-5 *2 (-882 *4)) (-5 *3 (-1 (-112) *5)) (-4 *4 (-1087)) + (-4 *5 (-1200)) (-5 *1 (-880 *4 *5)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-882 *4)) (-5 *3 (-635 (-1 (-112) *5))) (-4 *4 (-1087)) + (-4 *5 (-1200)) (-5 *1 (-880 *4 *5)))) 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